Circular synthetic aperture sonar (CSAS) is a method for improving the resolution and target detection capabilities of a synthetic aperture sonar system. CSAS data are difficult to focus because of their large aperture sizes and elevation sensitivity. This difficulty has sometimes been addressed by using transponders or distributing isotropic scatterers in the field of view of the system; however, this comes at the cost of reduced practicality. As an alternative, map-drift based multipoint autofocus ("multilateration") was proposed by Cantalloube and Nahum [IEEE Trans. Geosci. Remote Sens. 49, 3730-37 (2011)] for autofocusing analogous circular synthetic aperture radar data. Multilateration also solves the problem of aberration spatial variance by providing a three-dimensional navigation correction. In circular synthetic aperture focusing problems, though, correcting aberrations is a joint navigation and elevation estimation problem, and the present work extends the multilateration approach to simultaneously solve both a navigation solution and coordinate corrections for the multilateration control patches. Additionally, methods for addressing the stability and behavior of the inverse problem are addressed, and an adaptive weighting scheme for reducing the influence of outliers is presented. The field results demonstrate near optimal point-spread functions on distributions of natural isotropic scatterers and robustness in regions with bathymetric variability.