Polynomial Updates for the Unscented Kalman Filter
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914412113166336 |
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| author | Cherian, Chiran Servadio, Simone |
| author_facet | Cherian, Chiran Servadio, Simone |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomial Updates for the Unscented Kalman Filter Cherian, Chiran Servadio, Simone Systems and Control Probability 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. |
| title | Polynomial Updates for the Unscented Kalman Filter |
| topic | Systems and Control Probability |
| url | https://arxiv.org/abs/2603.20259 |