Variational-based robust adaptive multiplicative extended Kalman filter for micro-satellite attitude estimation

Abstract With the extended operational time of micro-satellites in orbit, the statistical characteristics of process and measurement noise often deviate from their nominal values, leading to a decline in the performance of traditional extended Kalman filters (EKFs) for attitude estimation and gyro drift compensation. The adaptive EKF algorithm based on variational Bayesian theory requires the nominal process noise matrix to closely match the true values; otherwise, its accuracy is significantly compromised. To address this challenge, this paper proposes an enhanced adaptive multiplicative EKF (AMEKF) algorithm based on variational methods. Compared to the traditional AMEKF, the proposed algorithm processes the gyroscope’s measured angular velocity using total variation, effectively removing the two zero-mean Gaussian noises that correspond to the process noise in this context. By using the processed angular velocity for attitude and gyro drift estimation, the algorithm bypasses the uncertain process noise, resulting in improved accuracy compared to traditional algorithms. Simulation results demonstrate that, in comparison with the traditional AMEKF, the proposed algorithm reduces gyro drift estimation error by approximately 99% and attitude estimation error by about 72%–93%. The simulation results of typical on-orbit operation modes for microsatellites show that, although the attitude estimation accuracy decreases under more complex angular velocity conditions, the three-axis attitude error angles can still reach <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mn>1.31</mml:mn> <mml:mtext> </mml:mtext> <mml:mn>1.37</mml:mn> <mml:mtext> </mml:mtext> <mml:mn>7.94</mml:mn> <mml:msup> <mml:mo stretchy="false">]</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> arcsec. The results further confirm that the proposed algorithm can effectively handle uncertain process and measurement noise, achieving high precision in both attitude and gyro drift estimation.