Identification of test mass stiffness based on dual sensitive axis decomposition

The coupling noise between test mass stiffness and displacement, as a significant component of the residual acceleration noise, critically impacts the performance of space gravitational wave detection, making stiffness identification essential for validating and optimizing control strategies and meeting the noise suppression requirements. For non-coaxial test mass configurations, this paper proposes a novel identification method based on dual sensitive axis decomposition. First, a relative dynamic model between the test mass and the spacecraft is constructed, and the model parameters are decomposed along the dual sensitive axis to isolate the influence of spacecraft acceleration disturbances and predominant angular acceleration disturbances on the on-orbit identification. Second, utilizing on-board laser interferometers, inertial sensors, and associated control loops, an on-orbit identification scheme is designed and a stiffness identification method using recursive least squares is proposed. Finally, numerical simulations are performed to verify the performance of the method. The experimental results demonstrate that the proposed stiffness identification method can effectively identify the stiffness of the test mass on the sensitive axis. Under the given simulation conditions, the mean absolute error is less than 5×10⁻⁹ s⁻², the root mean square error is less than 1.5×10⁻⁸ s⁻², and the maximum steady-state error is less than 2×10⁻⁹ s⁻². These findings suggest that the method can be applied to future gravitational wave science missions.