Analysis and implementation of calibration methods for magnetometers and accelerometers

Abstract

Throughout human history, navigation has always been an elementary necessity, from hunting to traveling overseas, and even outside of planet Earth. Agriculture is another area where navigation is progressively required, especially in the scope of the so-called precision agriculture, which considers and handles intrinsic spatial variabilities along cultivations. In order to meet the demands for navigation, numerous techniques have been developed; one of the most used and known is the GNSS (Global Navigation Satelite System) technology, which can provide navigation aid in a broad range of accuracy and cost. Navigation based on IMUs (Inertial Measurement Units) and AHRSs (Attitude and Heading Reference Systems), on the other hand, which basically consist of inertial and magnetic sensors, follows a complementary pattern in terms of cost benefit. Despite being possible, navigation systems based on only one navigation technique often do not produce a sufficiently accurate navigation solution, since those individual technologies, such as marine-grade IMUs and accurate GNSS signals, are generally too expensive. A possible solution for producing low-cost, high-precision navigation systems is the combination of different navigation techniques into an integrated system via sensor fusion. One of the biggest challenges involving low-cost inertial and magnetic sensors, especially the latter, is that their measurements are strongly corrupted by inherent and external errors. Such errors can be so compromising as to make it impossible to use the corrupted measurements for navigation purposes. In addition to sensor fusion, which contributes to the mitigation of errors, calibration techniques can precisely estimate systematic errors, which, then, can be compensated for. Therefore, this work analyzes and implements current calibration techniques for magnetometers and accelerometers. One of the objectives is to determine the suitability/robustness of the investigated algorithms for consumer-grade sensors. As the main contribution of this work, numerical and analytical solutions are presented for the compensation of systematic errors from intermediate estimates computed via one of the addressed methods. In addition, the work provides a complete mathematical description of the investigated calibration techniques, both for each type of sensor individually and for several types simultaneously. For validation purposes, the algorithms are subjected to simulations and comparisons with the results obtained via the proposed solutions, followed by implementations in hardware. Finally, a traditional magnetometer calibration method, for which new numerical and analytical solutions have been proposed, is adapted for the calibration of accelerometers.