SSUE: Simultaneous state and uncertainty estimation for dynamical systems

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 article, 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.

Automated summary

This article introduces a new method (SSUE) that can simultaneously estimate the internal state and parameter uncertainty of a system to address the challenge of parameter variability in practical dynamic systems. By developing a Bayesian framework and numerical methods, the estimation of parameter uncertainty and the update of the state vector are achieved, while observability analysis is conducted to assess consistency.