Distributed State Estimation for Discrete-Time Systems With Unknown Inputs: An Optimization Approach

TL;DR

This paper introduces a distributed optimization-based framework for state estimation in large-scale systems with unknown inputs, ensuring bounded errors and improved accuracy through normalization.

Contribution

It presents a novel Distributed Unknown Input Observer (DUIO) framework that combines local estimation with distributed optimization and normalization for enhanced accuracy.

Findings

Estimation error is bounded and depends on communication iterations.

Normalization improves estimation accuracy in poorly conditioned systems.

Simulation confirms the effectiveness of the proposed approach.

Abstract

This paper proposes a novel Distributed Unknown Input Observer (DUIO) framework for state estimation in large-scale systems subject to local unknown inputs. We consider systems where outputs are measured by a network of spatially distributed sensors and inputs are introduced through multiple dispersed channels. In this framework, each local node utilizes only its local input and output measurements to estimate the maximal locally reconstructible state. Subsequently, nodes collaboratively reconstruct the whole system state via a distributed optimization algorithm that fuses these partial estimates. We provide a rigorous analysis showing that the estimation error is bounded, with the error bound explicitly dependent on the number of communication iterations per time step and strongly convexity constant determined by the system parameters. Furthermore, to counteract curvature anisotropy induced by poor conditioned system geometry, we embed a normalization step into the distributed optimization procedure. Simulation results demonstrate the effectiveness of the proposed framework and the performance improvements yielded by the normalization procedure.