Globally optimal shape and spin pole determination with lightcurve inversion

Lightcurve inversion is an established technique in determining the shape and spin states of an asteroid. However, the front part of the processing pipeline, which recovers the spin pole and area of each facet, is a non-convex optimisation problem. Hence, any local iterative optimisation scheme can only promise a locally optimal solution. Apart from the obvious downsides of getting a non-optimal solution and the need for an initialisation scheme, another major implication is that it creates an ambiguous scenario - which is to be blamed for the remaining residual? The inaccuracy of the modelling, the integrity of the data, or the non-global algorithm? We address the last uncertainty in this paper by embedding the spin pole and area vector determination module in a deterministic global optimisation framework. To the best of our knowledge, this is the first attempt to solve these parameters globally. Specifically, given calibrated lightcurve data, a scattering model for the object, and spin period, our method outputs the globally optimal spin pole and area vector solutions. One theoretical contribution of this paper is the introduction of a lower bound error function that is derived based on 1) the geometric relationship between the incident and scattered light on a surface and 2) the uncertainty of the gap between the observed and estimated brightness at a particular epoch in a lightcurve. We validated our method’s ability in achieving global minimum with both simulated and real lightcurve data. We also tested our method on the real lightcurves of four asteroids.