We present a conceptually simple and computationally efficient algorithm, which is referred to as WRELAX, for the well-known time delay estimation problem. The method is a relaxation-based minimizer of a complicated nonlinear least squares criterion. WRELAX can be applied to detecting and classifying roadway subsurface anomalies by using an ultra-wideband ground-penetrating radar. Numerical and experimental examples are provided to demonstrate the performance of the new algorithm.