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

초록

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.

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