Adaptive and Nonlinear Kalman Filtering for GPS Navigation Processing

The Global Positioning System (GPS) is a satellite-based navigation system that provides a user with the proper equipment access to useful and accurate positioning information anywhere on the globe. The well-known Kalman filter (Gelb, 1974; Brown & Hwang, 1997; Axelrad & Brown, 1996) provides optimal (minimum mean square error) estimate of the system state vector, and has been widely applied to the fields of navigation such as GPS receiver position/velocity determination. To obtain good estimation solutions using the EKF approach, the designers are required to have good knowledge on both dynamic process (plant dynamics, using an estimated internal model of the dynamics of the system) and measurement models, in addition to the assumption that both the process and measurement are corrupted by zero-mean white noises. A conventional Kalman filter fails ensure error convergence due to limited knowledge of the system’s dynamic model and measurement noise. If the Kalman filter is provided with information that the process behaves a certain way, whereas, in fact, it behaves a different way, the filter will continually intend to fit an incorrect process signal. In actual navigation filter designs, there exist model uncertainties which cannot be expressed by the linear state-space model. The linear model increases modelling errors since the actual vehicle motions are non-linear process. It is very often the case that little a priori knowledge is available concerning the manoeuvring. Hence, compensation of the uncertainties is an important task in the navigation filter design. In the modelling strategy, some phenomena are disregarded and a way to take them into account is to consider a nominal model affected by uncertainty. The adaptive algorithm has been one of the approaches to prevent divergence problem of the EKF when precise knowledge on the system models are not available. To prevent divergence problem due to modelling errors using the EKF approach, the adaptive filter algorithm has been one of the strategies considered for estimating the state vector. Many efforts have been made to improve the estimation of the covariance matrices. Mehra (1970; 1971; 1972) classified the adaptive approaches into four categories: Bayesian, maximum likelihood, correlation and covariance matching. These methods can be applied to the Kalman filtering algorithm for realizing the adaptive Kalman filtering (Mehra, 1972; Mohamed & Schwarz, 1999). One of the adaptive fading methods (Ding, et al., 2007; Jwo & Weng, 2008) is called the strong tracking Kalman filter (STKF) (Zhou & Frank, 1996), which O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg