Thesis. 1975. Sc.D.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Vita. / Bibliography: leaves 318-319. / Sc.D.

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Motivated by the fact that anti-ship missiles present a serious threat to today's Navy, a tracking filter which will give superior tracking and trajectory extrapolation when tracking anti-ship missiles is desired. Because most anti-ship missiles use proportional navigation in their guidance systems, it is best to model their motion using the proportional navigation guidance law. An unbiased narrowband filter is required because the state estimate is used to extrapolate the trajectory over the long time of flight of the gun projectile used to intercept the anti-ship missile. Using the proportional navigation guidance law, a tracking filter is developed which meets the stated requirements. An advantage in using the proportional navigation model, which is not found in previous target models, is the end goal or destination constraint inherent in the proportional navigation guidance law: the anti-ship missile's goal is to strike ownership; the proportional navigation trajectory always passes through the origin. Because of model mismatch when tracking missiles using proportional navigation guidance, previous tracking filters, which use constant velocity, exponentially correlated acceleration, or constant acceleration models of target motion, must use a wide bandwidth or else develop significant bias errors. / M.S.

The engagement between an antiship missile and a ship’s defense system is investigated. The missile is equipped with proportional navigation guidance for homing in on its ship target. The ship’s defense system consists of a radar, an estimation system (the extended Kalman filter and the “jump filter” are used), and a gun system. The performance index is defined as the estimated number of hits (EHITS) of projectiles on the missile. The main objective of this dissertation is to determine maneuvering periods for the missile which minimize the EHITS to evade the ship’s gunfire under different engagement conditions. The maneuvering periods are design parameters in the missile’s controls of both the vertical and the horizontal planes. The engagement conditions are the follows: the maximum amplitude of the maneuvering functions, the homing in position of the missile on the ship, the measurement noise condition of the ship’s radar, and the missile’s model assumed in the ship’s filters. The missile’s control functions considered are periodic and of specific types (sinusoidal, square and sawtooth waveforms); therefore, the periods which minimize the EHITS in this study are suboptimal for the general engagement problem. Two methods are used to obtain the suboptimal periods: one is the ”brute force" method of computing the EHITS for certain equally spaced periods, the other uses an optimization software to search for the minimum point. The results show that the curve of EHITS vs. period is monotonically decreasing until it reaches a minimum point. The optimal period increases with an increase in measurement noise. Among the three waveforms used, the square wave gives the smallest optimal period and the sawtooth wave gives the largest one. The sinusoidal waveform with the period of 1.9 seconds is recommended. We consider the missile's performance against a perfect radar, a modern radar, and an earlier model radar. The optimum EHITS resulting from the optimal periods are between two and three EHITS for all three radars considered. / Ph. D.