Multipath effect is one of the many interference sources that degrade Global Positioning System (GPS) positioning performance. It is particularly prone to occur in places with reflective objects, such as high-rise buildings, Bridges and other buildings in the city. Usually, when the receiver is next to the reflected object, there will be interference of reflected signal, which will affect the subsequent positioning solution. Multipath is known to be one of the dominant error sources, and multipath mitigation is crucial for improvement of the positioning accuracy. It is not an easy task to establish precise statistical characteristics of measurement noise in practical engineering applications. The traditional Kalman filter (KF) is the best filter estimate when the noise is Gaussian, but most noise in real life is unknown, uncertain and non-Gaussian. When the signals are non-Gaussian, the performance of KF will be seriously deteriorated. The state estimation problem in non-Gaussian noise is discussed. Because of the Kalman filter using only second order signal information, the underlying system is disturbed by some heavy-tailed non-Gaussian impulsive noises, so in non-Gaussian noise environment, it is not optimal. A novel scheme using entropy principle based interacting multiple model (IMM) extended Kalman filter (EKF) is employed in which the maximum correntopy criterion (MCC) is utilized to address uncertainty of measurement noise, especially for the outlier types of multipath errors for the GPS navigation processing. The uncertainty of the noise can be described by a set of switching models using the multiple model estimation. Based on the filter structural adaptation, the IMM nonlinear filtering provides an alternative for designing the adaptive filter in the GPS navigation processing for time varying satellite signal quality. The MCC is a new approach to measure the similarity of two random variables using information from higher-order signal statistics. To improve the performance under non-Gaussian, the maximum correntropy Kalman filter (MCKF), which adopts the MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized. This method is more suitable for the unknown noise and uncertain parameters, and provides a new general solution for the study of random systems with generalized noise. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing as compared to other various system designs.

Keywords: multipath, GPS, correntropy, extended Kalman filter, interacting multiple model