High resolution Joint Time Delay and Frequency Estimation

Joint Time Delay and Frequency Estimation (JTDFE) problem of complex sinusoidal signals received at two separated sensors is an attractive problem that has been studied for many engineering applications. In this paper, the Rank-Revealing QR factorization is applied to the real data matrix obtained via the unitary transformation of the square Toeplitz complex data matrix. Then the MUSIC spectrum estimation function is used to estimate the frequencies. The time delay is estimated by applying RRQR to the complex data matrix. The unitary transformation from complex to real would reduce the processing time of frequency estimation by almost a factor of four, since the cost of complex manipulations is four times the real manipulations. Also RRQR is an important tool in numerical linear algebra because it provides accurate information about rank and numerical null space. The simulation results validate the performance of the proposed method.