Statistical Modeling of Random Walk Errors for Triaxial Rate Gyros

Abstract

Microelectromechanical systems (MEMS) gyroscope is a new type of inertial sensor with small size, light weight, low cost, and low power consumption. Thus, it has been widely used for guidance and stabilization of many platforms. Although these MEMS devices have such crucial advantages, the stochastic errors, mainly including random walk, bias instability, and quantization noise, may suddenly degrade the system performance in a short period of time. Therefore, a suitable modeling of these errors is vital to guarantee the system performance. In the previous work, Allan variance (AV) (time domain analysis) and power spectral density (frequency domain analysis) techniques are used to identify the random process and get the precise parameter estimation. However, they mainly deal with univariate situations and only give a suitable modeling of uniaxial gyro signal and not a precise estimation for an array of gyros. Aiming at an application in practical engineering and dealing with triaxial rate gyros’ stochastic errors, a new algorithm for estimating the statistical parameters of the triaxial rate gyros is proposed. The algorithm in this paper first extends the definition of AV from univariate to multivariable and gives the corresponding statistical properties, i.e., the theoretical mean, variance of the new AV, and covariance between different AV points, and then gives the algorithm based on the best linear unbiased estimator from statistical estimation theory. The performance of the algorithm is demonstrated using both simulated data and experimental data.