ON THE APPLICATION OF GAME THEORY AND TIME SERIES ANALYSIS TO PROBLEMS IN FIRE CONTROL

Two specific fire control problems are examined in this dissertation. One concerns the filter-predictor algorithms employed by an anti-aircraft (AA) artillery weapon system against an attacking, fixed-wing aircraft in a close ground-support bombing maneuver. The other deals with the determination of evasion strategies for an aircraft under attack by multiple air-to-air guided missiles. The concepts, methods and models of time series analysis and game theory are used to obtain new, minimum sensitivity high-order filter-predictor algorithms for the AA problem, and game theoretic concepts and models are employed to develop a mathematical model for multiple missile evasion in the air-to-air scenario. A central aspect of this dissertation is the use of authentic flight test data, which consists of eleven sample attack profiles an aircraft might perform when bombing a specific ground target in a hostile environment. These profiles, or flight paths, provide the attack aircraft motion for the simulation program in which the performance of fire control filter-predictor algorithms is evaluated. Although the eleven flight paths appear significantly different to the naked eye, the thirty-three acceleration-dot time series in the data base--eleven flight paths times three directions--are shown to be accurately modeled by a single robust fifth-order autoregressive (AR) model. The simulation results are presented for various predictors assuming noiseless observations of the aircraft motion by the AA weapon system, as well as for several filter-predictor algorithms with two levels of additive white noise in the observations. Substantial improvements in overall prediction capability achievable by using robust, high-order filter-predictor algorithms based on a fifth-order AR model of acceleration-dot instead of the benchmark third-order algorithms based on a first-order AR model of acceleration are demonstrated. A minimum sensitivity analysis of the eighth-order Kalman filters which are parameterized by the five AR coefficients is performed in a general, nth-order setting using a game theoretic approach. The analysis provides a technique for defining a least favorable AR acceleration-dot process, which in this dissertation is used to generate a worst case attack profile and to determine a minimum sensitivity Kalman filter. This technique, motivated by a new saddle-point theorem proven here for a linear nth-order system, can be applied to a range of problem areas, such as signal processing and process control. The missile evasion problem examined consists of one evading aircraft and two pursuing air-to-air guided missiles. For various formulations of the dynamics and optimization criterion, the existence, structure and behavior of a set of optimal evasion strategies are delineated, assuming the evader knows the guidance laws of each pursuing missle. Both fixed terminal time and free terminal time optimization criteria are studied. In the former case, the evader seeks to maximize the terminal miss distance between himself and each pursuer. In the latter case, the evader seeks to maximize the distance of closest approach between himself and each pursuer over some time interval. A game theoretic approach (maximization of the minimum miss) is taken to resolve these problems, which are most naturally formulated as multi-criterion or vector-valued optimization problems. The saddle-point theorems proven in this work provide a means of determining optimal evasion strategies which can be used as a baseline for the comparison of more heuristic algorithms capable of being implemented in real-time on current avionics computer hardware