Adaptive constraint-filtering method and its application to GPS positioning

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. The constraint-filtering method developed previously can accommodate the constraint in the filtering process for a nonlinear dynamic system. However, the assumption that the modelling noise and the sensor noise are known 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 modelling 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.