Gain-Constrained Recursive Filtering With Stochastic Nonlinearities and Probabilistic Sensor Delays

Abstract

Abstract-This paper is concerned with the gainconstrained recursive filtering problem for a class of timevarying nonlinear stochastic systems with probabilistic sensor delays and correlated noises. The stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step autocorrelated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraint. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.

Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties

“…Finally, an example has been given to illustrate the usefulness of the developed state estimation approach. The results in this paper could be further extended to the non-fragile state estimation problems for discrete neural networks with more complicated networkinduced phenomena such as fading measurements [4], [5], [10], [20], [26], missing measurements [8], sensor delays [9], randomly occurring faults [14] and mixed time-delays [31].…”

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

“…It is well recognized that the existence of the randomly occurring incomplete information would highly degrade the system performance if not handled properly. So far, a series of estimation and filtering schemes has been developed for networked systems with randomly occurring incomplete information in the literature, and great efforts have been made to deal with the randomly occurring nonlinearities in [49], [95]- [99], the randomly occurring uncertainties in [94], [97], the randomly occurring sensor saturations in [40], [72], the randomly occurring sensor delays in [31], [32], [38], [100], [101], the randomly occurring signal quantization in [41], [102], and the randomly occurring faults in [103]. Accordingly, several techniques for analysis and synthesis of the networked systems have been given, including innovation analysis approach [31], [32], linear matrix inequality approach [97], Hamilton-Jacobi-Isaacs inequality method [100], difference linear matrix inequality method [41], Riccati difference equation approach [101], [102], and game theory method [54].…”

“…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.…”

“…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. By using the recursive linear matrix inequality method, the robust H ∞ filter has been constructed in [45] for a class of time-varying networked systems with stochastic nonlinearities and variance constraints.…”

“…To mention a few, a Kalman-type filter has been designed in [52] for a class of time-varying nonlinear systems with random parameter matrices, correlated noises and fading measurements. Based on the result in [52], the recursive filtering problem has been investigated in [101] for time-varying nonlinear systems subject to finite-step correlated measurement noises, probabilistic sensor delays and gain-constraint. The developed filtering algorithm in [101] has the ability to attenuate the effects from the random sensor delays and gain-constraint onto the filtering performance and, moreover, it could be useful for addressing the gain-constrained issues arose in practical engineering with specified objectives, for example, to guarantee the unbiasedness property of the state estimates, simplify filter structure and handle the case of state estimates with linear equality constraint.…”