An improved central difference Kalman filter for satellite attitude estimation with state mutation

There are three problems in applying central difference Kalman filter (CDKF) to attitude estimation of low-cost satellite: (1) the negative definiteness and asymmetry of the covariance matrix caused by limited computing power and storage space of the onboard microprocessor may result in calculation divergence, (2) the system model uncertainty including model mismatch and state mutation caused by environmental disturbances from inside and outside the satellite will lead to filter divergence, (3) the addition operation on quaternions violates the normalization constraint, while enforced unitization will introduce approximation errors. To solve the above problems, this article proposes the multiplicative quaternion square root strong tracking CDKF (MQSRSTCDKF), in which three improvements to basic CDKF are made: (1) square roots of covariance matrices are adopted for information propagation in place of covariance matrices themselves, which always guarantees the symmetry and positive definiteness of covariance matrices, (2) multiple fading factors are employed to adjust square root of the covariance matrix of predicted state variables, and then adjust the gain matrix to make the filter attach more weight to sensor measurements than to corrupt state predictions caused by model uncertainties, (3) multiplication operation on quaternions is conducted instead of the addition one, which makes the normalization constraint on quaternions naturally satisfied without enforced unitization. Numerical simulation based on raw telemetry data from the on-orbit CubeSat NJUST-1 shows that MQSRSTCDKF has higher attitude estimation accuracy, faster convergence speed, and stronger robustness to filter divergence and calculation divergence than basic CDKF.