Fuzzy Enhancement of GPS – INS Synergy

The paper presents a new approach of enhancement of GPS – INS synergy by the use of a fuzzy system. A new membership function, which allows a better management of its shape, is used in Mamdani-type fuzzy inference systems. There are two main parameters in fuzzy control systems that influence the performances of a system. The first parameter is the overlapping of membership functions and the second is the output value after defuzzification. Both of them are related to the shape of membership functions. This is modified either by the change of classical membership functions or by the use of concentrator and dilator operators. We introduce a novel membership function which has an elliptical shape. This elliptical membership function provides for the same operation effects, but with much more accuracy. Essentially, the new membership function uses one parameter, the curvature, to obtain a flexible and useful set of functions. Furthermore, the curvature parameter is intuitively appealing. The theoretical fundamentals of the function are presented and the practical accuracy aspects are evaluated. A feed forward system using two Mamdani-type fuzzy inference subsystems is built, and then trained by the modification of the shapes of membership functions. INTRODUCTION During the past few years there are approaches focusing on using artificial intelligence to cope with problems arising from incertitude in hybrid navigation systems. The necessity of greater integrity of the navigation solution leads to approaches that do not put all eggs in the same basket. Although the GNSS is the most popular positioning system, when it comes to integrity most of the approaches use also the Inertial Navigation System (INS) as a backup. The synergy of GNSS and INS is the basis of the hybrid navigation systems. Loosely or tightly coupled, the two systems offer a solution for almost every customer. There is a huge literature on Kalman filtering of GPS and INS separately, when they are loosely coupled, or on GPS an INS together when they are tightly coupled. David McNeil Mayhew uses fuzzy techniques to overcome some problems in a loosely coupled hybrid system [1]. His approach is to weigh the GPS and INS outputs in function of the dynamic scenario. The weights are computed using fuzzy logic in different scenarios. For instance, if the vehicle speed is low the heading computed based on GPS fixes is not accurate and the weight is transferred to INS. Two years later, Escamilla-Ambrosio and Mort used a Fuzzy-adaptive Kalman Filter to adjust the measurement noise covariance matrix R employing a fuzzy inference system (FIS) [2]. In 2002, Rahbari, Leach, Dillon and de Silva approached the same problem of noise covariance matrix and tune this matrix, using fuzzy techniques, as function of aircraft maneuvers [3]. In [4] Loebis, Sutton and Chudley presents a very good review of multisensor data fusion and the papers published to date on artificial intelligence fusion using neural networks, fuzzy sets and genetic algorithms. The same authors will explore, one year later [5], a hybrid navigation system, which cope with the Kalman filter divergence problem caused by the insufficiently known filter statistics. The filter is adapted by use of fuzzy-rulebased scheme. Genetic algorithm techniques are then used to optimize the parameters of membership functions. A team of researchers from Department of Geomatics Engineering, University of Calgary, designed an adaptive fuzzy network to modify the Kalman filter that tightly coupled the GPS and INS [6]. The authors of the present paper explored in [7] the