Why are there so many functions for the error modeling? Isn't only the Allan variance sufficient to model IMU errors?

In contrast to high-end inertial sensors, Allan variance curves for the low-cost MEMS sensors do not provide anything except:

  1. ARW/VRW power
  2. Maximum averaging length for the sensor data

MEMS sensors have other error components which dominates the output error characteristics in more significant ways than the internal stability errors. Therefore, any analysis based on only Allan variance will be completely wrong for such sensors.

Here is an example showing the insufficiency of Allan variance method for the MEMS sensors. In the following figure the comparison of AV curves is provided for 2 gyroscopes. Gyroscope 1 (G1) is an ADIS16120 unit which has (had) a unit price around 1100USD. Gyroscope 2 (G2) is the sensor that is currently used in 4th generation iPhone/iPod. Its unit cost (per axis) is around 5USD.

Standard interpretation of these Allan variance curves suggests that G1 is only at most 4 times better than G2. In other words, if 4 G2 units are located on the same axis, the final accuracy in that axis will be much better than G1 (use of multiple sensors will also lower the flicker noise floor).

As a result:

In this case, what is the reason for this huge difference between the cost and accuracy(performance) of these 2 gyroscopes?

Is it the G1 that has a ridiculously high price tag, or is it just that the Allan variance curve is not capable of reflecting the real sensor performance for MEMS units?

Depending on all my past experiences, I can claim that the answer is the second one. The accuracy of the MEMS sensors depends on lots of other factors which do not appear (or at least not related to) Allan variance figures. That is why, any error budget analysis which is based on only Allan variance figures will be completely wrong for the MEMS sensors.

It is possible to present lots of other examples about the inconvenience/inconsistency of Allan variance analysis methods for the MEMS inertial sensors. Allan variance alone is simply not a suitable tool for the MEMS sensor error characterization. That is the reason why I added in this toolbox so many different error modeling routines to characterize the MEMS inertial sensor outputs.