On the robustness of parameter estimation of superimposed signals by dynamic programming

We analyze a recently proposed dynamic programming algorithm (REDP) for maximum likelihood (ML) parameter estimation of superimposed signals in noise. We show that it degrades gracefully with deviations from the key assumption of a limited interaction signal model (LISMO), providing exact estimates when the LISMO assumption holds exactly. In particular, 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 further quantified by a comparison to an ML algorithm with an exhaustive multidimensional search on a lattice in parameter space. We derive an explicit expression for the lattice spacing for which the two algorithms have equivalent optimization performance, which can be used to assess the robustness of REDP to deviations from the LISMO assumption. The values of this equivalent lattice spacing are found to be small for a classical example of superimposed complex exponentials in noise, confirming the robustness of REDP for this application.