A new method for the nonlinear transformation of means and covariances in filters and estimators

2000/03/01 by Simon Julier, S. Julier, J. Uhlmann +3 · 3,724 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Alpha beta filter #Artificial intelligence #Computer science #Control theory (sociology) #Covariance #Covariance intersection #Ensemble Kalman filter #Estimator #Extended Kalman filter #Fast Kalman filter #Filter (signal processing) #Filter design #Gaussian #Inertial Sensor and Navigation #Invariant extended Kalman filter #Kalman filter #Mathematics #Moving horizon estimation #Nonlinear filter #Nonlinear system #Physics #Scientific Research and Discoveries #Statistics #Target Tracking and Data Fusion in Sensor Networks #Transformation (genetics) #Unscented transform

paper · doi:10.1109/9.847726

published in IEEE Transactions on Automatic Control 45(3), 477-482 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2000/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This paper describes a new approach for generalizing the Kalman filter to nonlinear systems. A set of samples are used to parametrize the mean and covariance of a (not necessarily Gaussian) probability distribution. The method yields a filter that is more accurate than an extended Kalman filter (EKF) and easier to implement than an EKF or a Gauss second-order filter. Its effectiveness is demonstrated using an example.

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