  The noise and drift requirements for a navigation-grade gyroscope are widely
known, yet there is no simple analytic model of how the noise and drift of a
gyroscope influence the fix displacement error (FDE) of an inertial navigation
system (INS). This work derives simple analytical expressions for the
cross-track and along-track errors of an aircraft whose INS consists solely of
a three-axis gyroscope system with perfect knowledge of the vertical direction.
The error signal of each gyroscope is Gaussian white noise and drift modeled as
a first-order Markov random walk. These expressions provide a straightforward
mean of calculating the FDE of an aircraft as a function of the flight
duration, velocity, noise amplitude, drift amplitude, and drift's time
constant. These expressions are validated with Monte-Carlo simulations of long
flights. This model quantifies the noise-versus-drift trade-off for a gyroscope
in an inertial navigation system. It can save time when estimating the noise
and drift that a gyroscope must exhibit to satisfy a given position-error
requirement, or vice versa. They are used in particular to confirm the values,
often cited without demonstration, of the noise and drift required to meet the
maximum position error of an aircraft imposed by the Federal Aviation
Administration's required navigation performance 10 specification. Finally, it
demonstrates that using the minimum in the measured Allan deviation of a
gyroscope as a metric of the drift is incorrect, because it fails to capture
the drift's time constant. The proper metric is the maximum in the Allan
deviation.
