Navigation Sensor Stochastic Error Modeling and Nonlinear Estimation for Low-Cost Land Vehicle Navigation
Creators: name: Minaretzis, Chrysostomos
Publisher: name: Graduate Studies
Year: 2023
Subjects: subject: Inertial Sensor Stochastic Calibration
subject: Robust Estimation
subject: Generalized Method of Wavelet Moments
subject: Average Wavelet Variance Estimator
subject: Monte-Carlo Simulations
subject: Extended Kalman Filter
subject: Unscented Kalman Filter
subject: Engineering
subject: Statistics
subject: FOS: Mathematics

description: The increasing use of low-cost inertial sensors in various mass-market applications necessitates their accurate stochastic modeling. Such task faces challenges due to outliers in the sensor measurements caused by internal and/or external factors. To optimize the navigation performance, robust estimation techniques are required to reduce the influence of outliers to the stochastic modeling process. The Generalized Method of Wavelet Moments (GMWM) and its Multi-signal extensions (MS-GMWM) represent the latest trend in the field of inertial sensor error stochastic analysis, they are capable of efficiently modeling the highly complex random errors displayed by low-cost and consumer-grade inertial sensors and provide very advantageous guarantees for the statistical properties of their estimation products. On the other hand, even though a robust version exists (RGMWM) for the single-signal method in order to protect the estimation process from the influence of outliers, their detection remains a challenging task, while such attribute has not yet been bestowed in the multi-signal approach. Moreover, the current implementation of the GMWM algorithm can be computationally intensive and does not provide the simplest (composite) model. In this work, a simplified implementation of the GMWM-based algorithm is presented along with techniques to reduce the complexity of the derived stochastic model under certain conditions. Also, it is shown via simulations that using the RGMWM every time, without the need for contamination existence confirmation, is a worthwhile trade-off between reducing the outlier effects and decreasing the estimator efficiency. Generally, stochastic modeling techniques, including the GMWM, make use of individual static signals for inference. However, it has been observed that when multiple static signal replicates are collected under the same conditions, they maintain the same model structure but exhibit variations in parameter values, a fact that called for the MS-GMWM. Here, a robust multi-signal method is introduced, based on the established GMWM framework and the Average Wavelet Variance (AWV) estimator, which encompasses two robustness levels: one for protection against outliers in each considered replicate and one to safeguard the estimation against the collection of signal replicates with significantly different behaviour than the majority. From that, two estimators are formulated, the Singly Robust AWV (SR-AWV) and the Doubly Robust (DR-AWV) and their model parameter estimation efficiency is confirmed under different data contamination scenarios in simulation and case studies. Furthermore, a hybrid case study is conducted that establishes a connection between model parameter estimation quality and implied navigation performance in those data contamination settings. Finally, the performance of the new technique is compared to the conventional Allan Variance in a land vehicle navigation experiment, where the inertial information is fused with an auxiliary source and vehicle movement constraints using the Extended and Unscented Kalman Filters (EKF/UKF). Notably, the results indicate that under linear-static conditions, the UKF with the new method provides a 16.8-17.3% improvement in 3D orientation compared to the conventional setting (AV with EKF), while the EKF gives a 7.5-9.7% improvement. Also, in dynamic conditions (i.e., turns), the UKF demonstrates an 14.7-17.8% improvement in horizontal positioning and an 11.9-12.5% in terms of 3D orientation, while the EKF has an 8.3-12.8% and an 11.4-11.7% improvement respectively. Overall, the UKF appears to perform better but has a significantly higher computational load compared to the EKF. Hence, the EKF appears to be a more realistic option for real-time applications such as autonomous vehicle navigation.