Robust Wavelet Variance-based Approaches for the Stochastic Modeling of Inertial Sensor Measurement Noise

Abstract

The use of low-cost inertial sensors is nowadays wide-spread in many different mass-market applications, especially for navigation, for example in drones and smartphones. However, ensuring their performance is challenging since it is highly dependent on the available knowledge for the inertial sensor random error behavior, and which is hard to obtain accurately in practice. The main reason is that in many cases, the inertial sensor measurements collected during calibration contain outliers caused by either external (e.g., vibrations) or internal factors (e.g., ageing of the IMU). Therefore, it is essential that the modeling of that behavior is conducted by an estimator that has the capability to effectively reduce the influence of potential outliers from its estimation product (robustness), such that the estimated model parameters, when supplied to the chosen navigation algorithm, lead to optimal performances. The current state-of-the-art to handle the intricate nature of the stochastic errors, typically of low-cost inertial sensors, is the Generalized Method of Wavelet Moments (GMWM) and its Multi Signal extension (MS-GMWM). Although the GMWM possesses such a robustness feature thanks to an M-estimator for its fundamental quantity, the wavelet variance, it can be difficult to detect whether the analyzed data contain outliers or not, while this feature has not been extended to the multi signal approach. In this paper, it is demonstrated through simulations, that the utilization of the robust version of the GMWM in every scenario is a worthwhile trade-off between reduction of the outlier impact and reduction of the estimator’s efficiency. Furthermore, two new robust estimators in the context of the MS-GMWM are proposed and their performance is evaluated: the first one is able to decrease the influence of outliers in the analyzed data, while the second reinforces protection against calibration signal replicate(s) that present(s) significantly different stochastic error behavior compared to the others.