Fast recursive low-rank linear prediction frequency estimation algorithms

A class of fast recursive low-rank linear prediction algorithms for the tracking of time-varying frequencies of multiple nonstationary sinusoids in noise is introduced. Realizations with O(Nn) and O(Nn² ) arithmetic operations per time step are described, where N is the model order and n is the number of independent sinusoids. The key step towards an operations count that depends only linearly on the model order is fast eigensubspace tracking, and the property that the coefficients of a high-order N prediction filter itself constitute a perfectly (or almost perfectly) predictable sequence that can be annihilated using a low-order 2n prediction error filter that carries the desired signal frequency information in its roots. In this concept, root tracking is limited to a low-order filter polynomial, even if the overmodeling factor N/n is much larger than 1 for optimal noise suppression. Extraneous roots are not computed explicitly. Detailed simulation results confirm the tracking capabilities of the new algorithms