Improving UAV Remote Sensing Photogrammetry Accuracy Under Navigation Interference Using Anomaly Detection and Data Fusion

Abstract

Accurate and robust navigation is fundamental to Unmanned Aerial Vehicle (UAV) remote sensing operations. However, the susceptibility of UAV navigation sensors to diverse interference and malicious attacks can severely degrade positioning accuracy and compromise mission integrity. Addressing these vulnerabilities, this paper presents an integrated framework combining sensor anomaly detection with a Dynamic Adaptive Extended Kalman Filter (DAEKF) and federated filtering algorithms to bolster navigation resilience and accuracy for UAV remote sensing. Specifically, mathematical models for prevalent UAV sensor attacks were established. The proposed framework employs adaptive thresholding and residual consistency checks for the real-time identification and isolation of anomalous sensor measurements. Based on these detection outcomes, the DAEKF dynamically adjusts its sensor fusion strategies and noise covariance matrices. To further enhance the fault tolerance, a federated filtering architecture was implemented, utilizing adaptively weighted sub-filters based on assessed trustworthiness to effectively isolate faults. The efficacy of this framework was validated through rigorous experiments that involved real-world flight data and software-defined radio (SDR)-based Global Positioning System (GPS) spoofing, alongside simulated attacks. The results demonstrate exceptional performance, where the average anomaly detection accuracy exceeded 99% and the precision surpassed 98%. Notably, when benchmarked against traditional methods, the proposed system reduced navigation errors by a factor of approximately 2-3 under attack scenarios, which substantially enhanced the operational stability of the UAVs in challenging environments.

1. Introduction

Leveraging their efficiency and flexibility, Unmanned Aerial Vehicles (UAVs) have achieved widespread deployment in the field of remote sensing, with applications spanning critical domains such as environmental monitoring, precision agriculture, and engineering surveying [1,2,3,4,5,6]. Particularly in applications utilizing UAV photogrammetry—the process of generating high-accuracy three-dimensional (3D) digital models and orthomosaics from aerial imagery—extremely stringent requirements are placed on the accuracy of the flight platform’s navigation and positioning system since navigation errors directly impact the geometric fidelity and georeferencing precision of the final remote sensing product [7,8]. Consequently, achieving high-precision navigation has emerged as a critical challenge that warrants further investigation in the field of UAV photogrammetry [9,10,11].

In the UAV navigation system, different sensors provide specific measurements. For example, the Global Positioning System (GPS) utilizes the time of arrival data from multiple satellites to calculate the distance between the satellites and the receivers, thereby estimating the UAV’s position. Moreover, the Inertial Navigation System (INS), based on the Inertial Measurement Unit (IMU), processes the sensor inputs from the gyroscopes and accelerometers to determine the current navigation attitude, speed, and position. It provides high short-term accuracy and strong resistance to external interference. Furthermore, the magnetometer utilizes the Earth’s magnetic field or the artificial magnetic fields to estimate the UAV’s yaw angle. However, a single sensor cannot consistently guarantee accurate and seamless navigation for the UAV [12,13]. For example, the accumulating INS navigation errors over time reduce the long-term accuracy [14]. Magnetometers are susceptible to interference from nearby magnetic fields, significantly affecting their attitude estimation, while the GPS is vulnerable to signal blockage and multipath distortions in constrained environments [15].

In addition to static environmental factors, the GPS is particularly vulnerable to human-induced malicious interference and attacks. With the rapid expansion of GPS and magnetometer use, combined with advances in software-defined radio (SDR) technology, UAV sensors are increasingly exposed to security threats [16,17]. For example, the availability of affordable radio hardware enables SDR devices capable of GPS signal spoofing, thereby potentially compromising UAV positioning [18,19]. Moreover, the reliance on wireless communication between UAVs, ground control stations, and satellites renders these systems susceptible to a variety of attacks, including GPS spoofing, replay attacks, and magnetic jamming [20,21,22]. Although recent real-time detectors—such as the isolation-forest-based approach in [23]—can identify GPS spoofing and correct positioning errors using secure infrastructure data, they necessitate extensive trusted coverage. Notably, inertial sensors (e.g., accelerometers and gyroscopes) can perform consistency checks with GPS data at the acceleration and angular velocity levels to detect spoofing attacks; these inertial sensors are inherently immune to radio frequency (RF)-based spoofing or jamming attacks [24].

Due to the limitations inherent in relying on a single sensor for attack detection, numerous multi-source fusion (MSF) methods have been proposed to enhance state estimation accuracy in UAV navigation [25]. Dynamic black-box analysis has shown that MSF schemes can significantly reinforce security against GPS spoofing [26]. For example, Tao et al. [27] improved the positioning accuracy and stability by integrating low-cost sensors. Wang Y et al. [28] categorized vehicular cybersecurity challenges into two main areas: information-oriented and control-oriented. The control-oriented approaches were further divided into data-driven methods [29,30] and model-based methods [31]. However, while data-driven methods are effective only for attacks represented in the training data, model-based techniques detect deviations in sensor measurements from the expected behavior, as predicted by the UAV’s mathematical model—and have been validated over long-term operations [32]. In addition, Michieletto et al. [33] applied information-theoretic tools for threshold testing by assessing the consistency of multimodal measurements, yet this approach requires collaboration between multiple UAVs, thus limiting its applicability to single-UAV operations.

Motivated by these findings, we introduce an integrated navigation framework fusing the GPS, an IMU, and magnetic sensor data. This framework leverages mathematical model-based techniques within an adaptive MSF architecture to detect and isolate abnormal measurements effectively. A key feature is the dynamic selection of reliable sensor combinations based on real-time reliability assessments, ensuring that robust, high-precision navigation can be achieved using cost-effective sensors. The proposed framework for anomaly detection and multi-source fusion is illustrated in Figure 1. Accordingly, this paper presents the following three key contributions:

1. Problem: How can we achieve precise UAV navigation in environments subject to complex interference and deliberate attacks to ensure the success of photogrammetry missions?

2. Solution: To address this challenge, we propose a trusted navigation framework integrating sensor anomaly detection with adaptive sensor fusion.

3. Platform experiments: We conducted spoofing experiments using the SDR and rigorously evaluated the proposed framework’s performance with UAV flight data. The evaluation included comprehensive assessments of navigation error metrics and anomaly detection accuracy.

The remainder of this paper is organized as follows: Section 2 details the kinematic and measurement models for the UAV. In Section 3, we introduce the sensor attack detection method and two adaptive fusion algorithms. Section 4 presents experimental validations based on real flight data. Finally, Section 5 concludes the paper.

2. Preliminary Problem

This section presents the kinematic and measurement models for the UAV.

2.1. Kinematic Model of UAV

Kinematic and measurement models are critical for the accurate state estimation and control of UAVs. The UAV was assumed to satisfy the following conditions:

(1) The UAV was modeled as a bilaterally symmetrical rigid body;

(2) It was subject only to gravitational and aerodynamic forces;

(3) The effects of Earth’s rotation and curvature on the navigation system were neglected.

The kinematic model was established using two coordinate systems: an inertial (Earth-fixed) frame ${\sum }_n$ and a body-fixed frame ${\sum }_b$ attached to the UAV. Euler angles $(\varphi ,\theta ,\psi )$ were used to represent the orientation between ${\sum }_b$ and ${\sum }_n$, with a rotation order of $z-y-x$. The rotation matrix $\mathit{R}$, which transforms coordinates from the inertial system to the body-fixed frame, is given as follows:

$$\mathit{R}={\mathit{R}}_x\left(\varphi \right){\mathit{R}}_y\left(\theta \right){\mathit{R}}_z\left(\psi \right)$$

(1)

Subsequently, the rates of change of the Euler angles are expressed as

$$\left[\begin{array}{c}\dot{\varphi }\\ \dot{\theta }\\ \dot{\psi }\end{array}\right]=\left[\begin{array}{ccc}1& sin\varphi tan\theta & cos\varphi tan\theta \\ 0& cos\theta & -sin\varphi \\ 0& sin\varphi sec\theta & cos\varphi sec\theta \end{array}\right]\mathit{\omega }$$

(2)

where $\mathit{\omega }={\left[\begin{array}{c}{\omega }_x,{\omega }_y,{\omega }_z\end{array}\right]}^{\mathrm{T}}$ denotes the UAV’s angular velocity, reflecting its attitude changes. The UAV’s position is represented as $\mathit{P}={[P_n,P_e,P_d]}^{\mathrm{T}}$, and its linear velocity as $\mathit{V}={[V_n,V_e,V_d]}^{\mathrm{T}}$. This framework links sensor measurements from onboard gyroscopes to the UAV’s rotational motion.

2.2. Measurement Model of UAV

In this study, three sensors were utilized: the GPS, magnetometer, and an IMU. First, the GPS provides the UAV’s position measurement, $\tilde{\mathit{P}}$, and linear velocity measurement, $\tilde{\mathit{V}}$, modeled as follows:

$$\begin{array}{cc}\hfill \tilde{\mathit{P}}& =\mathit{P}+{\mathit{e}}_P\hfill \\ \hfill \tilde{\mathit{V}}& =\mathit{V}+{\mathit{e}}_V\hfill \end{array}$$

(3)

where ${\mathit{e}}_P$ and ${\mathit{e}}_V$ are Gaussian white noise terms with covariances ${\mathit{Q}}_P$ and ${\mathit{Q}}_V$, respectively.

The magnetometer provides the UAV’s yaw angle measurement, $\tilde{\psi }$, as follows:

$$\tilde{\psi }=\psi +e_{\psi }$$

(4)

where $e_{\psi }$ represents Gaussian white noise with covariance $Q_{\psi }$.

The IMU, comprising a gyroscope and an accelerometer, measures the UAV’s angular velocity and acceleration, respectively. The gyroscope measurement model is given by

$$\tilde{\mathit{\omega }}=\mathit{\omega }+{\mathit{b}}_w+{\mathit{e}}_{\eta }$$

(5)

where $\tilde{\mathit{\omega }}$ is the measured angular velocity, ${\mathit{b}}_w={[b_{{\mathit{\omega }}_x},b_{{\mathit{\omega }}_y},b_{{\mathit{\omega }}_z}]}^{\mathrm{T}}$ denotes the constant gyroscope bias, and ${\mathit{e}}_{\eta }={[e_{{\eta }_x},e_{{\eta }_y},e_{{\eta }_z}]}^{\mathrm{T}}$ is Gaussian zero-mean noise. Similarly, the accelerometer measurement model is given by

$$\tilde{\mathit{a}}=\mathit{R}(\mathit{a}+{\mathit{b}}_a)+{\mathit{e}}_a$$

(6)

where $\tilde{\mathit{a}}$ is the acceleration measurement, ${\mathit{b}}_a$ represents the constant accelerometer bias, and ${\mathit{e}}_a$ denotes Gaussian zero-mean noise.

2.3. State Estimation Based on EKF

Due to the nonlinear nature of the UAV’s kinematic model (state equations), this paper employs an adaptive EKF and federated filtering to implement an IMU/GPS/magnetometer loosely coupled integration model. The EKF addresses nonlinear problems via local linear approximations and has been widely applied [34,35].

First, we define the system state vector as

$$\mathit{x}={\left[\varphi \theta \psi \mathit{P}\mathit{V}{\mathit{b}}_w{\mathit{b}}_a\right]}^{\mathrm{T}}$$

(7)

The system motion model of the EKF is

$$\dot{\mathit{x}}=f\left(x\right)+\mathit{w}\left(t\right)$$

(8)

where f(x) is a nonlinear function of the state vector that represents the product of the state vector and the system matrix, and $\mathit{w}\left(t\right)$ is the Gaussian white noise term.

Combining Equations (3) and (4), the observation model is expressed as

$$\mathit{z}=h\left(\mathit{x}\right)+\mathit{v}\left(t\right)=\left[\begin{array}{c}{\mathit{z}}^{\mathrm{GPS}}\\ \\ {\mathit{z}}^{\mathrm{Mag}}\end{array}\right]=\left[\begin{array}{c}\tilde{\mathit{P}}\\ \\ \tilde{\mathit{V}}\\ \\ \tilde{\mathit{\psi }}\end{array}\right]+\mathit{v}\left(\mathit{t}\right)$$

(9)

where h(x) is a linear function that maps the state to the observation space that is updated using actual measurements.

Consequently, the measurement matrices for the GPS and magnetometer are defined accordingly:

$$\mathit{H}\left(t\right)={\left[{\mathit{H}}^{\mathrm{GPS}}{\left(t\right)}^{\mathrm{T}},{\mathit{H}}^{\mathrm{Mag}}{\left(t\right)}^{\mathrm{T}}\right]}^{\mathrm{T}}$$

(10)

where

${\mathit{H}}^{\mathrm{GPS}}\left(t\right)=[{\mathbf{0}}_{6\times 3},{\mathit{I}}_{6\times 6},{\mathbf{0}}_{6\times 6}],{\mathit{H}}^{\mathrm{Mag}}\left(t\right)=[0,0,1,{\mathbf{0}}_{1\times 12}]$

The EKF comprises two primary steps:

(1) Prediction step:

In this step, the current state is estimated from the previous state using the state transition equations, and the error covariance matrix is likewise propagated.

Discretizing Equations (8)–(10) using an improved Euler discretization method [36] introduces a subscript k to denote the discrete time index:

$$\begin{array}{cc}\hfill {\widehat{\mathit{x}}}_{k/k-1}& ={\mathit{F}}_{k/k-1}{\widehat{\mathit{x}}}_{k-1/k-1}\hfill \\ \hfill {\mathit{P}}_{k/k-1}& ={\mathit{F}}_{k/k-1}{\mathit{P}}_{k-1/k-1}{\mathit{F}}_{k/k-1}^{\mathrm{T}}+{\mathit{Q}}_{k-1}\hfill \end{array}$$

(11)

where ${\mathit{Q}}_k$ denotes the discrete process noise covariance at step $k-1$.

(2) Update step:

In the update step, the state estimate and error covariance are corrected based on the innovation—the difference between the observed and predicted values. The Kalman gain is calculated as follows:

$${\mathit{K}}_k={\mathit{P}}_{k/k-1}{\mathit{H}}_k^{\mathrm{T}}{\left({\mathit{H}}_k{\mathit{P}}_{k/k-1}{\mathit{H}}_k^{\mathrm{T}}+{\mathit{R}}_k\right)}^{-1}$$

(12)

The state update process utilizes the innovation ${\mathit{r}}_k={[{\left({\mathit{r}}_k^{\mathrm{GPS}}\right)}^{\mathrm{T}},r_k^{\mathrm{Mag}}]}^{\mathrm{T}}$, comprising the GPS residual ${\mathit{r}}_k^{\mathrm{GPS}}$ and the magnetometer residual $r_k^{\mathrm{Mag}}$. The residual ${\mathit{r}}_k$ can be estimated and calculated as the difference between the actual measurement and the predicted value:

$$\begin{array}{cc}\hfill {\mathit{r}}_k^{\mathrm{GPS}}& ={\mathit{z}}^{\mathrm{GPS}}-{\mathit{H}}^{\mathrm{GPS}}{\widehat{\mathit{x}}}_{k/k-1}\hfill \\ \hfill r_k^{\mathrm{Mag}}& =z^{\mathrm{Mag}}-{\mathit{H}}^{\mathrm{Mag}}{\widehat{\mathit{x}}}_{k/k-1}\hfill \end{array}$$

(13)

3. Trusted Navigation Framework for UAV in Different Sensor Interference Environments

UAVs are vulnerable to various sensor interferences during flight, which can significantly compromise the navigation accuracy. This study mainly investigated the sensor attacks on the GPS and magnetometer, and modeled GPS denial as a jamming attack. To mitigate these threats, we first outline the primary types of UAV sensor attacks. Subsequently, two robust navigation algorithms were developed for abnormal detection and for fusing trusted sensor information.

3.1. Types and Modeling of Sensor Attacks on UAV

GPS communications are frequently targeted by attackers, while magnetometers are particularly susceptible to environmental magnetic interference. Navigation sensor attacks are broadly categorized into jamming and spoofing attacks [37]. The characteristics of these two threats to UAV communications are outlined below:

(1) Jamming attacks

Jamming attacks employ specialized equipment to inject noise into sensor signals, degrading data quality and hindering the accurate collection of environmental information. For example, electromagnetic or physical interference can disrupt GPS signals. Mathematically, a jamming attack on the signal is modeled by reducing the signal to $NaN$:

$$\begin{array}{cc}\hfill {\tilde{\mathit{P}}}_{\mathrm{GPS},k}^{\mathrm{interrupted}}& =NaN\hfill \\ \hfill {\tilde{\mathit{V}}}_{\mathrm{GPS},k}^{\mathrm{interrupted}}& =NaN\hfill \end{array}$$

(14)

where ${\tilde{\mathit{P}}}_{\mathrm{GPS},k}^{\mathrm{interrupted}}$ and ${\tilde{\mathit{V}}}_{\mathrm{GPS},k}^{\mathrm{interrupted}}$ represent the jammed GPS position and velocity data, respectively.

Similarly, magnetic jamming attacks are modeled by injecting a random bias:

$${\tilde{\psi }}^{\mathrm{Mag}}=\tilde{\psi }+\delta {\psi }_{\mathrm{interference}}$$

(15)

where ${\tilde{\psi }}^{\mathrm{Mag}}$ denotes the jammed magnetic data and $\delta {\psi }_{\mathrm{interference}}$ is a random bias introduced as the attack parameter.

(2) Spoofing attacks

Spoofing attacks involve the injection of forged signals during data collection, which disrupts environmental perception, impairs decision-making, and compromises UAV flight safety. For instance, attackers may transmit counterfeit GPS signals to spoof a UAV. Mathematically, a spoofing attack is modeled by adding a fixed deviation:

$$\begin{array}{cc}\hfill {\tilde{\mathit{P}}}_{\mathrm{GPS},k}^{\mathrm{spoofed}}& =\tilde{\mathit{P}}+{\mathit{\delta }}_P^{\mathrm{spoofed}}\hfill \\ \hfill {\tilde{\mathit{V}}}_{\mathrm{GPS},k}^{\mathrm{spoofed}}& =\tilde{\mathit{V}}+{\mathit{\delta }}_V^{\mathrm{spoofed}}\hfill \end{array}$$

(16)

where ${\mathit{\delta }}_P^{\mathrm{spoofed}}$ and ${\mathit{\delta }}_V^{\mathrm{spoofed}}$ are the position and velocity offsets, respectively, used in the spoofing attack model.

Replay attacks involve recording previously transmitted signals and resending them later. The replay attack is modeled by introducing two distinct times t and ${\mathit{t}}^{\prime }$:

$$\begin{array}{cc}\hfill {\tilde{\mathit{P}}}_{\mathrm{GPS},k}^{\mathrm{replayed}}& ={\tilde{\mathit{P}}}_{\mathrm{GPS},k-\Delta }\hfill \\ \hfill {\tilde{\mathit{V}}}_{\mathrm{GPS},k}^{\mathrm{replayed}}& ={\tilde{\mathit{V}}}_{\mathrm{GPS},k-\Delta }\hfill \end{array}$$

(17)

where ${\tilde{\mathit{P}}}_{\mathrm{GPS},k}^{\mathrm{replayed}}$ and ${\tilde{\mathit{V}}}_{\mathrm{GPS},k}^{\mathrm{replayed}}$ represent the received GPS data corresponding to a previous time $\Delta =t^{\prime }-t$.

3.2. Anomaly Detection Mechanism for UAV in Sensor Attack Environment

Traditional methods for UAV sensor attack detection, such as model-driven mechanisms and statistical techniques (e.g., fixed-threshold and least-squares methods [38]), are widely applied. However, the complex operational environments and variable mission requirements of UAVs, coupled with their inherent strong nonlinearity and high dynamics, often limit the flexibility and adaptability of these methods when processing complex flight data, thereby hindering efficient and reliable detection in intricate scenarios.

To overcome the limitations of traditional methods, this paper proposes an anomaly detection mechanism for sensor attacks on UAVs. This mechanism employs a residual consistency check strategy that integrates continuous anomaly counting with dynamic adaptive thresholding. It is designed to monitor persistent inconsistencies between the UAV’s predicted state and actual sensor measurements, thereby enabling the more reliable detection of sensor attacks. Specifically, the detection logic initially identifies potential sensor attacks by evaluating the quadratic forms of the GPS residuals $d_k^{\mathrm{GPS}}$ and magnetometer residuals $d_k^{\mathrm{Mag}}$, along with their dynamic variations.

$$\begin{array}{cc}\hfill {\left(d_k^{\mathrm{GPS}}\right)}^2& ={\left({\mathit{r}}_k^{\mathrm{GPS}}\right)}^{\mathrm{T}}{\mathit{Cov}}^{-1}\left({\mathit{r}}_k^{\mathrm{GPS}}\right){\mathit{r}}_k^{\mathrm{GPS}}\hfill \\ \hfill {\left(d_k^{\mathrm{Mag}}\right)}^2& ={\left(r_k^{\mathrm{Mag}}\right)}^{\mathrm{T}}{\mathit{Cov}}^{-1}\left(r_k^{\mathrm{Mag}}\right)r_k^{\mathrm{Mag}}\hfill \end{array}$$

(18)

where $Cov\left({\mathit{r}}_k\right)$ represents the covariance matrix, and $d_k^2$ is expected to follow a chi-square distribution with degrees of freedom equal to dim(${\mathit{z}}_k$).

If $d_k^2$ ($d_{\mathrm{GPS},k}^2$, $d_{\mathrm{Mag},k}^2$) exceeds the corresponding threshold ${\tau }_{\mathrm{GPS}}$ (set to 20) or ${\tau }_{\mathrm{Mag}}$ (set to 25), the respective sensor measurement is deemed abnormal:

$$\left\{\begin{array}{cc}{d}_{\mathrm{GPS},k}^2>{\tau }_{\mathrm{GPS}}\hfill & \Rightarrow GPSanomaly\hfill \\ d_{\mathrm{Mag},k}^2>{\tau }_{\mathrm{Mag}}\hfill & \Rightarrow Maganomaly\hfill \end{array}\right.$$

(19)

3.2.1. Adaptive Threshold and Heading Rate Compensation

In highly dynamic environments, using only a fixed threshold can result in numerous misjudgments. To address this, we propose an adaptive threshold mechanism that is particularly optimized for scenarios with rapid heading angle changes:

$${\tau }_{\mathrm{Mag}}\left(k\right)={\tau }_{\mathrm{Mag},\mathrm{base}}·f\left({\dot{\psi }}_k\right)$$

(20)

where ${\tau }_{\mathrm{Mag},\mathrm{base}}$ is the initial threshold of the magnetic sensor mentioned in Equation (19); $f\left({\dot{\psi }}_k\right)$ denotes the heading angle change rate function:

$$\begin{array}{c}\hfill f\left({\dot{\psi }}_k\right)=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}|{\dot{\psi }}_k|\le {\dot{\psi }}_{\mathrm{threshold}}\hfill \\ 1+\lambda \left(\right|{\dot{\psi }}_k|-{\dot{\psi }}_{\mathrm{threshold}}),\hfill & \mathrm{if}|{\dot{\psi }}_k|>{\dot{\psi }}_{\mathrm{threshold}}\hfill \end{array}\right.\end{array}$$

(21)

where ${\dot{\psi }}_k={\displaystyle \frac{{\psi }_k-{\psi }_{k-1}}{\Delta t}}$ represents the rate of change of the heading angle; $\lambda$ is the compensation coefficient (set to 3.0); and ${\dot{\psi }}_{\mathrm{threshold}}$ is the threshold that triggers the compensation (set to 0.15 rad/s).

3.2.2. Consecutive Anomaly Counting and Residual Consistency Detection

To mitigate misjudgments caused by instantaneous fluctuations, a continuous anomaly counting mechanism is introduced:

$$C_{\mathrm{sensor},k}=\left\{\begin{array}{cc}min(C_{\mathrm{sensor},k-1}+1,C_{\max }),\hfill & \mathrm{if}\mathrm{sensor}\mathrm{abnormal}\mathrm{at}\mathrm{k}\hfill \\ max(C_{\mathrm{sensor},k-1}-1,0),\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(22)

where $C_{\mathrm{sensor},k}$ is a non-negative integer, and the upper limit of the count is $C_{\max }$ (set to 6).

At this time, the conditions judged as abnormal are

$$A_{\mathrm{sensor},k}=\left\{\begin{array}{cc}\mathrm{true},\hfill & \mathrm{if}{C}_{\mathrm{sensor},k}\ge C_{\mathrm{threshold}}\hfill \\ \\ \mathrm{false},\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(23)

where $C_{\mathrm{threshold}}$ (set to 6) is the threshold for the consistency of continuous residual signs. When the threshold is exceeded, it is considered that enough continuous anomalies are detected to reduce the interference of short-term peak noise.

Furthermore, to enhance the detection accuracy, a residual consistency check is also incorporated:

$$consisten{t}_{\mathrm{bias}}=\left(\left|\sum _{i=0}^{N-1}sign\left(r_{k-i}\right)\right|\ge {\eta }_{1}N\right)\wedge \left(\left|{\displaystyle \frac{1}{N}}\sum _{i=0}^{N-1}{r}_{k-i}\right|\ge {\eta }_2\right)$$

(24)

where $r_k$ represents the measurement residual, N is the history window length (set to 10), ${\eta }_1$ is the consistency threshold (set to 0.6), and ${\eta }_2$ is the deviation amplitude threshold (set to 0.05).

By combining $d_k^2$ with the residual consistency measure, we define a comprehensive reliability criterion for each sensor:

$$Re{l}_{\mathrm{sensor},k}=\neg \left(d_{\mathrm{sensor},k}^2>{\tau }_{\mathrm{sensor},k}\vee \mathrm{consistent}{\mathrm{bias}}_{\mathrm{sensor},k}\right)$$

(25)

where $Re{l}_{\mathrm{sensor},k}(Re{l}_{\mathrm{GPS},k},Re{l}_{\mathrm{Mag},k})$ denotes the reliability of the sensor at time k, and a true value means that the sensor is reliable.

Based on this analysis, if the $Re{l}_{\mathrm{sensor},k}$ value is true, the corresponding sensor measurement is used in the EKF update step. Conversely, if a sensor abnormality is detected, the measurement from that sensor is isolated (not used directly in the update), and the system relies on the fusion of the remaining reliable sensors or prediction only:

$$\begin{array}{cc}\hfill {\widehat{\mathit{x}}}_k& ={\widehat{\mathit{x}}}_{k/k-1}+{\mathit{K}}_k{\mathit{r}}_k\hfill \\ \hfill {\mathit{P}}_k& =\left(\mathit{I}-{\mathit{K}}_k{\mathit{H}}_k\right){\mathit{P}}_{k/k-1}\hfill \end{array}$$

(26)

3.3. Multi-Source Fusion Based on DAEKF

Following the sensor data anomaly detection, additional data processing and multi-source fusion are conducted. The abnormal data isolation and fusion scheme proposed in this paper is illustrated in Figure 2. Specifically, the primary innovation of the DAEKF is its ability to adaptively select reliable measurements for the update step based on the anomaly detection results. Based on the sensor reliability flags $Re{l}_{\mathrm{GPS}}$ and $Re{l}_{\mathrm{Mag}}$, four update modes are defined:

$$\begin{array}{c}{\mathrm{Mode}}_k=\left\{\begin{array}{cc}\mathrm{Both},\hfill & \mathrm{if}Re{l}_{\mathrm{GPS},k}\wedge Re{l}_{\mathrm{Mag},k}\hfill \\ \mathrm{GPS}\mathrm{only},\hfill & \mathrm{if}Re{l}_{\mathrm{GPS},k}\wedge \neg Re{l}_{\mathrm{Mag},k}\hfill \\ \mathrm{Mag}\mathrm{only},\hfill & \mathrm{if}\neg Re{l}_{\mathrm{GPS},k}\wedge Re{l}_{\mathrm{Mag},k}\hfill \\ \mathrm{IMU}\mathrm{only},\hfill & \mathrm{if}\neg Re{l}_{\mathrm{GPS},k}\wedge \neg Re{l}_{\mathrm{Mag},k}\hfill \end{array}\right.\end{array}$$

(27)

The covariance is updated using the Joseph form to ensure numerical stability:

$${\mathbf{P}}_{k|k}=(\mathbf{I}-{\mathbf{K}}_k{\mathbf{H}}_k){\mathbf{P}}_{k|k-1}{(\mathbf{I}-{\mathbf{K}}_k{\mathbf{H}}_k)}^{\mathrm{T}}+{\mathbf{K}}_k{\mathbf{R}}_k{\mathbf{K}}_k^{\mathrm{T}}$$

(28)

To further improve the system adaptability, both the process noise covariance matrix ${\mathit{Q}}_k$ and the measurement noise covariance matrix ${\mathit{R}}_k$ are dynamically adjusted based on the anomaly status:

$$\begin{array}{c}{\mathbf{Q}}_k=\left\{\begin{array}{cc}{\gamma }_Q·{\mathbf{Q}}_{\mathrm{base}},\hfill & \mathrm{if}\mathrm{in}\mathrm{anomaly}\mathrm{mode}\hfill \\ {\mathbf{Q}}_{\mathrm{base}},\hfill & \mathrm{otherwise}\hfill \end{array}\right.\end{array}$$

(29)

$$\begin{array}{c}{\mathbf{R}}_k=\left\{\begin{array}{cc}{\gamma }_R·{\mathbf{R}}_{\mathrm{base}},\hfill & \mathrm{if}\mathrm{in}\mathrm{effect}\mathrm{period}\hfill \\ {\mathbf{R}}_{\mathrm{base}},\hfill & \mathrm{otherwise}\hfill \end{array}\right.\end{array}$$

(30)

where ${\gamma }_Q$ and ${\gamma }_R$ are the augmentation factors, which are set to 2 and 3, respectively. This adjustment allows the system to increase the process uncertainty during anomalies and to augment the measurement uncertainty during the recovery phase, thereby achieving a smooth transition.

The proposed anomaly isolation and adaptive fusion mechanism was validated through four representative attack scenarios, as summarized in

Table 1. Proposed fusion scheme.

Case	GPS Status	Magnetic Status	Result	Fusion Strategy
1	No Alarm	No Alarm	No Attack	GPS + Magnetic + IMU
2	Alarm	No Alarm	GPS Attack	Magnetic + IMU
3	No Alarm	Alarm	Magnetic Attack	GPS + IMU
4	Alarm	Alarm	GPS and Magnetic Attack	IMU

, that encompassed the following: (1) no attacks or anomalies; (2) GPS-only attacks; (3) only magnetic interference attack exists; (4) simultaneous GPS and magnetic jamming attacks.

Case 1: No warning was generated, indicating an attack-free environment. In this scenario, the GPS, magnetometer, and IMU data were fused for navigation.

Case 2: Only a GPS anomaly was detected, which triggered a GPS attack warning. Consequently, the navigation system relied primarily on the magnetometer and IMU data.

Case 3: Only a magnetometer anomaly was detected, which led to a magnetic sensor warning; the GPS and IMU data were then used for navigation.

Case 4: Both GPS and magnetometer anomalies were detected. These sensors were isolated, and the system used solely IMU data to maintain short-term precise navigation.

We simulated these attack scenarios using GPS and magnetometer data to represent potential threats during UAV flights. When the anomaly detection mechanism did not flag any anomaly (as in Case 1), the sensors were considered reliable and their data was fused using the EKF. Conversely, when a sensor attack was identified, the compromised data was isolated, and information from the unaffected sensors was fused to ensure reliable navigation in complex environments.

Detector 1 is dedicated to detecting GPS attacks. When GPS sensor data is flagged as abnormal, a GPS attack warning is issued and the state estimate along with the error covariance are updated accordingly:

$$\begin{array}{cc}\hfill {\mathit{K}}_k& ={\mathit{P}}_{k/k-1}{\mathit{H}}_k^{\mathrm{T}}{\left({\mathit{H}}_k{\mathit{P}}_{k/k-1}{\mathit{H}}_k^{\mathrm{T}}+{\mathit{R}}_{\mathrm{GPS},k}\right)}^{-1}\hfill \\ \hfill {\widehat{\mathit{x}}}_k& ={\widehat{\mathit{x}}}_{k/k-1}+{\mathit{K}}_k{\mathit{r}}_k^{\mathrm{GPS}},{\mathit{P}}_k=\left(\mathit{I}-{\mathit{K}}_k{\mathit{H}}_k\right){\mathit{P}}_{k/k-1}\hfill \end{array}$$

(31)

In scenarios where only a GPS attack is present, the compromised GPS data is isolated while the unaffected magnetometer and IMU data are fused to update the UAV’s attitude and position (corresponding to Case 2 in Table 1).

Detector 2 is responsible for detecting magnetic interference attacks. When an anomaly is detected in the magnetometer data, a magnetic interference warning is triggered, and the state estimate along with the error covariance is updated accordingly:

$$\begin{array}{cc}\hfill {\mathit{K}}_k& ={\mathit{P}}_{k/k-1}{\mathit{H}}_k^{\mathrm{T}}{\left({\mathit{H}}_k{\mathit{P}}_{k/k-1}{\mathit{H}}_k^{\mathrm{T}}+{\mathit{R}}_{\mathrm{Mag},k}\right)}^{-1}\hfill \\ \hfill {\widehat{\mathit{x}}}_k& ={\widehat{\mathit{x}}}_{k/k-1}+{\mathit{K}}_k{r}_k^{\mathrm{Mag}},{\mathit{P}}_k=\left(\mathit{I}-{\mathit{K}}_k{\mathit{H}}_k\right){\mathit{P}}_{k/k-1}\hfill \end{array}$$

(32)

In scenarios where only magnetic interference is present (Case 3 in Table 1), the system isolates the affected magnetometer data. If both the GPS and magnetic sensors are compromised, both data sources are isolated, and the UAV relies solely on the IMU for short-term precise navigation (Case 4 in Table 1).

3.4. Multi-Source Fusion Based on Federated Filtering

When facing severe sensor attacks, a local single-point failure can result in a global deviation in navigation. To address this, we further investigated federated filtering for information isolation and global fusion. The federated filter stands as an advanced decentralized filtering architecture, leveraging the information sharing principle for robust state estimation and fault tolerance. It achieves this through meticulously designed update steps, information fusion, and information distribution mechanisms.

During the filtering process, each sub-filter performs a time update and measurement update independently, and the main (global) filter fuses the results of each sub-filter to obtain the global optimal estimate or conservative suboptimal estimate [39,40]. In our adaptive federated filtering algorithm, three sub-filters are implemented: (1) GPS sub-filter: mainly processes position and velocity information; (2) magnetometer sub-filter: mainly processes yaw angle information; (3) IMU sub-filter: mainly processes acceleration and angular velocity information.

The information allocation in the federated filter is governed by the following principle [41]:

$${\mathbf{P}}_{0,i}^{-1}={\beta }_i{\mathbf{P}}_0^{-1},\sum _i{\beta }_i=1$$

(33)

where ${\beta }_i$ denotes the proportion of information allocated to the i-th sub-filter. The initial weights are configured as 0.6 for the GPS sub-filter, 0.3 for the IMU sub-filter, and 0.1 for the magnetometer sub-filter, respectively.

The core innovation of the adaptive federated fusion framework lies in its dynamic adjustment of the trust levels of sensor subsystems based on real-time anomaly detection results. The trust assigned to each subsystem is updated continuously over time:

$$trus{t}_{i,k}=trus{t}_{i,k-1}+\Delta trus{t}_{i,k}$$

(34)

When an anomaly is detected:

$$\Delta trus{t}_{i,k}=-{\alpha }_{\mathrm{decay},i}·trus{t}_{i,k-1}$$

(35)

When the sensor is normal:

$$\Delta trus{t}_{i,k}={\alpha }_{\mathrm{increase},i}·(trus{t}_{i,\max }-trus{t}_{i,k-1})$$

(36)

where ${\alpha }_{\mathrm{decay},i}$ and ${\alpha }_{\mathrm{increase},i}$ are the decay rate and growth rate, and $trus{t}_{i,\max }$ is the maximum trust limit.

Based on the trustworthiness of the subsystems, normalized weights are calculated:

$${\omega }_{i,k}={\displaystyle \frac{trus{t}_{i,k}}{{\sum }_{j}trus{t}_{j,k}}}$$

(37)

Subsequently, fusion is performed in the information filter framework by combining the individual sub-filter information matrices.

$$\begin{array}{cc}\hfill {\mathbf{P}}_{\mathrm{global},k}^{-1}& =\sum _i{\omega }_{i,k}{\mathbf{P}}_{i,k}^{-1}\hfill \\ \hfill {\mathbf{P}}_{\mathrm{global},k}^{-1}{\widehat{\mathbf{x}}}_{\mathrm{global},k}& =\sum _i{\omega }_{i,k}{\mathbf{P}}_{i,k}^{-1}{\widehat{\mathbf{x}}}_{i,k}\hfill \end{array}$$

(38)

Thus, the global optimal estimate ${\widehat{\mathrm{x}}}_{\mathrm{global},k}$ is obtained:

$${\widehat{\mathbf{x}}}_{\mathrm{global},k}={\mathbf{P}}_{\mathrm{global},k}\sum _i{\omega }_{i,k}{\mathbf{P}}_{i,k}^{-1}{\widehat{\mathbf{x}}}_{i,k}$$

(39)

To prevent individual sub-filters from diverging and to contain the impact of an attack locally—thus avoiding a global collapse due to a single-point failure—a feedback mechanism was implemented. For example, if an attacker spoofs or jams the data of a particular sensor, only that sub-filter’s local estimation ${\widehat{\mathbf{x}}}_{i,k}$ will be affected. The main filter then mitigates the impact on the overall estimation by appropriately adjusting the corresponding weights ${\mathbf{P}}_{i,k}$:

$$\begin{array}{cc}\hfill {\widehat{\mathbf{x}}}_{i,k}& \leftarrow {\alpha }_{\mathrm{feedback},i}·{\widehat{\mathbf{x}}}_{\mathrm{global},k}+(1-{\alpha }_{\mathrm{feedback},i})·{\widehat{\mathbf{x}}}_{i,k}\hfill \\ \hfill {\mathbf{P}}_{i,k}& \leftarrow {\alpha }_{\mathrm{feedback},i}·{\mathbf{P}}_{\mathrm{global},k}+(1-{\alpha }_{\mathrm{feedback},i})·{\mathbf{P}}_{i,k}\hfill \end{array}$$

(40)

where ${\alpha }_{\mathrm{feedback},i}$ is the feedback coefficient.

4. Experimental Analysis

This section presents the experimental validation of our proposed navigation framework, specifically assessing its robustness for high-precision applications, like UAV photogrammetry. The fidelity of 3D environmental reconstructions, such as those of a university campus, is critically dependent on accurate vehicle trajectory data. However, the navigation sensors that provide this data are vulnerable to both environmental interference and malicious attacks. Therefore, the experiments herein were designed to quantitatively evaluate the framework’s ability to mitigate these threats. The evaluation focused on the efficacy of the dynamic adaptation and federated filtering algorithms in maintaining a high navigation accuracy under anomalous conditions, which ensured the data integrity required for successful 3D reconstruction in complex or adversarial environments.

The experimental hardware platform, depicted in Figure 3, comprised a DJI M350 RTK UAV manufactured by DJI (Shenzhen, China) and a ground station. The ground station included a GPS spoofing attack device (USRP B210) from Ettus Research (Austin, TX, USA), a portable power bank, and a laptop terminal for operation. The USRP B210 features a broad RF coverage range from 70 MHz to 6 GHz. During the experiments, the UAV’s flight controller logged a comprehensive suite of telemetry data, including the geodetic position (longitude, latitude, height), attitude (roll, pitch, yaw), inertial measurements (linear acceleration, angular velocity), velocity vectors, and magnetometer readings. All flight experiments, including the GPS attack scenarios, were conducted in an open-field environment at the Beihang University Hangzhou International Innovation College in Hangzhou, Zhejiang Province, China (coordinates: 119°58′14′′E, 30°21′34′′N).

Initially, a GPS attack experiment was conducted. In this experiment, a USRP B210 was connected to a laptop and used to generate a forged ephemeris file that corresponded to the target location (Xining, coordinates: 101°48′25′′E, 36°38′50′′N). The generated spoofing signal, mimicking GPS satellite signals, was then transmitted via a connected antenna. As shown in Figure 4, the position information on both Google Maps and the test software “Satellite Companion” confirmed that the smartphone’s location was successfully spoofed to the preset target. Furthermore, Figure 5 shows the map interface on the UAV controller, which presents map data corresponding to the spoofed location—thus demonstrating the feasibility of launching GPS attacks on the UAV.

Figure 6 demonstrates the comparison of the UAV photogrammetry under two different conditions. Figure 6a shows the normal flight state: the UAV flew along the planned route (red trajectory line) to cover the target mapping area. During this process, the UAV flew from the starting point to the end point and systematically collected a series of aerial images. The overlap rate between these images (with black rectangular boxes indicating their ground coverage)—primarily encompassed the forward overlap rate (the overlap between two consecutive photos as the UAV advanced along a single flight line) and the sidelap overlap rate (the overlap between adjacent photos from two parallel flight lines)—was precisely controlled. This ensured the integrity and spatial continuity of the data, which laid the foundation for subsequent high-precision three-dimensional scene reconstruction through the principles of photogrammetry. In contrast, Figure 6b demonstrates a scenario where the UAV encountered external interference or GPS spoofing attacks during flight. As a result, the actual flight trajectory of the UAV deviated significantly from the planned route, which presented an irregular and chaotic pattern. This directly led to disordered aerial image acquisition positions and uneven ground coverage. The overlap rate between the images became uncontrollable, which potentially resulted in rates that were too low, missing, or even large areas of coverage gaps. This unstructured and defective data collection mode greatly increased the difficulty of the 3D reconstruction and was likely to result in reconstruction failure or data loss in the final model, which made it impossible to fully and accurately reproduce the target scene.

To validate the proposed adaptive dynamic fusion and federated filtering algorithms, real flight data were collected from a UAV over a 380 s period. In the post-processing, various attack scenarios were simulated using the collected data: from 32 to 36 s, a spoofing attack was applied with a positional offset of [15, 15, 20] m; from 113 to 118 s, a replay attack was performed wherein the GPS received data from 4 s earlier; from 240 to 243 s, an interference/interruption attack was implemented, during which the GPS data became NaN; and from 320 to 323 s, a magnetic interference attack imposed a yaw angle offset of 0.25 rad (approximately 14.32°).

The performance of the navigation algorithms was evaluated using the RMSE [42,43], while the anomaly detection performance was assessed using the accuracy and precision metrics, which evaluated both the localization robustness and detection capability.

The position accuracy was quantified using the RMSE:

$${\mathrm{RMSE}}_{\mathrm{pos}}=\sqrt{{\displaystyle \frac{1}{N}}\sum _{k=1}^N{\parallel {\widehat{\mathbf{p}}}_k-{\mathbf{p}}_k^{\mathrm{true}}\parallel }^2}$$

(41)

where ${\widehat{\mathbf{p}}}_k$ is the position estimate, and ${\mathbf{p}}_k^{\mathrm{true}}$ is the real position.

The attitude accuracy was evaluated by the Euler angle RMSE:

$${\mathrm{RMSE}}_{\varphi ,\theta ,\psi }=\sqrt{{\displaystyle \frac{1}{N}}\sum _{k=1}^N{\parallel {\widehat{\mathsf{\Phi }}}_k-{\mathsf{\Phi }}_k^{\mathrm{true}}\parallel }^2}$$

(42)

where ${\widehat{\mathsf{\Phi }}}_k$ is the pose angle estimate.

Figure 7 illustrates the UAV flight trajectories. It is evident that the Classic EKF suffered from significant position deviations during the GPS attack periods. In practice, GPS spoofing may cause the UAV to be redirected to unintended locations—posing collision risks—while outdated data and interference interruptions can lead to severe positioning inaccuracies. The isolation and fusion algorithms proposed in this paper can mitigate these risks. As illustrated in Figure 8 (middle and bottom panels), the anomaly detection algorithm proposed in this study accurately identified GPS spoofing and magnetic interference attacks. Simultaneously, the federated filter adjusted the weights of the sub-filters (Figure 8, top panel) based on the detected anomalies. Moreover, by dynamically selecting more reliable data for subsequent fusion, the approach significantly mitigated the risks and navigation errors induced by sensor attacks. Even under sensor attacks, these algorithms delivered robust navigation.

To evaluate the performance of the proposed MSF algorithm, a comparative analysis was conducted against a Classic EKF that utilized a fixed-threshold anomaly detection mechanism. The experimental protocol was designed to compare the RMSE in the navigation solutions and the computational latency associated with the anomaly detection and judgment across the entire operational duration. Ten distinct sets of comparative experiments were executed, incorporating specific attack benchmarks: signal interruption (3 s), replay attack (5 s), magnetic interference (3 s), spoofing attack (3 s), yaw offset (0.25 rad), position offset ([10, 10, 20] m), and replay time offset (4 s). In addition, a series of interference and spoofing attacks of progressively increasing intensity were implemented, with detailed outcomes presented in

Table 2. Comparison of RMSE and anomaly detection times for three algorithms.

	Attack Events	Classic EKF (m|s)	DAEKF (m|s)	FF (m|s)
1	Attack benchmarks	3.00|0.264	1.54|0.079	1.01|0.481
2	Signal interruption 5 s	3.04|0.191	1.69|0.048	1.17|0.324
3	Replay attack 7 s	17.21|0.197	3.51|0.050	2.55|0.335
4	Mag interference 8 s	2.98|0.186	1.59|0.047	1.09|0.317
5	Spoofing attack 6 s	3.67|0.192	1.72|0.048	1.18|0.323
6	Spoofing offset [20, 20, 30] m	1.65|0.189	1.64|0.048	1.08|0.324
7	Spoofing offset [40, 40, 60] m	1.70|0.206	1.69|0.052	1.08|0.347
8	Spoofing yaw offset 0.35 rad	2.88|0.193	1.60|0.048	1.10|0.325
9	Spoofing yaw offset 0.50 rad	3.07|0.197	1.73|0.049	1.15|0.333
10	Replay time offset 8 s	2.95|0.197	1.63|0.049	1.03|0.329

FF: federated filtering.

. The experimental results reveal that the DAEKF achieved the shortest latency for algorithmic anomaly detection and judgment, whereas the federated filtering algorithm exhibited marginally longer processing times. Regarding the navigation accuracy, the conventional EKF demonstrated comparatively elevated the RMSE values; its performance was most substantially degraded under replay attack scenarios. In contrast, both the proposed DAEKF and the federated filtering algorithm yielded lower average RMSE values, indicating superior robustness and enhanced navigation accuracy across diverse attack and interference conditions.

Figure 9 presents the performance evaluation metrics for the anomaly detection concerning sensor attacks. Each experiment covered four typical attack events, namely, GPS spoofing attacks, replay attacks, interference/interruption attacks, and magnetic interference attacks. The results clearly demonstrate that the proposed algorithm achieved an average accuracy that exceeded 99% and an average precision that surpassed 98% across these attack scenarios.

5. Conclusions

This study addressed the critical challenge of maintaining navigation integrity for a UAV under sensor attacks or severe interference, particularly for precision-dependent applications, such as UAV-based remote sensing. We propose a robust navigation fusion framework that integrates an anomaly detection mechanism based on adaptive thresholding and residual consistency checks, with an adaptive sensor fusion strategy. By mathematically modeling sensor attacks, the system efficiently identifies and isolates anomalous data, thereby preventing error propagation. The proposed DAEKF adaptively reconfigures the fusion strategy upon attack detection, prioritizing trusted data sources, such as the IMU. To further bolster the resilience, a federated filtering architecture was implemented, which isolates sensor faults at the sub-filter level and dynamically adjusts information fusion weights based on assessed reliability, effectively mitigating fault propagation. Rigorous experimental evaluations that utilized real-world UAV flight data alongside simulated GPS spoofing, replay, interference, and magnetic interference attacks, empirically validated the framework’s performance. The anomaly detection mechanism achieved a high accuracy (>99%) and precision (>98%). Critically, compared with conventional methods, the proposed DAEKF and federated filtering algorithms significantly enhanced the navigation accuracy under attack conditions, where the DAEKF also substantially reduced the anomaly detection latency. These findings underscore the efficacy of the proposed framework in sustaining precise and reliable UAV navigation in complex or adversarial environments, thereby holding significant promise for improving UAV operational safety and mission success rates. Future research will focus on integrating reinforcement learning techniques to enhance system autonomy and robustness in unknown complex environments, and on optimizing the federated filter structure to further reduce the anomaly detection time.