This paper presents a novel class of self-organizing autonomous sensing agents that form a swarm and learn the static field of interest through noisy measurements from neighbors for gradient climbing. In particular, each sensing agent maintains its own smooth map which estimates the field. It updates its map using measurements from itself and its neighbors and simultaneously moves toward a maximum of the field using the gradient of its map. The proposed cooperatively learning control consists of motion coordination based on the recursive spatial estimation of an unknown field of interest with measurement noise. The convergence properties of the proposed coordination algorithm are analyzed using the ODE approach and verified by a simulation study.