Super resolution time delay estimation via MODE-WRELAX

We consider estimating time delays and amplitudes (real- or complex-valued) from the superposition of very closely spaced signals with known shapes. The well-known high resolution MODE (Method Of Direction Estimation) algorithm, which was originally proposed for angle estimation in array processing, is modified and used with our efficient time delay estimation method WRELAX (Weighted Fourier transform and RELAXation based) algorithm to deal with this problem. The proposed method is referred to as MODE-WRELAX. MODE-WRELAX provides better accuracy than MODE and higher resolution than WRELAX. Moreover, it can be used for both complex- and real-valued signals (including those with highly oscillatory correlation functions). Numerical results show that the MODE-WRELAX estimates can approach the corresponding Cramer-Rao bound. Efficient implementation of the algorithm is also discussed.