Gain-Constrained Extended Kalman Filtering with Stochastic Nonlinearities and Randomly Occurring Measurement Delays

Abstract

In this paper, the gain-constrained extended Kalman filtering problem is studied for discrete time-varying nonlinear system with stochastic nonlinearities and randomly occurring measurement delays. Both deterministic and stochastic nonlinearities are simultaneously present in the model, where the stochastic nonlinearities are described by first moment and can encompass several classes of well-studied stochastic nonlinear functions. A diagonal matrix composed of mutually independent Bernoulli random variables is introduced to reflect the phenomenon of randomly occurring measurement delays caused by unfavorable network conditions. The aim of the addressed filtering problem is to design a finite-horizon recursive filter such that, for all stochastic nonlinearities, randomly occurring measurement delays and gain constraint, the upper bound of the cost function involving filtering error is minimized at each sampling time. It is shown that the filter gain is obtained by solving matrix equations. A numerical simulation example is provided to illustrate the effectiveness of the proposed algorithm.

Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements

“…Hence, it is necessary to deal with the stochastic nonlinear functions to improve the accuracy of system state estimation. To mention but a few, in [24], a finite-horizon recursive filter was designed for discrete-time-varying nonlinear system with stochastic nonlinearities and randomly occurring measurement delays which made the filtering error minimum at each sampling time. The probability-constrained filtering problem was investigated in [25] for a class of time-varying nonlinear stochastic systems subject to estimation error variance constraint and a new filter was constructed to guarantee a minimized upper-bound on the estimation error variance.…”