Sigma-Point Filtering and Smoothing Based Parameter Estimation in Nonlinear Dynamic Systems

TL;DR

This paper explores advanced sigma-point filtering and smoothing techniques for maximum likelihood parameter estimation in nonlinear state-space models, comparing various schemes and demonstrating their effectiveness through simulated experiments.

Contribution

It introduces higher-order sigma-point schemes for filtering and smoothing, providing closed-form EM steps for certain models, and compares their performance with particle and extended Kalman filters.

Findings

Higher-order sigma-point methods can yield more accurate parameter estimates.

The methods outperform some traditional filtering techniques in specific nonlinear scenarios.

Experimental results validate the effectiveness of the proposed approaches.

Abstract

We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the maximization step in a class of models that are linear in parameters and have additive noise. To obtain approximations to the filtering and smoothing distributions needed in the likelihood-maximization methods, we focus on using Gaussian filtering and smoothing algorithms that employ sigma-points to approximate the required integrals. We discuss different sigma-point schemes based on the third, fifth, seventh, and ninth order unscented transforms and the Gauss--Hermite quadrature rule. We compare the performance of the methods in two simulated experiments: a univariate nonlinear growth model as well as tracking of a maneuvering target. In the experiments, we also compare against approximate likelihood estimates obtained by particle filtering and extended Kalman filtering based methods. The experiments suggest that the higher-order unscented transforms may in some cases provide more accurate estimates