Fitting real data to a pulse position jittered model

A disk channel model in which pulses of known shape and unknown amplitudes are jittered from a nominal regular spacing is proposed. The authors attempt to derive theoretical bounds on the accuracy of any estimation procedure based on this model and attempt to describe and evaluate an algorithm that produces estimates of the model parameters with accuracy close to the theoretical bound. A Cramer-Rao bound, which gives a finite lower bound on the variance of the estimation error, is presented. It is shown that by expressing amplitude estimates in terms of pulse positions, a search over the resulting function is equivalent to an estimation procedure that finds estimates close to the Cramer-Rao bound. The Cramer-Rao bound can be used to prove that the accuracy of amplitude estimates is independent of the amplitudes themselves. Accuracy of pulse-position estimates is dependent on pulse amplitudes and pulse positions. However, simulations have shown that as pulses move together it becomes more difficult to estimate the actual pulse positions and that position jitter may appear to be amplitude jitter. It is therefore difficult to distinguish between position and amplitude jitters when the pulses are closely spaced