  Inertial navigation systems generally consist of timing, acceleration, and
orientation measurement units. Although much progress has been made towards
developing primary timing sources such as atomic clocks, acceleration and
orientation measurement units often require calibration. Nuclear Magnetic
Resonance (NMR) gyroscopes, which rely on continuous measurement of the
simultaneous Larmor precession of two co-located polarized noble gases, can be
configured to have scale factors that depend to first order only on fundamental
constants. The noble gases are polarized by spin-exchange collisions with
co-located optically pumped alkali-metal atoms. The alkali-metal atoms are also
used to detect the phase of precession of the polarized noble gas nuclei. Here
we present a version of an NMR gyroscope designed to suppress systematic errors
from the alkali-metal atoms. We demonstrate rotation rate angle random walk
(ARW) sensitivity of 16 $\mu \text{Hz}/\sqrt{\text{Hz}}$ and bias instability
of $\sim$800 nHz.
