Distributed Kalman Estimation with Decoupled Local Filters

TL;DR

This paper introduces a novel distributed Kalman filtering approach that prevents error propagation across time steps, ensuring stable and accurate state estimation in networked systems without central coordination.

Contribution

The authors propose a new local filtering method that eliminates error propagation, guarantees stability under mild conditions, and aligns with centralized Kalman estimates asymptotically.

Findings

The new method prevents error carry-over between steps.

It guarantees stability under certain structural data conditions.

Numerical experiments show improved performance over existing methods.

Abstract

We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a local filter at each node using information obtained through some procedure for fusing data across the network. A common problem with existing methods is that the outcome of local filters at each time step depends on the data fused at the previous step. We propose an alternative approach to eliminate this error propagation. The proposed local filters are guaranteed to be stable under some mild conditions on certain global structural data, and their fusion yields the centralized Kalman estimate. The main feature of the new approach is that fusion errors introduced at a given time step do not carry over to subsequent steps. This offers advantages in many situations including when a global estimate in only needed at a rate slower than that of measurements or when there are network interruptions. If the global structural data can be fused correctly asymptotically, the stability of local filters is equivalent to that of the centralized Kalman filter. Otherwise, we provide conditions to guarantee stability and bound the resulting estimation error. Numerical experiments are given to show the advantage of our method over other existing alternatives.