Iterative observer-based state and parameter estimation for linear systems

TL;DR

This paper introduces an iterative approach combining back and forth nudging and Gauss-Newton steps for joint state and parameter estimation in linear systems, especially effective for systems with skew-adjoint generators.

Contribution

It presents a novel iterative method that integrates BFN and Gauss-Newton techniques for accurate joint state and parameter estimation in linear systems.

Findings

Effective for systems with skew-adjoint generators

Converges to fixed points minimizing output error

Applicable to both source and bilinear parameter estimation

Abstract

We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big impact on the parameter estimate. We propose to use the back and forth nudging (BFN) method for estimating the system's initial state and a Gauss--Newton step between BFN iterations for estimating the system parameters. Taking advantage of results on the optimality of the BFN method, we show that for systems with skew-adjoint generators, the initial state and parameter estimate minimizing an output error cost functional is an attractive fixed point for the proposed method. We treat both linear source estimation and bilinear parameter estimation problems.