On Refining Polynomial Phase Signal Parameter Estimates

Newton algorithms are commonly used in the final "refinement" stage of parameter estimation for sinusoids and higher order phase polynomial signals. Such parameter estimation scenarios arise commonly in radar applications where the radial target velocity (which is possibly time-varying) must be estimated. The author and coworkers have previously proposed an elegant and efficient alternative to a Newton gradient search type algorithm based on filtering and phase unwrapping. A statistical and computational analysis of this filtering/phase unwrapping method is presented here. The analysis shows the algorithm to be computationally efficient and much less sensitive to the accuracy of the initial guesses for the parameters than a Newton algorithm. A first-order statistical analysis of the filtering/phase unwrapping algorithm is performed, and guidelines are derived for the required accuracy of the initial estimates. Simulations are presented to confirm the analysis.