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Autonomous mobile sensor networks are employed to measure large-scale environmental fields. Yet an optimal strategy for mission design addressing both the cooperative motion control and the cooperative sensing is still an open problem. We develop strategies for multiple sensor platforms to explore a noisy scalar field in the plane. Our method consists of three parts. First, we design provably convergent cooperative Kalman filters that apply to general cooperative exploration missions. Second, we present a novel method to determine the shape of the platform formation to minimize error in the estimates and design a cooperative formation control law to asymptotically achieve the optimal formation shape. Third, we use the cooperative filter estimates in a provably convergent motion control law that drives the center of the platform formation to move along level curves of the field. This control law can be replaced by control laws enabling other cooperative exploration motion, such as gradient climbing, without changing the cooperative filters and the cooperative formation control laws. Performance is demonstrated on simulated underwater platforms in simulated ocean fields.