Abstract
The optimal linear estimation problems are investigated in this paper for a class of discrete linear systems with fading measurements and correlated noises. Firstly, the fading measurements occur in a random way where the fading probabilities are regulated by probability mass functions in a given interval. Furthermore, time-delay exists in the system state and observation simultaneously. Additionally, the multiplicative noises are considered to describe the uncertainty of the state. Based on the projection theory, the linear minimum variance optimal linear estimators, including filter, predictor, and smoother are presented in the paper. Compared with conventional state augmentation, the new algorithm is finite-dimensionally computable and does not increase computational and storage load when the delay is large. A numerical example is provided to illustrate the effectiveness of the proposed algorithms.
Highlights
NCSs have received significant attention for their successful applications in space exploration, target tracking, remote surgery, unmanned aerial vehicles, industrial monitoring, and other areas in recent years [1,2,3,4,5,6,7,8,9,10,11,12]
Yan et al [15] concentrated on the H∞ state estimator’s design problems for a kind of discrete-time artificial neural networks (ANNs) with multiple fading measurements. e phenomenon of multiple fading measurements is represented by a set of individual stochastic variables obeying a predetermined distribution on interval [0,1]
For a class of nonlinear systems with stochastic nonlinearities and multiple fading measurements, the stochastic nonlinearities are represented by statistical means which indicates multiplicative stochastic disturbances, and sufficient conditions are obtained to ensure stochastic stability of the modified unscented Kalman filter [17]
Summary
NCSs have received significant attention for their successful applications in space exploration, target tracking, remote surgery, unmanned aerial vehicles, industrial monitoring, and other areas in recent years [1,2,3,4,5,6,7,8,9,10,11,12]. Sun et al [7] consider that different sensor channels have different fading measurement rates, and the process and measurement noises are finitestep autocorrelated and/or cross correlated with each other In such complex systems, the optimal linear state estimators in the linear minimum variance (LMV) sense are presented by using the innovation analysis approach. By introducing the fictitious noises to compensate the stochastic uncertainties, the system under consideration can be converted into one with only uncertain noise variances [23, 24] In all these papers, the results focus on finding the optimal estimators, under which the state delay and observation delay are not considered simultaneously. Based on the discussions above, we aim to solve the optimal linear estimation problems for a class of state delay and observation delay systems with fading measurements and correlated noises.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
