Search Results (330)

This study presents a deep learning–assisted integrated navigation scheme implemented on an autonomous underwater vehicle carrying a Chinese domestically developed strapdown inertial navigation system, designed for operation in surface and littoral environments. The system integrates measurements from SINS, the global positioning system, and a Doppler velocity log, while integrating a Decoder-based covariance estimator into the error state-extended Kalman filter. This hybrid architecture adaptively models time-varying processes and measurement noise from raw sensor inputs, greatly improving robustness for surface navigation in dynamic marine environments. To improve learning efficiency, we design a compact and informative feature representation that can be adapted to navigation error dynamics. The novel structure captures temporal dependencies and the evolution of nonlinear error more effectively than typical sequence models, achieving faster convergence and superior accuracy compared to GRU and Transformer baselines. The experimental results based on real sea trial data show that our method significantly outperforms model-based and learning-based methods in terms of navigation solution accuracy and stability, and the adaptive estimation of noise covariance. Specifically, it achieves the lowest RMSE of 0.0274, reducing errors by 94.6–34.6%, compared to conventional ES-EKF-integrated navigation, Transformer, GRU, and a DCE variant. These findings underscore the practical significance of integrating domain-informed filtering methodologies with deep noise modeling frameworks to achieve robust and accurate AUV surface navigation. Full article

Accurate and reliable localization is crucial for autonomous systems operating in dynamic and semi-structured environments, such as precision agriculture and outdoor robotics. Advances in Global Navigation Satellite System (GNSS) technologies, particularly Differential GPS (DGPS) and Real-Time Kinematic (RTK) positioning, have significantly enhanced position estimation precision, achieving centimeter-level accuracy. However, GNSS-based localization continues to encounter inherent limitations due to signal degradation and intermittent data loss, known as GNSS outages. This paper proposes a novel complementary RTK-like position increment prediction model with the purpose of mitigating challenges posed by GNSS outages and RTK signal discontinuities. This model can be integrated with a Dual Extended Kalman Filter (Dual EKF) sensor fusion framework, widely utilized in robotic navigation. The proposed model uses time-synchronized inertial measurement data combined with the velocity inputs to predict GNSS position increments during periods of outages and RTK disengagement, effectively substituting for missing GNSS measurements. The model demonstrates high accuracy, as the total aDTW across 180 s trajectories averages at 1.6 m while the RMSE averages at 3.4 m. The 30 s test shows errors below 30 cm. We leave the actual Dual EKF fusion to future work, and here, we evaluate the standalone deep network. Full article

Arbitrary zones are commonly used to describe and monitor external load (EL) during training and competitions. However, in recent years, relative speed zones have gained interest as they allow a more detailed description of the demands of each individual player, with their benefits largely unknown. This study aimed to (i) identify differences in EL methodological approaches using arbitrary and relative running speed zones; (ii) examine the effect of the methodological approaches to identify fast and slow basketball players during competition and training; and (iii) determine the effect of the season stage on the methodological approaches. Twelve players from a Spanish fourth-division basketball team were observed for a full season of matches and training using inertial devices with ultra-wideband indoor tracking technology and micro-sensors. Relative velocity zones were based on the maximum velocity achieved during each match quarter and were retrospectively recalculated into four zones. A linear mixed model (LMM) compared fast and slow players based on speed profiles between arbitrary and relative thresholds and during each competition stage. All players surpassed peak speeds of 24 km·h⁻¹ during the season, exceeding typical values reported in elite basketball (20–24.5 km·h⁻¹). Arbitrary thresholds produced greater distances in high-speed running (Zones 3 and 4) and yielded lower values in low-speed activity (Zone 1), with differences of ~100 m and ~120–250 m, respectively (p < 0.001), particularly for fast-profile players. These discrepancies were consistent across most stages of the season, although relative zones better captured variations in Zone 1 across time. Training sessions also elicited +8.7% to +40.7% greater distances > 18 km·h⁻¹ compared to matches. The speed zone methodology substantially influenced EL estimates and affected how player EL was interpreted across time. Arbitrary and relative approaches offer unique applications, with coaches and sport scientists encouraged to be aware that using a one-size-fits-all approach may lead to misrepresentation of individual player demands, especially when tracking changes in performance or managing fatigue throughout a competitive season. Full article

Background: A single lumbar-mounted inertial sensor offers a practical alternative to optoelectronic systems for gait analysis, simplifying measurements and improving usability in the clinical field. However, its validity can be influenced by sensor placement and signal choice. This study aimed to develop and validate a novel algorithm for estimating spatiotemporal parameters using anteroposterior linear acceleration and angular velocity around the sagittal axis using a single inertial measurement unit (IMU) placed on the lumbar region. The proposed algorithm was validated comparing the parameters computed by the algorithm with the ones computed using a commercial wearable system based on a two-foot-mounted IMU configuration. Thirty healthy subjects underwent a 2 min walk test, and five spatiotemporal parameters were computed using the two methodologies. Study results showed that cadence and gait cycle time exhibited very high agreement, with only a small, statistically significant bias in cadence negligible for practical purposes. In contrast, swing, stance, and double-support parameters showed disagreement due to the presence of systematic proportional errors. This work introduces a novel algorithm for gait event detection and spatiotemporal parameter estimation, addressing uncertainties related to sensor placement, metric models, processing techniques, and signal selection, while avoiding synchronization issues associated with using multiple sensors. Full article

This study addresses the nonlinear estimation problem in the strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation by proposing an improved filtering algorithm based on $S{E}_2(3)$ Lie group state representation. A dynamic model satisfying the group affine condition is established to systematically construct both left-invariant and right-invariant error state spaces, upon which two nonlinear filtering approaches are developed. Although the fast unscented transformation method is not novel by itself, its first integration with the $S{E}_2(3)$ Lie group model for SINS/DVL integrated navigation represents a significant advancement. Experimental results demonstrate that under large misalignment angles, the proposed method achieves slightly lower attitude errors compared to linear approaches, while also reducing position estimation errors during dynamic maneuvers. The 12,000 s endurance test confirms the algorithm’s stable long-term performance. Compared with conventional unscented Kalman filter methods, the proposed approach not only reduces computation time by 90% but also achieves real-time processing capability on embedded platforms through optimized sampling strategies and hierarchical state propagation mechanisms. These innovations provide an underwater navigation solution that combines theoretical rigor with engineering practicality, effectively overcoming the computational efficiency and dynamic adaptability limitations of traditional nonlinear filtering methods. Full article

This paper presents a bionic extended Kalman filter (EKF) state estimation algorithm for agricultural planters, inspired by the bionic mechanism of migratory birds navigating in complex environments, where migratory birds achieve precise localization behaviors by fusing multi-sensory information (e.g., geomagnetic field, visual landmarks, and somatosensory balance). The algorithm mimics the migratory bird’s ability to integrate multimodal information by fusing laser SLAM, inertial measurement unit (IMU), and GPS data to estimate the position, velocity, and attitude of the planter in real time. Adopting a nonlinear processing approach, the EKF effectively handles nonlinear dynamic characteristics in complex terrain, similar to the adaptive response of a biological nervous system to environmental perturbations. The algorithm demonstrates bio-inspired robustness through the derivation of the nonlinear dynamic teaching model and measurement model and is able to provide high-precision state estimation in complex environments such as mountainous or hilly terrain. Simulation results show that the algorithm significantly improves the navigation accuracy of the planter in unstructured environments. A new method of bio-inspired adaptive state estimation is provided. Full article

Accurate and reliable pedestrian positioning service is essential for providing Indoor Location-Based Services (ILBSs). Zero-Velocity Update (ZUPT)-aided Strapdown Inertial Navigation System (SINS) based on foot-mounted wearable Inertial Measurement Units (IMUs) has shown great performance in pedestrian navigation systems. Though the velocity errors will be corrected once zero-velocity measurement is available, the navigation system errors accumulated during measurement outages are yet to be further optimized by utilizing historical data during both stance and swing phases of pedestrian gait. Thus, in this paper, a novel Forward–Backward navigation and Rauch–Tung–Striebel smoothing (FB-RTS) navigation scheme is proposed. First, to efficiently re-estimate past system state and reduce accumulated navigation error once zero-velocity measurement is available, both the forward and backward integration method and the corresponding error equations are constructed. Second, to further improve navigation accuracy and reliability by exploiting historical observation information, both backward and forward RTS algorithms are established, where the system model and observation model are built under the output correction mode. Finally, both navigation results are combined to achieve the final estimation of attitude and velocity, where the position is recalculated by the optimized data. Through simulation experiments and two sets of field tests, the FB-RTS algorithm demonstrated superior performance in reducing navigation errors and smoothing pedestrian trajectories compared to traditional ZUPT method and both the FB and the RTS method, whose advantage becomes more pronounced over longer navigation periods than the traditional methods, offering a robust solution for positioning applications in smart buildings, indoor wayfinding, and emergency response operations. Full article

Aimed at the problem of navigation performance degradation in inertial navigation system/global navigation satellite system (INS/GNSS)-integrated navigation systems due to measurement anomalies and non-Gaussian measurement noise in complex navigation environments, an adaptive unscented Kalman filter (AUKF) algorithm based on the maximum versoria criterion (MVC) is developed. The proposed method is designed to enhance INS/GNSS-integrated navigation system robustness and accuracy by addressing the limitations of conventional filtering approaches. An adaptive unscented Kalman filter is constructed to enable dynamic adjustment of filter parameters, allowing for real-time adaptation to measurement anomalies. This ensures accurate tracking of navigation parameter states, thereby improving the robustness of the INS/GNSS-integrated navigation system in the presence of abnormal measurements. On this basis, fully considering the high-order moments of estimation errors, the maximum versoria criterion is introduced as the optimization criterion to construct a novel cost function, further effectively suppressing deviations caused by non-Gaussian disturbances and improving system navigation accuracy. The effectiveness of the proposed method was verified through vehicle navigation experiments. The experimental results demonstrate that the proposed method outperforms traditional approaches, effectively handling measurement anomalies and non-Gaussian measurement noise while maintaining robust navigation performance. Specifically, compared to the EKF, UKF, and MCCUKF, the proposed method reduces the root mean square error of velocity and position by over 60%, 50%, and 30%, respectively, under complex navigation conditions. The algorithm exhibits good accuracy and stability in complex environments, showcasing its practical applicability in real-world navigation systems. Full article

Wearable sensors are used in gait analysis to obtain spatiotemporal parameters, with gait events serving as critical markers for foot and lower limb movement. Summarizing detection methods is essential, as accurately identifying gait events and phases are key to deriving precise spatiotemporal parameters through wearable technology. However, a clear understanding of how these sensors, particularly angular velocity and acceleration signals within inertial measurement units, individually or collectively, contribute to the detection of gait events and gait phases is lacking. This review aims to summarize the current state of knowledge on the application for both gyroscopes, with particular emphasis on the role of angular velocity signals, and inertial measurement units with both angular velocity and acceleration signals in identifying gait events, gait phases, and calculating gait spatiotemporal parameters. Gyroscopes remain the primary tool for gait events detection, while inertia measurement units enhance reliability and enable spatiotemporal parameter estimation. Rule-based methods are suitable for controlled environments, whereas machine learning offers flexibility to analyze complex gait conditions. In addition, there is a lack of consensus on optimal sensor configurations for clinical applications. Future research should focus on standardizing sensor configurations and developing robust, adaptable detection methodologies suitable for different gait conditions. Full article

Human gait motions differ depending on the age of the person. Previous studies have estimated age categories of walkers or have used age analysis for security or commercial surveillance purposes using images. However, few studies have estimated age from gait parameters alone. We estimated the age of people using kernel regression analysis based on their height, weight, and representative gait parameters, i.e., walking features that are interpretable with relative ease. Samples were obtained from 75 Japanese women aged 20–70 in a database. Through a variable selection based on sensitivity analysis, the established model estimated the ages of the women with a correlation coefficient of 0.78 with their actual ages, and the mean absolute error was 9.99 years. The sensitive variables included the minimum foot clearance, body weight, walking velocity, step width, and stride length. Estimation errors were significantly greater for elderly adults than for young people. Specifically, the mean absolute error for people in their 20s was $7.4$ years, whereas that for those over 60 was $13.1$ years. The proposed method uses gait parameters that can be measured with wearable devices, such as inertial measurement units; therefore, it offers an accessible approach to estimating a walker’s age with moderate certainty and promoting healthcare awareness in daily life. Full article

Under large azimuth misalignment conditions, the initial alignment of strapdown inertial navigation systems (SINS) is challenged by the nonlinear characteristics of the error model. Traditional particle filter (PF) algorithms suffer from the inappropriate selection of importance density functions and severe particle degeneration, which limit their applicability in high-precision navigation. To address these limitations, this paper proposes an adaptive mixed-order spherical simplex-radial cubature particle filter (MLG-AMSSRCPF) algorithm based on matrix Lie group representation. In this approach, attitude errors are represented on the matrix Lie group SO(3), while velocity errors and inertial sensor biases are retained in Euclidean space. Efficient bidirectional conversion between Euclidean and manifold spaces is achieved through exponential and logarithmic maps, enabling accurate attitude estimation without the need for Jacobian matrices. A hybrid-order cubature transformation is introduced to reduce model linearization errors, thereby enhancing the estimation accuracy. To improve the algorithm’s adaptability in dynamic noise environments, an adaptive noise covariance update mechanism is integrated. Meanwhile, the particle similarity is evaluated using Euclidean distance, allowing the dynamic adjustment of particle numbers to balance the filtering accuracy and computational load. Furthermore, a multivariate Huber loss function is employed to adaptively adjust particle weights, effectively suppressing the influence of outliers and significantly improving the robustness of the filter. Simulation and the experimental results validate the superior performance of the proposed algorithm under moving-base alignment conditions. Compared with the conventional cubature particle filter (CPF), the heading accuracy of the MLG-AMSSRCPF algorithm was improved by 31.29% under measurement outlier interference and by 39.79% under system noise mutation scenarios. In comparison with the unscented Kalman filter (UKF), it yields improvements of 58.51% and 58.82%, respectively. These results demonstrate that the proposed method substantially enhances the filtering accuracy, robustness, and computational efficiency of SINS, confirming its practical value for initial alignment in high-noise, complex dynamic, and nonlinear navigation systems. Full article

IMUs (inertial measurement units) and cameras are popular sensors for autonomous localization due to their convenient integration. This article proposes a collaborative localization method, the CICEKF (collaborative IMU-aided camera extended Kalman filter), with a loosely coupled and two-step structure for the autonomous locomotion estimation of collaborative robots. The first step is for single-robot localization estimation, fusing and connecting the IMU and visual measurement data on the velocity level, which can improve the robustness and adaptability of different visual measurement approaches without redesigning the visual optimization process. The second step is for estimating the relative configuration of multiple robots, which further fuses the individual motion information to estimate the relative translation and rotation reliably. The simulation and experiment demonstrate that both steps of the filter are capable of accomplishing locomotion estimation missions, standalone or collaboratively. Full article

In this paper, an adaptive control scheme composed of an estimated feed-forward compensation and a PD control law with three mutually independent estimators is proposed for the tracking of desired trajectories in joint space for a robotic arm. One of the estimators is used to identify inertial and geometrical parameters, while the others determine the two principal components of the friction phenomenon: the part whose magnitude is position-dependent but velocity-independent and the part whose magnitude is proportional to velocity. Next, the persistently exciting condition is satisfied for each regression matrix of the estimators in a way that is easier to prove than the classical structure. Then, uniform global asymptotic stability can be concluded for the tracking error, regardless of parametric convergence, by applying the direct Lyapunov theorem. This scheme has been applied experimentally for a robotic arm to verify the theoretical results. The experimental results yielded a better performance in both estimating the parameters and tracking, with a much simpler overall analysis than the alternatives consulted. Full article

Firstly, the Reynolds equation considering gas inertia force is theoretically deduced in the cylindrical coordinate system, and then a mathematical model of aerostatic thrust bearing with three degrees of freedom (3-DOF) is constructed. Secondly, the Reynolds equation and velocity control equation are solved by the finite difference method (FDM), and the characteristics of gas pressure and velocity distribution in the gas film under steady-state conditions are revealed. On this basis, in the single-factor analysis, the bearing capacity error and recovery torque error caused by the inertia force term are quantitatively analyzed. It is found that the bearing rotating speed has a significant influence on the inertial force error, and the bearing radius also has a certain influence on the inertial force error, while the initial clearance, gas supply pressure, and torsion angle have relatively little influence on the inertial force error. Finally, in the multi-factor analysis, the sample regression equation of relative error of bearing capacity and relative error of restoring torque is established by using the multiple regression analysis method. By comparing the estimated values with the simulation results, the validity of the constructed regression equation is verified. Full article

The Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integrated navigation technology is widely utilized in vehicle positioning. However, in complex environments such as urban canyons or tunnels, GNSS signal outages due to obstructions lead to rapid error accumulation in INS-only operation, with error growth rates reaching 10–50 m per min. To enhance positioning accuracy during GNSS outages, this paper proposes an error compensation method based on CNN-BiLSTM-Attention. When GNSS signals are available, a mapping model is established between specific force, angular velocity, speed, heading angle, and GNSS position increments. During outages, this model, combined with an improved Kalman filter, predicts pseudo-GNSS positions and their covariances in real-time to compute an aided navigation solution. The improved Kalman filter integrates Sage–Husa adaptive filtering and strong tracking Kalman filtering, dynamically estimating noise covariances to enhance robustness and address the challenge of unknown pseudo-GNSS covariances. Real-vehicle experiments conducted in a city in Jiangsu Province simulated a 120 s GNSS outage, demonstrating that the proposed method delivers a stable navigation solution with a post-convergence positioning accuracy of 0.7275 m root mean square error (RMSE), representing a 93.66% improvement over pure INS. Moreover, compared to other deep learning models (e.g., LSTM), this approach exhibits faster convergence and higher precision, offering a reliable solution for vehicle positioning in GNSS-denied scenarios. Full article