Precise measurement of the magnetic field vector with moving carriers 
Korepanov V., Dudkin F. 
Laboratory for Electromagnetic Innovations 

The geophysical research of Earth’s crust structure requires measurements of the Earth's magnetic field vector variations at big areas. Normally, this is made with fluxgate magnetometers (FGMs) in numerous stationary positions to cover all the area. To decrease time and money expenses, recently the attempts are known to do this with the help of moving carriers. The use of FGM onboard mobile carriers faces a number of difficulties that limit their implementation in the practice of geophysical research. This is due to the fact that the measurements of rather weak magnetic anomalies are executed in the presence of strong Earth’s magnetic field B0 (the absolute value B0 can reach 67 000 nT), which creates great interference unavoidably arising when the FGM rotates during its movement. This interference signal dB at the output of the FGM sensor is proportional to the derivative of the field vector projection onto the sensor axis with respect to the angle ζ between B0 and the sensor axis: dB=B_0 sinζ dζ, As follows from this formula, for a sensor being at given moment orthogonal to the vector B0, the change in the rotation angle dζ only by one thousandth of degree can lead to the appearance of an additional signal up to 1.2 nT. Therefore, the application of magnetometers for operation on mobile carriers is limited by the recording of variations of B0 absolute value. This decreases the useful information and is characteristic mostly for scalar magnetometers. The latter, however, are inferior to the FGMs by such important parameters as weight, size, and price. It is important to estimate whether FGMs may be competitive with scalar magnetometers also in the magnetic field measurement precision with acceptable for practice errors. So, let us analyze the possible ways to reduce the magnetic field values collected onboard moving carrier to the values in the stationary geomagnetic frame with acceptable errors. It is clear that for this the data about the orientation of the FGM axes during its motion are necessary. To obtain such information, a promising way is the use of an additional magnetometer installed on the ground at the site of work and properly oriented, as well as to use a tiltmeter in moving FGM. (Data from FGM of nearest geomagnetic observatories are not considered here because they do not contain magnetic disturbances of local origin). The axes direction of moving FGM relatively to the axes of stationary FGM may be then calculated by comparing the projections of the magnetic field vector in both magnetometers at every time moment. When calculating the rotations of the coordinate system, the Euler angles α, β, γ (respectively precession angle, nutation angle and angle of proper rotation) are most often used. Euler angles are convenient for physical interpretation of rotations, since they are intuitively understandable, and also when describing timeconstant rotations. However, the description of random rotation with the help of Euler angles has a number of significant drawbacks: rotations are not commutative; interpolation of rotations presents significant difficulty; and there is a problem of singularity (the socalled gimbal lock). To avoid them, the efficiency was estimated of use the quaternion formalism describing rotations with hypercomplex numbers in 4dimensional Euclidean space. It is shown that this way allows obtaining the final results with good resolution, acceptable for practice. The experimental tests confirmed these calculations and their results are discussed in the report. Also a new FGM version the best suitable for onboard light drones use is described and its parameters are discussed. 
Measurements 
oral 
