  Inertial sensors stimulate very large interest, not only for their
application but also for fundamental physics tests. Ring laser gyros, which
measure angular rotation rate, are certainly among the most sensitive inertial
sensors, with excellent dynamic range and bandwidth. Large area ring laser
gyros are routinely able to measure fractions of prad/s, with high duty cycle
and bandwidth, providing fast, direct and local measurement of relevant
geodetic and geophysical signals. Improvements of a factor $10-100$ would open
the windows for general relativity tests, as the GINGER project, an Earth based
experiment aiming at the Lense-Thirring test at $1\%$ level. However, it is
well known that the dynamics of the laser induces non-linearities, and those
effects are more evident in small scale instruments. Sensitivity and accuracy
improvements are always worthwhile, and in general there is demand for high
sensitivity environmental study and development of inertial platforms, where
small scale transportable instruments should be used. We discuss a novel
technique to analyse the data, aiming at studying and removing those
non-linearity. The analysis is applied to the two ring laser prototypes GP2 and
GINGERINO, and angular rotation rate evaluated with the new and standard
methods are compared. The improvement is evident, it shows that the
back-scatter problem of the ring laser gyros is negligible with a proper
analysis of the data, improving the performances of large scale ring laser
gyros, but also indicating that small scale instruments with sensitivity of
nrad/s are feasible.
