Estimation of Pulse Parameters by Autoconvolution and Least Squares

Let the parameter vector of a baseband pulse be mu = [D, A, W](T), where D = arrival time, A = amplitude, and W = width. A method for estimating mu for a pulse present in a noisy data segment is given. We start by performing an autoconvolution (AC) of the data segment, and then recording the shift where the AC peaks. By taking half of that shift, from the end of the segment, a point is placed near the middle of the pulse. Next, we partition the pulse at that point and perform two more ACs, (one on the left half of the pulse and another on the right half), and find two more shifts where the ACs peak. These two shifts provide coarse measurements on D and W. A further refinement by least squares (LS) then produces a final estimate for mu. Simulation results have corroborated the theoretical development and shown that the new estimator performs close to the Cramer-Rao lower bound (CRLB).