NEXO (Nonsingular Estimator for EXoplanet Orbits) fits exoplanet orbits to direct astrometric measurements using nonlinear batch estimation and nonsingular orbital elements. The estimation technique is based on the unscented transform, which approximates probability distributions using finite, deterministic sets of weighted sample points. Furthermore, NEXO uses Gaussian mixtures to account for the strong nonlinearities in the measurement model. As a fitting basis, it uses a set of orbital elements developed specifically for directly observed exoplanets, combining features of the Thiele–Innes constants and the Cohen–Hubbard nonsingular elements.