Using Adaptive Estimation to Minimize the Number of Samples Needed to Develop a Pattern to a Specified Uncertainty

Abstract

Obtaining far-field patterns in electromagnetics or acoustics, although generally not as computationally expensive as solving for the sources induced on an object, can none-the-less at times be a substantial fraction of the overall computer time associated with some problems. This can be especially the case in determining the monostatic radar cross section of large objects, since the current distribution must be computed for each incidence angle or when using physical optics to determine the radiation patterns of large reflector antennas. In addition, when employing the point sampling and linear interpolation of the far field that is most often used to develop such patterns, it can be necessary to sample very finely in angle to avoid missing fine details such as nulls. A procedure based on model-based parameter estimation is described here that offers the opportunity of reducing the number of samples needed while developing an easily computed and continuous representation of the pattern. It employs windowed, low-order, overlapping fitting models whose parameters are estimated from the sparsely sampled far-field values. The fitting models themselves employ either discrete-source approximations to the radiating currents or Fourier models of the far field. For the cases investigated, as few as 1.5 to 2 samples per far-field lobe are found to be sufficient to develop a radiation-pattern estimate that is accurate to 0.1 dB, and 2.5 samples per lobe for a simple scatterer. In general, however, the sampling density is not determined by the lobe count alone, but by the effective rank of the field over the observation window, which in turn is a function of both the aperture size and the spatial variation of the source distribution within that aperture.