Journal of Global Positioning Systems (2010) Vol.9, No.1 :33-40 DOI: 10.5081/jgps.9.1.33 Evaluating the Performances of Adaptive Kalman Filter Methods in GPS/INS Integration Ali Almagbile, Jinling Wang, and Weidong Ding School of surveying & Spatial Information Systems, University of New South Wales, Sydney, NSW 2052, Australia Abstract One of the most important tasks in integration of GPS/INS is to choose the realistic dynamic model covariance matrix Q and measurement noise covariance matrix R for use in the Kalman filter. The performance of the methods to estimate both of these matrices depends entirely on the minimization of dynamic and measurement update errors that lead the filter to converge. This paper evaluates the performances of adaptive Kalman filter methods with different adaptations. Innovation and residual based adaptive Kalman filters were employed for adapting R and Q. These methods were implemented in a loose GPS/INS integration system and tested using real data sets. Their performances have been evaluated and compared. Their limitations in real-life engineering applications are discussed. Keywords: GPS/INS integration; Kalman filter; Adaptive Kalman filter _____________________________________________ 1. Introduction The Kalman filter (KF) technique has been widely implemented for GPS/INS integration systems. Kalman filters rely on dynamic and stochastic models (e.g., Hu et al, 2003) that describe the behaviour of the state vector and the relationship between the measurements and the state vector respectively. The optimality of Kalman filter depends on the quality of prior assumptions about the process noise covariance matrix Q and the measurements noise covariance R (Mohamed and Schwarz, 1999). The quality of prior assumptions which are determined by certain knowledge about the measurements and test analysis are crucial factors that lead to the optimality of the Kalman filtering technique. For instance, inadequacy of prior assumptions to represent the real noise level could lead to unreliable results and sometimes to filter divergence (Ding et al, 2007). An adaptive Kalman filter has been used to tune the measurement and process noise covariance matrices R and Q respectively. Determining the suitable values of R and Q plays an important role to obtain a converged filter (Mohamed and Schwarz, 1999). For example, unreliable results will be yielded in case of determining small values of Q and R, on the other side, big diagonal element values of Q and R could produce filter divergence. Consequently, much attention has been paid to determine the disturbance matrices in order to obtain optimal Kalman filter parameters especially in GPS/INS integration applications (e.g., Mehra, 1970, 1971, 1972; Moghaddamjoo and Kirlin, 1989; Mohammad and Schwarz, 1999; Wang et al, 1999; Hide et al, 2003; Li and Wang, 2006; Ding et al, 2007). Adaptive Kalman filters have been developed using three different scenarios of adaptation. These adaptation scenarios are: adapting dynamic noise covariance matrix Q, measurement noise covariance matrix R, and the initial values of the error covariance matrix P. One of the philosophies for the Kalman filtering adaptation is to fix P and Q and vary R by trial and error to find the smallest value that gives stable state estimates, if this design does not give satisfactory performance, P and Q should also be varied (Grooves, 2008). Various approaches have already been proposed for estimating Q and R matrices. Mehra (1972) categorized these approaches as: Bayesian, Maximum likelihood, correlation and covariance matching methods. All of these methods have been tested in different applications in order to achieve high performance of Kalman filtering. For instance, the maximum likelihood (ML) method was employed in adaptive Kalman filtering (Mohamed and Schwarz, 1999). It is noted that this method provides reliable results for the GPS/INS integration algorithm. However, this method as well as Bayesian method need intensive computation and both are based on the assumption that the dynamic error is time-invariant, which is not realistic (Wang, 1999). In this paper, three innovation and residual based adaptive Kalman filtering techniques have been evaluated in a loosely coupled GPS/INS integrated system. A comparison has been conducted based on covariance analysis, and innovation and residual