Rank Revealing QR Factorization for Jointly Time Delay and Frequency Estimation

Abstract

The Rank-Revealing QR factorization (RRQR) is a valuable tool in numerical linear algebra because it provides accurate information about rank and numerical null-space. In this paper, we addressed the problem of estimating the time delay and the frequencies of noisy sinusoidal signals received at two spatially separated sensors using the well known RRQR, subspace decomposition technique. Although eigenvalue decomposition (EVD) of cross spectral matrix or Singular value decomposition SVD for the data matrix based techniques provide accurate estimation, they are hard to meet real time constraints due to computational load and cost. To explore compatibility with real time applications, we proposed a RRQR method in association with the well-known MUSIC/root-MUSIC algorithm to estimate unknown parameters without using any EVD or SVD. The simulation results verify that the proposed method provide better performance than the well known EVD or SVD based methods with less computational complexity. Index-Terms: Delay and Frequency estimation, Rank-Revealing