Robust Gaussian Process Quadrature Diffusion Filtering for Distributed Sensor Networks

In this article, we propose a robust diffusion nonlinear filtering algorithm based on Student-t distribution for distributed sensor networks (DSNs). Existing distributed state estimation (DSE) algorithms rely on the Gaussianity assumption of state and measurement, which may perform poorly in practical applications with outliers and heavy-tailed noise. Both state and measurement noises are characterized by Student-t distributions by the proposed algorithm. By employing the moment matching method, we approximate both the prior and posterior distributions as Gaussian distributions. Therefore, the Gaussian process quadrature (GPQ) moment transformation can be employed for nonlinear filtering. The local Student-t-based GPQ Kalman filter is then extended to the diffusion strategy framework for DSNs, resulting in the Student-t-based distributed diffusion GPQ Kalman filtering algorithm. We demonstrate that the classical diffusion Kalman filter in information form is a particular case of our proposed algorithm. Simulation results show the performance of our algorithm outperforms the classical diffusion filtering methods.