Fundamentals of Kalman Filtering: A Practical Approach, Second Edition
Containing numerous real-life problems and examples presented in detail, this text demonstrates the many ways in which Kalman filters can be designed.
TABLE OF CONTENTS Fundamentals of Kalman Filtering: A Practical Approach, Second Edition
Chapter 8: Drag and Falling Object
Introduction
In the preceding chapter we introduced extended Kalman filtering by trying to estimate the altitude and velocity of a falling object under the influence of drag. It was assumed in Chapter 7 that the amount of drag acting on the object was known in advance via knowledge of the object's ballistic coefficient. In that example we derived a two-state extended Kalman filter in which it was assumed that there were noisy measurements of the object's altitude and that the altitude and velocity of the object had to be estimated. In this chapter we will add further complexity to the problem by assuming that the drag or ballistic coefficient is unknown. Therefore, in this problem we desire to build another extended Kalman filter that will estimate the object's altitude, velocity, and ballistic coefficient based on noisy measurements of the object's altitude.
Problem Setup
Let us again reconsider the one-dimensional example of an object falling on a tracking radar, as was shown in Fig. 7.1 but is now redrawn for convenience in Fig. 8.1. This time the problem is different because we are assuming that the drag is unknown, which means that we have to estimate the ballistic coefficient in order to get a good estimate of the position and velocity of the object. Recall that the object was initially at 200,000 ft above the radar and had a velocity of 6000 ft/s toward the radar, which is located on the surface of a flat Earth. As was the case in...
Copyright American Institute of Aeronautics and Astronautics, Inc. 2005 under license agreement with Books24x7
