The Nonsingular Estimator for Exoplanet Orbits: An Unscented Batch Estimation Method for Direct Imaging Measurements

Abstract We present a new method for fitting exoplanet orbits to direct astrometric measurements, using nonlinear batch estimation and nonsingular orbital elements. Our estimation technique is based on the unscented transform, which approximates probability distributions using finite, deterministic sets of weighted sample points. Furthermore, we use Gaussian mixtures to account for the strong nonlinearities in the measurement model. As a fitting basis, we use a set of orbital elements developed specifically for directly observed exoplanets, combining features of the Thiele–Innes constants and the Cohen–Hubbard nonsingular elements. We validate the new method using simulated exoplanet orbits, and we demonstrate its use with real exoplanet data. Compared to state-of-the-art Markov Chain Monte Carlo and Bayesian rejection sampling techniques, the new method is found to give orbit estimates of comparable or higher accuracy but with much faster execution.