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Two Stages Time Delay and Frequency Estimator for Multiple Sinusoids

The problem of jointly estimating time delay and frequency of a signal received at two separated sensors is addressed in this paper. These methods require eigenvalue decomposition (EVD) of the covariance matrix of received data. Thus, the computational load and complexity is high especially when the number of samples is large. In addition, the noises field is assumed to be uncorrelated with constant variance. The objective of this paper is to develop an algorithm for estimating time delay and frequency without using any spectral decomposition techniques such as eigenvalue decomposition (EVD) or singular value decomposition (SVD) of the received data matrix. Proposed method only uses a linear transformation of the received data. Furthermore, this method accommodates more practical noise cases where the noise variance is not constant or in unknown correlated noise field. The proposed method can therefore is implemented with a reduced complexity compared to reference Y.Wu's method. Computer Simulation results demonstrate that the proposed method can estimate both the frequencies and time delay efficiently and accurately even at low signal to noise ratio (SNR).