Distributed Resilient Invariant Extended Kalman Fusion Filter Method for Target Tracking

ZHU Hongbo; ZHANG Yunkai

doi:10.11999/JEIT260273

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ZHU Hongbo, ZHANG Yunkai. Distributed Resilient Invariant Extended Kalman Fusion Filter Method for Target Tracking[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260273

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ZHU Hongbo, ZHANG Yunkai. Distributed Resilient Invariant Extended Kalman Fusion Filter Method for Target Tracking[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260273

ZHU Hongbo, ZHANG Yunkai. Distributed Resilient Invariant Extended Kalman Fusion Filter Method for Target Tracking[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260273

Citation:

ZHU Hongbo, ZHANG Yunkai. Distributed Resilient Invariant Extended Kalman Fusion Filter Method for Target Tracking[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260273

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Distributed Resilient Invariant Extended Kalman Fusion Filter Method for Target Tracking

doi: 10.11999/JEIT260273 cstr: 32379.14.JEIT260273

ZHU Hongbo^,,
ZHANG Yunkai

School of Electrical and Information Engineering, Anhui University of Science and Technology, Huainan 232001, China

Funds: The National Nature Science Foundation of China (62003001), Anhui Provincial Natural Science Foundation (2508085MF169), The Natural Science Research Project of Anhui Educational Committee (2023AH040157), Anhui University of Science and Technology Graduate Innovation Fundation (2023cx2093)

Received Date: 2026-03-16
Accepted Date: 2026-10-10
Rev Recd Date: 2026-10-10

Available Online: 2026-10-17

Abstract

Abstract

Objective Mobile Sensor Networks (MSNs) provide flexible deployment, dynamic sensing coverage, and cooperative observation capabilities for target tracking. However, nonlinear target motion, time-varying wireless communication topologies, intermittent measurements, and malicious attacks jointly complicate target tracking in MSNs. In open wireless communication environments, false data injection, denial-of-service, and replay attacks may corrupt measurement information and cause abnormal state estimates to propagate among neighboring nodes, thereby degrading estimation accuracy and potentially compromising filter consistency and stability. In addition, the target state considered in this study comprises orientation and position variables, whose evolution has an intrinsic non-Euclidean geometric structure. Conventional Extended Kalman Filter (EKF) methods generally linearize the system directly in Euclidean coordinates, which can introduce approximation errors and violate the orthogonality of the rotation matrix. Existing resilient distributed estimation methods also commonly rely on static sensor networks or restrictive linear-motion assumptions, limiting their applicability to nonlinear target tracking under dynamically switching network topologies. Therefore, reliable target tracking in MSNs requires a distributed state estimation method that accounts for geometric consistency, attack resilience, and dynamic network connectivity. Methods A distributed resilient invariant extended Kalman fusion filtering method is developed for nonlinear target tracking under network attacks. First, a Lie group-Lie algebra mapping is introduced into the EKF framework to construct an Invariant Extended Kalman Filter (IEKF). The target pose is represented on the two-dimensional Special Euclidean group (SE(2)), and the estimation error is defined through group multiplication. The error is then mapped to the corresponding Lie algebra, where linearization is performed. This geometric error representation preserves the structural properties of the rotation matrix during state propagation and avoids the loss of orthogonality caused by direct Taylor-expansion linearization. Prediction and measurement updates are formulated using the invariant error representation to obtain prior and posterior state estimates and their covariance matrices. Second, a dimensionality-reduced k-means attack detection mechanism is designed to assess local node credibility. For each neighboring node, the deviation between its posterior estimate and the local node’s fused prior estimate is reduced from a high-dimensional state difference to a scalar dissimilarity measure. These scalar dissimilarity measures are then clustered into two groups using k-means, and the cluster with the smaller centroid value is classified as the normal-node group. This mechanism identifies compromised or untrusted nodes without prior knowledge of the attack model and reduces the computational cost of clustering high-dimensional state deviations. The posterior estimates of identified compromised nodes are excluded from the trusted information set. Third, a covariance-intersection-based consensus fusion strategy is developed for time-varying network topologies. At each time step, a sensor node combines its own posterior estimate with the posterior estimates of trusted neighbors identified by k-means and the prior estimates of untrusted neighbors. The fusion weights are determined by the current network topology and node connectivity. Therefore, each node requires only local neighborhood information, and no global network information is needed. The resulting four-stage procedure consists of prediction, measurement update, attack detection, and consensus fusion. Results and Discussions MATLAB simulations are conducted to evaluate the estimation accuracy, stability, computational efficiency, and attack resilience of the proposed method. A mobile sensor network with six sensors is used to track a nonlinear moving target. The communication topology switches every two time steps, as shown in Fig. 1, and the target and sensor trajectories are presented in Fig. 2. Each sensor obtains a valid measurement only when the target is within its sensing range. The method is first evaluated in two cases: without attack detection and with the proposed attack detection mechanism. The corresponding state estimates are shown in Figs. 3 and 4. Without attack detection, malicious measurements cause the state estimates of several sensors to deviate markedly from the true target state. With the proposed detection mechanism enabled, corrupted measurements are screened out, and the state estimates from all six sensors gradually converge to the true target state, indicating improved estimation stability and tracking accuracy. A grouped false data injection attack is then simulated. Every 10 time steps, sensors 1 and 5 are attacked simultaneously, as are sensors 2 and 6, while the remaining sensors operate normally. Figs. 5 and 6 show the tracking trajectories without and with attack detection, respectively. The results indicate that the proposed detection mechanism identifies compromised nodes and prevents their abnormal measurements from dominating the distributed fusion process. Figs. 7 and 8 show the corresponding angular and relative-position estimation errors. Without attack detection, the estimation errors fluctuate significantly when attacks occur. When attack detection is combined with resilient fusion, the errors remain bounded and become more stable, indicating that the proposed method suppresses the propagation of malicious information under dynamic topology switching. For a quantitative comparison, the Root Mean Squared Error (RMSE) values for the angular and position estimates are compared among the proposed method, an adaptive-threshold detection method, and an invariant set-membership filtering method. All three methods are evaluated under the same target motion, network topology, noise, and attack conditions. As shown in Fig. 9, the proposed method maintains lower estimation errors and converges faster than both comparison methods. This improvement is attributable to two complementary components: the Lie group-Lie algebra-based IEKF, which preserves the geometric structure of the state representation, and the combined attack detection and covariance-intersection-based consensus fusion strategy, which limits the influence of abnormal information. Computational efficiency is also evaluated by running each method independently 100 times under identical conditions. As reported in Table 1, the average running time of the proposed method is 0.0340 s, compared with 0.0809 s for the adaptive-threshold detection method, 0.0816 s for the invariant set-membership filtering method, and 0.0357 s for the high-dimensional k-means method. The corresponding computation-time reductions are approximately 57.9%, 58.3%, and 4.7%, respectively. These results show that reducing high-dimensional state deviations to scalar dissimilarity measures lowers the computational cost of attack detection while preserving information about deviations caused by malicious measurements. Conclusions A distributed resilient invariant extended Kalman fusion filtering method is proposed for target tracking in MSNs subject to nonlinear target motion, time-varying communication topologies, and malicious measurement attacks. The Lie group-Lie algebra representation aligns the error definition and linearization with the system’s geometric structure, helping preserve consistency in nonlinear state estimation. The dimensionality-reduced k-means mechanism converts high-dimensional estimation deviations into scalar dissimilarity measures, enabling attack identification without a predefined attack model while reducing the computational burden. The covariance-intersection-based consensus fusion strategy combines each node’s own posterior estimate and trusted neighbors’ posterior estimates with untrusted neighbors’ prior estimates according to the current local topology, thereby limiting the influence of compromised nodes while preserving distributed operation. Simulation results show that the proposed method achieves lower estimation errors, more stable tracking performance, and lower computational cost than the comparison methods under the tested attack and dynamic-topology conditions. The proposed framework therefore provides an effective distributed solution for resilient target state estimation in attack-prone MSNs.
- Mobile Sensor Networks(MSN),
- Invariant Extended Kalman Filter(IEKF),
- Malicious attack,
- Target tracking

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References(23)

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