Optimal Trajectories for Underwater Vehicles by Quantization and Stochastic control

Huilong Zhang (1, 2) , Benoîte de Saporta (1, 2, 3) , François Dufour (1, 2) , Dann Laneuville (4) , Adrien Nègre (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 GREThA - Groupe de Recherche en Economie Théorique et Appliquée
4 DCNS - DCNS Group

We present in this paper a numerical method which computes the trajectory of a vehicle subject to some mission objectives. The method is applied to a submarine whose goal is to best detect one or several targets (we consider signal attenuation due to acoustic propagation) or/and to minimize its own detection range perceived by the other targets. Our approach is based on dynamic programming of a finite horizon Markov decision process. The position and the velocity of the targets are supposed to be known only up to a random estimation error, as a Kalman type filter is used to estimate these quantities from the measurements given by the on board sonar. A quantization method is applied to fully discretize the problem and solve it numerically.

Mots clés: Non linear filtering; Quantization; Markov decision processes; Dynamic programming; Underwater acoustic warfare

Domaines: Probabilités [math.PR]

Huilong Zhang, Benoîte de Saporta, François Dufour, Dann Laneuville, Adrien Nègre. Optimal Trajectories for Underwater Vehicles by Quantization and Stochastic control. Fusion 2014, Jul 2014, Salamanca, Spain. pp.8. ⟨hal-00990765⟩