Virtual Focal Plane Dynamics for Generalized Remote Sensing Coverage Analysis

Modern spaceborne remote sensing requirements necessitate a new paradigm of mission, leveraging distributed platforms for short revisit time at global scale. The distributed spacecraft mission (DSM), from constellations to heterogenous trains, can meet science goals moving forward into the next decade, while lowering risk and cost through novel rideshare opportunities. However, in light of an increased number of satellites is an increased mission complexity, expanding the trade space, leading to a computationally demanding optimization task. There are techniques to intelligently search the trade space for optimal architectures, but in order to compare one design to another, they must first be given value through figures of merit from coverage simulation. In traditional coverage calculators, the Earth is discretized into many grid points (GPs) that define a region of interest. Some or all of these GPs are iterated over to determine whether they lie within a simulated satellite’s field-of-view (FOV) at a given time-step. If so, they are considered accessed GPs, and the time of access is recorded. Past coverage algorithms are inefficient because 1) time-steps are required and 2) many more GPs are iterated over than is necessary to produce coverage metrics. The Envelope Grid Point Approach (EGPA) algorithm is an improvement on existing state-of-the-art coverage calculators, reducing calculation time by up to 3 orders of magnitude, depending on simulation scenario. However, EGPA has a simple access time model; simulated off-nadir maneuvering, orbit regime and eccentricity, and FOV type are restricted. Common remote sensing designs are simulated well, but future DSMs may utilize non-traditional orbit regimes and dynamic off-nadir maneuvering to maximize science return. While traditional coverage calculators are less efficient, they retain an unmatched generality, which is particularly important for realistic mission design. In this study, we develop a new access time model called Virtual Focal Plane Dynamics (VFPD), replacing the brittle nonlinear access evaluation in EGPA, meeting the same generality as prior methods, while retaining high efficiency. In VFPD, for each GP, we query satellite position, velocity, and acceleration over a series of tie points from an initial guess, and fit multiple 2nd order parametric curves to the relative motion of the GP as projected on the sensor focal plane. The intersections of the GP relative trajectory with the FOV boundary uniquely identify the start and end of access events for each GP. With VFPD, we are able to produce average access time, access start, access end, and access period. We compare VFPD to three representative cases, for a circular and an eccentric orbit with e = 0.2, and an off-nadir case at up to 45° roll for circular and rectangular FOVs of 30°. As compared to traditional methods, VFPD covers ~98% of the same GPs within <1 sec average access time RMSE, and <0.1 sec access start and end time at a 90% confidence interval. The efficiency of VFPD depends on the coverage calculator it is equipped with; for EGPA, VFPD retains the same low order of runtime complexity.