Total least squares approach for frequency estimation using linear prediction

The resolution of the estimated closely spaced frequencies of the multiple sinusoids degrades as the signal-to-noise ratio (SNR) of the received signal becomes low. This resolution can be improved by using the total least squares (TLS) method in solving the linear prediction (LP) equation. This approach makes use of the singular value decomposition (SVD) of the augmented matrix for low rank approximation to reduce the noise effect from both the observation vector and the LP data matrix simultaneously. Comparison is made to the principle eigenvector (PE) method of Tufts and Kumaresan, both on theoretical and experimental grounds. The TLS algorithm exhibits superior performance over the PE method where low rank approximation is applied to the data matrix only.