Abstract
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.
Highlights
Over the last few decades, research on the estimation problem for networked stochastic systems has gained considerable attention, due to the undeniable advantages of networked systems, whose applicability is encouraged, among other causes, by the development and advances in communication technology and the growing use of wireless networks. As it is well known, the Kalman filter provides a recursive algorithm for the optimal least-squares estimator in stochastic linear systems, assuming that the system model is exactly known and all of the measurements are instantly updated
Important extensions of the Kalman filter have been proposed for conventional sensor networks in which the measured outputs of the sensors always contain the actual signal contaminated by additive noises, and the transmissions are carried through perfect connections
A numerical example is presented with the following purposes: (a) to show that, the current covariance-based estimation algorithms do not require the evolution model generating the signal process, they are applicable to the conventional formulation using the state-space model, even in the presence of state-dependent multiplicative noise; (b) to illustrate some kinds of uncertainties which can be covered by the current model with random measurement matrices; and (c) to analyze how the estimation accuracy of the proposed algorithms is influenced by the sensor uncertainties and the random delays in the transmissions
Summary
Over the last few decades, research on the estimation problem for networked stochastic systems has gained considerable attention, due to the undeniable advantages of networked systems, whose applicability is encouraged, among other causes, by the development and advances in communication technology and the growing use of wireless networks. The development of sensor networks motivates the necessity of designing new estimation algorithms that integrate the information of all the sensors to achieve a satisfactory performance; using different fusion techniques, the measurements from multiple sensors are combined to obtain more accurate estimators than those obtained when a single sensor is used In this framework, important extensions of the Kalman filter have been proposed for conventional sensor networks in which the measured outputs of the sensors always contain the actual signal contaminated by additive noises, and the transmissions are carried through perfect connections (see, e.g., [1,2,3] and references therein). Random failures in the transmission of measured data, together with the inaccuracy of Sensors 2017, 17, 1151; doi:10.3390/s17051151 www.mdpi.com/journal/sensors
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