This article envisions surveillance and estimation in a future data-rich space environment, wherein spacecraft and other systems sense and record myriad environmental parameters incidentally to their primary missions. In this future environment, a wide range of sensor data will be available, but much of the data may be incidental, and hence subject to fluctuation, gaps, and low fidelity. Here, we explore estimation using such incidentalmeasurement data streams. Specifically, two canonical incidental-measurement-based estimation problems are posed -one concerned with recovering diffusive processes from an incidentally-mobile sensor, the other concerned with object (target) tracking using incidental measurements. Basic formal analyses of these estimation problems are pursued, and simulation results are also presented.