Robust filtering with stochastic nonlinearities and multiple missing measurements

Abstract

This paper is concerned with the filtering problem for a class of discrete-time uncertain stochastic nonlinear time-delay systems with both the probabilistic missing measurements and external stochastic disturbances. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. Such a probabilistic distribution could be any commonly used discrete distribution over the interval [0 1]. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing, stochastic disturbances, norm-bounded uncertainties as well as stochastic nonlinearities, the error dynamics of the filtering process is exponentially mean-square stable. By using the linear matrix inequality (LMI) method, sufficient conditions are established that ensure the exponential mean-square stability of the filtering error, and then the filter parameters are characterized by the solution to a set of LMIs. Illustrative examples are exploited to show the effectiveness of the proposed design procedures.

Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

“…It is worth mentioning that, in most reported results, the measurement signal has been assumed to be either completely lost or successfully transferred, and a typical way is to model the missing measurements by the Bernoulli distribution. However, in practical applications, owing to the sensors aging, sensor temporal failure or some of the data coming from a highly noisy environment, the measurement missing might be partial and individual sensor could have different missing probability in the data transmission process [26]. It is noted that most available results with respect to filtering problem with missing measurements have been concentrated on linear systems only, and the corresponding results for nonlinear systems have been very few.…”

“…, q). As discussed in [26], the random variable α i k can take any value over the interval [0, 1] and the probability for α i k to take different values may vary with the sensors. Moreover, α i k can obey any discrete probability distributions over the interval [0, 1] that includes the Bernoulli (binary) distribution as a special case.…”

“…In fact, such stochastic nonlinearities include the state-multiplicative noises as spe-cial cases. Recently, the filtering problem with stochastic nonlinearities described by statistical means has already stirred some research interests, and some latest results can be found in [26,35] and the references therein. On the other hand, almost all real-time systems are timevarying and therefore finite-horizon filtering problem is of practical significance.…”

A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements

“…It should be pointed out that, among the reported results regarding the state estimation with missing measurements, the Bernoulli distribution is commonly employed to characterize the case where the measurements are successfully transmitted or completely missing. Nevertheless, such way of modeling missing measurements has certain limitations in practice as it fails to describe the case where only partial information is missing or fading in a networked environment [24]. To the best of the authors' knowledge, the recursive state estimation problem for time-varying stochastic complex networks with missing measurements has not been fully investigated, and the purpose of this paper is to shorten such a gap.…”

“…However, due to the complexity of large-scale networks, the measurement signals may be missing/fading during the network transmission resulting from various causes such as sensors aging, intermittent sensor failures, limited bandwidth, network congestion or accidental loss of some collected data [6,8,16,18,19]. As such, in order to improve the estimation performance, it is vitally important to take the phenomenon of the missing measurements into account when designing the state estimator especially in the network settings [11,13,24]. In the past decade, the state estimation problems with missing measurements have drawn considerable research interest and a huge amount of results have been reported.…”