A Distributed Optimization Scheme for State Estimation of Nonlinear Networks with Norm-bounded Uncertainties

TL;DR

This paper presents a distributed optimization-based approach for state estimation in complex nonlinear networks with uncertainties, ensuring bounded errors and verified through simulation.

Contribution

It introduces a novel distributed estimation scheme that models uncertainties and nonlinearities uniformly and simplifies feasibility checking compared to traditional methods.

Findings

Estimation errors are proven to be bounded under the proposed scheme.

The method effectively handles Gaussian noise, uncertainties, and nonlinearities.

Numerical simulations confirm the theoretical advantages of the approach.

Abstract

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach, the estimation problem is reformulated as an optimization problem, solving for a solution in a distributed way by utilizing a decoupling technique. Then, based on this solution, a class of estimators is designed to handle the system dynamics and constraints. A novel feature of this design lies in the unified modeling of uncertainties and nonlinearities, the decoupling of nodes, and the construction of recursive approximate covariance matrices for the optimization problem. Furthermore, the feasibility of the proposed estimators and the boundedness of the mean-square errors are ensured under a developed criterion, which is easier to check than some typical estimation strategies including the linear matrix inequalities-based and the variance-constrained ones. Finally, the effectiveness of the theoretical results is verified by a numerical simulation.