A Robust Parallel Interacting Multi‐Model Kalman Filter Based on Expectation‐Maximization for Packet Loss and Non‐Gaussian Noise

ABSTRACT In practical applications, systems are frequently subjected to the dual challenges of packet loss and non‐Gaussian noise. Simultaneously, state estimation algorithms based on information entropy often suffer from practical limitations owing to their substantial computational burden and time cost. To address these limitations, this paper proposes a novel parallel interacting multi‐model Kalman filter with packet loss (PIMM‐PLKF) to achieve robust and efficient state estimation. The method begins by employing the expectation‐maximization (EM) algorithm to train a Gaussian mixture model (GMM), which accurately captures the characteristics of non‐Gaussian noise. This trained GMM is then integrated into a linear discrete‐time system model with packet loss, enabling precise reconstruction of the system dynamics. The core of the PIMM‐PLKF lies in its parallel architecture, which comprises two sets of IMM‐PLKFs. Each set contains multiple Kalman filters tailored to specific GMM noise components, which exchange information through input‐output interactions to enhance estimation precision. In addition, the transition probability matrix (TPM) is dynamically updated in real time, using both current and historical model information to address the limitations of fixed TPMs and improve robustness in dynamic environments. Simulation results demonstrate the superior estimation accuracy, robustness, and computational simplicity of the PIMM‐PLKF. Compared to traditional methods, particularly those based on information entropy, it achieves better performance while maintaining ease of implementation. These findings highlight the PIMM‐PLKF's potential for applications such as sensor networks and target tracking, where non‐Gaussian noise and incomplete data transmission pose critical challenges.