Accuracy Issues in Kalman Filtering State Estimation of Stiff Continuous-Discrete Stochastic Models Arisen in Engineering Research

Abstract

This paper aims at exploring accuracy of Kalman-like filters. Its particular interest lies in estimation of stochastic systems whose drift coefficients expose a stiff behavior. The latter means that the Jacobian of the drift coefficient in such a continuous-discrete system, which is presented by an Itô-type stochastic differential equation (SDE) for modeling the plant’s dynamic behavior and a discrete-time equation for simulating its measurement process, has large eigenvalues at the solution trajectory. Here, we employ the so-called “discrete-discrete” approach, which is grounded in SDE discretization schemes, and compare the outcome accuracy of EKF-, CKF- and UKF-type methods when these are based on the Euler-Maruyama and Itô-Taylor discretizations of the strong convergence orders 0.5 and 1.5 and applied for estimating the Van der Pol oscillator and Oregonator reaction models. We evidence that state estimation errors committed in our stiff stochastic scenarios are sensitive to both the type of Kalman filtering method utilized and the SDE discretization scheme implemented. So these must be chosen carefully in accurate and robust state estimation algorithms intended for treating stiff continuous-discrete stochastic systems.