Identification and Compensation of Detection Electrode Errors in Hemispherical Resonator Gyroscopes via Bidirectional Turntable Rotations

The increasing demand for whole-angle mode operation in hemispherical resonator gyroscopes (HRGs) necessitates the development of precise calibration and compensation methods for angle-dependent bias (ADB) that preserves their long-term stability and high-accuracy properties. Besides the anisoelasticity and anisodamping of the resonator, the interference between control loops induced by electrode errors, including the actuation electrode error (AEE) and the detection electrode error (DEE), has also become one of the major factors that limit the accuracy of rate-integrating gyroscopes (RIGs). In this paper, a novel bi-directional rotations-based method for the DEE identification is proposed, which significantly improves the compensation accuracy compared to existing techniques. An evaluation criterion based on the invariance of the magnitudes and signs of the residual ADB across varying turntable speeds is further proposed. Notably, this study presents the first explicit demonstration that the DEE must be compensated before the AEE to avoid cross-coupled errors and ensure calibration accuracy. Both gap unevenness and angle misalignment are considered in the error model, and they are found to be proportional with the amplitudes of the Cos4θ and Sin4θ components of the DEE-induced additional ADB. After the compensation of the DEE, AEE and anisodamping error, the real-time bias stability (1σ) of a WA mode HRG was improved to 0.0081°/h. Additionally, this identification and compensation method for the DEE can be widely extended to other resonant gyroscopes with annular sensing elements.