Constrained State Estimation -- A Review

TL;DR

This paper reviews Bayesian and constrained state estimation techniques for nonlinear, non-Gaussian dynamic systems, covering Kalman filters, particle filters, and methods for incorporating physical constraints.

Contribution

It provides a comprehensive overview of constrained state estimation methods, comparing their advantages and disadvantages in nonlinear, non-Gaussian contexts.

Findings

Review of Kalman filter extensions for nonlinear systems

Discussion of particle filters for nonlinear estimation

Analysis of constrained estimation approaches and their trade-offs

Abstract

The real-world applications in signal processing generally involve estimating the system state or parameters in nonlinear, non-Gaussian dynamic systems. The estimation problem may get even more challenging when there are physical constraints on the system state. This tutorial-style paper reviews the Bayesian state estimation for (non)linear state-space systems and introduces the formulation of constrained state estimation in such scenarios. Specifically, we start by providing a review of unconstrained state estimation using Kalman filters (KF) for the linear systems and their extensions for nonlinear state-space systems, including extended Kalman filters (EKF), unscented Kalman filters (UKF), and ensemble Kalman filters (EnKF). Next, we present particle filters (PFs) for nonlinear state-space systems. Finally, we review constrained state estimation using various filtering techniques and highlight the advantages and disadvantages of the different constrained state estimation approaches.