Resilient distributed Kalman filtering for cyber-physical systems via mean subsequence reduction

• Resilient DKF using dot-product Mean Subsequence Reduction (MSR-DP) for CPS state estimation • No thresholds or voting; effective even in sparse, adversarial networks • Ensures resilience via graph-based (r,s)-robustness and r-reachability • Outperforms prior DKFs under multiple false data injection attack types • Verified through simulations with realistic CPS network attack scenarios This paper presents a novel resilient distributed Kalman filtering (DKF) framework based on the Mean Subsequence Reduction mechanism that involves the dot-product (MSR-DP), designed to address security challenges in cyber-physical systems. Unlike conventional methods based on clustering or fixed threshold criteria to isolate compromised sensor data, the proposed resilient MSR-based distributed Kalman Filter algorithm (hereafter referred to as MSR-DP-DKF) dynamically identifies and excludes malicious nodes by leveraging the intrinsic connectivity properties of the network. We rigorously develop the algorithm using graph theoretical concepts such as r -reachability and ( r, s )-robustness to ensure sufficient redundancy against adversarial influences—even in sparsely connected networks. Simulations across diverse network topologies demonstrate the magnitude of our contribution: in challenging sparse networks, MSR-DP-DKF achieves complete resilience (0% compromised agents), whereas threshold-based and cluster-based methods fail in up to 100% of runs. This robustness is paired with markedly superior estimation accuracy, reducing the error of non-compromised agents by at least 97.6% compared with threshold-based approaches and by at least 96% compared with cluster-based methods. Furthermore, a discussion on the computation and communication overhead is presented. This work paves the way for more adaptive and robust filtering solutions in critical cyber-physical system applications, ranging from smart grids to autonomous systems.