Nonlinear deterministic and stochastic radar tracker modeling and analysis

This dissertation addresses a problem in applied mathematics that is strongly motivated by decision processes that take place within advanced technology anti-ship cruise missiles (ASCMs) The ASCMs use a tracking mechanism to home-in on ship targets. Understanding, and ultimately defeating, the tracker process is a fundamental goal of electronic warfare (EW). An overview of EW and the role it plays in defending ships from ASCMs is given. Additionally, the operation of a typical ASCM is discussed with the aim of narrowing the focus on those modules of the missile that are needed for the study of EW techniques that attack the missile's ability to track real ship targets. These essential components are described by the radar target interaction and the missile tracking system. The radar signal return from complex targets is reviewed. Then, nonlinear dynamical models for the automatic gain control (AGC) aided, gated radar range and angle trackers are developed for two common types of loop dynamics. Both discrete-time and continuous-time dynamical models are presented for each type of tracking loop. These dynamical models are driven by random fluctuations that enter into the tracker dynamics via the radar signal and are the result of the stochastic nature of radar target reflections.; The combined range and angle tracker models are reduced to AGC-aided range trackers. As an ASCM closes with a target group, and the target radar returns of a ship and a decoy separate beyond the limits of the gate, the tracker can no longer follow the ensemble of returns and it ultimately commits to one of the targets. The study of the resolution phenomena is initiated for deterministic targets. Each of the reduced order models is analyzed for a deterministic target return condition. General stability criteria for asymptotic stability of equilibrium points is studied and used to evaluate the tracker's ability to resolve two competing targets. The tracker's resolution capability is also examined in the context of a bifurcation in the model equations. Under the assumption of constant targets, a bifurcation diagram is obtained.; A fundamental tracker analysis problem is to determine how the tracker resolves multiple statistically fluctuating targets that are crossing and separating in space, and with what probability individual targets are selected. The continuous-time simulation model of the AGC-aided range tracker is studied using Monte Carlo techniques. Numerical computation of the evolution of the probability density is employed to study sensitivity to certain model parameters, especially noise correlation time, relative intensity of target fluctuations, target separation rate, and the AGC bandwidth. A simpler model results from the study.; Stochastic stability is studied using Liapunov functions or sample path analysis and singular perturbations, depending on the assumed noise characteristics. The stochastic stability results are in the spirit of results on partial stability, a topic heretofore considered mainly for deterministic problems. That is, it is shown that one state variable (the tracker's range estimate) may display stable behavior, although another state variable (the AGC voltage) behaves erratically.; Some preliminary results are given for the combined range and angle tracker. They are limited to a short study of the nature of the bifurcation in the model equations describing range and azimuth tracking.