A Model Fusion Distributed Kalman Filter for Non-Gaussian Measurement Noise

Wireless sensor networks (WSNs) represent a critical research domain within the Internet of Things (IoT) technology. The distributed Kalman filter (DKF) has garnered significant attention as an information fusion method for WSNs. However, effectively handling non-Gaussian environments remains a crucial challenge for DKF. This article proposes a solution by partitioning the noise distribution into multiple Gaussian components, thereby approximating the measurement model with submodels. We introduce a model fusion DKF (MFDKF) that combines submodels by assuming independent random processes for the model’s transition probabilities. The expectation-maximization (EM) algorithm is employed to estimate the relevant parameters. To address specific requirements in WSNs that demand high consensus or have limited communication, two derivative algorithms, namely, consensus MFDKF (C-MFDKF) and simplified MFDKF (S-MFDKF), are proposed based on consensus theory. The convergence of MFDKF and its derivative algorithms is analyzed. A series of simulations demonstrate the effectiveness of MFDKF and its derivative algorithms.