Continuous-discrete unscented Kalman filtering framework by MATLAB ODE solvers and square-root methods

TL;DR

This paper introduces a MATLAB-based continuous-discrete UKF framework that enhances state estimation accuracy and robustness by leveraging MATLAB ODE solvers and stable square-root methods.

Contribution

It proposes a novel implementation framework for continuous-discrete UKF using MATLAB ODE solvers and J-orthogonal transformations for improved accuracy and stability.

Findings

Discretization error is effectively controlled by MATLAB ODE solvers.

The proposed methods demonstrate enhanced robustness to roundoff errors.

Stable square-root UKF methods outperform traditional Cholesky-based approaches.

Abstract

This paper addresses the problem of designing the {\it continuous-discrete} unscented Kalman filter (UKF) implementation methods. More precisely, the aim is to propose the MATLAB-based UKF algorithms for {\it accurate} and {\it robust} state estimation of stochastic dynamic systems. The accuracy of the {\it continuous-discrete} nonlinear filters heavily depends on how the implementation method manages the discretization error arisen at the filter prediction step. We suggest the elegant and accurate implementation framework for tracking the hidden states by utilizing the MATLAB built-in numerical integration schemes developed for solving ordinary differential equations (ODEs). The accuracy is boosted by the discretization error control involved in all MATLAB ODE solvers. This keeps the discretization error below the tolerance value provided by users, automatically. Meanwhile, the robustness of the UKF filtering methods is examined in terms of the stability to roundoff. In contrast to the pseudo-square-root UKF implementations established in engineering literature, which are based on the one-rank Cholesky updates, we derive the stable square-root methods by utilizing the $J$-orthogonal transformations for calculating the Cholesky square-root factors.