Abstract
In this paper, we first present a Weighted Fourier transform and RELAXation based method, which is both computationally and statistically efficient, for the well-known time delay estimation problem. Later WRELAX is extended to multiple look cases where the receiver noise is assumed to be zero- mean colored Gaussian noise with unknown covariance matrices. Numerical examples show that both WRELAX and its extensions can approach the corresponding Cramer-Rao bound, the minimum attainable variances for any unbiased estimators, for a wide range of signal-to-noise ratios. The new algorithm can be applied to detecting and classifying roadway subsurface anomalies by using an ultra wideband ground penetrating radar. Experimental examples are also provided to demonstrate the performance of the new algorithm.
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