Bias and variance calculation of a principal component based frequency estimator

The authors address the performance evaluation of the state variable algorithm based on singular value decomposition in frequency estimation. The bias and the variance expressions of the estimated frequency are obtained analytically to study the characteristics and the performance of the algorithm with respect to the free parameters. The calculations are based on the second-order Taylor series approximation of the principal singular vectors and values of the data matrix and its related derivatives with respect to its elements. The derived bias and variance expression are verified to be valid via simulation results. The estimated bias and variance are compared for variation in the dimensions of the data matrix and for wide range of signal-to-noise ratio