Iterative algorithm for matched-filter design in minimum variance spectral estimation

The minimum variance spectral estimation based on matched filter bank is a non-parametric approach; it uses the output of a bank of band-pass matched filters to calculate the spectral estimation value of the input signal. Traditional solution method of the matched filter is based on autocorrelation matrix inversion, which is limited by the dimension and singularity of the matrix. An iterative algorithm is proposed to directly calculate the matched-filter, which is implemented based on the simplified complex coefficient convex quadratic optimization problem and avoids the matrix inversion. The proposed algorithm has quadratic termination property and is solved with conjugate gradient method; the optimal solution can be reached in finite number of iterations. Limiting the number of iterations can achieve a tradeoff between frequency resolution and spectral line unmatching, and higher spectral peak amplitudes are obtained. The proposed new algorithm was applied in experiment, (minimum variance distortionless response, MVDR) and (canonical correlation analysis, CCA) algorithm matched filters were implemented, and the spectral estimation results were compared.