Laplace ℓ₁ Huber based cubature Kalman filter for attitude estimation of small satellite

This paper offers a solution to the attitude estimation of small satellite with the existence of model error and heavy-tailed noise, which is referred as to the Laplace ℓ₁ Huber Based Kalman filter (ℓ₁-HBKF). It employs the Laplace distribution and Huber based method to update the measurement covariance to deal with different types of model error or heavy-tailed noise for robust design. Then, the majorization minimization approach is discussed to improve the estimation accuracy by an iterative algorithm. In addition, the proposed ℓ₁-HBKF is implemented in the Kalman filtering framework and is further extended by the strategy of fifth-degree cubature rule for high accuracy. Finally, the attitude estimation of small satellite is simulated and compared with conventional cubature Kalman filter (CKF), which can prove the accuracy and robustness of the proposed methods for the attitude estimation with low precision sensors.