Under the assumption that the surrounding environment remains unchanged, multipath contamination of GPS measurements can be formulated as a function of the sidereal repeatable geometry of the satellite with respect to the fixed receiver. Hence, multipath error estimation amounts to a regression problem. We present a method for estimating code multipath error of GPS ground fixed stations. By formulating the multipath estimation as a regression problem, we construct a nonlinear continuous model for estimating multipath error based on well-known sparse kernel regression, for example, support vector regression. We will empirically show that the proposed method achieves state-of-the-art performance on code multipath mitigation with 79 % reduction on average in terms of standard deviation of multipath error. Furthermore, by simulation, we will also show that the method is robust to other coexisting signals of phenomena, such as seismic signals.