Data fitting by low-rank polynomials

Doing my research I faced a problem of low-rank approximation of a function of 2 coordinates, given as a number of points, empirically obtained during an experiment. Basically, this function has exponent shape surface image, but we need necessarily its polynomial approximation with no more than about 5-6 first terms. Also, some of the surface points need to be fixed hardly to preserve the physical meaning of the approximant (several points). So, the question is what’s the most appropriate way to get such an approximation using Matlab tools (cutting off outliers, fitting data with some curvilinear surface and make its low-rank approximation; possibly, with verification of approximation quality later on and obtaining a polynomial formula). It’d be awesome if you provide any code examples/links. Thank you in advance!