  We present a simple analysis of the design of a passive miniature resonant
optical gyroscope. By combining the requirements on the angular random walk and
the bias stability, we end up with simple expressions of the minimum diameter
of the ring waveguide cavity and the maximum power that should be used to probe
it. Using state-of-the-art performances of photonic integrated circuit and
whispering gallery mode technologies in terms of propagation losses and mode
size, we show that tactical grade gyroscope performances can be achieved with a
diameter of a few cm provided the detrimental influence of Kerr effect is
mitigated, using for instance an active control of the unbalance in the
intensities. We further extend the analysis to medium performance gyroscope and
give some hints on the efforts to be made to potentially demonstrate a
miniature resonant optical gyroscope with this level of performance.
