We consider a multiuser MIMO Mobile Satellite System (MSS) and model its channel as a cascade of a slow varying component, directivity vector, and a fast fading component, propagation component. We study the estimation of the slow varying part of the satellite channel at the gateway. Since the channel model is nonlinear, we propose a nonlinear parametric least squares approach. This optimization problem is shown to be equivalent to an eigenvalue complementary problem. The equivalent problem does not require an intermediate estimation of the nuisance (fast fading component) with relevant benefits in terms of computational complexity. The performance of the proposed algorithm is assessed by simulations based on realistic satellite channels.