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arXiv · 2603.20259

Polynomial Updates for the Unscented Kalman Filter

Chiran Cherian·Simone Servadio
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Abstract

Most nonlinear filters used in spacecraft navigation are based on a linear approximation of the optimal minimum mean square error estimator. The Unscented Kalman Filter (UKF) handles nonlinear dynamics through a sigma-point transform, but the resulting state estimate remains a linear function of the measurement. This paper proposes a polynomial approximation of the optimal Bayesian update, leading to a Polynomial Unscented Kalman Filter that retains the structure of the standard UKF but enriches the measurement update with higher-order (polynomial) terms. To compute the moments required by this polynomial estimator, we employ a Conjugate Unscented Transformation (CUT), which accurately captures higher-order central moments of the state and measurement. Numerical examples, including Clohessy-Wiltshire and Circular Restricted 3-Body dynamics with non-Gaussian measurement noise, illustrate that the resulting polynomial-CUT filters improve both state estimation accuracy and covariance consistency when compared with their linear counterparts.

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Chiran Cherian, Simone Servadio. 2026-03-11. Polynomial Updates for the Unscented Kalman Filter. https://arxiv.org/abs/2603.20259

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