Extended Kalman Filter

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

An estimation algorithm that linearizes the nonlinear state and measurement equations via first-order Taylor expansion around the current estimate, then applies standard Kalman filter recursive formulas. The paper uses EKF for libration point orbit celestial navigation: the state equation is the three-body problem dynamics, the measurement equation is the nonlinear relation between starlight angle and position, and a first-order linearized state transition matrix suffices for accuracy. Simulation results show EKF in the barycentric rotating frame converges position error to approximately 7.5 km (2 navigation stars, 10 s sampling period).

Application Value

The extended Kalman filter handles nonlinear problems through linearization, widely used in libration point orbit celestial navigation, converging to high accuracy.

  • Geometric Dilution of Precision
  • Very Long Baseline Interferometry
  • Deep Space Network

References

  • 赵书阁 等 - 2013 - 日地系统L2点Halo轨道自主天文导航及精度分析
  • Colagrossi 等 - 2021
  • Pesce 等 - 2023 - Modern spacecraft guidance, navigation, and control
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Contributors: ouyangjiahong, Ou Yang Jiahong