Pursuit-evasion game for normal distributions

In this paper we consider a probabilistic model of a pursuit-evasion game on Rn, in which neither pursuer nor evader positions are known with certainty. Both parties are represented by normal distributions that evolve according to a Kalman filter as new sensor readings (observation from overhead camera/satellite images) are obtained. The objective is to design the control commands issued by the pursuer (which is executed noisily). The control commands issued by the evader are unknown - only sensor measurements are given. Even with such limited knowledge we prove boundedness of a distance between the pursuer´s distribution and the evader´s true distribution (one that takes into account the evader´s control commands). Our simulation results support the claimed guarantees.