SSUE: Simultaneous State and Uncertainty Estimation for Dynamical Systems

TL;DR

This paper presents SSUE, a Bayesian method for simultaneously estimating the internal state and parameter uncertainty of dynamical systems, improving accuracy despite variability in system parameters.

Contribution

The paper introduces a novel Bayesian framework and computational algorithm for joint state and uncertainty estimation in dynamical systems, with theoretical analysis and simulations.

Findings

Effective joint estimation demonstrated through simulations.

Observability analysis links system properties with estimation consistency.

Algorithm based on maximum a posteriori estimation shows practical viability.

Abstract

Parameters of the mathematical model describing many practical dynamical systems are prone to vary due to aging or renewal, wear and tear, as well as changes in environmental or service conditions. These variabilities will adversely affect the accuracy of state estimation. In this paper, we introduce SSUE: Simultaneous State and Uncertainty Estimation for quantifying parameter uncertainty while simultaneously estimating the internal state of a system. Our approach involves the development of a Bayesian framework that recursively updates the posterior joint density of the unknown state vector and parameter uncertainty. To execute the framework for practical implementation, we develop a computational algorithm based on maximum a posteriori estimation and the numerical Newton's method. Observability analysis is conducted for linear systems, and its relation with the consistency of the estimation of the uncertainty's location is unveiled. Additional simulation results are provided to demonstrate the effectiveness of the proposed SSUE approach.