Subspace approach for two-dimensional parameter estimation of multiple damped sinusoids

In this paper, we tackle the two-dimensional (2-D) parameter estimation problem for a sum of K≥2K≥2 real/complex damped sinusoids in additive white Gaussian noise. According to the rank-property of the 2-D noise-free data matrix, the damping factor and frequency information is contained in the dominant left and right singular vectors. Using the sinusoidal linear prediction property of these vectors, the frequencies and damping factors of the first dimension are first estimated. The parameters of the second dimension are then computed such that frequency pairing is automatically achieved. Computer simulations are included to compare the proposed approach with several conventional 2-D estimators in terms of mean square error performance and computational complexity.

► The parameter information is contained in the K principal singular vectors.
► The WLS technique is employed to estimate the parameters in the first dimension.
► The estimate of the rest parameters is reduced to K1-D single-tone problem.
► The parameter estimates in both dimensions are automatically paired up.