Sigma-Point Filter for Terrain Referenced Navigation

Abstract

This paper deals with a navigation system based on inertial navigation combined with terrain referenced navigation (TRN). A TRN system is able to provide an aiding source for the inertial navigation system (INS) using radar altimeter measurements and a digital terrain elevation reference. This setup is self sucien t and does not need any external signal sources to provide a long term stable navigation solution for civil and military avionics. Especially in military applications, where GPS signals can be jammed, a combined TRN/INS system allows high performance and integrity of the navigation system. This paper describes the integration of the TRN functionality in a non-linear lter, commonly known as sigma-point lter. Furthermore, it will show the advantages this non-linear approach over the Extended Kalman lter (EKF). The sigma-point approach uses deterministically calculated and weighted points which capture the probability density function of the state. To determine the sigma points over the time, it is not necessary to calculate the linearization of the measurement and system model. Therefore, it allows the strongly non-linear measurement model of TRN-systems to be considered properly. Simulations show the superiority of the sigma-point lter compared to the extended Kalman lter. or almost all applications in civil and military avionics it is mandatory to determine position, velocity and attitude accurate and with a high update rate. These requirements cannot be sucien tly guaranteed with a single sensor. Therefore, the optimal integration of dieren t sensor signals is mandatory for navigation systems. Probably the most widely used setup is based on an inertial and a satellite navigation system like the global positioning system (GPS). The INS allows short term stable calculation of position, velocity and attitude based on acceleration and rotation rate measurements and initial position, velocity and attitude. Because of the degrading navigation solution of the INS for longer measurement periods, the satellite navigation system usually provides a position aiding using external satellite signals. Considering a situation where these external signals are disturbed, it is not possible to accomplish a long term stable navigation solution because of the failing satellite navigation system. In military applications the intentional jamming, while ying over hostile areas, has to be expected and a method has to be found to enable navigation even in this situation. Due to extensive use of satellite navigation systems in domestic applications and the simplicity to build jammers, the chances of disturbances in civil navigation has to be considered. To avoid the dependency on external signals, a self sucien t navigation system has to be used to aid the INS. A TRN system is self sucien t because it determines the position based on radar height measurements and a digital elevation reference that is stored on board of the aircraft. The dicult y by using a TRN system is based on the strong non-linearity of the measurement model. It cannot be covered properly by the Extended Kalman lter normally used to integrate the INS and GPS data. Therefore, a so called sigma-point lter is used to perform the integration for the non-linear measurement model. In the following sections a principle of terrain referenced navigation is presented and TRN algorithms based on comparison and ltering methods are introduced. Afterwards, the sigma-point lter is described and adaptations for the TRN measurement model are explained. Finally, simulation results are discussed.