Simplified LMS algorithms in the case of non-uniformly sampled signals

In a previous paper (Lahalle et al. (2000)) we introduced an adaptive ARMA estimation method for time series with missing samples. Due to the non-linearity of the optimization criterion in the case of missing observations, the proposed method has led to an LMS-like algorithm with a higher computational complexity than the standard LMS. As many applications require very low complexity algorithms, the purpose of the present paper is to introduce simplified versions of the LMS adapted to the non-uniform sampling context. Both waveform reconstruction performance and computational costs are evaluated as a function of probability density of the sampling process. Stationary and non-stationary contexts are considered.