This paper presents an explorative navigation method using sparse Gaussian processes for mobile sensor networks. We first show that a near-optimal approximation is possible with a subset of measurements if we select the subset carefully, i.e., if the correlation between the selected measurements and the remaining measurements is small and the correlation between the prediction locations and the remaining measurements is small. An estimation method based on a subset of measurements is desirable for mobile sensor networks since we can always bound computational and memory requirements and unprocessed raw measurements can be easily shared with other agents for further processing (e.g., consensus-based distributed algorithms or distributed learning). We then present an explorative navigation method using sparse Gaussian processes with a subset of measurements. Using the explorative navigation method, mobile sensor networks can actively seek for new measurements to reduce the prediction error and maintain high-quality estimation about the field of interest indefinitely with limited memory.