Multipath is known to be one of the dominant error sources in high accuracy positioning systems, and multipath parameter estimation is crucial for multipath mitigation and subsequently improvement of the positioning accuracy. This paper investigates the minimum entropy extended Kalman filter (MEEKF) for GPS multipath parameter estimation, which is effective for dealing with non-Gaussian systems. Most of the existing multipath estimation algorithms are usually designed for Gaussian noise. However, non-Gaussian noise is often encountered in many practical environments and their performances degrade dramatically in non-Gaussian cases. The mean square error criterion is limited to the assumption of linearity and Gaussianity. Although the particle filter can deal with non-Gaussian, nonlinear system, it is computationally expensive for an online realization. If a better performance is expected, one reasonable way is to obtain an optimal estimation under the minimum entropy criterion. The scheme is designed by introducing an additional term, which and is tuned according to the higher order moment of the estimation error. The algorithm has a high accuracy in estimation because entropy can characterize all the randomness of the residual. A multipath estimation algorithm based on kernel minimum error entropy filter is proposed, where the minimum error entropy criterion is applied. The extended Kalman filter (EKF) is designed to give a preliminary estimation of the state. A RBF network is added to the EKF innovation term to compensate for the non-Gaussianity of the whole system. The Renyi’s entropy of the innovation is introduced and parameters of the RBF-network are updated using minimum entropy criterion at each time step. According to the stochastic information gradient method, an optimal filer gain matrix is obtained. The scheme is designed by introducing an additional term, which and is tuned according to the higher order moment of the estimation error. The algorithm provides better estimation accuracy because the entropy can characterize all the randomness of the residual. The I (in-phase) and Q (quadrature) accumulator outputs from the GPS correlators are used as the observational measurements of nonlinear filters to estimate the multipath parameters such as amplitude, code delay, phase, and carrier Doppler. Since the measurement of (I and Q) for the filter and the system states are highly nonlinearly related, the nonlinear filters are potentially useful. Performance evaluation will be conducted to evaluate the effectivity of the proposed algorithm for multipath estimation based on various configurations and system designs.

Keywords: entropy, extended Kalman filter, multipath, GPS, tracking loop