Sensor scheduling criterion for space surveillance based on relative orbit analysis

To exploit the observation effectiveness of the space surveillance network comprehensively and provide a mathematical explanation of a sensor scheduling result, the analytical sensor scheduling criterion is required. This paper presents an analytical sensor scheduling criterion of the space surveillance network based on the relative orbit analysis. A virtual chief orbit and the relative orbit elements, which are the set of orbit element differences of the real satellite relative to the virtual chief satellite, are used to describe the motion of the real satellite. Because the virtual chief orbit, which is selected under the constraint that the relative orbit radius is less than 0.3% of that of the chief orbit radius, is accurately known, the uncertainty of the relative motion will describe the uncertainty of orbit determination of the real satellite. Then one can obtain an analytical criterion derived from the covariance matrix of the relative orbit elements to measure the observation effectiveness of a sensor scheduling. This criterion is valid for the observation of the general elliptic orbit satellite with arbitrary observation data types and is expressed explicitly in terms of influencing factors, such as the sensor type, measurement accuracy, observation time, fit span, and observation geometry. The individual effectiveness and tradeoffs of these influencing factors can be explored quantitatively by this criterion. To get a clear view of how these factors individually or cooperatively affect the predicted position error, a closed-form expression of this criterion is presented under the planar orbit assumption. This simplified criterion, which is valid for the observation of near-circular orbit satellites, can provide the mathematical explanation of the traditional sensor scheduling strategies. Finally, some simple sensor scheduling strategies are analyzed based on this criterion.