Rate-driven adaptive recursive compensation for asymmetric thermal hysteresis in MEMS disk resonant gyroscope

Bias drift and asymmetric thermal hysteresis limit the measurement accuracy of MEMS disk resonant gyroscopes (DRGs) under wide temperature variation conditions. This paper proposes an adaptive recursive piecewise polynomial (ARPP) compensation architecture that addresses thermal-state asymmetry and dynamic residual hysteresis while meeting real-time implementation requirements. First, a Kalman hysteresis preprocessing (KHP) mechanism is introduced to suppress measurement noise and identify heating and cooling states using a dual-timescale temperature-rate criterion with adaptive thresholds. Based on the identified thermal states, separate heating adaptive recursive polynomial (HARP) and cooling adaptive recursive polynomial (CARP) sub-models are constructed. Each sub-model incorporates a temperature-rate-driven recursive factor (TDRF), which adjusts the recursive feedback gain according to the measured temperature variation rate. The model order is selected using the Akaike information criterion (AIC). Independent validation experiments were conducted at temperature variation rates of \pm0.5, \pm1.0, and \pm{1.5}^\circ\mathrm{C}/\mathrm{min}. The proposed method reduces the average angle random walk (ARW) from {0.19}^\circ/\sqrt\mathrm{h} to {0.03}^\circ/\sqrt\mathrm{h} and the average bias instability (BI) from {36.04}^\circ/\mathrm{h} to {3.70}^\circ/\mathrm{h}, corresponding to reductions of 84.21% and 89.72%, respectively. The compensation algorithm was implemented on an field-programmable gate array (FPGA) and operated in real time during the experiments. These results support the effectiveness of the proposed method in compensating temperature-dependent bias and thermal hysteresis over the tested temperature-rate range, while maintaining suitability for real-time embedded implementation.