Probability-Dependent Gain-Scheduled Filtering for Stochastic Systems With Missing Measurements

Abstract

This paper addresses the gain-scheduled filtering problem for a class of discrete-time systems with missing measurements, nonlinear disturbances and external stochastic noises. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability is time-varying with securable upper and low bounds that can be measured in real time. The multiplicative noise is a state-dependent scalar Gaussian white noise sequence with known variance. The addressed gain-scheduled filtering problem is concerned with the design of a filter such that, for the admissible random measurement missing, nonlinear parameters and external noise disturbances, the error dynamics is exponentially mean-square stable. The desired filter is equipped with time-varying gains based primarily on the timevarying missing probability and is therefore less conservative than the traditional filter with fixed gains. It is shown that the filter parameters can be derived in terms of the measurable probability via the semi-definite programme method. Index Terms-Filtering; missing measurements; gain scheduling; time-varying Bernoulli distribution; probability-dependent Lyapunov functions I. INTRODUCTION The general idea of filtering problems is to form a kind of "best estimate" for the true value of some certain system based on some potentially noisy observations [1]-[4], [8], [13]-[16]. Filtering problem serves as one of the fundamental problems in the areas of control and signal processing. During the past few decades, the filtering problem has attracted considerable attention and some effective filtering strategies have been exploited in the literature that include Kalman filtering scheme [9] and H ∞ filtering methods [10]. The developed filtering approaches have been applied in a variety of systems such as uncertain time-delay systems [10], stochastic systems [11] and nonlinear systems [6], [11].

Fusion Predictors for Multisensor Stochastic Uncertain Systems With Missing Measurements and Unknown Measurement Disturbances

“…However, it is optimal in the linear unbiased minimum variance sense under the given form (11) of Kalman-like recursive predictor. Due to its simple recursive form, similar estimators have been also designed in many systems such as [4], [5], [13], [14], and [17]. The globally optimal filter in linear unbiased minimum variance sense has been reported in [18].…”

“…Caballero-Águila et al [3] design the centralized and distributed fusion filters and smoothers for multi-sensor linear discrete-time stochastic systems with missing measurements which are described by Bernoulli distributed variables assumed to be correlated at instants that differ m units of time. Wei et al [4] and Hu et al [5] study the gain-scheduled filter and optimal H ∞ filter for a class of nonlinear systems with missing measurements. Zhang et al [6] design an estimator based on the packet dropout compensation.…”

Almost sure state estimation withH2-type performance constraints for nonlinear hybrid stochastic systems

“…On the other hand, the H ∞ filtering can be regarded as a suboptimal filtering due to its capability of providing a smaller bound for the worst-case estimation error [1,2]. It might be worth emphasizing that, in most of the existing results, the estimators are designed to guarantee that the dynamics of the estimation error converges in terms of certain stability concepts such as the stochastic asymptotic stability [23], the mean-square stability [6][7][8]11], the mean-square exponential stability [29], the pth moment stability [14], and the asymptotic stability in probability [24].…”

Bounded H∞ synchronization for time‐varying networks with probability‐dependent information

“…It is worth mentioning that when modeling the RONs, the Bernoulli distribution sequence is usually supposed to have invariant probability, whereas such an assumption may be violated because the probability for the occurrence of the nonlinearities is time‐varying in certain situations. In this case, the time‐varying Bernoulli distribution introduced in should be utilized, where the missing probability is given in a range that can be measured in practice. Similar ideas have been proposed in and , where the delayed state‐feedback control problem and the H ∞ synchronization control problem have been studied respectively for the stochastic systems with RONs based on a probability‐dependent gain scheduled method.…”