State Estimation Using a Network of Distributed Observers With Unknown Inputs

TL;DR

This paper introduces a novel distributed observer design for linear systems with unknown inputs and limited local measurements, ensuring accurate state estimation across a network with switching topologies.

Contribution

It develops a new distributed observer framework that handles unknown inputs and limited local information, filling a gap in existing distributed estimation methods.

Findings

The proposed observer guarantees convergence under mild detectability conditions.

Effective in both undirected and directed switching communication graphs.

Simulation results confirm improved estimation accuracy in various scenarios.

Abstract

State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state vector of the entire system can be estimated, while each observer (or node) has access to only local output measurements that may not be sufficient on its own to reconstruct the entire system's state. Existing results in the literature on distributed state estimation assume either that the system does not have inputs, or that all the system's inputs are globally known to all the observers. Accordingly, we address this gap by proposing a distributed observer capable of estimating the overall system's state in the presence of inputs, while each node only has limited local information on inputs and outputs. We provide a design method that guarantees convergence of the estimation errors under some mild joint detectability conditions. This design suits undirected communication graphs that may have switching topologies and also applies to strongly connected directed graphs. We also give existence conditions that harmonize with existing results on unknown input observers. Finally, simulation results verify the effectiveness of the proposed estimation scheme for various scenarios.