A stochastic pursuit-evasion differential game with noise-corrupted measurements of the bearing

Abstract

A stochastic pursuit-evasion differential game involving two players, E and P, moving in the plane is considered. It is assumed that both players can measure the distance d(P, E) between P and E while receiving noise-corrupted measurements of the bearing β of E from P. Using the noise-corrupted measurements of β, player E applies a 'Line-of-Sight' (L.O.S.) guidance law, whereas player P applies: (i) the L.O.S. guidance law; and (ii) the Proportional Navigation (P.N.) guidance law. In both cases, the probability of the event E, where E = {player E is intercepted by P before leaving P's detection range}, is computed. In addition, the cases where (a) E receives measurements of d(P, E) and β, whereas P receives only measurements of d(P, E) and uses an estimate β̂ of β, and (b) both players have complete observation of d(P, E) and β are dealt with, and Prob(E) is computed. In all cases, the computation of Prob(E) led to the numerical solution of a partial differential equation on a kind of a 'generalized torus' in R3. The results obtained can be used for the evaluation of the performance of the L.O.S. and P.N. guidance laws when only noise-corrupted measurements are available. © 1985.