Joint State and Parameter Estimation Using the Partial Errors-in-Variables Principle

TL;DR

This paper introduces a novel joint state and parameter estimation method based on the partial errors-in-variables principle, improving accuracy in uncertain dynamical systems through iterative Kalman smoothing and regularized least squares.

Contribution

It formulates a new PEIV regression approach that explicitly considers parameter prior uncertainty and integrates Kalman smoothing for enhanced estimation accuracy.

Findings

Improved estimation accuracy over existing methods

Effective handling of parameter prior uncertainty

Demonstrated superiority through simulations

Abstract

This letter proposes a new method for joint state and parameter estimation in uncertain dynamical systems. We exploit the partial errors-in-variables (PEIV) principle and formulate a regression problem in the sense of weighted total least squares, where the uncertainty in the parameter prior is explicitly considered. Based thereon, the PEIV regression can be solved iteratively through the Kalman smoothing and the regularized least squares for estimating the state and the parameter, respectively. The simulations demonstrate improved accuracy of the proposed method compared to existing approaches, including the joint maximum a posterior-maximum likelihood, the expectation maximisation, and the augmented state extended Kalman smoother.