Distributed adaptive Bernoulli filtering for multi-sensor target tracking under uncertainty

This paper addresses the challenges posed by imperfect detection and uncertain parameters, such as detection probability and noise covariances, in target tracking. We introduce an Adaptive Bernoulli Filter (ABF) capable of handling multiple sources of uncertainty simultaneously. The ABF employs a Gaussian Inverse Gamma Inverse Wishart Mixture (GIGIWM) to represent the spatial probability density function of the augmented state. Using a variational Bayesian approach, we derive a closed-form solution for the filter, providing estimates for target existence probability, kinematic and feature states, measurement noise covariance matrix, and predicted error covariance matrix. Additionally, we extend the ABF to incorporate prior knowledge through constrained distributions. In a distributed multi-sensor scenario, we propose a fusion approach to combine local posteriors, extending existing fusion techniques to handle local posteriors that depend on both global and local variables. Simulation results show the effectiveness and robustness of the proposed filter and distributed fusion framework.