Asteroid shapes are currently modeled using the shape software package. shape takes a model for the asteroid, which is based on both shape and spin parameters, and projects that model into radar space. This projection is compared to observed data for the asteroid, and changes are made to the model parameters in an attempt to minimize the residuals. shape uses increasing model complexity to build up a representation for the asteroid, from a basic ellipsoid model to capture gross features, to a spherical harmonic model which can represent finer surface elements (See section ? (results)).
shape currently uses a Sequential Parameter Fit (SPF) mechanism to adjust the model following a comparison between the projected radar image and the asteroid data. The SPF iterates through each parameter of the model and minimizes the \(\chi^2\) for that individual parameter using a brent and bracket method [reference: numerical recipes]. This process is not only slow, but it also does not guarantee convergence on a local maximum. My work has been to replace the SPF currently implemented in shape with a modified Square Root Information Filter, as outlined in section ?.