ON THE ROBUSTNESS OF PARAMETER-ESTIMATION OF SUPERIMPOSED SIGNALS BY DYNAMIC-PROGRAMMING

We analyze a recently proposed dynamic programming algorithm (REDP) fo r maximum likelihood (ML) parameter estimation of superimposed signals in noise. We show that it degrades gracefully with deviations from th e key assumption of a Limited interaction signal model (LISMO), provid ing exact estimates when the LISMO assumption holds exactly. In partic ular, we show that the deviations of the REDP estimates from the exact ML are continuous in the deviation of the signal model from the LISMO assumption. These deviations of the REDP estimates From the MLE are f urther quantified by a comparison to an ML algorithm with an exhaustiv e multidimensional search on a lattice in parameter space. We derive a n explicit expression for the lattice spacing for which the two algori thms have equivalent optimization performance, which can be used to as sess the robustness of REDP to deviations from the LISMO assumption. T he values of this equivalent lattice spacing are found to be small for a classical example of superimposed complex exponentials in noise, co nfirming the robustness of REDP for this application.