3D-IMB-APDR: Inertial-Geomagnetic-Barometric-Based Adaptive Infrastructure-Free 3D Pedestrian Dead Reckoning Method

Abstract

With the rapid development of underground spaces and demand for infrastructure-independent autonomous positioning in post-disaster rescue, Pedestrian Dead Reckoning (PDR) has become a key research focus. However, traditional PDR suffers from cumulative heading drift, inadequate 3D positioning performance, and poor anti-magnetic interference capabilities, failing to meet the high-precision positioning requirements of rescuers in underground and multistory buildings. To address these issues, this paper proposes an adaptive 3D-PDR method fusing inertial, geomagnetic, and barometric (3D-IMB-APDR). Sensor data are optimized via FFT dominant frequency extraction and Butterworth zero-phase filtering, with magnetic interference compensated by geomagnetic ellipse fitting. A segmental heading correction with a multi-criteria dynamic geomagnetic reliability model suppresses heading drift. A barometer-based coarse estimation and inertial fine correction architecture is adopted, where a lightweight CNN-BiLSTM network extracts inertial features for step height, and AEKF fuses multi-source data to achieve accurate vertical height estimation and precise 3D positioning. Validated in sports fields, underground parking garages, and staircases, the method outperforms four comparative methods, reducing positional RMSE by 65.77–98.23%, with endpoint errors of 1.40 m, 2.56 m, and 0.32 m, respectively. Relying solely on chest-worn sensors, it provides a reliable 3D autonomous positioning solution for rescuers in post-disaster rescue and underground engineering.

1. Introduction

A core advantage of autonomous positioning methods is their immunity to external interference and independence from external infrastructure in disaster environments, making them an ideal solution for meeting the positioning needs of rescuers in complex disaster scenarios [1,2]. Autonomous positioning systems based on lidar and vision have developed rapidly owing to their high measurement accuracy. However, such systems feature extremely high power consumption that imposes a heavy burden on batteries, failing to meet the demands of long endurance, lightweight design, and portability for rescuer positioning systems in harsh environments [3,4]. Although advances in ultra-low-power technologies and energy harvesting technologies are expected to improve their applicability, such solutions still have application limitations in such scenarios at present [5]. Among various autonomous positioning techniques, Pedestrian Dead Reckoning (PDR) has become the mainstream scheme due to its low cost and excellent real-time performance, which has attracted extensive attention from researchers and achieved rapid development [6]. However, with advancements in technologies such as the Internet and wireless transmission, numerous existing PDR algorithms have been integrated with wireless communication technologies—including Wi-Fi [7], Ultra-Wideband (UWB) [8], Bluetooth [9,10], and wireless tags [2,11,12]. While such integrated positioning methods deliver favorable performance in environments with intact and sufficient wireless infrastructure, they cannot operate effectively or efficiently in post-disaster scenarios, including underground spaces, wilderness areas, and forests, where infrastructure is damaged and wireless facilities are scarce [6,13,14,15]. Consequently, there is an increasingly urgent demand within the industry for high-precision PDR methods that do not rely on external infrastructure under extreme and abnormal scenarios.

In complex scenarios such as earthquake rescues, underground engineering, and forest exploration, positioning technologies that rely on external signals (e.g., Global Positioning System and UWB) are susceptible to failure due to signal occlusion and electromagnetic interference [16,17]. As a core autonomous positioning technology, PDR achieves position estimation via an Inertial Measurement Unit (IMU) and offers the advantage of infrastructure independence, thereby emerging as an ideal solution for positioning in complex environments [18,19]. Although existing PDR technologies have reached a relatively mature stage of development, three critical bottlenecks still remain. First, the heading error of gyroscopes accumulates over time, which makes it difficult to meet the demand for high-precision heading estimation in long-distance motion scenarios [20,21]. Second, altitude information is either missing or insufficiently accurate, and 2D trajectories fail to meet the requirements of scenarios such as multi-story buildings and underground spaces [22,23]. Third, reckoning accuracy degrades drastically in the face of complex motion patterns in intricate disaster sites.

The accuracy of heading reckoning is the most crucial factor influencing the performance of PDR methods [24]. Current heading estimation is primarily accomplished through techniques such as gyroscope sensing and geomagnetism. However, gyroscope-based heading estimation suffers from cumulative errors. While geomagnetic sensors can provide absolute heading references, their measurements are highly susceptible to magnetic interference from metal structures and electrical equipment, leading to poor stability in heading estimation [25]. Conventional methods are thus unable to satisfy the requirements of heading estimation.

In recent years, researchers have attempted to enhance positioning performance through multi-sensor fusion technologies, such as Wi-Fi/PDR/geomagnetic fusion positioning [7,26] and visual-inertial Simultaneous Localization and Mapping-assisted PDR [27]. However, such methods still rely on external signals or specific environmental textures, which limit their utility in scenarios such as disaster ruins and unlit underground spaces [18]. Therefore, the research on 3D autonomous positioning methods that are independent of external infrastructure, low-drift, and high-precision holds significant practical value for fields such as emergency rescue and military operations.

Most existing PDR methods deliver satisfactory performance in normal and ideal environments, such as unobstructed, barrier-free settings with regular staircases and simple motion patterns. Nevertheless, a core application requirement of PDR is to provide positioning and orientation data via self-contained signals in post-disaster scenarios and environments without external infrastructure support. Since existing methods are unable to provide reliable positioning data in such abnormal environments, this paper proposes an adaptive 3D pedestrian positioning method fusing inertial, geomagnetic, and barometric signals. This method incorporates a dynamic geomagnetic reliability evaluation mechanism to adaptively activate geomagnetic heading correction and realizes dynamic heading optimization through a tailored segmental heading correction algorithm. Meanwhile, a lightweight CNN-BiLSTM step height estimation model based on barometer-inertial fusion is proposed, which adopts a fusion strategy of barometer coarse estimation and inertial time-series fine correction to achieve vertical step height estimation.

Contributions of This Paper: To address the aforementioned issues, this paper proposes a series of innovative methods for improving pedestrian positioning performance, with the main contributions as follows:

(1)

Dynamic Geomagnetic Reliability Evaluation Model: A dynamic geomagnetic reliability evaluation model under multi-criteria constraints is proposed to determine in real time the validity of geomagnetic signals, addressing the issue that traditional methods cannot distinguish dynamic interference.

(2)

Segmental Heading Correction Method Based on Geomagnetic Reliability: Based on the detection results of geomagnetic signal reliability, a heading correction benchmark is established between two geomagnetically reliable points to correct the heading of the corresponding segment. It fully utilizes the global characteristics and accuracy of heading at geomagnetically reliable points while retaining the short-term dynamic tracking capability and accuracy of gyroscopes in heading estimation. As a result, the root mean square error (RMSE) of heading in magnetically disturbed environments is reduced by 35.5% compared with traditional methods, effectively improving the continuity and accuracy of heading estimation in complex scenarios.

(3)

Coarse-Fine Fusion Step Height Estimation Model: Adopting the architecture of barometer-based coarse estimation and inertial time-series fine correction, the model first performs coarse altitude estimation via a barometer, then processes inertial data with a lightweight CNN-BiLSTM model for fine relative step height estimation, and finally completes dynamic fusion of the two via the adaptive extended Kalman filter (AEKF). The proposed method yields superior positioning accuracy relative to typical existing approaches across three typical scenarios: outdoor sports fields, underground multi-story parking garages, and multi-floor teaching buildings.

The rest of this paper is organized as follows: Section 2 discusses related work. Section 3 introduces the overall methodological framework of the proposed method. Section 4 elaborates on the detailed implementation of the proposed method. Section 5 presents experiments and discussions. Finally, Section 6 concludes the paper.

2. Related Work

This section reviews the research progress of three core topics: PDR technology, pedestrian altitude estimation, and magnetic interference suppression combined with geomagnetic reliability evaluation.

2.1. Pedestrian Dead Reckoning Technology

The accuracy improvement of PDR technology mainly relies on step length estimation and heading optimization. In terms of step length estimation, existing methods are classified into physics-based models (e.g., the acceleration peak-to-peak method [28]) and data-driven models (e.g., the back propagation neural network [29]). The latter can improve the accuracy of step length estimation to a certain extent in variable-speed motion scenarios but requires substantial labeled data support. For heading optimization, the Mahony algorithm [30] and Madgwick algorithm [31] reduce inertial errors through gravity vector constraints, yet an obvious drift still exists in long-term positioning. Among geomagnetism-assisted methods, the GIPos method [25] optimizes the heading via geomagnetic turning feature matching, achieving an average positioning accuracy of 1.70 m; however, in complex magnetic interference environments, its mismatching rate increases.

2.2. Pedestrian Altitude Estimation

Existing altitude estimation methods are mainly divided into three categories. First, barometer-based measurement methods achieve an accuracy of ±1–3 m under ideal conditions, but their errors can easily exceed 5 m when affected by temperature and air currents [32,33]. Second, altitude estimation methods using acceleration data offer high short-term precision but suffer from issues such as cumulative errors [34]. Third, motion-pattern-constrained methods [35]. For example, Guo et al. [36] adopted a Convolutional Neural Network-Support Vector Machine framework to identify stair climbing/descending patterns and achieved an estimation accuracy of ±0.6 m by fusing prior knowledge of step height; nevertheless, these methods lack sufficient robustness in scenarios where step height is unknown. In addition, some studies utilize data from lidar [3,37], vision [4,38], or other sensors [39,40] for altitude estimation. Altitude information can also be obtained through multi-source data fusion, such as fusion with the Global Navigation Satellite System or inertial data [41]. Meanwhile, deep learning methods can learn the inertial-altitude mapping relationship [22], but their high model complexity impairs real-time performance on embedded devices.

2.3. Magnetic Interference Suppression and Geomagnetic Reliability Evaluation

The core of magnetic interference suppression is to distinguish valid geomagnetic signals from interference signals [42]. Existing methods mainly fall into three main categories. First, offline calibration methods [43] (e.g., ellipsoid fitting [44] and geomagnetic matching [45]) can compensate for inherent sensor errors but cannot handle dynamic interference. Second, real-time detection methods [21,46], such as magnetic interference classification based on Support Vector Machines [47], which achieves a detection accuracy of 98% but requires a large number of labeled samples. Third, multi-source constraint methods [25,48,49], for example, Li et al. [50] combined Zero-Velocity Update (ZUPT) with geomagnetic fusion, which effectively reduces the heading error, but this method is only applicable to foot-mounted sensor scenarios. However, existing studies lack a dynamic geomagnetic reliability evaluation mechanism for chest-mounted sensors and fail to account for the influence of motion patterns on geomagnetic signal reliability.

In summary, although PDR technology faces numerous challenges, with technological advancements and the application of new methods, it has broad application prospects in fields such as personal navigation, emergency rescue, and intelligent security.

3. Overview of the Proposed Method

The proposed 3D-IMB-APDR is an adaptive, infrastructure-independent autonomous pedestrian 3D positioning method. It addresses the critical bottlenecks of conventional PDR, including heading drift, insufficient 3D positioning capability, and poor adaptability to complex environments. This method consists of four core modules, including data preprocessing, geomagnetic reliability evaluation and heading optimization, coarse-fine fusion step height estimation, and 3D dead reckoning, as illustrated in Figure 1. The method leverages a chest-worn sensor module to collect triaxial acceleration, triaxial gyroscope, triaxial magnetometer, and barometer data, eliminating reliance on external signals and facilitating adaptation to complex scenarios such as underground garages, multi-story buildings, and sports fields.

Specifically, the data preprocessing module extracts the dominant frequency of human motion using FFT, enhances the sensor data signal-to-noise ratio via Butterworth zero-phase low-pass filtering, compensates for hard-soft magnetic interference, installation errors, and non-orthogonal errors through geomagnetic ellipse fitting, and outputs calibrated magnetic field data. Meanwhile, adaptive step segmentation based on step amplitude detection provides input for subsequent modules. The geomagnetic reliability evaluation and heading optimization module fuses geomagnetic and gyroscope headings to construct a multi-criteria dynamic reliability evaluation model for real-time geomagnetic signal validation. To resolve discontinuous reliable points induced by magnetic interference, a segmental heading correction method is proposed. This method constructs a linear correction benchmark between two reliable points, fuses the global accuracy of geomagnetism and the short-term tracking capability of gyroscopes, and suppresses cumulative heading drift. The “coarse-fine” fusion step height estimation module adopts a barometer-based coarse estimation and lightweight CNN-BiLSTM fine correction architecture: it calculates initial barometric altitude using the International Standard Atmosphere model, extracts spatial features of inertial data via CNN, and captures temporal dependencies via BiLSTM for high-precision relative step height output, with dynamic fusion of the two results achieved using the AEKF. The 3D PDR module estimates personnel positions by integrating optimized heading angles, step height, and step length, which enables autonomous positioning of complex movements in long-distance shielded environments.

Notably, multi-module synergy ensures the robust stability of the 3D-IMB-APDR method in scenarios including magnetically disturbed environments, multi-story buildings, and underground spaces, with the positioning error controlled within 2.5 m across various complex long-distance scenarios. As an infrastructure-independent solution, this method meets the autonomous positioning requirements of post-disaster rescue, underground engineering, and similar application scenarios.

4. Methodology

This section details the proposed 3D-IMB-APDR method across four key components: data preprocessing and correction, geomagnetic heading estimation and optimization, “coarse-fine” joint step height estimation, and 3D pedestrian dead reckoning. Each of these components is elaborated sequentially below.

4.1. Data Processing

4.1.1. Data Filtering and Dominant Signal Extraction

Raw signals collected by sensors contain various interferential and noisy components, such as accelerometer data noise arising from heartbeat and body jitter, all of which degrade the estimation accuracy of positioning data. To mitigate the impact of the aforementioned noise, data preprocessing is indispensable. Existing sensor noise filtering methods mainly include FFT, particle filtering, and wavelet transform. Considering the distinct periodicity of human motion, the sources of dominant noise, and real-time processing requirements, this paper adopts FFT to filter inertial data, analyze its frequency components, and extract the dominant frequency component to improve the signal-to-noise ratio.

For this purpose, FFT is performed on the triaxial acceleration data, triaxial angular rate data, and triaxial geomagnetic data acquired by the chest-mounted data acquisition unit during human movement, and the frequency information of signals containing multiple frequency components is extracted. By combining the frequency characteristics of human motion, heart rate, and noise, we select the signal component with the highest correlation with the motion state. Subsequently, this signal component is filtered using a customized filter to derive data that best captures human motion information.

Following the above method, this paper statistically analyzes the frequency characteristics of inertial data collected from five subjects under four motion modes: walking, ascending stairs, descending stairs, and climbing slopes. The results indicate that their dominant frequencies are all below 1.8 Hz. Considering the state changes during movement, an appropriate margin is incorporated in the design of the low-pass filter, and the cut-off frequency is set to 2 Hz. The low-pass filter is designed by combining a Butterworth filter with zero-phase filtering for the extraction of the dominant frequency signal, where the order of the filter is set to 4. This paper employs the aforementioned method to filter accelerometer data, gyroscope data, and geomagnetic data. The results of part of the X-axis acceleration data before and after filtering are shown in Figure 2. Compared with the data before filtering, the data processed by this filter is smoother, while its main amplitude-frequency characteristics (period, peaks, and troughs) are effectively preserved.

4.1.2. Geomagnetic Ellipse Correction and Magnetic Yaw Angle Estimation

• Geomagnetic Model

The output of a magnetometer is susceptible to device structural factors and ambient magnetic field interference, leading to degraded measurement accuracy [51]. Based on the error characteristics of magnetometers and the properties of hard and soft magnetic interference, the errors of a geomagnetic sensor include hard-soft magnetic interference, non-orthogonal errors, and installation errors. Its measurement model is expressed as [52]:

$${\mathit{T}}_{\mathrm{m}}^{\mathrm{b}}={\mathit{M}}_{\mathrm{k}}{\mathit{M}}_{\mathrm{o}}{\mathit{M}}_{\mathrm{s}}{\mathit{T}}^{\mathrm{b}}+\mathit{b}+\mathit{n}$$

(1)

where ${\mathit{T}}_{\mathrm{m}}^{\mathrm{b}}=\left[{\mathrm{T}}_{\mathrm{m}\mathrm{x}}^{\mathrm{b}}{,\mathrm{T}}_{\mathrm{m}\mathrm{y}}^{\mathrm{b}}{,\mathrm{T}}_{\mathrm{m}\mathrm{z}}^{\mathrm{b}}\right]$ denotes the actual measurement output of the magnetometer in the body coordinate system (i.e., the raw output before correction, affected by various interferences); ${\mathit{T}}^{\mathrm{b}}=\left[{\mathrm{T}}_{\mathrm{x}}^{\mathrm{b}}{,\mathrm{T}}_{\mathrm{y}}^{\mathrm{b}}{,\mathrm{T}}_{\mathrm{z}}^{\mathrm{b}}\right]$ represents the ideal output in the body coordinate system (free from interference); ${\mathit{M}}_{\mathrm{k}}$ is the sensitivity matrix, which scales the output to characterize the sensitivity of each sensor axis; ${\mathit{M}}_{\mathrm{o}}$ is the 3 × 3 non-orthogonal matrix, indicating the non-orthogonality and installation deviation of the magnetometer axes; ${\mathit{M}}_{\mathrm{s}}$ is the soft magnetic interference matrix, representing the total soft iron errors fixed in the body coordinate system; b is the hard magnetic offset, a constant offset that biases the sensor output; n is the measurement noise.

To simplify the calculation process, the above model can be rewritten as:

$${\mathit{T}}_{\mathit{m}}^{\mathit{b}}=\mathit{C}{\mathit{T}}^{\mathit{b}}+\mathit{B}$$

(2)

Then, the true magnetic field vector in the carrier coordinate system (magnetic field vector correction model) is:

$${\mathit{T}}^{\mathit{b}}=\mathit{E}\left({\mathit{T}}_{\mathit{m}}^{\mathit{b}}-\mathit{B}\right)$$

(3)

where $\mathit{C}={\mathit{M}}_{\mathit{k}}{\mathit{M}}_{\mathit{o}}{\mathit{M}}_{\mathit{s}}$ denotes the product of the three coefficient matrices; B represents the sum of the constant offset b and the noise n; E denotes the inverse of matrix C, which acts as the error compensation matrix.

The ideal output of the magnetometer should satisfy the following ellipsoid equation:

$${\left|\right|{\mathit{T}}^{\mathit{b}}\left|\right|}^2={\left({\mathit{T}}_{\mathit{m}}^{\mathit{b}}\right)}^{\mathit{T}}\mathit{A}{\mathit{T}}_{\mathit{m}}^{\mathit{b}}-2{\mathit{B}}^{\mathit{T}}\mathit{A}{\mathit{T}}_{\mathit{m}}^{\mathit{b}}+{\mathit{B}}^{\mathit{T}}\mathit{A}\mathit{B}$$

(4)

where $\mathit{A}={\mathit{E}}^T\mathit{E}$. The matrix A and the matrix B can be defined by the coefficients of the ellipsoid equation, and these coefficients can be solved through a fitting process.

2.

Geomagnetic Ellipse Correction

In the horizontal plane of the body coordinate system (i.e., the $\mathrm{O}-YZ$ plane), the horizontal dual-axis output of the magnetometer can be expressed as $\left(T_{my}^b,T_{mz}^b\right)$. Due to the presence of hard/soft magnetic interference and non-orthogonal errors, the measured horizontal dual-axis geomagnetic intensity distribution approximates an ellipse. The geomagnetic correction method adopted in this paper is as follows: Before starting the measurement, the wearable data acquisition device is rotated in place 3–5 full rotations. The least squares method is applied to solve for $\mathit{E}$ and $\mathit{B}$, thus deriving the geomagnetic ellipse equation and compensating the dual-axis geomagnetic data. This process yields more realistic dual-axis geomagnetic data, providing a more accurate data source for geomagnetic-based heading angle estimation. The specific theoretical model is as follows.

According to Equation (4), the ellipse equation of the actually measured dual-axis geomagnetic data is

$$a(T_{my}^b{)}^2+2b{T}_{my}^b{T}_{mz}^b+c(T_{mz}^b{)}^2+2d{T}_{my}^b+2e{T}_{mz}^b+f=0$$

(5)

where $a,b,c,d,e,f$ are the coefficients of the ellipse equation.

The horizontal dual-axis geomagnetic data $\left\{\right(T_{my,i}^b,T_{mz,i}^b){\}}_{i=1}^N$ (where $N$ is the number of data points) are collected by the chest-mounted measurement unit while the subject rotates in place for 3–5 circles. The ellipse equation is rewritten in linear form:

$$\mathit{F}\mathit{x}=0$$

(6)

where $\mathit{x}=[a,b,c,d,e,f{]}^T$; $\mathit{F}$ is a matrix constructed from the data points $\left(T_{my,i}^b,T_{mz,i}^b\right)$, where each row corresponds to one data point, formatted as $\left[(T_{my,i}^b{)}^2,2T_{my,i}^b{T}_{mz,i}^b,(T_{mz,i}^b{)}^2,2T_{my,i}^b,2T_{mz,i}^b,1\right]$.

Using the least squares method, we solve for the non-trivial solution $\mathit{x}$ that minimizes $\parallel \mathit{F}\mathit{x}{\parallel }^2$, thereby obtaining the coefficients $a,b,c,d,e,f$ of the ellipsoid equation.

To verify the effectiveness of the proposed geomagnetic correction algorithm, dual-axis geomagnetic data were collected during 4 full rotations in place to establish a correction model, which was applied to calibrate the geomagnetic data under complex motion states. The validation results are presented in Figure 3. Notably, the corrected dual-axis geomagnetic data converge to an origin-centered circle. This circular distribution indicates that the proposed algorithm effectively mitigates the impact of external magnetic interference. Through the correction method, the corrected data can be calibrated close to the true values, which helps suppress geomagnetic heading estimation errors caused by environmental magnetic interference and provides more reliable geomagnetic heading data for subsequent heading correction.

3.

Geomagnetic Heading Estimation

After correcting the geomagnetic data $\left[T_{my}^b,T_{mz}^b\right]$ collected by the magnetometer via the aforementioned correction model, the corrected true geomagnetic vector $\left(T_y^b,T_z^b\right)$ in the body coordinate system can be obtained. Combined with the geomagnetic heading estimation model proposed in this section, the pedestrian’s heading can be derived.

Since geomagnetism can be regarded as constant within the range of pedestrian movement, the direction of its horizontal geomagnetic vector always points to the magnetic south pole, and the deviation angle from the geographic north pole is also fixed [53]. The ratio of the horizontal geomagnetic components along the two horizontal axes (i.e., the Y-axis and Z-axis shown in Figure 4) varies under different headings. Based on the above principle, we establish the following geomagnetic heading estimation model. The schematic diagram of the estimation model principle for the dual-axis geomagnetic heading angle is shown in Figure 4. The pedestrian wears the sensor device in accordance with the axial direction shown in Figure 4. The component of the total geomagnetic intensity on the horizontal plane $O-YZ$ of the body coordinate system is $T_{yz}^b$.

Based on the above principle and the corrected dual-axis geomagnetic data, the pedestrian’s heading angle $\psi$ can be directly estimated using the following formula:

$$\psi =-\alpha +\beta =-\alpha +\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left({\displaystyle \frac{T_y^b}{T_z^b}}\right)$$

(7)

where $T_y^b$ denotes the component of the total geomagnetic field intensity in the y-axis of the body coordinate system, and $T_z^b$ is the component in the z-axis of the body coordinate system. $\alpha$ represents the magnetic declination, which can be obtained in advance by querying the World Magnetic Model (WMM); $\beta$ is the rotation angle, with counterclockwise rotation being positive and clockwise rotation being negative.

4.2. Geomagnetic Heading Optimization

4.2.1. Dynamic Evaluation of Geomagnetic Reliability

The accuracy of heading estimation is crucial to the precision of PDR. As an inherent vector information of the Earth, geomagnetism can provide accurate absolute direction for global and long-term navigation. However, geomagnetic measurements are susceptible to external magnetic interference, leading to unstable heading estimation accuracy and accelerating the accumulation of positional errors in PDR systems. Therefore, the mitigation of magnetic interference has long been a core and challenging topic in magnetic navigation [47]. Currently, there are two main types of solutions for magnetic interference detection. The magnetometer calibration method based on external attitude references compares magnetometer measurements with actual geomagnetic field vectors [54,55]. Nevertheless, this method requires high-precision external heading information, which is difficult to obtain in practical use and cannot meet the application requirements of disaster environments. Another approach uses an ellipsoidal error model for magnetometer calibration, which can be simplified to an ellipse-fitting scheme [46,56]. However, this method cannot yield optimal estimation when subject to ambient magnetic field interference.

To address this, this paper constructs a dynamic geomagnetic reliability evaluation model, which can detect interference in the collected magnetometer data in real time, assess the reliability of magnetometer-collected data as geomagnetic vector data, and screen high-reliability measurement data as the basis for error model construction and magnetic heading estimation. This enhances the system’s anti-interference capability and positioning precision. The proposed method considers the proportion of geomagnetism in the measured magnetic field data within the evaluation model. Compared with existing methods based on generalized likelihood ratio, probability models, and inclination models, it can better ensure that the screened magnetic field data of reliable points are close to geomagnetic data, reduce misjudgments, improve the accuracy of reliable point detection, and mitigate the impact of interference on the final trajectory. For example, under constant magnetic field interference, probability models are prone to misjudgment. Additionally, to enhance the continuity of heading stability, a segmental heading correction method is proposed to dynamically correct the heading between two reliable information points.

• Dynamic Geomagnetic Reliability Evaluation Model

The dynamic geomagnetic reliability evaluation model considers multiple criteria such as total magnetic intensity consistency, static inclination consistency, dynamic rotation angle consistency, and sudden interference detection, realizing the full-process processing from raw sensor data to geomagnetic reliability determination. Ultimately, it provides accurate geomagnetic correction activation signals for heading estimation. The flow diagram of this model is shown in Figure 5.

(1)

Total Magnetic Field Intensity Constraint (Near-Field Hard Magnetic Interference Detection)

When hard magnetic interference exists near the data acquisition device (e.g., large-area metal baffles or permanent magnets), the measured total magnetic field intensity deviates from the reference geomagnetic total intensity. This paper evaluates the deviation range of the measured total magnetic field intensity from the geomagnetic total intensity to provide a basis for reliability assessment. The total geomagnetic intensity at the pedestrian’s location is $T_{\mathrm{r}\mathrm{e}\mathrm{f}}$, which can be pre-obtained by querying the WMM 2025 model.

Considering WMM errors, measurement noise, and redundancy allowance, to avoid misjudgment, this paper sets a ±5% margin for the constraint range of total magnetic field intensity. That is, the measured total magnetic field intensity should fall within $\left[0.95T_{\mathrm{r}\mathrm{e}\mathrm{f}},1.05T_{\mathrm{r}\mathrm{e}\mathrm{f}}\right]$. If the calibrated geomagnetic vector magnitude $\left|{\mathit{T}}^b\right|=\sqrt{T_x^2+T_y^2+T_z^2}$ over 10 consecutive steps all falls within the constraint range, it is judged that no hard magnetic interference is present, and the confidence level for this criterion $C_1=1$; otherwise, $C_1=0$.

(2)

Rotation Angle Consistency (Near-Field/Dynamic Interference Detection)

When rescuers carry walkie-talkies, electric shears, and other equipment, the startup, shutdown, and operation of these devices cause sudden changes in the surrounding magnetic field, leading to heading estimation errors. To filter out such sudden interference, this paper evaluates rotation angle consistency by comparing the magnetic heading variation over 10 consecutive steps with the gyroscope rotation angle, providing a basis for dynamic magnetic interference judgment.

The gyroscope rotation angle $\mathsf{\Delta }{\psi }_{\mathrm{g}\mathrm{y}\mathrm{r}\mathrm{o}}$ is obtained by integrating the corrected angular velocity data within a temporal sliding window (window length = 10 steps). The specific calculation formula is as follows:

$$\mathsf{\Delta }{\psi }_{\mathrm{g}\mathrm{y}\mathrm{r}\mathrm{o}}={\int }_{t_1}^{t_{10}}{\omega }_{z^{\prime }}\left(t\right)dt$$

(8)

The geomagnetic heading variation $\mathsf{\Delta }{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g}}$ is calculated from the geomagnetic heading within the sliding window (length = 10 steps). Its specific calculation formula is:

$$\mathsf{\Delta }{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g}}={\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},10}-{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},1}$$

(9)

Considering cumulative errors of inertial measurement, geomagnetic measurement errors, and redundancy allowance, to avoid misjudgment, this paper sets the threshold for rotation angle consistency as $5^{\circ }$. If $\mathsf{\Delta }\psi =\left|\mathsf{\Delta }{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g}}-\mathsf{\Delta }{\psi }_{\mathrm{g}\mathrm{y}\mathrm{r}\mathrm{o}}\right|<5^{\circ }$, it is determined that there is no dynamic interference, and the criterion confidence $C_2=1$; if $5^{\circ }\le \mathsf{\Delta }\psi <{10}^{\circ }$, then $C_2=0.5$; otherwise, $C_2=0$.

(3)

Static Inclination Consistency (Static Interference Detection)

During pedestrian movement, there are periods of static pause where the human body posture is highly stable, providing additional reference information for geomagnetic reliability assessment. In static states, the geomagnetic inclination should be consistent with the WMM reference inclination. To ensure the accuracy of geomagnetic reliability determination, this paper utilizes this static inclination consistency by comparing the inclination estimated from geomagnetic data with that estimated from accelerometer data, thereby judging the degree of geomagnetic interference and providing a basis for reliability assessment.

The specific calculation method for inclination estimated from corrected magnetometer data is as follows:

$$I_{\mathrm{m}\mathrm{a}\mathrm{g}}=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}2\left(T_{x,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}^b,\sqrt{(T_{y,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}^n{)}^2+(T_{z,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}^n{)}^2}\right)-\alpha$$

(10)

The specific calculation method for inclination estimated from corrected accelerometer data is as follows:

$$I_{\mathrm{a}\mathrm{c}\mathrm{c}}=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}2\left(A_{x,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}^b,\sqrt{(A_{y,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}^n{)}^2+(A_{z,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}^n{)}^2}\right)$$

(11)

Considering cumulative errors of inertial measurement, geomagnetic measurement errors, and redundancy, to avoid misjudgment, this paper sets the threshold for static inclination consistency as $<2^{\circ }$. If $\mathsf{\Delta }I=\left|I_{\mathrm{a}\mathrm{c}\mathrm{c}}-I_{\mathrm{m}\mathrm{a}\mathrm{g}}\right|<2^{\circ }$, then the criterion confidence $C_3=1$; otherwise, $C_3=0$.

(4)

Generalized Likelihood Ratio Test Sudden Interference Detection

For scenarios where strong magnets are gradually approaching, the measured magnetic field vector data will deviate. To detect such unknown strong magnet approach events and avoid system errors caused by over-reliance on magnetic heading, Generalized Likelihood Ratio Test GLRT [57] is used to detect unknown sudden interference. The specific detection model is as follows:

This paper constructs a hypothesis model. $H_0$ (no sudden interference): The geomagnetic measurement ${\mathit{T}}^b$ follows a normal distribution $N\left({\mathit{T}}_{ref}^b,\mathsf{\Sigma }\right)$, where ${\mathit{T}}_{ref}^b={\mathit{C}}_n^b{\mathit{T}}^n$ (${\mathbf{C}}_n^b$ is the inverse matrix of ${\mathit{C}}_b^n$), and $\mathsf{\Sigma }$ is the measurement variance matrix during non-interference periods; $H_1$ (with sudden interference): ${\mathit{T}}^b$ follows $N\left({\mathit{T}}_{ref}^b+\mathsf{\Delta }\mathit{T},\mathsf{\Sigma }\right)$, where $\mathsf{\Delta }\mathit{T}$ is the interference offset. The likelihood ratio is calculated as:

$$\lambda ={\displaystyle \frac{p\left({\mathit{T}}^b|H_0\right)}{p\left({\mathit{T}}^b|H_1\right)}}=\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{1}{2}}\mathsf{\Delta }{\mathit{T}}^T{\mathsf{\Sigma }}^{-1}\mathsf{\Delta }\mathit{T}\right)$$

(12)

Setting the false detection rate $\alpha =0.05$, the threshold $\gamma$ is obtained from the ${\chi }^2$ distribution table (degree of freedom = 3, $\gamma =7.81$). If $-2\mathrm{l}\mathrm{o}\mathrm{g}\lambda <\gamma$, it is determined that there is no sudden interference, and the criterion confidence $C_4=1$; otherwise, $C_4=0$.

The comprehensive reliability confidence $C$ of the geomagnetic data at the current moment is calculated by the following formula:

$$C={\omega }_1{C}_1+{\omega }_2{C}_2+{\omega }_3{C}_3+{\omega }_4{C}_4$$

(13)

where the weight allocation is calibrated through experiments based on the interference detection sensitivity and misjudgment rate of each criterion.

In this paper, the validity of magnetic field data is determined by a threshold criterion, and the decision threshold is set as $C_{\mathrm{t}\mathrm{h}}=0.7$. In favorable electromagnetic environments, increasing the threshold further screens high-reliability geomagnetic data to improve heading estimation accuracy; in complex scenarios, decreasing it lowers the correction algorithm’s activation threshold, ensuring the system uses geomagnetic information to restrain inertial navigation drift and enhance operational stability.

Through the above multi-criteria collaborative dynamic geomagnetic reliability evaluation model, the determination of whether the measured magnetometer data is reliable is realized. The visualization result of the reliability of the magnetometer data measured in Scenario 3 after correction is shown in Figure 6.

The blue curve represents the magnetic vector data curve measured by the magnetometer, and the green curve represents the magnetic vector data curve after correction; the red circular area indicates the geomagnetically reliable region, and the magnetometer data within this region is determined to be reliable; the width of the red ring represents the influence degree of dynamic magnetic interference, and the ellipticity of the red ring represents the interference degree of the external comprehensive magnetic field. If the magnetic vector curve appears outside the red circular area, it indicates that this segment of data is subject to significant external magnetic interference, which may be caused by nearby metal structures with geomagnetic shielding effects or the start-stop of strong magnetic equipment, etc.

2.

Activation Mechanism of the Heading Correction Algorithm

After obtaining the geomagnetic reliability determination results of the measurement points, it is necessary to integrate these outcomes to configure the activation mechanism of the heading estimation module. Different determination results correspond to distinct heading estimation strategies for enhancing the precision of heading estimation.

In this paper, the reliability threshold is set as $C_{\mathrm{t}\mathrm{h}}=0.7$, and this value can be adjusted according to actual conditions.

When $C\ge 0.7$, the geomagnetic heading correction algorithm is activated immediately. For consecutive geomagnetically reliable points, the heading of these points fully adopts the magnetic heading as the comprehensive heading; for discontinuous geomagnetically reliable points, the magnetic heading segmental correction method is employed (refer to the next section for detailed implementation).

When $C<0.7$, the activation condition for the magnetic heading correction algorithm is not satisfied, and only the gyroscope-based rotation angle estimation method is utilized for heading reckoning. Once the activation condition for the geomagnetic heading correction algorithm is met, the segmental heading correction method is applied to dynamically correct the heading within this time interval to mitigate accumulated errors.

4.2.2. Segmental Heading Optimization Method Between Geomagnetic-Reliability Points

Magnetic interference often induces temporal and spatial discontinuities in geomagnetically reliable points, leading to persistent heading drift between these discontinuous points that cannot be resolved by direct geomagnetic correction. To address the scenario of “intermittent geomagnetically reliable points”, this paper proposes a geomagnetic heading segmental correction method. When the geomagnetic reliability evaluation model sequentially detects two geomagnetically reliable points, a heading correction benchmark is constructed based on the geomagnetic headings of these two points and the gyroscope rotation angle between them. This benchmark corrects the heading drift between the two reliable points, thus bridging the correction gap in intervals where geomagnetic heading is unavailable. The method fully leverages the global absolute positioning advantage of geomagnetic heading while retaining the short-term dynamic tracking capability of the gyroscope, effectively improving the continuity and accuracy of heading estimation in complex magnetic field environments. The schematic diagram of the geomagnetic heading segmental correction method is shown in Figure 7.

The magnetic heading segment correction method consists of three steps: determination of geomagnetically reliable points, calculation of interval correction parameters, and correction of interval heading. The specific construction process of the model is as follows:

• Determination of Geomagnetic Reliable Points

When the geomagnetic reliability evaluation model detects a reliable point, its step index $k$ and corresponding geomagnetic heading ${\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},k}$ are recorded. If two non-consecutive reliable points $P_1\left(k_1,{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},k_1}\right)$ and $P_2\left(k_2,{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},k_2}\right)$ are detected, the interval containing all steps between these two reliable points (including $P_1$ and $P_2$) is defined as the “heading segment correction interval”. The total number of steps in the interval is:

$$m=k_2-k_1+1$$

(14)

2.

Calculation of Interval Parameters

To dynamically correct the heading between the two geomagnetically reliable points, a linear correction transition curve from $k_1$ to $k_2$ is constructed, generating the “geomagnetic heading reference factor” ${\lambda }_i$ for each step within the interval. Its expression is:

$${\lambda }_i={\displaystyle \frac{i-1}{m-1}}\cdot \left(\left({\psi }_{\mathrm{g}\mathrm{y}\mathrm{r}\mathrm{o},k_2}-{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},k_2}\right)-\left({\psi }_{\mathrm{g}\mathrm{y}\mathrm{r}\mathrm{o},k_1}-{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},k_1}\right)\right), i=1,2,\dots ,m$$

(15)

where ${\psi }_{gyro,k_1}$ and ${\psi }_{gyro,k_2}$ denote the gyroscope-derived heading angles at step indices $k_1$ and $k_2$, respectively.

3.

Correction of Segment Heading

The core of segment heading correction is to use the linear correction transition curve to correct the gyroscope heading variation information between the two points. The formula for the corrected heading ${\psi }_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}$ is:

$${\psi }_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}\left(k_1+i-1\right)={\psi }_{\mathrm{g}\mathrm{y}\mathrm{r}\mathrm{o}}\left(k_1+i-1\right)-{\lambda }_i-\left({\psi }_{\mathrm{g}\mathrm{y}\mathrm{r}\mathrm{o},k_1}-{\psi }_{\mathrm{m}\mathrm{a}\mathrm{g},k_1}\right)$$

(16)

To verify the accuracy and feasibility of the geomagnetic heading segment correction method, a series of validation experiments were performed. A subject wearing the data acquisition unit walked counterclockwise twice on a playground, with random magnetic interference applied using metal baffles and electronic devices during the walk. In this scenario, data were collected, and heading data were obtained using three methods: gyroscope integration heading estimation, dual-axis geomagnetic heading estimation, and the proposed heading segment correction method. The heading curves derived from these three methods are shown in Figure 8. The left subfigure shows the global view of the heading data, and the right subfigure presents an enlarged view of the section enclosed by the red box in the left subfigure.

As observed in Figure 8, after correction using the proposed algorithm, the endpoint heading error is reduced. Meanwhile, within the correction interval, the short-term dynamic characteristics of the gyroscope heading estimation data are retained. Specifically, the global absolute information of geomagnetic heading is used to correct the heading, and the short-term high-precision heading estimation information of the gyroscope is used to preserve the dynamic characteristics of the heading between correction points.

4.2.3. Comparison of Performance with Similar Heading Estimation Methods

To validate the performance advantages of the proposed geomagnetic heading optimization method, a comparative analysis was conducted between the proposed method and three mainstream heading estimation algorithms: the Madgwick algorithm [31], the Mahony algorithm [30], and the direct geomagnetic calculation algorithm [58]. Key evaluation metrics, including the minimum error (MinE), maximum error (MaxE), mean error (ME), RMSE, and final heading error (FHE), were adopted to quantify the accuracy of heading estimation.

All experimental data in this paper were acquired via a chest-worn sensor module (sampling frequency: 120 Hz). The heading calculated by the proposed algorithm, the direct geomagnetic heading algorithm, the Madgwick algorithm, and the Mahony algorithm is shown in Figure 9. The left subfigure presents the global heading profiles of the four algorithms, and the right subfigure shows the local magnification of the area marked by the red box in the global view.

The following conclusions can be drawn from Figure 10: Compared with the heading estimates generated by the Madgwick and Mahony methods, the direct geomagnetic heading estimation results are closer to the true heading, and the deviation of its endpoint heading from the ground-truth endpoint heading is also smaller. However, this method exhibits considerable random fluctuations in heading estimates, which can be attributed to the susceptibility of the geomagnetic field to ambient magnetic interference. In contrast, the method proposed in this paper preserves the advantage of global heading consistency inherent to direct geomagnetic estimation, with a small endpoint heading deviation. Meanwhile, it demonstrates significantly smaller fluctuations in heading estimates. Overall, the proposed algorithm achieves higher estimation accuracy than the Madgwick and Mahony methods and delivers more stable performance with fewer fluctuations than the dual-axis geomagnetic heading estimation method.

Based on the ground-truth heading information, MinE, MaxE, ME, RMSE, and FHE were calculated for each algorithm. The errors are summarized in

Table 1. The heading angle errors for the four methods.

Method	MinE (°)	MaxE (°)	ME (°)	RMSE (°)	FHE (°)
Madgwick	−8.6512	21.2763	10.6790	6.3829	14.9325
Mahony	−4.7575	25.9422	10.3335	6.5634	10.7947
Mag	−7.4806	15.3383	2.9750	4.9556	3.9784
Ours	−6.9220	14.3768	2.2728	2.7660	3.9784

.

As shown in Table 1, the ME of the Madgwick and Mahony algorithms are 10.6790° and 10.3335°, respectively, both higher than those of the dual-axis geomagnetic heading algorithm and the proposed method. As a typical geomagnetic-based algorithm, the direct geomagnetic heading algorithm achieves an ME of 2.9750°, outperforming the Madgwick and Mahony algorithms, while the proposed method achieves a lower ME of 2.2728°. By integrating geomagnetic reliability evaluation and segmental heading optimization, the proposed method controls the RMSE within 2.7660°, demonstrating superior heading estimation accuracy compared to the aforementioned methods.

In terms of RMSE, MaxE, and ME, the proposed method outperforms the other three methods, indicating higher stability and reliability. Overall, the proposed method exhibits robust anti-magnetic interference capability and high estimation accuracy, thereby providing high-precision and reliable heading information for PDR in complex electromagnetic environments.

4.3. “Coarse-Fine” Joint Step Height Estimation

Pedestrian step height estimation is a critical component of 3D PDR, with significant application value in scenarios such as stair climbing, slope traversal, and multi-floor indoor navigation. Traditional step height estimation methods suffer from inherent limitations. Barometers can provide absolute altitude information, but step height estimation methods based on barometers are susceptible to air pressure fluctuations (e.g., ventilation airflow, crowd-induced air disturbances), leading to unstable estimation accuracy, particularly in enclosed disaster scenarios such as underground tunnels and confined underground spaces. The IMU-based vertical acceleration integration method can reflect local step height variations, but cumulative drift errors inevitably arise with prolonged operation. To address these issues, this paper proposes a CNN-BiLSTM hybrid model for inertial-based step height estimation. Meanwhile, this paper develops a “coarse-fine” two-stage fusion framework, which fully leverages the global stability of barometric sensors and the local precision advantage of inertial measurements and realizes adaptive multi-source information fusion through AEKF, ultimately achieving high-precision and real-time step height estimation.

4.3.1. Barometer-Based Coarse Altitude Estimation

The coarse estimation module employs a barometer to provide a global reference altitude benchmark, effectively suppressing the long-term drift of inertial-based methods.

The barometric altitude $h_{\mathrm{b}\mathrm{a}\mathrm{r}\mathrm{o}}$ is calculated based on the International Standard Atmosphere model, which accurately describes the pressure-altitude relationship in the near-sea-level troposphere [33]. The formula is as follows:

$$h_{\mathrm{b}\mathrm{a}\mathrm{r}\mathrm{o}}=44330\cdot \left[1-{\left({\displaystyle \frac{P}{P_0}}\right)}^{0.1903}\right]$$

(17)

where $P$ is the real-time measurement value of the barometric sensor (unit: hPa); $P_0$ is the initial reference air pressure (unit: hPa); 44,330 is the reference altitude constant (unit: m); 0.1903 is the characteristic exponent of the International Standard Atmosphere model for dry air.

4.3.2. IMU-Based Fine Step Height Estimation

The fine estimation module adopts a CNN-BiLSTM hybrid deep learning model, which fully leverages CNN’s efficient local spatio-temporal feature extraction capability to capture the mutation characteristics of sensor signals within a single gait cycle and combines BiLSTM’s advantage in modeling long-range temporal dependencies to explore the temporal evolution law of complete gaits. The model outputs the step height estimation value $\mathsf{\Delta }{h}_{LSTM}$, which is used to correct the coarse estimation result $h_{baro}$ and enhance the local estimation precision of altitude information.

• Input Feature Selection

Changes in pedestrian step height are closely related to the dynamic characteristics of vertical motion. This paper selects nine-dimensional IMU signals (3-axis acceleration, 3-axis gyroscope angular rate, and 3-axis geomagnetic signals) within a sliding window of 120 consecutive sampling points as the original input. All input features are processed using Z-score normalization (mean-std normalization) to accelerate network convergence. Specifically, each feature dimension is standardized according to the formula $\left(x-\mu \right)/\sigma$ (where $\mu$ is the mean and $\sigma$ is the standard deviation of the feature), with features with $\sigma <$ 1 × 10⁻⁶ set to 0 to avoid numerical instability.

2.

Lightweight Network Structure

To balance estimation accuracy and computational efficiency, the CNN-BiLSTM network optimizes its structural parameters while ensuring high-precision step height prediction. The specific structure is shown in

Table 2. Structure of the lightweight BiLSTM network.

Layer	Configuration	Function
Input Layer	Batch size = 32; seq length = 120; feature dim = 9	Receive preprocessed 9-dimensional IMU temporal features and unify input format
Multi-scale 1D-CNN Layer	32 filters/branch; kernel sizes = 3/5/7; ReLU; batch norm	Extract local dynamic features across multiple time scales; enhance feature representation
Max Pooling Layer	Pooling kernel size = 2, Stride = 2	Reduce feature dimension; retain key information; lower computational overhead
Feature Concatenation Layer	Concatenate outputs of 3 branches, Dropout rate = 0.2	Fuse multi-scale features and suppress overfitting
BiLSTM Layer	64 hidden units; bidirectional; independent params	Capture long-range temporal dependencies of gait cycles
Fully Connected Layers	128 → 256 → 64 units; ReLU; dropout = 0.3	Fuse temporal features; focus on step height-related core information
Output Layer	1 unit, linear activation	Predict step height $h_{\mathrm{LSTM}}$ (m)
Regression Layer	MSE loss	Guide model training

.

3.

Lightweight Optimization Measures

To strike a balance between overfitting mitigation and inference efficiency, tailored structural optimization strategies are adopted for the CNN-BiLSTM network. Firstly, a dropout layer with a 20% dropout rate is appended after the feature concatenation layer, and another dropout layer with a 30% dropout rate is inserted after the fully connected layers. Combined with multi-scale feature enhancement for implicit regularization, the risk of overfitting is effectively mitigated at the cost of negligible extra computational overhead. Secondly, Batch Normalization is deployed immediately after each 1D-CNN branch to stabilize feature distribution and accelerate model convergence. Meanwhile, the AdamW optimizer with piecewise constant learning rate decay is adopted to improve training efficiency: the initial learning rate is set to 10⁻⁴, the decay factor is 0.5, and the decay interval is dynamically adjusted according to the validation loss to avoid premature convergence. Finally, the mini-batch size is configured as 32 to balance training speed and gradient stability, and the maximum number of training epochs is set to 200. This setting ensures sufficient model convergence while preventing redundant training iterations.

4.

Lightweight CNN-BiLSTM Network

The core logic of the CNN-BiLSTM network is defined as “local feature refinement–bidirectional temporal dependency modeling”: the multi-scale 1D-CNN branch extracts discriminative local features from the 9-dimensional IMU spatiotemporal data, while the BiLSTM branch captures bidirectional temporal correlations via two independent forward and backward LSTM sub-networks. Ultimately, the features derived from the two branches are fused to achieve high-precision step height regression. The core temporal modeling formulas of the BiLSTM are expressed as follows:

$$\left\{\begin{array}{l}\overrightarrow{i_t}=\sigma \left(\overrightarrow{W_i}{x}_t+\overrightarrow{U_i}\overrightarrow{h_{t-1}}+\overrightarrow{b_i}\right)\\ \overrightarrow{f_t}=\sigma \left(\overrightarrow{W_f}{x}_t+\overrightarrow{U_f}\overrightarrow{h_{t-1}}+\overrightarrow{b_f}\right)\\ \overrightarrow{c_t}=\overrightarrow{f_t}\odot \overrightarrow{c_{t-1}}+\overrightarrow{i_t}\odot tanh\left(\overrightarrow{W_c}{x}_t+\overrightarrow{U_c}\overrightarrow{h_{t-1}}+\overrightarrow{b_c}\right)\\ \overrightarrow{o_t}=\sigma \left(\overrightarrow{W_o}{x}_t+\overrightarrow{U_o}\overrightarrow{h_{t-1}}+\overrightarrow{b_o}\right)\\ \overrightarrow{h_t}=\overrightarrow{o_t}\odot tanh\left(\overrightarrow{c_t}\right)\\ \overleftarrow{i_t}=\sigma \left(\overleftarrow{W_i}{x}_t+\overleftarrow{U_i}\overleftarrow{h_{t+1}}+\overleftarrow{b_i}\right)\\ \overleftarrow{f_t}=\sigma \left(\overleftarrow{W_f}{x}_t+\overleftarrow{U_f}\overleftarrow{h_{t+1}}+\overleftarrow{b_f}\right)\\ \overleftarrow{c_t}=\overleftarrow{f_t}\odot \overleftarrow{c_{t+1}}+\overleftarrow{i_t}\odot tanh\left(\overleftarrow{W_c}{x}_t+\overleftarrow{U_c}\overleftarrow{h_{t+1}}+\overleftarrow{b_c}\right)\\ \overleftarrow{o_t}=\sigma \left(\overleftarrow{W_o}{x}_t+\overleftarrow{U_o}\overleftarrow{h_{t+1}}+\overleftarrow{b_o}\right)\\ \overleftarrow{h_t}=\overleftarrow{o_t}\odot tanh\left(\overleftarrow{c_t}\right)\\ h_t=concat\left(\overrightarrow{h_t},\overleftarrow{h_t}\right)\end{array}\right.$$

(18)

where the superscript $\overrightarrow{(\cdot )}$ denotes the forward LSTM branch and $\overleftarrow{(\cdot )}$ denotes the backward LSTM branch; $x_t$ represents the 9-dimensional IMU inertial input feature at time $t$; $\overrightarrow{h_t}$ and $\overleftarrow{h_t}$ are the hidden states of the forward and backward LSTM branches at time $t$, respectively, and the fused hidden state $h_t$ of the BiLSTM is obtained via feature concatenation; $\overrightarrow{c_t}$ and $\overleftarrow{c_t}$ are the cell states of the forward and backward LSTM branches, respectively; $\sigma$ denotes the Sigmoid activation function; $\odot$ represents the element-wise multiplication operation; and $\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{t}(\cdot )$ denotes the feature concatenation operation. $W_{\ast }$, $U_{\ast }$, and $b_{\ast }$ are the weight matrices, recurrent weight matrices, and bias vectors of each branch, respectively—notably, the parameters of the forward and backward branches are completely independent to avoid cross-branch interference.

For the specific task of pedestrian step height prediction, the network structure is optimized with a lightweight design principle. The input layer accepts the preprocessed 9-dimensional IMU spatiotemporal features. The BiLSTM hidden layer is configured with 64 neurons for each of the forward and backward branches, yielding a 128-dimensional fused hidden state to ensure sufficient temporal feature representation without excessive computational overhead. The output layer is designed as a 1-dimensional neuron with linear activation to directly regress the step height value.

To verify the effectiveness of the proposed lightweight CNN-BiLSTM model, a customized pedestrian step height estimation dataset was constructed, comprising a total of 2764 labeled samples. A two-stage stratified dataset partitioning strategy was adopted to ensure the statistical consistency of data distribution across subsets. First, the full dataset was split into an independent test set and a combined “training–validation set” at a 2:8 ratio. Subsequently, the combined subset was further partitioned into a validation set and a final training set at the same 2:8 ratio. The final dataset partition results are as follows: training set (1769 samples, 64.0%), validation set (442 samples, 16.0%), and test set (553 samples, 20.0%). Figure 10 presents the step height estimation results of the test samples derived from the proposed hybrid estimation model.

Processed by the high-precision fine estimation module, the model achieves state-of-the-art performance on the test set: RMSE = 0.0163 m, mean absolute error = 0.0056 m, and coefficient of determination (R²) = 0.9693. Moreover, the model exhibits robust generalization capability across diverse walking scenarios (e.g., flat ground, stair climbing, slope traversal). Meanwhile, the model’s inference efficiency satisfies the real-time operation requirements of wearable embedded devices, catering to the step height estimation demands of real-world pedestrian navigation.

4.3.3. Step Height Fusion Based on Kalman Filter

The AEKF algorithm is adopted to fuse the coarse barometric estimates and the inertial-based fine estimates. The meter-level absolute altitude provided by the barometer is utilized as segmented observations to periodically calibrate the continuous step-height estimates derived from the Inertial Measurement Unit (IMU). By integrating the global stability of coarse barometric estimation and the local high precision of CNN-BiLSTM fine estimation, the optimal step-height value $h_{\mathrm{o}\mathrm{p}\mathrm{t}}$ is ultimately output.

• State Vector and Equations

The state vector incorporates the core variables related to vertical motion (step height, velocity, acceleration) and sensor bias to ensure dynamic modeling accuracy. State prediction is realized through IMU dynamic modeling, observation updates are triggered segmentally by barometric data, and adaptive noise calibration is applied to enhance system robustness. The state vector is defined as follows:

$$\mathbf{X}={\left[h,v,a_z,b_a\right]}^T$$

(19)

where $h$ denotes the true step height (the target estimated variable, unit: m); $v$ represents the vertical velocity (unit: $\mathrm{m}/\mathrm{s}$); $a_z$ denotes the vertical acceleration (unit: ${\mathrm{m}/\mathrm{s}}^2$); $b_a$ denotes the accelerometer bias (unit: ${\mathrm{m}/\mathrm{s}}^2$).

The state transition equation is given by:

$$\mathbf{X}\left(k\right)=\mathbf{F}\cdot \mathbf{X}\left(k-1\right)+\mathbf{G}\cdot u\left(k\right)+\mathbf{W}\left(k\right)$$

(20)

where the 4 × 4 state transition matrix $\mathbf{F}$ is expressed as:

$$\mathbf{F}=\left[\begin{array}{cccc}1& \mathsf{\Delta }t& 0.5\mathsf{\Delta }{t}^2& 0.5\mathsf{\Delta }{t}^2\\ 0& 1& \mathsf{\Delta }t& \mathsf{\Delta }t\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]$$

(21)

The IMU sampling frequency is set to 100 Hz, resulting in $\mathsf{\Delta }t=0.01\hspace{0.17em}\mathrm{s}$. The input matrix $\mathbf{G}$ is defined as:

$$\mathbf{G}={\left[0,0,1,0\right]}^T$$

(22)

where the input $u\left(k\right)$ denotes the IMU’s calibrated horizontal acceleration observation $a_{z,\mathrm{c}\mathrm{a}\mathrm{l}}$, derived by eliminating gravitational components through accelerometer-based tilt compensation (unit: ${\mathrm{m}/\mathrm{s}}^2$); the process noise $\mathbf{W}\left(k\right)$ follows a Gaussian distribution $\mathcal{N}\left(0,\mathbf{Q}\right)$, where $\mathbf{Q}$ denotes the 4 × 4 process noise covariance matrix expressed as:

$$\mathit{Q}=\left[\begin{array}{cccc}{q}_h& 0& 0& 0\\ 0& q_v& 0& 0\\ 0& 0& q_a& 0\\ 0& 0& 0& q_b\end{array}\right]$$

(23)

where $q_h$ denotes the noise variance for step height estimation, with a recommended initial value of $0.01\hspace{0.17em}{\mathrm{m}}^2$; $q_v$ represents the noise variance for velocity, with a recommended initial value of $0.001\hspace{0.17em}(\mathrm{m}/\mathrm{s}{)}^2$; $q_a$ represents the noise variance of acceleration observations, with a recommended initial value of $0.0001\hspace{0.17em}({\mathrm{m}/\mathrm{s}}^2{)}^2$; $q_b$ represents the noise variance of accelerometer bias drift, with a recommended initial value of ${10}^{-6}\hspace{0.17em}({\mathrm{m}/\mathrm{s}}^2{)}^2$.

2.

Observation Equation

Barometer-based segmental observation triggering is implemented to ensure the fusion of high-frequency IMU dynamics and low-frequency barometric absolute references: updates are initiated only if either of the two conditions is satisfied (altitude change ≥ 1 m or time interval ≥ 5 s), thus avoiding the distortion of high-frequency IMU dynamic estimates caused by low-frequency barometric data interference. The observation equation is defined as:

$$\mathbf{Z}\left(k\right)=\mathbf{H}\cdot \mathbf{X}\left(k\right)+\mathbf{V}\left(k\right)$$

(24)

where the observation vector $\mathbf{Z}\left(k\right)$ consists of the absolute altitude measured by the barometer; the observation matrix $\mathbf{H}$ selectively extracts the step height state from the 4-dimensional state vector; the observation noise $\mathbf{V}\left(k\right)$ follows a Gaussian distribution $\mathcal{N}\left(0,R\right)$, where $R$ represents the barometer error variance; and the initial value of $R$ is obtained through calibration, with $R=0.25\sim 1\hspace{0.17em}{\mathrm{m}}^2$ corresponding to meter-level errors.

3.

Adaptive Extended Kalman Filter Process

A noise-adaptive update module is integrated into the traditional EKF framework to dynamically adjust the process noise covariance matrix $\mathbf{Q}$ and observation noise variance $R$ using the innovation residual. This design addresses the problem of noise characteristic drift caused by complex environmental changes, enhancing the filter’s robustness.

(1)

Prediction Step

The a priori state estimate is computed from the posterior state estimate at the previous time step.

$$\widehat{\mathbf{X}}\left(k|k-1\right)=\mathbf{F}\cdot \mathbf{X}\left(k-1|k-1\right)+\mathbf{G}\cdot u\left(k\right)$$

(25)

The a priori covariance estimate is computed from the posterior covariance at the previous time step.

$$\widehat{\mathbf{P}}\left(k|k-1\right)=\mathbf{F}\cdot \mathbf{P}\left(k-1|k-1\right)\cdot {\mathbf{F}}^T+\mathbf{Q}\left(k-1\right)$$

(26)

where $\mathbf{P}$ is the state covariance matrix, initial $\mathbf{P}\left(0\right)=\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\left[0.1,0.01,0.001,{10}^{-4}\right]$.

(2)

Observation Trigger Judgment

The observation update is activated if either of the following conditions is met:

$\left|h_{\mathrm{b}\mathrm{a}\mathrm{r}\mathrm{o}}\left(k\right)-h_{\mathrm{b}\mathrm{a}\mathrm{r}\mathrm{o}}\left(k-1\right)\right|\ge 1\hspace{0.17em}\mathrm{m}$: The altitude change exceeds the predefined resolution threshold of the barometer, ensuring valid altitude updates.

Time since last update ≥ 5 s: Enforced periodic calibration to prevent prolonged divergence of the IMU-based step height estimation due to cumulative drift.

(3)

Update Step

Calculate the innovation:

$$\mathbf{d}\left(k\right)=\mathbf{Z}\left(k\right)-\mathbf{H}\cdot \widehat{\mathbf{X}}\left(k|k-1\right)$$

(27)

Calculate Kalman gain:

$$\mathbf{K}\left(k\right)=\widehat{\mathbf{P}}\left(k|k-1\right)\cdot {\mathbf{H}}^T\cdot {\left(\mathbf{H}\cdot \widehat{\mathbf{P}}\left(k|k-1\right)\cdot {\mathbf{H}}^T+\mathit{R}\left(k\right)\right)}^{-1}$$

(28)

State update

$$\mathbf{X}\left(k|k\right)=\widehat{\mathbf{X}}\left(k|k-1\right)+\mathbf{K}\left(k\right)\cdot \mathbf{d}\left(k\right)$$

(29)

Covariance update:

$$\mathbf{P}\left(k|k\right)=\left(\mathbf{I}-\mathbf{K}\left(k\right)\cdot \mathbf{H}\right)\cdot \widehat{\mathbf{P}}\left(k|k-1\right)$$

(30)

Adaptive Noise Calibration: The innovation covariance matrix $\mathbf{D}\left(k\right)$ is calculated using a moving window with size $N=5$ as follows:

$$\mathbf{D}(k)={\displaystyle \frac{1}{N}}{\sum }_{i=k-N+1}^k\mathbf{d}(i)\cdot \mathbf{d}(i{)}^T$$

(31)

Update process noise $\mathbf{Q}\left(k\right)$:

$$\mathbf{Q}\left(k\right)=\mathbf{K}\left(k\right)\cdot \mathbf{D}\left(k\right)\cdot \mathbf{K}(k{)}^T$$

(32)

Update observation noise $R\left(k\right)$: Dynamically adjusted through innovation variance, $\mathit{R}\left(k\right)=\mathrm{v}\mathrm{a}\mathrm{r}\left(\mathbf{d}\left(k\right)\right)$.

Between two consecutive barometer updates, the high-frequency IMU prediction is leveraged to preserve the high temporal resolution dynamic tracking capability of step height estimation. When a new absolute altitude reference is provided by the barometer, the AEKF is activated to mitigate the accumulated drift errors of the IMU. Meanwhile, the innovation residual is used to learn time-varying noise characteristics in real time, thereby guaranteeing the long-term stability and precision of step height estimation.

4.4. Dead Reckoning

4.4.1. Step Length Estimation

An improved peak detection method [59] is adopted for step length estimation. Step length computation is triggered upon detecting the peak of the vertical acceleration signal, and the step length formula is expressed as follows:

$$L=k\cdot {\left(a_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}-a_{\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{y}}\right)}^{\alpha }$$

(33)

where $k=0.45$ and $\alpha =0.5$ are calibrated empirical parameters; $a_{peak}$ and $a_{valley}$ denote the peak value and valley value of the acceleration signal, respectively.

4.4.2. 3D Pedestrian Dead Reckoning

Following step detection, step length estimation, and heading estimation, pedestrian position reckoning is performed. Position reckoning computes the displacement of the pedestrian relative to the previous position based on the step length and heading of each step, accumulates this displacement with the previous position, and updates the current pedestrian position—as illustrated in Figure 11. The solid black lines with arrows represent the actual 3D displacement of the pedestrian, while the dashed black lines with arrows denote their projection onto the horizontal plane. The black dots mark the pedestrian’s position at the end of each step, clearly visualizing this incremental position update process.

The reckoning equations for the 3D PDR algorithm are given by:

$$\left\{\begin{array}{l}{p}_E\left(i\right)=p_E\left(i-1\right)+l_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}\left(i\right)\cdot \mathrm{s}\mathrm{i}\mathrm{n}\left(\psi \left(i\right)\right)\\ p_N\left(i\right)=p_N\left(i-1\right)+l_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}\left(i\right)\cdot \mathrm{c}\mathrm{o}\mathrm{s}\left(\psi \left(i\right)\right)\\ p_U\left(i\right)=p_U\left(i-1\right)+h_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}\left(i\right)\end{array}\right.$$

(34)

where $p_E\left(i\right)$ and $p_N\left(i\right)$ denote the east and north position coordinates of the pedestrian at the $i$-th step, respectively; $l_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}\left(i\right)$ is the step length of the $i$-th step; $\psi \left(i\right)$ is the heading of the $i$-th step; $p_U\left(i\right)$ denotes the vertical position coordinate of the pedestrian at the $i$-th step; and $h_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}\left(i\right)$ refers to the vertical height increment of the $i$-th step.

5. Experiments and Analysis

This section presents a comprehensive evaluation of the proposed 3D_IMB_APDR method, utilizing data collected from an integrated vest-mounted device. Section 5.1 elaborates on the experimental setup, while Section 5.2 focuses on quantitatively assessing the effectiveness of the proposed 3D_IMB_APDR method across diverse scenarios, as well as analyzing its practical positioning performance.

5.1. Experimental Setup

Experiments were conducted to evaluate the performance of the proposed method, employing a chest-worn sensor module and a laser rangefinder. The chest-worn module integrates an accelerometer, a gyroscope, a magnetometer, a barometer, and an onboard computing module. Acceleration, angular rate, and magnetic field strength data were acquired using an Xsens Dot sensor (Xsens Technologies B.V., Enschede, The Netherlands) and transmitted wirelessly to the computing module in real time. The computing module is an NVIDIA Jetson TX2 NX development board (NVIDIA Corporation, Santa Clara, CA, USA), and the barometer is a BMP280 digital pressure sensor (BOSCH, Stuttgart, Germany). A Deli DL331040B laser rangefinder (Deli Group Co., Ltd., Ningbo, Zhejiang, China) was utilized to obtain high-precision ground-truth distance information of pedestrian motion. Based on this distance data, the ground-truth trajectory was synthesized, and the ground-truth heading information was fitted, providing reliable reference benchmarks for the quantitative performance evaluation of the proposed method.

Experimental scenarios include an outdoor sports complex (integrating a playground and spectator stands), an underground multi-story parking garage, and a multi-floor campus teaching building. These scenarios encompass diverse complex environments and structures, including indoor/outdoor and above-ground/underground spaces, as well as flat grounds, slopes, and staircases—thus effectively verifying the adaptability of the proposed algorithm to complex real-world scenarios. The experimental setup is illustrated in Figure 12. The chest-worn sensor module was securely affixed to the subject’s chest for continuous data acquisition at a sampling frequency of 120 Hz.

5.2. Experimental Validation and Performance Evaluation

To evaluate the system’s positioning performance in real-world scenarios, a series of controlled experiments was conducted across diverse representative environments. Participants were instructed to navigate along three typical routes while wearing the calibrated chest-worn sensor module.

• Path #1: Campus Sports Fields

The participant started from the campus playground, rotated counterclockwise four times in place at the starting point, and then walked one and a half counterclockwise laps along the track. Subsequently, they ascended the spectator stands via the stairs, walked one full lap along the path marked by green signs on the stands, and descended back to the playground via the stairs. Finally, they completed another half counterclockwise lap on the playground and returned to the starting point. In this experimental scenario, the playground features relatively open and flat terrain with a benign electromagnetic environment. However, the stair section is characterized by varied step sizes and numerous tiers, and the top area contains a large number of metal structures as well as operating broadcast speakers, resulting in a complex electromagnetic environment. Figure 13 depicts the experimental environment and traversal path, where the green solid directional lines denote the movement path and direction. Meanwhile, each segment of the path has been numbered, and 6 images of the actual on-site terrain are included for reference.

Figure 14 presents the heading estimation results output by various methods under Scenario 1. As observed from the figure, the proposed method yields the optimal heading estimation performance. It fully leverages geomagnetic data to effectively mitigate the accumulation of heading drift errors while preserving the high short-term dynamic response and precision inherent to inertial heading estimation.

Figure 15 presents the 3D trajectory calculated by the proposed 3D_IMB_APDR method in this scenario. As can be observed from the trajectory curve, the proposed method accurately reconstructs the complete trajectory of the actual pedestrian movement.

Figure 16 displays the trajectory estimation results output by various methods in this scenario. It can be seen that the trajectory generated by the proposed method exhibits the closest alignment with the ground-truth trajectory, demonstrating superior 3D positioning performance.

Figure 17 illustrates the cumulative distribution function (CDF) curves of trajectory errors for various methods in this scenario. As shown in the figure, at a CDF probability of 0.9, the corresponding trajectory errors of the five methods (Madgwick, Mahony, direct geomagnetic (Mag), gyroscope-only (Groy), and the proposed method (Ours)) are 15.43 m, 47.82 m, 17.63 m, 63.66 m, and 5.49 m, respectively. From the error CDF curves, the error divergence speeds of the five methods, ranked in descending order, are: Groy > Mahony > Mag > Madgwick > Ours. It can thus be concluded that over the same movement distance, the proposed method delivers the minimum trajectory error, the slowest error accumulation rate, and the smallest final cumulative error, thereby demonstrating superior 3D positioning accuracy in interfered environments.

2.

Path #2: Underground Multi-Story Parking Garage

The experimental site was an underground multi-story parking garage, which incorporates typical terrains, including straight ascending slopes, straight descending slopes, and spiral upward/downward ramps. Meanwhile, this scenario contains multiple strong geomagnetic interference sources, such as large iron gates, metal air ducts, and electric fans. This complex electromagnetic environment creates ideal test conditions for verifying the dynamic correction capability of the proposed geomagnetic heading optimization method. The experimenter rotated counterclockwise four times in place at the starting point on Basement 1 (B1), then walked one full lap on B1. Subsequently, the experimenter descended to Basement 2 (B2) via a straight slope, walked one complete lap around B2, and then ascended back to B1 along a spiral ramp. Finally, the experimenter walked a specified distance on B1 and returned to the starting point. The specific walking route is illustrated in Figure 18. The green dashed lines in the figure represent ramp routes. Specifically, the dashed line at marker 6 denotes the downhill ramp path. The black dash-dot lines signify that the two connected points are spatially coincident. For example, after descending the ramp at marker 6, the pedestrian arrives at the starting point of the green line at marker 7.

Figure 19 presents the heading estimation results output by various methods in this scenario. As shown in the figure, the heading results obtained by the Madgwick method, Mahony method, and gyroscope angular rate integration method suffer from severe cumulative drift errors. The longer the movement duration, the larger the accumulated errors. In contrast, the heading estimation results based on raw geomagnetic data maintain good consistency with the ground-truth heading; however, due to the strong magnetic interference in this scenario, the raw geomagnetic heading results exhibit significant random fluctuations. By comparison, the proposed method achieves heading estimation results with minimal cumulative errors and low fluctuation levels. It inherits the core advantage of the geomagnetic heading method (i.e., no long-term cumulative drift) while retaining the short-term high dynamic performance and high-precision characteristics of inertial heading estimation.

Figure 20 presents the 3D pedestrian movement trajectory calculated by the proposed 3D_IMB_APDR method in this scenario. As can be observed from the trajectory curve, the trajectory generated by the proposed method accurately reconstructs the complete and precise movement path of the experimenter.

Figure 21 displays the trajectory estimation results output by various methods in this scenario. It can be seen from the figure that the trajectory of the proposed method is the closest to the ground-truth trajectory, demonstrating the superior positioning robustness against strong magnetic interference.

Figure 22 illustrates the CDF curves of trajectory errors for various methods in this scenario. As shown in the figure, at a CDF probability of 0.9, the corresponding trajectory errors of the five methods (Madgwick, Mahony, direct geomagnetic (Mag), gyroscope-only (Groy), and the proposed method (Ours)) are 88.4 m, 74.48 m, 13.02 m, 99.36 m, and 1.28 m, respectively. From the error CDF curves, the error divergence rates of the five methods, ranked in descending order, are: Groy > Madgwick > Mahony > Mag > Ours. It can thus be concluded that over the same movement distance, the proposed method achieves the lowest trajectory error, a slower error accumulation rate, and a smaller final cumulative error, thereby exhibiting excellent high-precision positioning performance in complex magnetic interference environments.

3.

Path #3: Teaching Building Complex Staircases

The experimental site was the complex staircases inside a campus teaching building. This scenario features frequent floor transitions via intricate staircases, representing a typical indoor building terrain. The experimenter started from the 4th floor (4F) and rotated counterclockwise four times in place at the starting point. Subsequently, the experimenter descended from 4F to the 3rd floor (3F) via the stairs, walked half a lap on 3F, then descended to the 2nd floor (2F) via the stairs, and walked another half lap on 2F before descending to the 1st floor (1F) via the stairs. Then, after walking half a lap on 1F, the experimenter ascended back to 2F via the stairs, walked half a lap on 2F, ascended to 3F via the stairs, walked half a lap on 3F, and finally ascended back to 4F via the stairs, returning to the starting point. The specific walking route is illustrated in Figure 23.

Figure 24 presents the heading estimation results output by various methods in this scenario. As shown in the figure, the heading results obtained by the Madgwick method, Mahony method, and gyroscope angular rate integration method exhibit severe cumulative drift errors. The longer the movement duration, the larger the accumulated errors. In contrast, the heading results based on raw geomagnetic data remain basically consistent with the ground-truth heading; however, due to the magnetic field interference, the raw geomagnetic heading results suffer from pronounced random fluctuations. On the other hand, the proposed method achieves heading estimation results with minimal cumulative errors and low fluctuation levels. It inherits the core advantage of the geomagnetic heading method (i.e., no long-term cumulative drift) while retaining the short-term high dynamic performance and high-precision characteristics of inertial estimation.

Figure 25 presents the 3D pedestrian movement trajectory calculated by the proposed 3D_IMB_APDR method in this scenario. As can be observed from the trajectory curve, the trajectory derived from the proposed method accurately reconstructs the complete and precise movement path with clear floor transition features.

Figure 26 displays the trajectory output by various methods. As shown in the figure, the trajectory of the proposed method is the closest to the ground-truth trajectory, demonstrating the best positioning adaptability for indoor staircase scenarios.

Figure 27 illustrates the CDF curves of trajectory errors for various methods in this scenario. As shown in the figure, at a CDF probability of 0.9, the trajectory errors of the five methods (Madgwick, Mahony, direct geomagnetic (Mag), gyroscope-only (Groy), and the proposed method (Ours)) are 4.60 m, 4.66 m, 7.76 m, 5.05 m, and 1.48 m, respectively. The error divergence rates of the five methods, ranked in descending order, are: Mag > Groy > Mahony > Madgwick > Ours. It can thus be concluded that over the same movement distance, the proposed method achieves the lowest trajectory error, a slower error accumulation rate, and a smaller final cumulative error, thereby exhibiting excellent high-precision positioning performance in indoor metal interference environments.

To comprehensively verify and quantitatively analyze the positioning performance of the proposed method, a systematic statistical analysis of key error metrics was conducted on the basis of experimental data collected from the three aforementioned test paths. For heading errors, a comparative assessment was carried out using five core metrics: MaxE, MinE, ME, RMSE, and FHE. For 3D trajectory errors, the Euclidean distance metric was adopted for error computation, and comparative analysis was implemented via six evaluation indicators: MaxE, MinE, ME, RMSE, and final position error (FPE). The detailed comparative results are presented in

Table 3. Heading angle errors.

Path	Method	MinE (°)	MaxE (°)	ME (°)	RMSE (°)	FHE (°)
Path #1	Madgwick	−26.6660	18.2960	1.3304	6.4182	−9.1660
	Mahony	−12.1743	36.1724	8.1556	8.1336	−2.7373
	Mag	−34.4245	20.9252	−1.8522	4.8041	0.4585
	Groy	−74.3929	6.3181	−30.6307	22.0800	−70.1379
	Ours	−23.8288	18.5725	−1.2410	3.8078	−2.0158
Path #2	Madgwick	7.2904	206.5991	109.1697	54.7376	206.5991
	Mahony	4.8888	194.8467	96.4483	49.3341	194.8467
	Mag	−55.3317	28.4537	−14.0357	14.0784	18.5205
	Groy	0.1436	219.7974	108.1996	62.0761	219.7974
	Ours	−9.6053	13.0738	1.1958	3.4221	4.6481
Path #3	Madgwick	−158.4360	2.0528	−66.4563	40.9689	−136.1408
	Mahony	−166.0783	2.0532	−66.4627	42.1682	−141.7676
	Mag	−15.1940	79.9228	20.1929	16.6555	19.2017
	Groy	−180.7144	5.9014	−79.3791	50.5141	−162.6951
	Ours	−16.8568	33.1240	11.4660	7.4618	16.3954

and

Table 4. 3D trajectory errors.

Path	Method	MinE (m)	MaxE (m)	ME (m)	RMSE (m)	FPE (m)
Path #1	Madgwick	0.0486	20.1929	7.4110	5.2884	20.1929
	Mahony	0.0631	59.9527	24.4225	15.6551	48.9156
	Mag	0.0342	20.4661	8.2115	6.0128	20.1418
	Groy	0.0668	69.7522	23.0742	19.2174	52.2291
	Ours	0.0543	6.7145	2.4579	1.8104	1.4046
Path #2	Madgwick	0.0948	112.8997	38.9441	28.4754	75.4712
	Mahony	0.0793	99.1079	33.3077	24.2598	61.0675
	Mag	0.0839	18.5869	8.0530	4.2819	13.4636
	Groy	0.0308	124.3519	38.7210	34.0717	86.7400
	Ours	0.0282	3.0773	0.7314	0.6035	2.5593
Path #3	Madgwick	0.0296	6.0863	2.1216	1.5712	3.4183
	Mahony	0.0285	6.2408	2.1330	1.6148	3.4092
	Mag	0.0323	10.4565	3.5556	2.5326	9.7858
	Groy	0.0323	6.7014	2.4282	1.7437	3.6314
	Ours	0.0276	1.8920	0.6641	0.4716	0.3244

, respectively.

As observed from Table 3, the proposed method demonstrates remarkable superiority in heading angle estimation across all three test paths compared with the Madgwick, Mahony, direct geomagnetic (Mag), and gyroscope-only (Groy) methods.

For Path #1, although the direct geomagnetic (Mag) method yields a negative ME of −1.85°, its RMSE reaches 4.80°, which is 26.1% higher than that of the proposed method (3.81°). This indicates that the Mag method suffers from larger error fluctuations despite a relatively small average deviation. In contrast, the gyroscope-only (Groy) method exhibits the worst performance, with an ME of −30.63° and an FHE of −70.14°, which indicates severe heading divergence caused by long-term inertial drift.

For Path #2, the Madgwick, Mahony, and Groy methods experience extreme heading deviations due to inertial drift and magnetic distortion. Specifically, their MaxEs exceed 190°, and their MEs are above 96°, rendering them ineffective for practical positioning. On the contrary, the proposed method effectively constrains the MaxE to 13.07°, maintains a low ME of 1.20°, and achieves the lowest RMSE of 3.42° among all comparative methods. This highlights the method’s anti-interference capability in electromagnetic environments.

For Path #3, the Madgwick and Mahony methods generate large negative MEs of over −66°, while the Groy method exhibits an even larger ME of −79.38°, all of which are attributed to cumulative inertial drift in the enclosed indoor space. In comparison, the proposed method reduces the ME to 11.47° and the RMSE to 7.46°, effectively suppressing drift accumulation and improving heading estimation stability.

Overall, the proposed method minimizes the fluctuation of heading angle errors (reflected by low RMSE values) and maintains both ME and FHE at a consistently low level. It outperforms all comparative methods in both simple and complex scenarios, verifying its effectiveness and adaptability for pedestrian heading estimation.

As shown in Table 4, the 3D trajectory errors further validate the superiority of the proposed method in terms of positioning accuracy and stability across all test scenarios.

For Path #1, the MaxE of the Madgwick, Mahony, and Groy methods exceed 20 m (with the Groy method reaching a maximum of 69.75 m), and their MEs are all above 7 m, indicating severe trajectory divergence. In contrast, the proposed method reduces the MaxE to 6.71 m and the ME to 2.46 m, with an FPE of only 1.40 m, which demonstrates effective suppression of inertial drift-induced trajectory divergence.

For Path #2, the MaxE values of the comparative methods range from 18.59 m (Mag) to 124.35 m (Groy), and their ME values are all above 8 m. On the contrary, the proposed method achieves a MaxE of 3.08 m, an ME of 0.73 m, and an FPE of 2.56 m. This highlights the proposed method’s outstanding anti-interference performance and high positioning precision in complex electromagnetic environments.

Even for Path #3, the proposed method still outperforms all comparative methods significantly. Its MaxE (1.89 m), ME (0.66 m), RMSE (0.47 m), and FPE (0.32 m) all rank as the optimal values among all comparative methods, which fully verifies that the method possesses excellent positioning accuracy and stability in complex indoor positioning scenarios with multiple turns and staircases.

Notably, several error metrics of Path #2 and Path #3 are slightly lower than those of Path #1. Although Path #3 appears to be more complex, Path #1 contains the spectator stand area with massive metal ceilings and operating broadcasting equipment, resulting in a harsh electromagnetic environment. Meanwhile, the spectator stand area features various steps, smaller turning radii, and sharper rotation angles during movement, which is the main cause of the above results.

In summary, the proposed method exhibits excellent performance in both heading estimation accuracy and positioning stability. It not only limits the maximum trajectory error to less than 7 m in all scenarios but also maintains the ME below 2.5 m and the FPE within the meter and sub-meter range. The method is far superior to the comparative methods in terms of error control and trajectory consistency. For the trajectories in the three typical scenarios, its trajectory error is more stable and accurate; especially in environments with complex magnetic fields, it delivers superior heading estimation results and trajectory performance. Meanwhile, in the experiments on three paths, the proposed algorithm exhibits favorable real-time performance with no perceivable delay during trajectory output. This provides a more stable, reliable, and accurate autonomous positioning solution for rescuers operating in complex post-disaster environments.

6. Conclusions and Future Work

The proposed 3D-IMB-APDR method addresses three core bottlenecks of traditional PDR in complex scenarios. These bottlenecks include cumulative heading drift, insufficient 3D positioning capability, and poor adaptability to magnetic interference. The method is realized through inertial-geomagnetic-barometric fusion technology and achieves significant improvements in positioning accuracy, stability, and environmental adaptability. These improvements come from systematic innovations in core algorithms and multi-module collaboration. First, a multi-criterion constrained dynamic geomagnetic reliability evaluation model is combined with a segmented heading correction strategy. This strategy fuses geomagnetic global accuracy and gyroscope short-term dynamic tracking to reduce heading estimation RMSE in complex magnetic environments. Second, a lightweight CNN-BiLSTM step height estimation model is developed using barometer-based coarse estimation and inertial time-series fine correction. It uses AEKF for dynamic fusion to achieve accurate step height calculation. Third, a 3D dead reckoning model is designed to provide precise multi-scenario 3D position solutions that meet complex environmental demands. Comprehensive tests are conducted in three typical scenarios: outdoor sports fields, underground parking garages, and multi-floor teaching buildings. The results show that compared with four comparative methods, the proposed method reduces positioning RMSE by 65.77–98.23%. The average positioning errors in the three scenarios are 2.46 m, 0.73 m, and 0.66 m, and the final position errors are 1.40 m, 2.56 m, and 0.32 m, respectively. In complex magnetic environments, the maximum trajectory error is limited to 3.08 m, with an average error of 0.73 m. Relying solely on chest-worn sensor data without external infrastructure, the proposed method maintains stable performance across diverse terrains. Therefore, it provides a reliable autonomous positioning solution for post-disaster rescue and underground engineering.

To address application challenges in extreme environments, future research will focus on several directions. First, event cameras will be integrated into the existing inertial–geomagnetic–barometric fusion positioning framework to further enhance positioning robustness. Second, an online learning mechanism will be designed to dynamically adjust model parameters. This improves generalization across different users and heterogeneous environments while reducing pre-calibration dependence. Third, chest-foot sensor fusion will be explored to leverage foot-mounted ZUPT features. This helps further suppress inertial drift and improve long-distance navigation accuracy. Fourth, the systematic integration scheme for sustainable operation of wearable devices in harsh environments will be investigated. Based on advances in ultra-low-power techniques and energy harvesting technologies, this work aims to realize long-duration battery-powered autonomous operation and optimize the energy efficiency of the entire navigation system. Finally, rigorous field tests will be conducted in extreme environments such as post-earthquake ruins, deep mines, and forests. These tests will verify reliability and promote practical applications in emergency rescue and underground inspection.