Adaptive Precision Geolocation Algorithm with Multiple Model Uncertainties

Abstract

In the unmanned ground vehicle (UGV) case, the estimation of a future position with a present one is one of the most important techniques (Madhavan & Schlenoff, 2004). Generally, the famous global positioning system (GPS) has been widely used for position tracking because of its good performance (Torrieri, 1984; Kim et al., 2006). However, there exist some defects. For example, it needs a separate receiver and it must have at least three available satellite signals. Moreover it is also vulnerable to the indoor case (Gleanson, 2006) or the reflected signal fading. There have been many researches to substitute or to assist the GPS. One of them is the method of using the time difference of arrival (TDoA) which needs no special equipment and can be operated in indoor multipath situation (Najar & Vidal, 2001). The TDoA means an arrival time difference of signals transmitted from a mobile station to each base station. It is the basic concept of estimation that the position of a mobile station can be obtained from the crossing point of hyperbolic curves which are derived from the definition of TDoA. Including some uncertainties, there have been several approaches to find the solution of TDoA based geolocation problem using the least square method, for example, Tayler series method (Xiong et al., 2003), Chan’s method (Ho & Chan, 1993), and WLS method (Liu et al., 2006). However in case of a moving source, it demands a huge amount of computational efforts each step, so it is required to use a method which demands less computational time. As a breakthrough to this problem, the application of EKF can be reasonable. The modeling errors happen in the procedure of linear approximation for system behaviors to track the moving source’s position. The divergence caused from the modeling errors is a critical problem in Kalman filter applications (Julier & Uhlmann, 2004). The standard Kalman filter cannot ensure completely the error convergence because of the limited knowledge of the system’s dynamical model and the measurement noise. In real circumstances, there are uncertainties in the system modeling and the noise description, and the assumptions on the statistics of disturbances could be restrictive since the availability of a precisely known model is very limited in many practical situations. In practical tracking filter designs, there exist model uncertainties which cannot be expressed by the linear statespace model. The linear model increases modeling errors since the actual mobile station moves in a non-linear process. Especially even with a little priori knowledge it is quite