Filtering for Multi-sensor System with Random and Fixed Out-of-order Measurements

This paper addresses the critical challenge of spatial out-of-order measurements in multi-sensor networked systems, which degrade state estimation accuracy. We propose tailored solutions for two scenarios: random and fixed out-of-order conditions. For random out-of-order with unpredictable sequences, a cumulative measurement method and a minimum-innovation-based recovery algorithm are developed to enhance estimation precision. For fixed out-of-order with consistent yet unknown patterns, a fast restoration algorithm leveraging cumulative innovation evaluation is introduced to reconstruct correct sequences within finite time. Theoretical analysis establishes upper bounds on error covariance, while numerical simulations validate the algorithms’ efficacy in both stable and unstable systems, achieving recovery accuracies exceeding 70% and 80%, respectively. The proposed methods significantly outperform conventional fusion techniques, offering robust solutions for real-world applications in networked control systems.