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This paper describes an optimization framework to design guidance for apossibly heterogeneous team of multiple mobile sensors to estimate aspatiotemporal process modeled by a 2D diffusion-advection process. Owing tothe abstract linear system representation of the process, we apply theKalman-Bucy filter for estimation, where the sensors provide linear outputs. Wepropose an optimization problem that minimizes the sum of the trace of thecovariance operator of the Kalman-Bucy filter and a generic mobility cost ofthe mobile sensors, subject to the sensors' motion modeled by linear dynamics.We establish the existence of a solution to this problem. Moreover, we proveconvergence to the exact optimal solution of the approximate optimal solution.That is, when evaluating these two solutions using the original cost function,the difference becomes arbitrarily small as the approximation gets finer. Tocompute the approximate solution, we use Pontryagin's minimum principle afterapproximating the infinite-dimensional terms originating from thediffusion-advection process. The approximate solution is applied in simulationto analyze how a single mobile sensor's performance depends on two importantparameters: sensor noise variance and mobility penalty. We also illustrate theapplication of the framework to multiple sensors, in particular the performanceof a heterogeneous team of sensors.

Optimal guidance and estimation of a 2D diffusion-advection process by a team of mobile sensors