Estimation of radio refractivity structure using radar clutter

In radar meteorology, "anomalous propagation" (AP) clutter is usually viewed as a contaminant in the retrieval of information (e.g., rain rate) using Dopper radar. For naval forces, however, the characterization of the atmospheric refractivity structure that leads to AP clutter is important information as non-standard refractivity structures significantly change where targets can and cannot be seen using shipboard radars.

The refractivity structures of interest fall into two general categories: evaporation ducts that arise from the refractivity profile in the surface layer above bodies of water, and surface based ducts that are associated with an inversion layer. The inference of the evaporation duct from radar sea clutter is a fairly simple parameter estimation problem [see Rogers, Hattan and Stapleton, Estimating evaporation duct heights from radar sea echo, Radio Science, 35(4), 2000]. The inference of parameters characterizing surface based ducts, though, is a multi-parameter inverse problem. A conventional inverse problem approach is to cast the problem in the form

E^*=arg _E opt [ f ( d , m( E ) )]

where E is a vector of global environmental parameters (e.g., the trapping layer base-height (z_T), change in refractivity across the inversion, etc.), d is the observed clutter power as a function of range, m( ) is the forward model that maps E into the space of d, and f( ) is an objective function. The forward model is non-linear and thus finding the estimate E^* requires a global search under most circumstances.

Presently, we have a mixture of results. We believe that most of the poor results stem from range-dependency of the environmental parameters, in particular, that of z_T. This leads to shifting the range where features such as clutter rings occur, a behavior that is problematic when the objective function f( ) is the squared error. One approach is to continue using global parameters but to augment E so as to characterize the range dependency of z_T, etc. Of course, this increases the dimensionality of the problem. A more appealing approach is to develop a marching algorithm that massages local parameters (that are horizontally correlated) at each range step. If the state and observeration equations were linear, refractivity estimation could be achieved by this approach using well-known Kalman filtering. However, the highly non-linear way in which refractivity impacts propagation necessitates something more general. In this paper, sequential importance sampling for recursively approximating the conditional expectation of refractivity given observed clutter data is presented.

We demonstrate: (a) the success and a failure of the conventional algorithm using range-independent parameters, (b) the sensitivity of the clutter field to refractivity parameters whose changes in range are modeled as a Markov process, (c) the use of conventional algorithm where E has been augmented to include parameters describing the range dependency of z_T, and (d)) the use of a non-linear recursive Bayesian state estimation algorithm.