Doppler Mean Velocity Estimation: Small Sample Analysis and a New Estimator

Abstract : Optimal Doppler velocity estimation, under the constraint of small sample size, is explored for a standard Gaussian signal measurement model and thematic maximum likelihood (ML) and Bayes estimation. Because the model considered depends on a vector parameter VELOCITY, SPECTRUM WIDTH, AND SIGNAL- TO-NOISE RATIO (SNR), the exact formulation of an ML or Bayes solution involves a system of equations that is neither uncoupled nor explicit in form. Historically, iterative methods have been the most suggested approach to solving the required equations. In addition to being computationally intensive, it is unclear whether iterative methods can be constructed to perform well given a small-sample size and low signal strength. This report takes a different approach and seeks to construct approximate (ML and Bayes) estimators based on the notion of using constrained adaptive models to deal with nuisance parameter removal. A Monte Carlo simulation is used to determine small-sample estimator statistics and to demonstrate true performance bounds in the case of known nuisance values. Performance comparisons between these optimal forms and other standard estimators PULSE PAIR (PP) and a frequency domain wind profiler (WP) method are presented. Performance sensitivity of the optimal algorithms, with respect to uncertainty in the values of model nuisance parameters, is explored and provides the foundation for the recommendation to seek an adaptive method. An adaptive estimation method, closely allied with the derived ML and Bayes formulas, is developed using information theoretic methods to constrain the adaptation process.