The singular case and robust linear prediction

Linear Prediction (LP) and the well known fast algorithms of the Levinson type have already widely proven their efficiency in various fields. But these algorithms fail to be applicable when one of the principal minors of the signal covariance matrix happens to be singular (or close to singularity). This paper investigates this singular case both for scalar and vector (multichannel) time series. It is shown that the standard lattice may be replaced by a convenient lossless lattice. Various techniques are proposed to leap over the singular case. They are analysed in terms of generalized choleski factors. The paper then deals with the multichannel case which is attached by a reduction of redundant outputs leading back to the scalar singular case. The results are applicable to the design of robust LPC algorithms and to the use of ARMA models in antenna array processing.