Nonlinear Bayesian Filter: Alternative to the Extended Kalman Filter in the GPS/INS Fusion Systems

Yudan Yi and Dorota A. Grejner-Brzezinska

Abstract:	The complementary error characteristics of GPS and inertial sensors result in a multi-sensor fusion system providing high-accuracy continuous 3-dimensional position and orientation solutions. Due to the nonlinearity of the system and measurement models in the GPS/INS integration, and under the Gaussian probability density assumption, the Extended Kalman Filter (EKF) has been the standard technique used to provide a sub-optimal nonlinear estimation (estimation of the state of the nonlinear dynamic system) by means of a linearization procedure using the first-order Taylor approximation. EKF is currently widely used in a number of GPS/INS integrated systems. In order to overcome the sub-optimal performance of EKF, several alternative nonlinear Bayesian filters have been proposed, and have already demonstrated performances superior to EKF in some nonlinear applications. For example, the nonlinear derivative-free filters, such as the Unscented Kalman Filter (UKF), can result in more accurate approximation up to the 3rd order Taylor series expansion for any nonlinearity, even based on the same Kalman filter framework with the Gaussian probability density assumption,. Due to more accurate approximation of the nonlinear derivative-free filters, it may allow large errors in the initial state vector; therefore it is theoretically possible to eliminate the initial coarse and fine alignments for inertial sensors using the nonlinear derivative-free filters. The focus of this paper is to improve the accuracy and reliability of the currently implemented GPS/INS system by employing the nonlinear derivative-free Bayesian filters, as compared to the traditional EKF. The OSU-developed AIMS. GPS/INS system is used as the EKF reference to test the possible improvements in the navigation solution. An overview of the nonlinear Bayesian filtering technique will be introduced first, and then detailed algorithms of one nonlinear derivative-free filter Bayesian filter, UKF, will be presented. A kinematic experimental GPS/INS dataset, including dual-frequency carrier phase data and inertial measurements from two different grade inertial sensors (H764G and IMU400C) installed in the same vehicle will be used to validate the proposed filtering technique. Special consideration, in the comparison including UKF and EKF, will be given to the orientation convergence speed and free navigation performance. The effects of the alternative Bayesian filter on the navigation performance as a function of the grade of inertial sensors will be investigated through the use of a high-end navigation grade INS (e.g. H764G) and a low-cost consumer grade IMU (e.g. Crossbow MEMS IMU400C) in the example dataset.
Published in:	Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005) September 13 - 16, 2005 Long Beach Convention Center Long Beach, CA
Pages:	1391 - 1400
Cite this article:	Yi, Yudan, Grejner-Brzezinska, Dorota A., "Nonlinear Bayesian Filter: Alternative to the Extended Kalman Filter in the GPS/INS Fusion Systems," Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, CA, September 2005, pp. 1391-1400.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In