New Fast Algorithm for Simultaneous Identification and Optimal Reconstruction of Non Stationary AR Processes with Missing Observations

Abstract

This paper deals with the problem of adaptive reconstruction and identification of AR processes with randomly missing observations. A new real time algorithm is proposed. It uses combined pseudo-linear RLS algorithm and Kalman filter. It offers an unbiased estimation of the AR parameters and an optimal reconstruction error in the least mean square sense. In addition, thanks to the pseudo-linear RLS identification, this algorithm can be used for the identification of non stationary AR signals. Moreover, simplifications of the algorithm reduces the calculation time, thus this algorithm can be used in real time applications.

Lattice Algorithm for Adaptive Stable Identification and Robust Reconstruction of Nonstationary AR Processes With Missing Observations

“…Finally, examples illustrate the performances of the new algorithm. It is compared to the Kalman pseudo-linear RLS algorithm [19]. Both algorithms are applied to the identification and reconstruction of non stationary AR processes and to the reconstruction of audio signals with random missing samples.…”

“…It is based on the reflection coefficients calculated in [14]. In section 3, the Kalman filter presented in [19] for the prediction of an AR process subject to missing samples is described. In section 4, an extension of the RLSL algorithm to the identification of signals with missing samples is presented.…”

“…Several methods, such as in [1], [2], [8], [12], [16], [18], have already been developed for on line processing of AR signals with missing data. They use at each time only the past available data.…”

“…However these two algorithms converge toward biased estimation of the parameters. In [18], we proposed an alternative to the LMSlike algorithm based on the incomplete past predictor [2]. It offers simultaneous optimal identification and reconstruction.…”

“…However, this algorithm is quite time consuming. Recently [19], we proposed to use a Kalman filter for the prediction with the pseudo linear RLS algorithm. This algorithm is fast.…”