A Mathematical Foundation for Selecting Radar Locations for Operational Testing of Inertial Systems

One in a series of memoranda exploring new techniques in ICBM testing and improvements in the test-range configuration. It contains the mathematical foundations for a computer program that determines the optimal locations of the radar trackers on a missile test range, such that a certain statistical estimate of miss, relative to the actual impact point, is minimized. The memorandum considers the problem of radar-tracking, during boost phase, a rocket vehicle navigated by an inertial measurement unit (IMU). If the maximum likelihood estimate of the IMU parameters that produced a given set of noisy range data is determined, and if the maximum likelihood estimate of miss is calculated from this parameter estimate, then the vehicle miss covariance matrix is a function of the radar map locations. The study presents an optimization scheme for locating the radars such that the maximum eigenvalue of the covariance matrix is minimized.