Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2013 IEEE.This paper is concerned with the gain-constrained recursive filtering problem for a class of time-varying 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.This work was supported in part by the National Natural Science Foundation of China by Grants 61273156, 61028008, 60825303, 61104125, and 11271103, National 973 Project by Grant 2009CB320600, the Fok Ying Tung Education Fund by Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China by Grant 2007B4, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. by Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Optimal Fusion Estimation with Multi-Step Random Delays and Losses in Transmission

This paper is concerned with the optimal fusion estimation problem in networked stochastic systems with bounded random delays and packet dropouts, which unavoidably occur during the data transmission in the network. The measured outputs from each sensor are perturbed by random parameter matrices and white additive noises, which are cross-correlated between the different sensors. Least-squares fusion linear estimators including filter, predictor and fixed-point smoother, as well as the corresponding estimation error covariance matrices are designed via the innovation analysis approach. The proposed recursive algorithms depend on the delay probabilities at each sampling time, but do not to need to know if a particular measurement is delayed or not. Moreover, the knowledge of the signal evolution model is not required, as the algorithms need only the first and second order moments of the processes involved. Some of the practical situations covered by the proposed system model with random parameter matrices are analyzed and the influence of the delays in the estimation accuracy are examined in a numerical example.This research is supported by the “Ministerio de Economía y Competitividad” and “Fondo Europeo de Desarrollo Regional” FEDER (Grant No. MTM2014-52291-P)

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the 'perturbed Kalman filter' (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified

Centralized filtering and smoothing algorithms from outputs with random parameter matrices transmitted through uncertain communication channels

The least-squares linear centralized estimation problem is addressed for discrete-time signals from measured outputs whose disturbances are modeled by random parameter matrices and correlated noises. These measurements, coming from different sensors, are sent to a processing center to obtain the estimators and, due to random transmission failures, some of the data packet processed for the estimation may either contain only noise (uncertain observations), be delayed (sensor delays) or even be definitely lost (packet dropouts). Different sequences of Bernoulli random variables with known probabilities are employed to describe the multiple random transmission uncertainties of the different sensors. Using the last observation that successfully arrived when a packet is lost, the optimal linear centralized fusion estimators, including filter, multi-step predictors and fixed-point smoothers, are obtained via an innovation approach; this approach is a general and useful tool to find easily implementable recursive algorithms for the optimal linear estimators under the least-squares optimality criterion. The proposed algorithms are obtained without requiring the evolution model of the signal process, but using only the first and second-order moments of the processes involved in the measurement model.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigaciónand Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)