Consensus variational Bayesian moving horizon estimation for distributed sensor networks with unknown noise covariances

This paper deals with state estimation over distributed sensor networks with unknown process noise covariance matrix (PNCM) and measurement noise covariance matrices (MNCMs). The unknown PNCM and MNCMs are modeled with constrained inverse Wishart distributions and estimated together with the state trajectory within a moving horizon window. Each local node computes its local estimates by combining variational Bayes (VB) inference with Moving Horizon Estimation (MHE). Then, in order to diffuse the information through the network, at each time instant three consensus tasks are performed in parallel: the first one is a consensus on the parameters of the local approximated PNCM posterior; the second one is a consensus on the prior information on the state trajectory over the moving window; the third one is a consensus on the measurements over the moving window. The resulting consensus-based distributed VBMHE (D-VBMHE) algorithm generalizes existing consensus filters to the problem of jointly estimating the state trajectory over a window as well as to unknown PNCM and MNCMs. Simulation and experimental results on target tracking case-studies demonstrate the outperformance of the proposed D-VBMHE compared to state-of-the-art conventional and adaptive consensus filters.