Reducing noise sensitivity in F-esprit using weighting matrices

In this paper we explore the possibility of using a weighting matrix to improve the accuracy of F-ESPRIT - a recently developed frequency estimation algorithm. In F-ESPRIT, the estimation is based on frequency domain data, and the algorithm is developed to enable a frequency selective estimation. The estimation is based on forming a data matrix which for i.i.d. measurement noise, is perturbed by a non-diagonal noise matrix. Since F-ESPRIT is a subspace based algorithm, the non-diagonal perturbation matrix will for low Signal to Noise Ratios (SNR) reduce the estimation accuracy. In this paper, we derive an exact expression for the perturbation matrix, and evaluate a weighting strategy for improving the performance. Empirical results show a large improvement in the low SNR case.