Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

Abstract

In this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0,1]. Such a probability distribution is allowed to be any commonly used distribution over the interval [0, 1] with known conditional probability. The aim of the addressed filtering problem is to design a filter such that, in the presence of both the stochastic nonlinearities and multiple missing measurements, there exists an upper bound for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati-like difference equations that are of a form suitable for recursive computation in online applications. An illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme.

Filtering and fault detection for nonlinear systems with polynomial approximation

“…[8,20,39] (18) helps to achieve a better approximation and estimation performance in the sequel, which will be demonstrated in the simulation.…”

Estimation, filtering and fusion for networked systems with network-induced phenomena: New progress and prospects

“…The filtering problems for networked systems with stochastic nonlinearities have already stirred some research interests and some latest results can be found in [16], [43], [45], [52], [101] based on several analysis techniques. For example, by using the Riccati-like difference equation approach, the extended Kalman filter has been designed in [16] for a class of time-varying networked systems with stochastic nonlinearities and multiple missing measurements.…”

“…The filtering problems for networked systems with stochastic nonlinearities have already stirred some research interests and some latest results can be found in [16], [43], [45], [52], [101] based on several analysis techniques. For example, by using the Riccati-like difference equation approach, the extended Kalman filter has been designed in [16] for a class of time-varying networked systems with stochastic nonlinearities and multiple missing measurements. Moreover, the locally optimal Kalman-like filtering algorithms have been developed in [52], [101] for time-varying networked systems with stochastic nonlinearities, where the compensation schemes have been proposed to attenuate the effects from random sensor delays, random parameter matrices and gain-constraints onto the filtering performance.…”

“…For example, the recursive filtering problems have been studied in [16], [53] for two general classes of nonlinear networked time-varying systems with the multiple missing measurements and quantization measurements respectively, where some new recursive filtering algorithms have been developed by properly estimating the linearization error and based on the stochastic analysis technique. It has been shown that an optimal upper bound of the filtering error covariance can be obtained at each sampling instant by employing the filtering schemes in [16], [53]. In addition, more freedom degree and better filtering performance can be achieved by tuning the weight parameters, and the explicit forms of the filter parameters have been given in terms of the solutions to Riccati-like difference equations.…”

“…Linear matrix inequality method time-invariant complex dynamical systems feasible [25], [40]- [44] Difference linear matrix inequality method time-varying complex dynamical systems feasible [21], [27], [45], [46] Innovation analysis approach linear time-invariant/time-varying systems optimal [30]- [32], [39], [47], [48] Hamilton-Jacobi-Isaacs inequality approach general nonlinear time-invariant systems feasible [35] Backward Riccati difference equation method nonlinear time-varying systems sub-optimal [37], [49], [50] Forward Riccati difference equation method nonlinear time-varying systems sub-optimal [7], [16], [51]- [54] [49], [56], [57], the N-order Rice fading channel has been modeled by sequences of independent and identically distributed Gaussian random variables with known means and variances, where the multi-path induced fading stemming mainly from multi-path propagation has been considered when dealing with the control and estimation problems for networked systems and the impact from the fading measurements onto the control/estimation performance has been examined.…”