A framework for inertial sensor calibration using complex stochastic error models

Modeling and estimation of gyroscope and accelerometer errors is generally a very challenging task, especially for low-cost inertial MEMS sensors whose systematic errors have complex spectral structures. Consequently, identifying correct error-state parameters in a INS/GNSS Kalman filter/smoother becomes difficult when several processes are superimposed. In such situations, the classical identification approach via Allan Variance (AV) analyses fails due to the difficulty of separating the error-processes in the spectral domain. For this purpose we propose applying a recently developed estimation method, called the Generalized Method of Wavelet Moments (GMWM), that is excepted from such inconveniences. This method uses indirect inference on the parameters using the wavelet variances associated to the observed process. In this article, the GMWM estimator is applied in the context of modeling the behavior of low-cost inertial sensors. Its capability to estimate the parameters of models such as mixtures of GM processes for which no other estimation method succeeds is first demonstrated through simulation studies. The GMWM estimator is also applied on signals issued from a MEMS-based inertial measurement unit, using sums of GM processes as stochastic models. Finally, the benefits of using such models is highlighted by analyzing the quality of the determined trajectory provided by the INS/GNSS Kalman filter, in which artificial GNSS gaps were introduced. During these epochs, inertial navigation operates in coasting mode while GNSS-supported trajectory acts as a reference. As the overall performance of inertial navigation is strongly dependent on the errors corrupting its observations, the benefits of using the more appropriate error models (with respect to simpler ones estimated using classical AV graphical identification technique) are demonstrated by a significant improvement in the trajectory accuracy.