Gaussian Filtering for Stiff Continuous–Discrete Stochastic Modeling Tasks

This chapter presents the first insight into the theory of nonlinear Kalman filtering techniques intended for treating stiff continuous–discrete stochastic systems. In particular, it introduces the notion of stiffness in the SDE framework and extends it then to continuous–discrete stochastic state estimation tasks of such sort. Based on the stability analysis of Dahlquist elaborated in Sect.  1.5 of Chap. 1, our consideration focuses on stiffness features of the specific ODE have arisen and been solved within the time-update steps in the non-SR and SR implementations of the traditional DL-EKF and universal DL-KF methods with deterministically sampled expectation and covariance, which are grounded on the GHQF, UKF, third- and fifth-degree CKF parameterizations as well as on the derivative-free EKF one. All this creates a solid theoretical background for designing advanced state estimation procedures for treating stiff continuous–discrete stochastic systems in practice. The theoretical analysis of A-stable Gaussian filters with deterministically sampled expectation and covariance, which are summarized in the form of pseudo-codes placed in appendixes of Chaps.  4 ,  6 and this chapter, is supported with illustrative calculations performed in MATLAB.