Use of Extended Interval Kalman Filter on Integrated GPS/INS System

GPS/INS integration with uncertain dynamics modelling and uncertain measurement noise is studied. An extended interval Kalman filter is applied to such an uncertain integrated system, since the traditional extended Kalman filter is no longer applicable. The results of a computer simulation indicate that the extended Kalman filtering algorithm is consistent with the traditional extended Kalman filtering scheme, and is also effective for the nonlinear integrated system with uncertainty. Introduction GPS and INS systems have complimentary features that can improve performance of navigation and give a highly reliable and accurate navigation solution. The Kalman filter has been applied to the integrated GPS/INS (e.g., Cannon 1991, Da 1997, He et al. 1998). For a Kalman filter to be optimal, a main assumption is that the dynamic model and noise statistical parameters should exactly be known. This, however, is not the case in most practical situations. For instance, the variances of system noise and measurement errors in an integrated system are often not accurately known. The parameters in the dynamic model may be uncertain due to several reasons, such as unstable ION GPS '99, 14-17 September 1999, Nashville, TN 190 error characteristics of the inertial sensors (Titterton et al. 1997), the linearization process of the observation model, changes in environmental conditions, Selective Availability (SA), aircraft manoeuvres, etc. The traditional Kalman filter can not deal with such situations with inaccurate dynamics and statistical parameters. The effects of system uncertainty on the performance of a filter have been extensively studied by several authors. For instance, Neal (1967), Koussoulas and Leondes (1986) investigated the effects of parameter uncertainty in dynamic models, and Heffes (1966), Sangsuk-Iam (1990) discussed the effects of noise uncertainty; Griffin and Sage (1969) and Lainiotis and Slims (1970) studied the influence of uncertainty in the parameters in both dynamic and statistical models by a sensitivity analysis approach. Although robustness for some linear systems has been investigated in the last two decades, robust Kalman filtering for uncertain linear systems is still an active research topic. Several approaches have been proposed using the H ∞ criteria (Nagpal 1991, Xie et al. 1991). A new interval Kalman filter (IKF) developed by Chen (1997) has the same recursive structure as the traditional Kalman filter, escaping the additional computation required for the above H ∞ methods. On the other hand, the IKF has been shown to be better than some existing robust Kalman filtering (Chen et al, 1997). Since the measurement equations are nonlinear and also as the inertial system equations themselves are nonlinear, it is necessary to use an extended interval Kalman filter (EIKF) for the integrated navigation system. Siouris (1997) successfully applied the EIKF to tracking of an incoming ballistic missile system. However, noise uncertainty for the tracking problem has not been studied by using intervals. This paper is focused on the application of the interval system analysis to the integrated GPS/INS with uncertainty. The parameter uncertainties of dynamics model and the noise uncertainties are described by intervals, and the EIKF is established for the nonlinear integrated system.