Continuous-Discrete Cubature Kalman Filter With Log-Euclidean Metric-Based Covariance Integration

Jiaolong Wang, Chengxi Zhang, Choon Ki Ahn, Jin Wu, Ming Liu

Research output: Contribution to journalArticlepeer-review


For continuous-discrete filtering with strong nonlinearity and large measurement intervals, a Log-Euclidean metric (LEM) based novel continuous-discrete cubature Kalman filter (LEMCDCKF) is proposed by shifting the cubature rule-based covariance propagation to Riemannian manifold. In conventional CDCKFs, the covariance differential equation based on cubature points is solved with Euclidean space integration schemes, which inevitably ignore the geometric property and restrict the performance of CDCKF. To remedy this shortage, we propose to define covariance on Riemannian symmetric positive definite (SPD) manifold and integrate the cubature rule-based covariance differential equation with the LEM-based novel scheme, which can successfully account for the manifold property of covariance matrices and provide accurate results. Moreover, by refining CDCKF with the LEM based scheme, the proposed LEMCDCKF shifts the covariance integration process to SPD manifold, which can break through the limitation of Euclidean numerical scheme. Numerical investigations verify the superior performance of the proposed LEMCDCKF in air traffic control scenarios with large measurement intervals.

Original languageEnglish
Pages (from-to)4281-4285
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number11
Publication statusPublished - 2023 Nov 1

Bibliographical note

Publisher Copyright:
© 2023 IEEE.


  • Log-Euclidean metric
  • Nonlinear continuous-discrete system
  • covariance propagation
  • cubature Kalman filter
  • symmetric positive definite

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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