ESTIMATION TECHNIQUE USING COVARIANCE INFORMATION IN LINEAR DISCRETE-TIME-SYSTEMS

This paper contributes to a new development in the estimation problems of the signal by using the covariance information of the signal and observation noise without usage of any of the realization techniques from the covariance information for the state-space model of the signal. It is assumed that the signal is observed with additive white Gaussian noise. The recursive least-squares filtering algorithm is devised for the estimation problems from the autocovariance data of the signal process, the observed value and the variance of the observation noise process in linear discrete-time systems. The filter requires the autocovariance data K(m), m = 0, 1, 2,..., M, of the signal process in calculating the coefficients in the filtering equations, provided that the signal data is fitted to the autoregressive (AR) process of order M. In the numerical examples, the proposed filter is applied to the noise reduction problem for a signal generated by the AR(2) model and a stochastic binary signal.