Rapid Initial Alignment of Dual-Axis Rotational Inertial Navigation Using Phase-Preserving Angular-Rate Reconstruction and Dynamic Lever-Arm Compensation

Dual-axis rotation can modulate constant and low-frequency errors of inertial sensors; however, low-frequency platform motion introduces dynamic lever-arm velocity into GNSS-aided alignment measurements. We propose a rapid initial alignment framework that integrates encoder-aided compensation for mechanism-induced angular velocity, multi-axis dominant frequency estimation, phase-preserving robust harmonic regression, dynamic lever-arm velocity transfer, period-matched velocity/position integral measurements, and component-wise robust filtering. The frequency estimator employs reliability gating to handle competing non-harmonic spectral peaks and propagates reconstruction quality into the measurement covariance. In static eight-position experiments, the peak-to-peak variation in heading repeatability ranged from 15.12 arcseconds to 52.20 arcseconds. In vehicle-mounted experiments against a known 50 mil heading reference, compared with a conventional error-state Kalman filter using velocity/position matching, the proposed method reduced the heading RMSE from 62.3 arcseconds to 27.3 arcseconds and the within-series peak-to-peak spread from 149.9 arcseconds to 65.1 arcseconds, both by about 56%. In the shipborne experiment, the dominant component of the joint attitude spectrum of the moored vessel was identified at 0.0430 Hz; with identical hardware, identical data, and an identical navigation solver, the proposed alignment method reduced the horizontal position RMSE of 15-day pure inertial navigation from 1033.02 m to 437.23 m (a 57.7% reduction) and the maximum horizontal error from 3438.69 m to 1011.30 m compared with the conventional alignment algorithm.