—To deal with the estimation problem for systems subject to constraints while the corresponding noise processes are not completely known, the adaptive constraint-filtering method is proposed in this paper. As having been shown in [1], the constraint-filtering method can accommodate the constraint in the filtering process for a nonlinear dynamic system. The method is based on the knowledge of the modeling noise and the sensor noise, which may not be practical. Here, we use the fuzzy innovation adaptive estimation (FIAE) approach to deal with the unknown noise processes, and use the fading-memory method to tackle the modeling errors. The synthesized algorithm is then applied to solve the ill-conditioned GPS positioning problem. It is shown by the experimental results that the proposed algorithm can enhance the accuracy significantly.