Ground testing of space-based gravitational-wave missions requires causal and low-noise horizontal-velocity estimation for vibration-isolation platforms. Fixed sensor fusion becomes suboptimal when sensor noise power varies, especially when complementary sensors have strongly frequency-dependent colored-noise spectra. This paper proposes a colored-noise power-adaptive Kalman filtering algorithm (CN-PAKF) for fusing laser interferometric displacement sensor (IFO) and broadband seismometer (SEIS) observations. The method constructs a motion-canceling synchronous difference channel and uses band-decomposed power statistics with asymmetric spectral priors to estimate sensor noise-power scales online. Scaling only the corresponding colored-noise drive covariances preserves the normalized spectral shapes of the modeled colored components and avoids unrestricted covariance adaptation; bounded physical-process and residual measurement-covariance safeguards may alter the total modeled error spectrum. In paired open-loop simulations, CN-PAKF reduced the target-band velocity RMSE by 31.3% and 70.5% relative to the IFO and SEIS observations under nominal noise conditions, while remaining within 1% of causal colored-noise baseline filters. When the IFO noise power increased 30-fold, CN-PAKF reduced the stage-wise target-band RMSE by 36.8% compared with a fixed colored-noise Kalman filter. These results indicate that CN-PAKF provides a causal, structure-preserving, and performance-tested fusion algorithm for synchronized sensors with time-varying noise power and approximately fixed colored-noise spectral shapes.

For space-based gravitational-wave detection, a released test mass in an inertial sensor may retain appreciable residual angular motion, while electrostatic actuation authority is finite. This work investigates single-axis test-mass capture about the suspension-wire axis using a torsion-pendulum platform integrating differential capacitive sensing, electrostatic actuation, and digital control in the same hardware loop. Capacitive-readout calibration, free-oscillation identification, and static torque-balance actuation calibration establish quantitative relations among test-mass motion, suspension dynamics, control voltage, and electrostatic torque, and characterize the nominal near-center actuation authority. At controller activation, the measured angular offset is approximately 15.6 mrad, and the estimated angular velocity is approximately 800 μrad/s. Under limited electrostatic actuation, the control output remains at or near saturation for approximately 110 s during the initial braking stage; the test mass then reverses direction, the output desaturates, and the response converges toward the housing center. The maximum angular displacement after activation is approximately 0.067 rad, with no further test-mass–electrode-housing contact observed. After approximately 550 s, the test mass enters a stable near-center region, where an out-of-loop autocollimator measures an angular RMS of 1.81 μrad. The corresponding command-equivalent electrostatic control torque has an RMS value of $2.6\times {10}^{-11}$ N·m. These results provide a quantitative experimental characterization of single-axis test-mass capture from a large initial dynamic state under limited electrostatic actuation authority.