Application of an evolution strategy in planetary ephemeris modeling

Abstract

Classical planetary ephemeris construction comprises three major steps which are to be performed iteratively: numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of observations (reduction step), and optimization of model parameters (adjustment step). In future, this approach may become challenged by further refinements in force modeling (e.g. inclusion of much more significant minor bodies than in the past), an ever-growing number of planetary observations (e.g. the vast amount of spacecraft tracking data), and big data issues in general. In order to circumvent the need for both the inversion of normal equation matrices and the determination of partial derivatives, and to prepare the ephemeris for applications apart from stand-alone solar-system planetary orbit calculations, here we propose an alternative ephemeris construction method. The main idea is to solve it as an optimization problem by straightforward direct evaluation of the whole set of mathematical formulas, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and potential numerical difficulties. The usual gradient search is replaced by a stochastic search, namely an evolution strategy, the latter of which is perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach allows for multi-criteria optimization and time-varying optima. These issues will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of a generalized physical state (orbit, size, shape, rotation, gravity, ...) of celestial bodies (planets, satellites, asteroids, or comets), and/or if one seeks near real-time solutions. Here, we outline the general idea and exemplarily optimize high-correlated asteroidal ring model parameters (total mass and heliocentric radius), and individual asteroid masses, based on simulated observations.