Breaking Through GNSS Outage: Advanced Stochastic Model for MEMS IMU in Navigation

Inertial navigation systems (INS) are widely recognised for providing precise location, velocity, and attitude data over short durations. However, their accuracy deteriorates over time. To maintain accurate navigation, it is crucial to characterise and model both deterministic and stochastic error components of inertial sensors. This paper employs three techniques for modelling stochastic errors: the autocorrelation function (ACF), the Allan variance (AV), and the generalised method of wavelet moments (GMWM). Two different-grade inertial measurement units (IMUs) evaluate the effectiveness of ACF, AV, and GMWM in modelling inertial sensor noise: the ADIS low-cost micro-electromechanical systems (MEMS) grade IMU and the Spatial MEMS tactical-grade IMU. A laboratory calibration test is conducted to eliminate deterministic errors. A strategy for modelling stochastic errors of MEMS inertial sensors is presented, involving selecting the best model for each sensor using the three techniques rather than applying a single model. Based on a comparison of the three techniques, GMWM measurements are used for the navigation algorithms. GMWM's performance modelling stochastic errors are analysed using real dynamic in-field datasets collected by both IMUs, with induced GPS signal outages. Three extended Kalman filter (EKF) INS/GNSS integrated navigation algorithms are implemented based on ACF analysis and GMWM-based model selection. A 15-state algorithm based on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1^{st}$</tex-math></inline-formula> order Gauss-Markov (GM) estimated by ACF, a 45-state algorithm based on ADIS IMU data, and a 57-state algorithm based on Spatial IMU data are compared. The experimental results demonstrate that the proposed 45-state navigation algorithm reduces the 2D position RMSE by approximately 67% compared to the conventional 15-state algorithm, while the 57-state algorithm achieves an improvement of around 64%.