RLS Wiener estimators from observations with multiple and random delays in linear discrete-time stochastic systems

This paper designs a new recursive least-squares (RLS) Wiener fixed-point smoother and filter from randomly delayed observed values by multiple sampling times in linear discrete-time stochastic systems. The actual observed value is generated in terms of the observed values y¯(k-(j-1)) with the probability pj(k),1⩽j⩽N. It is assumed that the delay measurements are characterized by Bernoulli random variables. y¯(k) is given as a sum of the signal and the white observation noise. The RLS Wiener estimators use the following information: (a) the system matrix; (b) the observation matrix; (c) the variance of the state vector; (d) the delay probabilities pj(k) and (e) the variance of white observation noise.