A pursuit-evasion differential game with noisy measurements of the evader's bearing from the pursuer (Q1068736)

A stochastic pursuit-evasion differential game involving two players, E and P, moving in the plane is considered. It is assumed that player E (the evader) has complete observation of the position and velocity of player P, whereas player P (the pursuer) can measure the distance d(P,E) between P and E but receives noise-corrupted measurements of the bearing \(\beta\) of E from P. Three cases are dealt with: (a) using the noise- corrupted measurements of \(\beta\), player P applies the proportional navigation guidance law; (b) P has complete observation of d(P,E) and \(\beta\) (this case is treated for the sake of completeness); (c) using the noise-corrupted measurements of \(\beta\), P applies an erroneous line- of sight guidance law. For each of the cases, sufficient conditions on optimal strategies are derived. In each of the cases, these conditions require the solution of a nonlinear partial differential equation on a torus in \({\mathbb{R}}^ 2\). Finally, optimal strategies are computed by solving the corresponding equations numerically.