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Session A3: Inertial Measurement Units

A Two-Step Computationally Efficient Procedure for IMU Classification and Calibration
Gaetan Bakalli, University of Geneva, Switzerland; Ahmed Radi, University of Calgary, Canada; Stéphane Guerrier, Yuming Zhang, Roberto Molinari, Pennsylvania State University; Sameh Nassar, University of Calgary, Canada
Location: Big Sur

Over the last couple of decades, the integration of Inertial Navigation System (INS) with Global Navigation Satellite System (GNSS) has become a standard approach for many different applications that require accurate position fixing, velocity measuring, and orientation computing of moving objects. In the typical INS/GNSS architecture, the GNSS is responsible for positioning information while the INS is at the helm of attitude determination. In ideal conditions, navigation solutions based on integration architecture can usually reach a level of positioning accuracy in the range centimetres, if not millimetres, when considering kinematic applications. However, these settings suffer from various limitations associated with a frequent occurrence of GNSS signal outages caused by Radio Frequency (RF) signal blockages such as those due to tunnels and urban areas (Nassar et al., 2006). In such cases, positioning information is provided using the INS, used as a stand-alone system, until RF signals are obtained again with sufficient accuracy. Based on this, the overall system positioning accuracy is totally dependent on the quality of the INS sensor data which, in turn, could be improved if precise inertial sensor error models are implemented.
Generally, inertial sensor error modelling is a challenging and time-consuming task in the process of designing inertial navigation systems, and particularly for low-cost Micro-Electro Mechanical Systems (MEMS)-based ones that become attractive candidates for INS/GNSS integrated architecture (Yuksel et al., 2010). Although MEMS-based inertial sensors have various advantages regarding cost and size reduction as well as low power consumption and light weight, some limitations concerning the overall accuracy should be addressed. To be more specific, the fact that such cheap and small MEMS-based sensors rarely provide the required accuracy, in some applications, is undeniable (Niu et al., 2007). The reason for this lies in the silicon material used during MEMS fabrication process, which on one hand possesses significant electrical and mechanical advantages over other materials and leads to be much cheaper to manufacturing. On the other hand, such a material makes the sensor highly sensitive to many environmental variations (Woodman, 2007). Based on the above, various error signals are being added to the true value measured by the sensor, categorised as deterministic and stochastic error components, which then are integrated through navigation algorithms and accumulated. Consequently, these accumulated errors can have a significant influence on the estimated position, velocity, and attitude which, in turn, reflects as a performance degradation of the overall navigational accuracy, especially when INS is working as a standalone system in areas of poor GNSS signals. Therefore, precise modelling of the inertial sensor errors is a prerequisite to enhance navigation precision, where the parameters characterizing the error models should be accurately determined allowing to correct the errors directly within the system firmware.
Based on this necessity, numerous compensation techniques have been used according to the grade of the IMU and the intended applications in order to mitigate the inertial sensors error terms. For instance, considering solely deterministic error modelling, a few standard calibration methods are proposed in Xiao et al. (2008) and multi-position calibration methods are introduced by Syed et al. (2007). However, the present proposal focuses on stochastic calibra- tion/modelling for which the literature is increasing but still lacking solutions in a series of important settings. Some highly cited methods such as Auto-correlation based methods (see Li et al., 2015 and Niu et al., 2002), Power Spectral Density (Lim et al., 2013) and the Allan Variance (El-Sheimy et al., 2008) are used to identify random nature errors related to inertial sensor. A recent approach called the Generalized Methods of Wavelets Moments (GMWM), introduced in Guerrier et al. (2013) uses the Wavelet Variance (WV) for identifying the latent random processes that characterize the stochastic error part of inertial sensors and estimating their corresponding parameters.
Nevertheless, all the previously mentioned traditional noise characterization tools only take into account one sequence of observations, while it is more com- mon in practice to observe several of these sequences coming from the same sensor. Taking this setting into account, Bakalli et al. (2017) investigated the properties of an extension of the GMWM. For lower-grade IMUs they observed that if the different observed sequences have the same model structure, they don’t have the same parameter values. Based on this observation, the concept of near-stationary processes was introduced for a certain type of MEMS-IMU while these processes have not been detected for higher-grade IMU where the parameter values remain the same for all sequences.
The goal of this proposal is to provide a general two-step approach that aims at classifying IMUs with respect to whether they are near-stationary or not, and if they are not, calibrate them automatically according to the methods in Radi et al. (2017) using the Cross-Validated Wavelet Variance Information Criterion. Unlike common statistical data ,error signal from IMUs require the handling of large data sets with more complex models, for which the consequences are increasing numerical and computational issues. In this proposal, we will present new methods to tackle this problem that are numerically tractable and computationally efficient based on new algorithm. We will show the efficiency of these methods with real data from low cost-sensors and discuss their applications with micro-aerial vehicles. This framework will be presented in a freely available software, the gui4gmwm, developed in the widely used statistical tool R using C++ language. This software will enable the user to investigate with ease the error signal of an IMU, perform the near-stationary test and automatically calibrate the signal of interest.
References
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