Distributed Sequential State Estimation Over Binary Sensor Networks With Inaccurate Process Noise Covariance: A Variational Bayesian Framework

In this paper, the distributed sequential state estimation problem is addressed for a class of discrete time-varying systems with inaccurate process noise covariance over binary sensor networks. First, with the purpose of reducing communication costs, a special class of sensors called binary sensors, which output only one bit of data, is adopted. The Gaussian tail function is then used to describe the likelihood of the binary measurements. Subsequently, the process noise covariance matrix is modeled as a inverse Wishart distribution. By employing a variational Bayesian approach combined with diffusion filtering strategies, the parameters (i.e., mean and variance) of the prior and posterior probability density functions are formalized for the sequential estimator and the sequential predictor. Then, the fixed-point iteration is utilized to receive the approximate optimal distributions of both system states and estimated covariance matrices. Finally, a simulation example of target tracking demonstrates that our algorithm performs effectively using binary measurement outputs.