Beat Frequency Estimation in a Square He-Ne Ring Laser Gyroscope: Joint I/Q Channel Calibration and Kalman Filtering

A gain-phase-calibrated four-channel in-phase/quadrature (I/Q) fusion and recursive beat-frequency estimation framework is developed for a square He-Ne ring laser gyroscope. Calibration-derived channel parameters enable ordinary least-squares (OLS) fusion, while residual covariance estimation provides a generalized least-squares (GLS) extension. Known-ground-truth simulations verify the theoretical fusion gain, covariance propagation, and consistency of the recursive estimation framework. A chronologically partitioned experimental record is used for calibration, parameter tuning, and held-out validation. The proposed fusion improves spectral signal-to-noise ratio compared with individual channels, and the independently tuned extended and unscented Kalman filters achieve millihertz-level frequency estimation accuracy. Innovation analysis further reveals remaining carrier-synchronous temporal correlations, indicating the importance of more complete residual modeling for future stochastic refinement.