Cooperative exploration requires multiple robotic sensor platforms to navigate in an unknown scalar field to reveal its global structure. Sensor readings from the platforms are combined into estimates to direct motion and reduce noise. We show that the combined estimates for the field value, the gradient and the Hessian satisfy an information dynamic model that does not depend on motion models of the platforms. Based on this model, we design cooperative Kalman filters that apply to general cooperative exploration missions. We rigorously justify a set of sufficient conditions that guarantee the convergence of the cooperative Kalman filters. These sufficient conditions provide guidelines on mission design issues such as the number of platforms to use, the shape of the platform formation, and the motion for each platforms.