Learning aLinearDynamical SystemModel for Spatio- temporal FieldsUsing aGroupofMobile SensingRobots

This paper considers the problem of learning dynamic spatiotemporal fields using sensor measurements from a group of mobile sensing robots. We first introduce a general dynamical model for the spatiotemporal field. We then propose a family of motion strategies that can be used by a group of mobile robotic sensors to move along a uniformly observable periodic trajectory to collect point samples about the field. Our motion strategies are designed to collect enough information from enough locations at enough different times for the robots to learn the dynamics of the field. In conjunction with these motion strategies, we propose a new learning algorithm based on subspace identification to learn the parameters of the dynamical model. We prove that as the number of data collected by the robots goes to infinity, the parameters learned by our algorithm will converge to the true parameters. The performance of our algorithm is demonstrated in numerical simulations and verified by considering the surface water temperature in the Caribbean Sea, which is a physical spatio-temporal field.