  Orbit determination (OD) is a fundamental problem in space surveillance and
tracking, crucial for ensuring the safety of space assets. Real-world
ground-based optical tracking scenarios often involve challenges such as
limited measurement time, short visible arcs, and the presence of outliers,
leading to sparse and non-Gaussian observational data. Additionally, the highly
perturbative and nonlinear orbit dynamics of resident space objects (RSOs) in
low Earth orbit (LEO) add further complexity to the OD problem.
  This paper introduces a novel variant of the higher-order unscented Kalman
estimator (HOUSE) called $w$-HOUSE, which employs a square-root formulation and
addresses the challenges posed by nonlinear and non-Gaussian OD problems. The
effectiveness of $w$-HOUSE was demonstrated through synthetic and real-world
measurements, specifically outlier-contaminated angle-only measurements
collected for the Sentinel 6A satellite flying in LEO. Comparative analyses are
conducted with the original HOUSE (referred to as $\delta$-HOUSE), unscented
Kalman filters (UKF), conjugate unscented transformation (CUT) filters, and
precise orbit determination solutions estimated via onboard global navigation
satellite systems measurements.
  The results reveal that the proposed $w$-HOUSE filter exhibits greater
robustness when dealing with varying values of the dependent parameter compared
to the original $\delta$-HOUSE. Moreover, it surpasses all other filters in
terms of positioning accuracy, achieving three-dimensional root-mean-square
errors of less than 60 m in a three-day scenario. This research suggests that
the new $w$-HOUSE filter represents a viable alternative to UKF and CUT
filters, offering improved positioning performance in handling the nonlinear
and non-Gaussian OD problem associated with LEO RSOs.
