Approximating a Laplacian Prior for Joint State and Model Estimation within an UKF

TL;DR

This paper presents a method to improve state estimation in systems with poor models by jointly estimating states and model uncertainties using an extended UKF with a sparsity-promoting prior.

Contribution

It introduces a novel approach combining a square root UKF with a regularized horseshoe prior to estimate sparse model parameters and improve model accuracy.

Findings

Small estimation errors achieved

Automated model reduction detected model improvements

Effective approximation of missing dynamics

Abstract

A major challenge in state estimation with model-based observers are low-quality models that lack of relevant dynamics. We address this issue by simultaneously estimating the system's states and its model uncertainties by a square root UKF. Concretely, we extend the state by the parameter vector of a linear combination containing suitable functions that approximate the lacking dynamics. Presuming that only a few dynamical terms are relevant, the parameter vector is claimed to be sparse. In Bayesian setting, properties like sparsity are expressed by a prior distribution. One common choice for sparsity is a Laplace distribution. However, due to some disadvantages of a Laplacian prior, the regularized horseshoe distribution, a Gaussian that approximately features sparsity, is applied. Results exhibit small estimation errors with model improvements detected by an automated model reduction technique.