Smoothing Criteria for Regularized Matrix Inversion of Bistatic Radar Echoes

In 2005, the planet Mars was illuminated 56 times for 20 min each by an unmodulated 75-cm wavelength circularly polarized wave transmitted from the SRI International 46-m antenna in the Stanford foothills. The direct signal and a Martian surface echo, separated by differential Doppler frequency shifts, were received simultaneously at the Mars Odyssey orbiter. The surface echoes exhibit both fluctuating amplitude and varying spectral width, which are responses to surface reflectivity and roughness variations along the surface track, described by a surface scattering function. We analyze the echo data using quasi-specular scattering theory and exploit high-resolution Mars orbiter laser altimeter topographic maps to model the scattering surface in 3-D at positions along the specular track of the echo, assuming a two-scale classical scattering model. We solve for a surface scattering function via regularized matrix inversion using the measured data and our surface scattering model. Optimizing the matrix inversion regularization over the course of each experiment requires consideration of the changing properties of the surface echoes caused by different viewing geometries. At one extreme the echoes appear as a strong narrowband signal, but on the other extreme the echo signals are weak and have a wide bandwidth. In this paper, we describe a scheme for determining a set of regularization constants that result in physically plausible scattering functions over the full range of echo types.