Estimation technique using covariance information with uncertain observations in linear discrete-time systems

Abstract This paper proposes the recursive estimation technique using the covariance information in linear stationary discrete-time systems when the uncertain observations are given. At first, recursive least-squares algorithms for the filtering, fixed-point smoothing and one-step ahead prediction estimates are designed. The estimators use the crossvariance function of the state variable, that generates the signal process, with the signal, the observation vector, the system matrix, the variance of white Gaussian observation noise, the observed value and the probability that the signal exists in the uncertain observation. Second, to obtain the necessary information related to the covariance function of the signal in the estimators, we show the factorization method for the observation vector, the crossvariance function and the system matrix from the autocovariance function of the signal. As a result, the proposed technique uses finite number of autocovariance data of the stationary stochastic signal, the variance of white Gaussian observation noise, the uncertain observations and the probability.