RLS Wiener Predictor with Uncertain Observations in Linear Discrete-Time Stochastic Systems

This paper proposes recursive least-squares (RLS) l-step ahead predictor and filtering algorithms with uncertain observations in linear discrete-time stochastic systems. The observation equation is given by         y k k z k v    k  , , where is a binary switching sequence with conditional probability. The estimators require the information of the system state-transition matrix     z k Hx k     k   , the observation matrix H , the variance   , K k k of the state vector   x k , the variance   R k of the observation noise, the probability       1 p k P k    that the signal exists in the uncertain observation equation and the   2, 2 element   2, | P k j 2     of the conditional probability of   k  , given .   j 