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Earth magnetic field mapping from planetary orbiting satellites requires a spacecraft magnetic field environment control program combined with the deployment of the magnetic sensors on a boom in order to reduce the measurement error caused by the local spacecraft field. Magnetic mapping missions (Magsat, Oersted, CHAMP, SAC-C MMP and the planned ESA Swarm project) carry a vector magnetometer and an absolute scalar magnetometer for in-flight calibration of the vector magnetometer scale values and for monitoring of the inter-axes angles and offsets over time intervals from months to years. This is done by comparing the two magnetometer outputs for several days and for as many different external field directions and amplitudes in the satellite frame as available. The vector and the scalar sensor may be placed of the order of 2 m apart and at the end of an about 10 m long boom counted from the spacecraft centre-of-gravity. In line with the classical dual vector sensors technique for monitoring the spacecraft magnetic field, this paper proposes and demonstrates that a similar combined scalar/vector gradiometry technique is feasible by using the measurements from the boom-mounted scalar and vector sensors onboard the Oersted satellite. For Oersted, a large difference between the pre-flight determined spacecraft magnetic field and the in-flight estimate exists causing some concern about the general applicability of the dual sensors technique.

A novel highly stable magnetic fluxgate vector gradiometer is presented in this paper. It is based on two triaxial fluxgate sensors with the Compact Spherical Coil (CSC) feedback to demonstrate the feasibility of such instrument (the full gradient instrument will consist of at least four triaxial sensors for measuring all the components of the gradient tensor). The sensors have been designed and constructed for the geopotential German satellite CHAMP, and are based on the instrument flying on the Danish satellite Orsted dedicated to measure the Earth's magnetic field with very high precision. The transducers are of the ringcore type with very low noise and high thermal stability. They use amorphous metal magnetic core (Vitrovac 6025). The cores have been annealed in two different processes with different temperatures and stress. With this instrument, three components of the gradient tensor can be measured with a precision better than 100 pT rms /m. The noise of the gradiometer is 93 pT rms /m in the band 0.01–10 Hz (30.1 pT rms /(Hz 1/2 m) at 1 Hz).

The shift of the NMR spectral line frequency in a proton free precession absolute scalar magnetometer using the omni-directional toroid container for a proton-rich liquid depends on the magnetic susceptibility of the liquid and on the direction of the external field relative to the axis of the toroid. The theoretical shift is estimated for water by computing the additional magnetic field from the magnetization of the liquid and comparing it to the theoretical field in a spherical container. Along the axis the estimated average shift is −0.08 nT and perpendicular to the axis the shift is +0.08 nT relative to that of a spherical sensor. The field inhomogeneity introduced by the toroid shape amounts to 0.32 nT over the volume of the sensor and is not expected to significantly affect the signal decay time, when considering the typical water line width of about 2.5 nT.

The compact spherical coil (CSC) vector-feedback magnetometer on the Danish Orsted geomagnetic mapping satellite underwent extensive calibrations and verifications prior to integration and launch. The theory of the 'thin shell' calibration procedure is introduced. Spherical harmonic modelling was developed and tested over several years and used for Orsted and other missions at test facilities in Europe, the United States and the Republic of South Africa. The verification of the test coil system using an Overhauser absolute scalar proton magnetometer is explained and the overall calibration results are given. The temperature calibrations are explained and reported on. The overall calibration model standard deviation is about 100 pT rms. Comparisons with the later in-flight calibrations show that, except for the unknown satellite offsets, an agreement within 4 nT was obtained. Finally an rf interference between the CSC and the Overhauser magnetometer is discussed, which may account for some of this discrepancy.

The vector fluxgate magnetometer of the Orsted satellite is routinely calibrated by comparing its output with measurements of the absolute magnetic intensity from the Overhauser instrument, which is the second magnetometer of the satellite. We describe the method used for and the result obtained in that calibration. Using three years of data the agreement between the two magnetometers after calibration is 0.33 nT rms (corresponding to better than ± 1 nT for 98% of the data, and better than ± 2 nT for 99.94% of the data). We also report on the determination of the transformation between the magnetometer coordinate system and the reference system of the star imager. This is done by comparing the magnetic and attitude measurements with a model of Earth’s magnetic field. The Euler angles describing this rotation are determined in this way with an accuracy of better than 4 arcsec.

The single axis magnetic gradiometer based on two compact detector compensation (CDC) fluxgate ringcore sensors separated 20 cm is described. Despite its high stability and precision better than 1 nT, the calibration procedures are not straightforward. Firstly, the mono-axial measurement does not provide vector information about the magnetic field. Secondly, one of the sensors measures the ambient magnetic field and is used to compensate for the main field at both sensors. Several methods have been developed for characterization of the gradiometer, and the calibration of the gradient measurements is achieved by using a magnetic dipole of strength 2 mAm 2 . In a coil facility, the gradient can be determined with an accuracy of 0.3 nT/m RMS .

The current-output fluxgate may be tuned by using a serial capacitor. Such tuning increases the sensor sensitivity in the situation when the pick-up coil has a low number of turns. We achieved a signal/feedthrough ratio improvement by a factor of 5. The measured parameters fit the simplified theoretical model within 20% deviation.

The construction of a triaxial fluxgate sensor with very high axis stability and low temperature coefficients is described. The axis orthogonalities change less than 2.1 s of are in the whole testing temperature range +20 to −10°C. The temperature coefficients for the sensitivities of the three axes are 6.7, 10.1 and 13.3 ppm K −1 , respectively. This high stability is achieved by using a newly developed ceramic, CSiC, as the supporting construction material.

A model of a fluxgate magnetometer based on the field interactions in the fluxgate core has been derived. The non-linearity of the ringcore sensors due to large uncompensated fields transverse to the measuring axis are calculated and compared with measurements. Measurements of the non-linearity are made with a spectrum analyzer measuring the higher harmonics of an applied sinusoidal field. For a sensor with a permalloy ringcore of 1 in. in diameter the deviation from linearity is measured to about 15 nT p-p in the earth's field and the measurements are shown to fit well the calculations. Further, the measurements and the calculations are also compared with a calibration model of the fluxgate sensor onboard the ‘MAGSAT’ satellite. The later has a deviation from linearity of about 50 nT p-p but shows basically the same form of non-linearity as the measurements.

The experiments and theoretical considerations leading to the construction of a high-performance three-axis fluxgate magnetometer are described. The magnetometer will be used (1996) in the Earth's field mapping satellite named 'OErsted'. The fluxgate sensors are based on stress-annealed metallic glass ribbons as core materials. It is shown that very simple physical models can be used to explain the fluxgate mode of operation, thereby making it easy to calculate the overall sensor performance from first principles. Special attention is drawn to the core excitation current which is analysed on the basis of nonlinear electrical circuitry. It is furthermore shown that the ring-core demagnetizing field obeys a simple cosine law which permits the calculation of the sensor sensitivity with high accuracy. The sensitivity, that is the signal-to-noise ratio, is ultimately determined by the sensor noise which is about 15 pT RMS (0.06-10 Hz), corresponding to a noise power density (1/f noise) of 6.2 pT Hz-1/2 at 1 Hz. The actual magnetometer operating range and sensitivity is determined by the 1 bit resolution of the Earth's field represented by the output from the 18 bit AD converted used in the instrument (+or-65536 nT with 0.5 nT resolution). The maximum attainable bandwidth is half the sensor excitation frequency (1/2*15 kHz) but the OErsted magnetometer bandwidth is limited to 250 Hz. The thermal stability of the sensor has been measured to be better than 1 nT in the temperature range -20 to +60 degrees C.

This paper describes an experiment where the flux-gate sensor broad band output signal is digitized with 8-bit resolution at a high rate, and subsequently numerically analysed in order to extract information on the external magnetic field. The results show that it is feasible to obtain a noise level of 1 nT for a data output rate of 100 Hz. The method will allow construction of a magnetometer based entirely on digital techniques, with only a minimum of analogue circuits.

The fluxgate null feed-through signal is discussed theoretically giving an expression for the excitation current and for the core flux coupling coefficients to the secondary coil. Experimental results show that the two signals cannot be nulled simultaneously by rotating the core inside the secondary coil, and give the two coupling coefficients. The excitation current coupling depends critically on the symmetry of the winding, and it is shown that the two signals are associated with excess noise adding to the basic core noise.

The output current impulses of the short-circuited fluxgate depend on the input magnetic field, and on a number of core parameters such as the demagnetization factor, the cross sectional area, the time spent in saturation, etc. Following a theoretical treatment, experimental tests of the parameter dependences are reported, and additional experimental evidence of the noise performance is presented.

The sensor offset as a function of the ring rotation angle with respect to the detector coil has been studied for three different fluxgate sensors of the ringcore type. The core material consists of metallic glass ribbons which have been heat treated in different ways so that different magnetization curves and noise levels are obtained. For the best core the offsets are rather low (a few nT) and only slightly dependent on the rotation angle.

This is a reply to a comment on our paper. The comment suggests an inconsistency in the relation between the magnetic field and the magnetometer measurements. This is resolved, once the existence of two physically different sensor systems is appreciated, as has also been discussed in some detail in our paper.

A method for measuring the demagnetisation of fluxgate sensors is introduced and used to evaluate the demagnetising factors for four ring-core sensors having 5, 10, 15 and 20 wraps of magnetic core ribbon. The demagnetising factor is proportional to the number of wraps, and the noise is also proportional to the number of wraps except for the more noisy 5-wrap core. The estimated internal core noise was 1 pT RMS taking into consideration the demagnetising factor and the relative permeability of the core material.

The calibration parameters of a vector magnetometer are estimated only by the use of a scalar reference magnetometer. The method presented in this paper differs from those previously reported in its linearized parametrization. This allows the determination of three offsets or signals in the absence of a magnetic field, three scale factors for normalization of the axes and three non-orthogonality angles which build up an orthogonal system intrinsically in the sensor. The advantage of this method compared with others lies in its linear least squares estimator, which finds independently and uniquely the parameters for a given data set. Therefore, a magnetometer may be characterized inexpensively in the Earth's magnetic-field environment. This procedure has been used successfully in the pre-flight calibration of the state-of-the-art magnetometers on board the magnetic mapping satellites Orsted, Astrid-2, CHAMP and SAC-C. By using this method, full-Earth-field-range magnetometers (± 65536.0 nT) can be characterized down to an absolute precision of 0.5 nT, non-orthogonality of only 2 arcsec and a resolution of 0.2 nT.

The reference coordinate axes of a magnetic vector field sensor are related to the instrument digital output vector Ū by the calibration matrix and the offset vector Ō. In addition, this reference coordinate system must be related to (at least) two externally accessible optical or geometrical axes in order to be able to determine the precise orientation of the magnetic coordinate axes in an external reference system. Two methods for determining a reference axis in the sensor coordinates are discussed: (1) using a triaxial coil facility to measure the sensor orientation for two different positions, rotated about a fixed reference axis; (2) in the Earth's field the magnetometer sensor is rotated about a fixed axis into a number of (at least three) positions.

The construction of an orthogonal reference frame based on a set of three skew axes for a magnetic coil system and a magnetic sensor is discussed and presented. For a skew system, it is possible to define the coil axes and the magnetic axes as a dual set of axes that are linked to the system. Therefore, one orthogonal reference frame can be identified from the coil axes and another from the magnetic axes. Although this representation is not unique, it is the most intuitive visual representation as it is shown. The parametrizations based on the operation of the fluxgate transducer for the magnetic sensors compact spherical coil (CSC) (Orsted satellite) and compact detector coil (CDC) (Astrid-2 satellite) are analyzed and identified. In principle, only the transformation matrix that orthogonalizes the sensor is needed, but it is customary to express this matrix as a function of some non-orthogonal angles. Therefore, most relevant conventions from the literature are presented for comparison. All the representations agree for the case of small angle approximation, which is valid for most sensors.

Fluxgate sensors are mostly used in closed-loop d.c. magnetometer systems; they can also measure alternating fields up to several kilohertz, either in open-loop mode or from an error signal in the slow-feedback loop as in the Thunderstorm rocket magnetometer, which has 0.1 nT resolution up to 3 kHz. The alternative is to use the direct induction effect in the pick-up or feedback coil. While the low L/R constant of the pick-up coil causes a high −3 dB frequency corner, the spherical feedback coil has narrow frequency characteristics and low noise up to 10 kHz when used as a search coil. The noise level achieved is 56 pT r.m.s. from 123 Hz to 10 kHz.

The design and performance of the Astrid-2 magnetometer are described. The magnetometer uses mathematical routines, implemented by software for commercially available digital signal processors, to determine the magnetic field from the fluxgate sensor. The sensor is from the latest generation of amorphous metal sensors developed by the Department of Automation at the Technical University of Denmark.

A large number of measured demagnetizing factors for fluxgate ring cores of a wide range of cross section shapes have been compiled from the literature and plotted against the core cross-sectional area over the squared mean core diameter. The points group close to a straight line through the origin. The local demagnetizing factor is used, and the conversion to the average or global factor is derived. Three approximate analytical/numerical calculations of the internal field in the ring-core magnetic material are made. The results are close to the experimental data, supporting the conclusion that the demagnetizing factor for thin rings is proportional to the ring cross-sectional area divided by the diameter squared.

A new full Earth's field dynamic feedback fluxgate magnetometer is described. It is based entirely on digital signal processing and digital feedback control, thereby replacing the classical second harmonic tuned analogue electronics by processor algorithms. Discrete mathematical cross-correlation routines and substantial oversampling reduce the noise to 71 pT root-mean-square in a 0.25 - 10 Hz bandwidth for a full Earth's field range instrument.