Performance analysis and enhancement of proportional navigation guidance systems

Abstract

Proportional navigation has long been an active area of research in the guidance and control community. It is easy to implement and effective in most applications. However, proportional navigation leads to poor observability problems when using bearings-only measurements. Bearings-only measurement systems are common in guidance and target tracking, as they are low-cost and free from jam noise. Proportional navigation guidance systems with bearings-only measurements are not only practically important, but also theoretically interesting and nontrivial, due to their time-varying dynamics, highly nonlinear measurements, and complex engagement geometry when the target is maneuverable. This thesis is concerned with observability enhancement and performance analysis of proportional navigation guidance systems. To tackle the low observability problem involved in proportional navigation systems with angle-only information, observability analysis is rigorously performed in order to grasp a better understanding of the essence of the problem. Necessary and sufficient conditions for system observability are firmly established, and are general enough to encompass most previous results. Extensions of these conditions are readily applicable to observability checks with practical guidance laws in closed loop. The observability analysis paves the way for improvement of system performance and development of new guidance laws. Among existing guidance laws proposed to improve system observability as well as interception performance, additive proportional navigation is a class of guidance that preserves the simplicity in design and realization, while enhancing system observability by incorporating a measure of information content. Based on the thermal noise model, a new form of additive observable proportional navigation is presented in this thesis. Analysis undertaken demonstrates that this new guidance law outperforms true proportional navigation, which is the most accepted guidance law, by offering a better possibility of observable systems and a larger region of interception. The effectiveness of this new control law is also confirmed by simulations. Bounds of system navigation constants to ensure interception are provided as guidelines for system design. To account for the finite acceleration capability of real-world guidance systems due to physical limitations, effects of acceleration saturation constraint are investigated. In contrast to the ideal system with infinite acceleration capability, more stringent requirements on system initial launch conditions and different bounds of design parameters must be met to achieve interception, using more total control effort. The degradation of system performance due to saturation constraint is verified by extensive simulations.