Distributed Kalman Filter for A Class of Nonlinear Uncertain Systems: An Extended State Method

TL;DR

This paper introduces a distributed Kalman filter for nonlinear uncertain systems using an extended state approach, enabling real-time estimation covariance bounds and robustness over time-varying sensor networks.

Contribution

It proposes a novel extended state distributed Kalman filter that guarantees bounded estimation covariance under mild conditions for nonlinear uncertain systems.

Findings

Estimation covariance is bounded under mild assumptions.

The filter provides real-time upper bounds on estimation error.

Numerical simulations confirm the filter's effectiveness.

Abstract

This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the original state and the nonlinear dynamics is constructed. By analyzing the extended system, we provide a design method for the filtering gain and fusion matrices, leading to the extended state distributed Kalman filter. It is shown that the proposed filter can provide the upper bound of estimation covariance in real time, which means the estimation accuracy can be evaluated online.It is proven that the estimation covariance of the filter is bounded under rather mild assumptions, i.e., collective observability of the system and jointly strong connectedness of network topologies. Numerical simulation shows the effectiveness of the proposed filter.