Abstract
Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise vc(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k); 2) the observation matrix H; 3) the variance of the state vector x(k); 4) the system matrix for the colored observation noise vc(k); 5) the variance of the colored observation noise; 6) the input noise variance in the state equation for the colored observation noise.
Highlights
Like the Kalman estimators, the recursive leastsquares (RLS) Wiener estimation problems have been researched extensively
This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems
The RLS Wiener fixed-point smoother and filter have been designed for the colored observation noise
Summary
Like the Kalman estimators, the RLS Wiener estimation problems have been researched extensively. In [1], the RLS Wiener filter and fixed-point smoother are designed in linear discrete-time systems. Contrary to the Kalman estimators, the RLS Wiener estimators are advantageous in the point that the RLS Wiener estimators do not require the information of the input noise variance and the input matrix in the state equation for the state vector. In spite of the fruitfulness as aforementioned above, in the area of the estimation problems for the colored observation noise, the studies on the RLS Wiener estimation problems in discrete-time stochastic systems might not be seen hitherto in discrete-time stochastic systems From this viewpoint, this paper, especially, examines to design a new estimation technique of recursive leastsquares (RLS) Wiener fixed-point smoother and filter for the colored observation noise in linear discrete-time wide-sense stationary stochastic systems. A numerical simulation example, in Section 4, shows the estimation characteristics of the current fixed-point smoother and filter for the colored observation noise
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