Modified multiplicative quaternion cubature Kalman filter for attitude estimation

Abstract

SummaryIn this paper, a modified multiplicative quaternion cubature Kalman filter (CKF) for attitude estimation is proposed. For high‐dimensional state estimation, the CKF that uses third‐degree spherical‐radial cubature rule can provide a more accurate estimation than the unscented Kalman filter. However, for the attitude estimation in the case of larger initial conditional errors, the results may be reversed. To take full advantage of the CKF, the Lagrange cost function method is introduced to solve the quaternion weighted mean, then, the mean is used as the reference quaternion for the measurement update in the CKF framework. The choice of the reference quaternions and the quaternion update method is different from the existing literature to avoid the algorithm from failing. In addition, the unconstrained three‐component vectors represent the attitude error quaternion in the filtering algorithm, whereas the quaternion is used to perform attitude propagation. Simulation results demonstrate the better performance of the proposed modifying filter algorithm in comparison with the multiplicative extended Kalman filter, the unscented Kalman filter, and the CKF under larger initial condition errors.

A novel Gaussian sum quaternion constrained cubature Kalman filter algorithm for GNSS/SINS integrated attitude determination and positioning system

“…However, the use of quaternions as state variables is bound by normalization constraints in practical applications. If these constraints are overlooked during data processing, the resulting accuracy of the filter and the positive quality of covariance will be compromised ( Huang et al, 2016 ; Qiu and Qian, 2018 ). In addition, these previous studies are based on the assumption that the random model is the white Gaussian noise, and the actual process noise and measurement noise in GNSS/SINS-IADPS deviate from ideal Gaussian distribution.…”

A new Gaussian–Student's t mixing distribution‐based Kalman filter with unknown measurement random delay rate

“…1 In many applications such as navigation system, target tracking, signal processing, the KF has been wildly used. [2][3][4][5][6][7][8] The KF assumes that the measurement is received in real time and the measurement noise is Gaussian noise with known statistical characteristics. However, the phenomenon of measurement random delay often occurs in engineering applications which due to the unreliable communication transmissions, and the estimation accuracy of KF will significantly decrease or even diverge in this case.…”

“…For linear systems, the Kaiman filter (KF) is the optimal estimator under minimum mean square error criterion 1 . In many applications such as navigation system, target tracking, signal processing, the KF has been wildly used 2–8 . The KF assumes that the measurement is received in real time and the measurement noise is Gaussian noise with known statistical characteristics.…”

Multiplicative modified Rodrigues-parameters-based strong tracking unscented Kalman filter for satellite attitude estimation

“…This will lead to singularity of covariance matrices unless complicated additional measures are taken. In addition, a variable cannot be added directly to the quaternion because it will spoil the normalization constraint and bring extra challenges to the prediction of state variables and calculation of covariance matrices in nonlinear filters [7]. Euler angles are not subject to normalization constraint and are free from singularity of covariance matrices as they are the minimal attitude representations, but they suffer from another form of singularity in which two of the angles become indeterminate in certain orientations and vary dramatically with only small attitude changes, which makes the filter difficult to converge to a certain solution [8].…”