State Estimation Methods for Continuous-Discrete Nonlinear Systems involving Stochastic Differential Equations

TL;DR

This paper compares various state estimation techniques for nonlinear systems with stochastic differential equations, demonstrating their effectiveness through simulation of a modified four-tank system.

Contribution

It introduces and evaluates multiple state estimation methods, including EKF, UKF, EnKF, and particle filter, for continuous-discrete nonlinear stochastic systems.

Findings

All methods successfully estimated system states.

The extended Kalman filter showed numerical stability with Joseph form.

Performance varied among methods based on accuracy and computational cost.

Abstract

In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and a particle filter. We implement the state estimation methods in Matlab. We evaluate the performance of the methods on a simulation of the modified four-tank system. We implement the state estimation methods for non-stiff systems, i.e., using an explicit numerical integration scheme. The implementation of the extended Kalman filter utilises the Joseph stabilising form for numerical stability. We evaluate the accuracy of the state estimation methods in terms of the mean absolute percentage error over the simulation horizon. We show that each method successfully estimates the states and unmeasured disturbances of the simulated modified four-tank system. Finally, we present conclusions.