Iterative filtering for multiple frequency estimation

It is well-known that Prony´s least-squares estimator gives inconsistent estimates for multiple frequency estimation. In a recent attempt to diminish this problem, Dragosevic and Stankovic (1989) couple the least-squares method of autoregressive (AR) estimation with an iterative filtering scheme discussed by Kay (1988) using an all-pole filter. But the inconsistency still persists. This paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work. It is shown that the inconsistency can be eliminated with an appropriately parametrized filter. The clue for the correct parametrization comes from a formula for the bias of the least squares AR estimator. The fact of the matter is that as long as a filter satisfies the parametrization requirement, consistent estimates can be obtained from the least-squares AR estimator on the basis of the filtered data. In particular, the all-pole filter considered by Dragosevic and Stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator. Experimental results show that the modified method has a higher resolution than the discrete Fourier transform and that its overall performance is quite remarkable