Misalignment calibration of geomagnetic vector measurement system using parallelepiped frame rotation method

https://doi.org/10.1016/j.jmmm.2016.06.019Get rights and content

Highlights

  • •

    A new misalignment calibration method by rotating a parallelepiped frame is proposed.

  • •

    It does not need to know sensor attitude information or local dip angle.

  • •

    The calibration system attitude change angle is not strictly required.

  • •

    It can be widely used when sensors measure different physical information.

  • •

    Geomagnetic vector measurement error is reduced evidently.

Abstract

Misalignment error is one key factor influencing the measurement accuracy of geomagnetic vector measurement system, which should be calibrated with the difficulties that sensors measure different physical information and coordinates are invisible. A new misalignment calibration method by rotating a parallelepiped frame is proposed. Simulation and experiment result show the effectiveness of calibration method. The experimental system mainly contains DM-050 three-axis fluxgate magnetometer, INS (inertia navigation system), aluminium parallelepiped frame, aluminium plane base. Misalignment angles are calculated by measured data of magnetometer and INS after rotating the aluminium parallelepiped frame on aluminium plane base. After calibration, RMS error of geomagnetic north, vertical and east are reduced from 349.441 nT, 392.530 nT and 562.316 nT to 40.130 nT, 91.586 nT and 141.989 nT respectively.

Introduction

Three axis magnetometers are widely used because they can measure magnetic field components [1], [2], [3], [4], [5]. The measured values are the magnetic field projection on magnetometer axis [6], [7], [8]. The magnetic field components on local geography coordinate should be measured by geomagnetic vector measurement system, in which three axis magnetometer and attitude measurement instrument should be used [9], [10], [11]. Providing that the attitude information of three axis magnetometer is known, the magnetic field components on local geography coordinate can be known: north magnetic field, vertical magnetic field, east magnetic field [12], [13], [14], [15]. One key factor influencing the measurement result of geomagnetic measurement system is the attitude measurement accuracy.

Geomagnetic vector measurement system mainly contains three axis magnetometer and inertia instrument, in which inertia instrument is used to provide attitude for three axis magnetometer. Geomagnetic vector can be obtained by combining with magnetic field measurement value and attitude measurement value. Inertia instrument contains three axis gyroscope and three axis accelerometer. After alignment and calibration, accelerometer coordinate can be considered as gyroscope coordinate, which is also considered as INS coordinate [16]. In the installation process, misalignment error between inertia instrument coordinate and magnetometer coordinate cannot be avoided. Misalignment error is a key factor influencing the measurement accuracy of geomagnetic measurement system. 1° misalignment error can lead to geomagnetic vector measurement error about hundreds of nT. Thus, it is rather important to calibrate misalignment error. There are two difficulties to calibrate misalignment: (1) Inertia instrument coordinate and magnetometer coordinate are invisible. (2) It is different from sensor array calibration because they measure different physical information, which makes it more difficult.

Some researchers proposed related methods for misalignment calibration in different systems. Pang et. al proposed a method for magnetic sensor array misalignment calibration. It can only calibrate misalignment when sensors measure the same physical information [17]. Zhu et al used a six sides optics mirror and optics reference frame system for misalignment calibration in integrative sensor system. It used the projection of magnetic field and gravity on optics reference frame system. Misalignment angles between magnetic sensor coordinate and optics reference coordinate were calculated, and misalignment angles between accelerometer coordinate and optics reference coordinate were calculated. This method should accurately adjust three dimension optics reference coordinate, and the fixed optics reference coordinate should be selected as North-East-Ground direction. In addition, local dip angle should be known [18]. Renk et. al used a six dimension robot to calibrate misalignment error. Also, this method need accurately control attitude. Yaw, roll, pitch angles of robot arm should be provided [19]. Vcelak et. al used a three dimension rotation table to calibrate misalignment error in compass. Attitude information provided by accelerometer should be used for roll misalignment error calibration of magnetometer [20]. Jurman et al. deployed a MEMS compass composing of magnetometer and accelerometer in a plastic box. The calibration principle is similar with the method in [20], which should provide attitude information [21]. In a whole, the mentioned methods have several disadvantages: (1) The operation of equipment is complex. (2) Accurate attitude information should be provided.

In this paper, a calibration method for misalignment error of geomagnetic measurement system is proposed, which is easy to operate, and it is not necessary to know attitude information. The proposed method is effective for misalignment calibration of other kinds of system when sensors measure different physical information.

Section snippets

Calibration theory

The calculation process is shown in Fig. 1. The process details can be expressed as:

  • (1)

    Nonmagnetic rotation table is deployed on a flat ground, but it is not necessary to strictly deploy it at the level plane.

  • (2)

    Magnetometer and accelerometer of geomagnetic measurement system are fixed in a nonmagnetic parallelepiped frame deployed on nonmagnetic rotation table. Nonmagnetic parallelepiped frame coordinate is set as X,Y,Z.

  • (3)

    At the initial attitude, X axis of nonmagnetic parallelepiped frame coordinate

Simulation

  • (1)

    Three axis magnetometer and INS are fixed in parallelepiped frame. The true misalignment angles between magnetometer and parallelepiped frame are set as: [αmagβmagγmag]=[1°0.5°0.5°]. The true misalignment angles between accelerometer and parallelepiped frame are set as: [αaccβaccγacc]=[1°0.5°0.5°]. Magnetometer measurement noise is set as: 5 nT. Accelerometer measurement noise is set as: 0.005 m/s2. At initial attitude, the projection of geomagnetic field on parallelepiped frame are [ 35,000; −

Experimental system

As shown in Fig. 9, the experimental system contains DM-050 three-axis fluxgate magnetometer, INS with 90 type laser gyroscope triads (It is the type of the laser gyro, which is manufactured by National University of Defense Technology in China) and accelerometer triads, aluminium parallelepiped frame, GPS (to measure longitude, latitude and altitude), notebook computer (to record and save measurement results), data acquisition software and data processing software. The information of DM-050

Discussion

  • (1)

    The measurement average of geomagnetic field projection on rotation axis influences the estimation accuracy of misalignment calibration. In simulation, X axis measurement RMS error after misalignment calibration is reduced to 3.6 nT. Magnetometer Z axis measurement RMS error after calibration can still reach 8.6 nT. The major reason is that the magnetometer rotation axis measurement average is different from the true value. The measured error can be further reduced when the measurement average is

Conclusion

In conclusion, it suggests an effective way for the misalignment calibration of geomagnetic field vector measurement instrument. Using the rotation method, misalignment angles can be estimated effectively and geomagnetic vector measurement error is reduced evidently. Compared with traditional misalignment calibration method, this calibration method has several advantages: (1) It does not need to know sensor attitude information with regard to geography coordinate or local dip angle. (2) The

Acknowledgments

This research is supported by National Natural Science Foundation of China (Project number: 51175507), Distinguished Postgraduate Fund of Hunan Province (CX2012B012) and Distinguished Postgraduate Fund of National University of Defense Technology (B120302), and the authors are very grateful to Prof. Wenqi Wu, Prof. Xiaoping Hu and Prof. Meiping Wu for their support.

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