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.