# Constrained State Estimation -- A Review

arXiv: https://arxiv.org/abs/1807.03463 · HTML: https://mlsanity.com/paper/1807.03463/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2018.

## Built on by (most cited first, 2 of 2)

- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Preserving linear invariants in ensemble filtering methods](https://mlsanity.com/paper/2404.14328/) (2024)

## Abstract (arXiv)

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.