Optimal subspace selection for non-linear parameter estimation applied to refractivity from clutter

We consider the problem of constructing an optimal reduced-rank subspace for parameter estimation, in models where the data is a non-linear function of the parameters. The solution which minimizes mean-squared error is a compromise between the prior distribution and the measurement model, reducing to the Karhunen-Loeve transform when only the prior is considered. The measurement model determines which parameters the measured data is less sensitive to, and which are therefore less estimable. Our approach obtains parameterizations in which the influence of these parameters is reduced, so that limited resources may be allocated to more estimable features. We apply it to the problem of estimating tropospheric index-of-refraction profiles from sea-surface clutter returns received from ship-based microwave radars.