| Four estimators are applied to the problem of tactical ballistic missile (TBM) parameter estimation and prediction. This research compared the accuracy and efficiency of several implementations of batch, sequential (Kalman), extended Kalman, and Bayes filters. It examined how well each performed in determining the position, velocity and thrust acceleration of a TBM. Azimuth, elevation, and range measurements are used as inputs to the filters. Some of the filters used angle-only measurements while others used range in addition to the angle observations. This research looked at observations from space-based sensors, ground-based sensors and a combination of both. The filters estimated a seven parameter state consisting of the position and velocity components, and the thrust acceleration magnitude; an eight parameter state consisting of the exhaust velocity and the ratio of the mass flow rate to the initial mass, in addition to the position and velocity vectors; and a seven parameter state of range, range rate, argument of latitude and its rate, inclination, right ascension of the ascending node, and net acceleration.; The launch and impact points were estimated using states taken at different points in the missile trajectory. The states, which varied from the position and velocity vectors to the full eight parameter state, were numerically integrated either forward or backward in time until the oblate Earth was intersected. The launch impact estimates were good (within 1.5 km) until the state reached 50 seconds after launch. The impact point estimation results were poor and varied from within 2 km to 40 km of the actual point.; Based on the various factors examined, the eight state Batch filter using range, azimuth and elevation measurements was selected for the filter to better handle the TBM tracking and prediction problem. |
