A Structure-Preserving Power-Adaptive Colored-Noise Kalman Filtering Algorithm for Four-Wire Pendulum Velocity Monitoring

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.