Resolution of overlapping echoes of unknown shape

An algorithm for detecting and estimating the parameters of an unknown number of closely spaced, superimposed noisy echoes of a signal of unknown and arbitrary shape is derived. The algorithm exploits an approximate invariance structure in the frequency domain that allows the ESPRIT algorithm to be used for parameter estimation. An extension of the algorithm is applicable to the resolution of superimposed pulses of unknown and possibly different shapes. Computer simulation results for the algorithm are compared with the corresponding Cramer-Rao performance bounds