An algorithm for automatic inertial sensor calibration

We present an algorithm for determining the nature of stochastic processes together with its parameters based on the analysis of time series of inertial errors. The algorithm is suitable mainly (but not only) for situations when several stochastic processes are superposed. In such cases, classical approaches based on the analysis of Allan variance or PSD are likely to fail due to the difficulty of separating the underlying error-processes in the spectral domain. The developed alternative is based on the recently proposed method called the Generalized Method of Wavelet Moments (GMWM), which estimator was proven to be consistent and asymptotically normally distributed. The principle of this method is to match the empirical and model-based wavelet variances (WV). In this study we propose a goodness-of-fit criterion which can be used to determine the suitability of a model candidate and apply it to low-cost inertial sensors. The suggested approach of model selection relies on an unbiased estimate of the distance between the theoretical WV and the empirical WV which would be obtained on an independent sample issued from the stochastic process of interest. Such goodness-of-fit criterion is however “penalized” by the complexity of the model. In some sense, the proposed methodology is a generalization of Mallow’s Cp applied to models estimated by the GMWM. By allowing to rank candidate models, this approach permits to construct an algorithm for automatic model identification and determination. The benefits of this methodology are highlighted by providing practical examples of model selection for two types of MEMS- IMUs, the latter of higher quality.