Statistical modeling of rate gyros and accelerometers

Gyroscopes and accelerometers are important components of inertial measurement units (IMUs), which are used for guidance and stabilization of many platforms. Two important statistical parameters that influence the performance of inertial sensors are the spectral densities R and Q of the additive noise and random drift components, respectively. Previous work on the modeling of inertial sensors is based on computing the Allan variance of a sensor signal and fitting the result with two lines, one for R and the other for Q. It is shown in this paper that the line for Q is often inaccurate. This paper provides a statistical algorithm for jointly estimating Q and R. The performance of the algorithm is demonstrated using simulated data. A bound on the error in the integral of a gyro output, as a function of Q and R, is derived, as is a bound on the error in the double integral of an accelerometer output.