Minimum-observation method for rapid and accurate satellite coverage prediction

Satellite coverage is one of the most important elements of satellite applications, which determines the range and duration of the service provided by the satellite. We propose a rapid one-dimensional method to predict when a ground target is visible from the satellite, which means the ground target is within the footprint of the satellite, for an arbitrary sensor field. The field is defined as the shape of the observable range of the sensor placed on the satellite. For instance, the cone field means the shape of the observable range of the sensor is a circle, while the rectangle field means the shape of the observable range of the sensor is a rectangle. First, the minimum-observation function is defined to describe the geometric properties of the sensor field of a satellite. Based on the geometric relationship between the satellite and a target, visible conditions at a ground point given the satellite field of view are obtained, considering the field and earth-occlusion constraints. In order to calculate the visible set during a given period, the Hermite cubic interpolation method is used to obtain the earth-occlusion-off intervals rapidly, and the field-constraint function is fitted by the linear fixed-step method. The visible intervals of the ground point from the sensor are obtained by finding the zero points of the fitting field-constraint function limited by the earth-occlusion-off intervals. To demonstrate the effectiveness of the proposed method, a series of numerical simulations are conducted. The simulation results indicate that the proposed method can balance computation time and precision, which is suitable for various types of satellite orbits and sensor fields. Thus, as a practical method, the proposed method can provide efficient communication, navigation, and remote sensing tool.