Abstract
In this paper, we consider the problem of estimating a periodic sequence of pulses driving an AR transfer system from its output pulse sequence contaminated by an observation noise. For this problem we discuss three estimation methods, Methods 1, 2 and 3, to estimate the input pulse sequence whenever one cycle is finished. Methods 1 and 2, which we present in this paper, are based on operations of taking an average with explicit consideration of the periodicity. Method 3 is obtained by applying a least square method, which is optimal in the sense of minimization of the noise power, to this problem. Asymptotic behavior of estimation errors by the three methods are examined, and it is shown that under any of these the error variance converges to zero asymptotically with the same order. Also, it is indicated that if the observation starts with some delay from driving start time the delay may have a considerable effect on transient behavior of the estimation error of each method. Furthermore, by numerical examples, it is shown that each method has similar estimation accuracy when there is no delay of the observation start time but when there is some delay the accuracy of Method 3, a least square method, grows down ramarkably while Methods 1 and 2, with rather simple operations of taking an average, hold their accuracy in a satisfactorily high range.
