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.
Optimal linear weighted cooperative spectrum sensing for clustered-based cognitive radio networks
