Kalman Filtering for Discrete Stochastic Systems with Multiplicative Noises and Random Two-Step Sensor Delays

Dongyan Chen,Long Xu,Yonglong Yu,Xiaohui Liu

doi:10.1155/2015/809734

Abstract

This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE). Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method.

Highlights

The filtering problem has been a mainstream research topic in the control theory due to its wide and important engineering applications such as signal processing, econometrics communication, guidance, navigation, and control of vehicles [1,2,3,4]
In [7], based on the minimum mean square error (MMSE) principle and the projection theory, the traditional Kalman filtering algorithm has been proposed for a class of linear discrete stochastic systems
The problem of the optimal Kalman filtering has been investigated for a class of linear discrete stochastic systems with multiplicative noises and random two-step sensor delays

Summary

Introduction

The filtering problem has been a mainstream research topic in the control theory due to its wide and important engineering applications such as signal processing, econometrics communication, guidance, navigation, and control of vehicles [1,2,3,4]. In [7], based on the minimum mean square error (MMSE) principle and the projection theory, the traditional Kalman filtering algorithm has been proposed for a class of linear discrete stochastic systems. The Kalman filtering problems have been widely investigated for different systems [8, 9]. The theoretical results of the extended Kalman filter (EKF) have been proposed and applied in many practical engineering problems [10,11,12,13]. A new terminal slidingmode control scheme has been designed in [15] by using the EKF observer

Objectives

Results

Conclusion