North-finding with 0.004 radian precision using a silicon MEMS quadruple mass gyroscope with Q-factor of 1 million

We demonstrate north-finding capability with a measured 4 milliradian (mrad) 1-σ uncertainty using an in-house developed vibratory silicon MEMS quadruple mass gyroscope (QMG). We instrumented a vacuum packaged QMG with isotropic Q-factor of 1.2 million and bias instability of 0.1°/hr for azimuth detection by measuring the Earth's rotation. Continuous rotation (“carouseling”) produced azimuth datapoints with uncertainty diminishing as the square root of the number of turns. Integration of 100 datapoints with normally distributed errors reduced uncertainty to 4 mrad, beyond the noise limit of the QMG. We also implemented self-calibration methods, including temperature compensation and discreet ±180° turning (“maytagging”) as potential alternatives to the carouseling.