Further Results on the Joint Time Delay and Frequency Estimation Without Eigendecomposition

Abstract

Joint Time Delay and Frequency Estimation (JTDFE) problem of complex sinusoidal signals received at two separated sensors is an attractive problem that has been considered for several engineering applications. In this paper, a high resolution null (noise) subspace method without eigenvalue decomposition is proposed. The direct data Matrix is replaced by an upper triangular matrix obtained from Rank-Revealing LU (RRLU) factorization. The RRLU provides accurate information about the rank and the numerical null space which make it a valuable tool in numerical linear algebra. The proposed novel method decreases the computational complexity of JTDFE approximately to the half compared with RRQR methods. The proposed method generates estimates of the unknown parameters which are based on the observation and/or covariance matrices. This leads to a significant improvement in the computational load. Computer simulations are included in this paper to demonstrate the proposed method.