AR spectral analysis with random missing observations

This communication deals with parametric spectral estimation in the case of missing observations: the signal is periodically sampled and samples are lost. We assume that the original signal is an autoregressive process and that misses verify a random Bernouilli pattern. The objective is to develop a parametric PSD estimation algorithm that does not require optimization and involves the random nature of the misses. The investigated solution is to perform a PSD estimation on an interpolated version of the measured signal. An advantage of this approach is that it allows the use for example of the well known Burg algorithm that gives better results than Yule-Walker for short or medium data length. However in this context a crucial point is of course the lost samples reconstruction step. A recursive interpolation scheme is introduced, the stationarity of the interpolated signal is studied and the relation between the interpolated and the original signal PSD is derived. From this result, the optimal interpolator parameters are determined as a function of the signal parameters and the probability of misses. Two iterative algorithms are proposed and their performance demonstrated by computer simulation