Moving-Window Weighted Least Squares with Edge Optimization for Schuler Oscillation Suppression in Inertial Navigation Systems

To address the reliance of damping-network-based Schuler oscillation suppression on external aids in pure inertial navigation systems, as well as the edge effects and low computational efficiency of time–frequency transform methods, this paper proposes a moving-window weighted least-squares edge optimization (MWLS-EO) algorithm. By exploiting a priori knowledge of the Schuler carrier frequency and the slow variation in the complex envelope modulated at the Foucault frequency, the proposed method reformulates Schuler oscillation suppression as an envelope estimation problem at a known carrier frequency. On a sparse grid, the slowly varying component is estimated via weighted least squares, interpolated onto the original sampling grid, and subtracted from the original signal. At the boundaries, measured samples are used instead of zero padding. The proposed method is validated through static simulations and a 227-h shipborne field experiment conducted aboard the research vessel “Dayang”. The shipborne trajectory includes moderate turns and speed variations, which represent typical long-endurance marine navigation conditions. Experimental results demonstrate that the proposed method achieves velocity accuracy comparable to that of the Normal Time–Frequency Transform (NTFT) in the middle segment of the trajectory. At the trajectory boundaries, it improves velocity accuracy by 64.7–96.1% compared with pure INS and by 42.7–73.4% compared with NTFT. Moreover, the latitude and longitude errors are reduced by 36.6% and 3.0%, respectively, relative to INS, and by 29.0% and 2.4%, respectively, relative to NTFT. Moreover, the computation time for envelope estimation and Schuler component extraction is reduced from 18.7 h to 87 s, while edge effects are significantly attenuated. This demonstrates an effective trade-off between accuracy and efficiency for long-endurance autonomous navigation.