Application of an Adaptive Kalman Filter for the Estimation of Position, Velocity & Acceleration of a Moving Body from GPS Measurements

The use of moving platforms in order to carry out measurements on the ground, on the sea or in the air is very important for geophysical applications. This renders possible the quasi continuous measurement of physical values in a short time over wide areas, but requires the estimation of the motion of the measurement module. At the Institute for Geodesy and Photogrammetry of the Swiss Federal Institute of Technology in Zurich, airborne gravimetry flights are performed in order to measure quasi continuous gravity values over Swiss territory. Due to the complexity of the dynamics of an aircraft, and to the high accuracy needed in the gravity measurements required for Geophysical applications (10-5 [m1s2]), the estimation of the motion, and in particular, of the acceleration of the aircraft, the effects of which on the meter are dramatically higher than the anomalies expected in the gravitational field, is of great importance.
In this work a method for the estimation of the motion of moving platforms is presented. This method is the adaptive extended Kalman filter. After a short introduction to the filtering theory, two applications are discussed. In the first one, the circular motion of a machine for testing the surface of a road (see Figure 1) is es ti mated. The position of one rotating arm is measured by differential GPS measurements. The main task is the recursive estimation of the tangential acce1eration of the arm. In the analysis of this application, the following points will be addressed:

- A dynamic system is described by a state vector, which is a set of physical variables, and the relative differential equations. From many different state vector representations, the one exhibiting the best properties must be chosen. - The use of a model for the system dynamics allows also with a deterioration of the measurements to estimate the state vector (even in absence of measurements an estimation of the state vector is available, that is the apriori estimate) - The use of an adaptive algorithm is a good alternative for problems with unknown input function.