sensors

Review Recent Progress of Fluxgate Magnetic Sensors: Basic Research and Application

Songrui Wei 1 , Xiaoqi Liao 2,3, Han Zhang 1, Jianhua Pang 4 and Yan Zhou 5,*

1 Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, China; [email protected] (S.W.); [email protected] (H.Z.) 2 College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China; [email protected] 3 Ångström Laboratory, Department of Engineering Sciences, Uppsala University, 75121 Uppsala, Sweden 4 Shenzhen Institute of Guangdong Ocean University, International Biological Valley, Dapeng District, Shenzhen 518060, China; [email protected] 5 School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China * Correspondence: [email protected]

Abstract: Fluxgate magnetic sensors are especially important in detecting weak magnetic fields. The mechanism of a fluxgate magnetic sensor is based on Faraday’s law of electromagnetic induction. The structure of a fluxgate magnetic sensor mainly consists of excitation windings, core and sensing windings, similar to the structure of a transformer. To date, they have been applied to many fields such as geophysics and astro-observations, wearable electronic devices and non-destructive testing. In this review, we report the recent progress in both the basic research and applications of fluxgate magnetic sensors, especially in the past two years. Regarding the basic research, we focus on the progress in lowering the noise, better calibration methods and increasing the sensitivity. Concerning



 applications, we introduce recent work about fluxgate magnetometers on spacecraft, unmanned aerial vehicles, wearable electronic devices and defect detection in coiled tubing. Based on the above Citation: Wei, S.; Liao, X.; Zhang, H.; work, we hope that we can have a clearer prospect about the future research direction of fluxgate Pang, J.; Zhou, Y. Recent Progress of magnetic sensor. Fluxgate Magnetic Sensors: Basic Research and Application. Sensors Keywords: magnetic sensor; fluxgate; noise; sensitivity; calibration 2021, 21, 1500. https://doi.org/ 10.3390/s21041500

Academic Editor: Guo-Hua Feng 1. Introduction Received: 29 December 2020 Sensors are devices for detecting, collecting and transmitting various kinds of infor- Accepted: 5 February 2021 mation from the environment. It is the first step of most forms of artificial intelligence Published: 22 February 2021 and they play more and more important roles in many fields of industry and daily life. Among them, magnetic sensors detect magnetic fields and currents and are widely used Publisher’s Note: MDPI stays neutral in astro-observation, geophysics observation, non-destructive testing and wearable in- with regard to jurisdictional claims in telligent devices, etc. [1–5]. To date, many types of magnetic sensors based on different published maps and institutional affil- mechanisms have been developed. The magnetic sensors based on fluxgate, Hall effect iations. and magnetoresistance effect are the most widely investigated [5]. In this review, we will focus on the recent progress of fluxgate magnetic sensors regarding both basic research and applications. Compared with other magnetic sensors, fluxgate magnetic sensors have advantages Copyright: © 2021 by the authors. such as high sensitivity, high accuracy, high resolution, simple and compact structures, and Licensee MDPI, Basel, Switzerland. low noise [6–14]. What’s more, they can be used in different kinds of environment and This article is an open access article even hostile environments, and they have important applications in weak magnetic field distributed under the terms and measurements. The basic structures of parallel and orthogonal fluxgate magnetometers conditions of the Creative Commons are schematically shown in Figure1[ 15]. They are mainly composed of three parts: the Attribution (CC BY) license (https:// magnetizing windings, the sensing windings and the core. The basic working principle creativecommons.org/licenses/by/ of a fluxgate sensor is about the periodic change of the magnetic permeability of the soft 4.0/).

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the magnetizing windings, the sensing windings and the core. The basic working princi- ple of a fluxgate sensor is about the periodic change of the magnetic permeability of the soft ferromagneticferromagnetic core which core is whichdriven isby driven a periodic by a periodicexciting excitingcurrent. current.The periodic The periodic cur- current in rent in the excitingthe exciting windings windings will induce will induce a periodic a periodic magnetic magnetic field in field the in magnetic the magnetic core core and this and this will furtherwill further induce induce a periodic a periodic current current in the in sensing the sensing windings. windings. When When there there is no is no ambient ambient magneticmagnetic field, field, the current the current of the of exciting the exciting windings windings and andthe sensing the sensing windings windings matches. matches. However,However, when when the thesoft soft core core is expo is exposedsed to toan anambient ambient magnetic magnetic field, field, the the soft soft core will be core will be moremore easily easily saturated saturated in in the the ambient ambient magnetic magnetic field’s field’s direction direction and and less less easily easily saturated in saturated in thethe opposite opposite direction. direction. In In this this ca case,se, the the currents currents of of the the exciting exciting windings windings and and the sensing the sensing windingswindings do do not not match. match. The The differ differenceence between between the current the current of exciting of exciting wind- windings and sensing windings are used to estimate the strength of the magnetic field and the output ings and sensing windings are used to estimate the strength of the magnetic field and the signal is usually integrated to the form of a voltage. For the orthogonal fluxgate sensor, output signal is usually integrated to the form of a voltage. For the orthogonal fluxgate the case is a little different. The noise of orthogonal fluxgate sensor is mainly originated sensor, the case is a little different. The noise of orthogonal fluxgate sensor is mainly orig- from the domain walls movement. This is the so called Barkhausen noise. To reduce the inated from the domain walls movement. This is the so called Barkhausen noise. To reduce noise, a DC excitation current which is sufficiently larger than the AC excitation current is the noise, a DC excitation current which is sufficiently larger than the AC excitation cur- applied to reduce the movement of the domain walls. This describes fundamental mode rent is applied to reduce the movement of the domain walls. This describes fundamental orthogonal fluxgates (FM-OFG). mode orthogonal fluxgates (FM-OFG).

Figure 1. TheFigure schematical 1. The diagramschematical of: ( adiagram) parallel of: fluxgate (a) parallel magnetic fluxgate sensor magnetic and (b) orthogonalsensor and fluxgate(b) orthogonal magnetic sensor. The word “parallel”fluxgate andmagnetic “orthogonal” sensor. The in theword name “parallel” meanthe and orientation “orthogonal” between in the thename excitation mean the magnetic orientation field and the between the excitation magnetic field and the probed magnetic field. In (a), the excitation magnetic probed magnetic field. In (a), the excitation magnetic field Hex is parallel to the probed magnetic field Hdc. In (b), the field Hex is parallel to the probed magnetic field Hdc. In (b), the excitation current is along the axial excitation current is along the axial direction. So, the excitation magnetic field is around the circle and orthogonal to the direction. So, the excitation magnetic field is around the circle and orthogonal to the probed field probed field H . Only the orthogonal fluxgate sensor needs the DC exciting current which should be sufficiently larger Hdcdc. Only the orthogonal fluxgate sensor needs the DC exciting current which should be sufficiently than the AClarger exciting than current. the AC exciting current. To date, many kinds of fluxgate sensors have been developed. According to the To date, many kinds of fluxgate sensors have been developed. According to the ori- orientation between the magnetic field of excitation current and target magnetic field, entation between the magnetic field of excitation current and target magnetic field, fluxgate sensors can be divided into parallel fluxgate sensors and orthogonal fluxgate fluxgate sensors can be divided into parallel fluxgate sensors and orthogonal fluxgate sen- sensors, as shown in Figure1. They are named after the orientation between the excitation sors, as shown in Figure 1. They are named after the orientation between the excitation magnetic field and the probed magnetic field. According to the measured signal, they can be magnetic field and the probed magnetic field. According to the measured signal, they can divided into voltage fluxgate sensors and time domain fluxgate sensors. In voltage fluxgate be divided into voltage fluxgate sensors and time domain fluxgate sensors. In voltage sensors, the voltage on the sensing windings is measured to estimate the ambient field. In fluxgate sensors, the voltage on the sensing windings is measured to estimate the ambient time domain fluxgate sensors, the time difference between the positive and negative signal field. In time domain fluxgate sensors, the time difference between the positive and neg- will be used to estimate the ambient field. The working principle of the voltage fluxgate ative signal will be used to estimate the ambient field. The working principle of the voltage sensor is described in the last paragraph. The working principle of the residence time- fluxgate sensordifference is described (RTD) in fluxgatethe last paragraph. magnetometer The isworking schematically principle shown of the in residenceFigure2[16 ]. Figure2a time-differenceis (RTD) an ideal fluxgate square magnetometer hysteresis loop. is When schematically there is noexternal shown in Figure magnetic 2 [16]. field, Fig- the relationship ure 2a is an idealbetween square the hyster magneticesis loop. field When and time there will is noexternal be shown magnetic as the solid field, black the linere- in Figure2b. lationship betweenThe time the intervalsmagnetic between field and the time positive will be and shown negative as the saturation solid black states line are in equal. Namely, Figure 2b. TheRT timeD =intervals T+ − T −between= 0. When the anpositi externalve and magnetic negative fieldsaturation in applied states on are the equal. magnetic core, the + − Namely, RT Dfigure = T − will T = be 0. lifted When in an the external H direction magnetic and the field equilibrium in applied is on broken the magnetic as shown in Figure2c. core, the figureUnder will be this lifted condition, in the H the direct timeion difference and the isequilibrium no longer zerois broken as shown as shown in Figure in 2d.

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Figure 2c. Under this condition, the time difference is no longer zero as shown in Figure 2d. Their high cost of fabrication has limited the application of fluxgate sensors in more daily necessity fields. The recent trend of fluxgate sensors in industry is to reduce the fabrication cost. Many new fabrication methods have been proposed and the pad-printing technique is one of them. The pad-printing technique is one of the micro-printing tech- niques which have the advantages of being fast and simple. The micro-printing technique provides new features such as flexibility to fluxgate magnetic sensors. Compared with other micro-printing techniques, pad-printing has advantages such as high printing rates (more than 1500 prints per hour), fast drying of the motif, mass production, precise layer- by-layer printing, and the option of printing on non-flat surfaces [17–19]. The structure of this review is arranged as follows: Firstly, it is divided into two main parts, covering basic investigations and applications. In the basic investigation part, recent works about the Sensors 2021, 21, 1500 noise, calibration method and the sensitivity are discussed. For the application part,3 of ap- 18 plications in astro-observation, geographical observation, wearable electronic devices and non-destructive testing are discussed.

FigureFigure 2.2. SchematicSchematic diagram diagram of of the the working working prin principleciple of ofRTD RTD fluxgate fluxgate magnetometer. magnetometer. (a) Ideal (a) Ideal squaresquare hysteresishysteresis loop,loop, ((bb)) magneticmagnetic inductioninduction intensityintensity correspondingcorresponding toto thethe hysteresishysteresis looploop inin (a), ((ca)), sinusoidal (c) sinusoidal excitation excitation signal signal of an of RTD an RTD fluxgate fluxga withte with and withoutand without a target a target magnetic magnetic field, field, and (d) inducedand (d) induced voltage signalvoltage from signal sensing from coilsensing with coil and with without and awithout target magnetica target magnetic field. field.

2. BasicTheir Research high cost of fabrication has limited the application of fluxgate sensors in more daily2.1. Noise necessity fields. The recent trend of fluxgate sensors in industry is to reduce the fabrication cost. Many new fabrication methods have been proposed and the pad-printing Butta et al. investigated the relationship between the noise of an orthogonal fluxgate technique is one of them. The pad-printing technique is one of the micro-printing tech- and the composition of the wire-core [20]. The noise of a fundamental mode orthogonal niques which have the advantages of being fast and simple. The micro-printing technique fluxgate is usually ascribed to Barkhausen noise [21,22]. The origin of this noise is the move- provides new features such as flexibility to fluxgate magnetic sensors. Compared with ment of the domain wall in the alloy wires which make up the core of magnetic sensor. To other micro-printing techniques, pad-printing has advantages such as high printing rates date, most works are devoted to eliminating this kind of noise and much progress has been (more than 1500 prints per hour), fast drying of the motif, mass production, precise layer- made. Researchers have applied various methods such as optimizing the geometry to re- by-layer printing, and the option of printing on non-flat surfaces [17–19]. The structure duce the demagnetization and using multiple wires and the Barkhausen noise has thus been of this review is arranged as follows: Firstly, it is divided into two main parts, covering reduced to a very low level [23], but the total noise is still in a high level and the origin of basic investigations and applications. In the basic investigation part, recent works about thethe noise,remaining calibration noise is method unclear. and In [20], the sensitivityButta et al.are proposed discussed. that Forthe theremaining application noisepart, may applicationscome from the in magnetostriction astro-observation, of the geographical wire. According observation, to the definition wearable of electronic magnetostriction, devices andon one non-destructive hand, when an testing external are discussed.magnetic field is applied on magnetic materials, there will be a deformation on the direction of the magnetic field. On the other hand, when stress is 2.applied Basic Researchon the magnetic material, the magnetization of the material will also be changed. In 2.1. Noise Butta et al. investigated the relationship between the noise of an orthogonal fluxgate and the composition of the wire-core [20]. The noise of a fundamental mode orthogonal

fluxgate is usually ascribed to Barkhausen noise [21,22]. The origin of this noise is the movement of the domain wall in the alloy wires which make up the core of magnetic sensor. To date, most works are devoted to eliminating this kind of noise and much progress has been made. Researchers have applied various methods such as optimizing the geometry to reduce the demagnetization and using multiple wires and the Barkhausen noise has thus been reduced to a very low level [23], but the total noise is still in a high level and the origin of the remaining noise is unclear. In [20], Butta et al. proposed that the remaining noise may come from the magnetostriction of the wire. According to the definition of magnetostriction, on one hand, when an external magnetic field is applied on magnetic materials, there will be a deformation on the direction of the magnetic field. On the other hand, when stress is applied on the magnetic material, the magnetization of the material will also be changed. In the production process of alloy wires, many kinds of stress are introduced. What’s more, when the magnetic sensor is working, stress can also be induced because of the thermal expansion of the wire and the substrate. This means that for a certain Sensors 2020, 20, x FOR PEER REVIEW 4 of 18

Sensors 2021, 21, 1500the production process of alloy wires, many kinds of stress are introduced. What’s more, 4 of 18 when the magnetic sensor is working, stress can also be induced because of the thermal expansion of the wire and the substrate. This means that for a certain magnetic field, there will be differentmagnetic magnetizations field, there in the will wire be du differente to the stress magnetizations and magnetostriction. in the wire The due fluc- to the stress and tuation of the magnetostriction.magnetization under The a fluctuationconstant external of the magnetizationfield, by definition, under isa the constant noise. externalAs field, by the magnetostrictiondefinition, is usually is the noise.dependent As the on magnetostriction the composition isof usually the magnetic dependent materials, on the in composition of this work different compositions of (Co1−xFex)75Si15B10 systems were investigated in which x the magnetic materials, in this work different compositions of (Co1−xFex)75Si15B10 systems = 0.05, 0.055, 0.06,were 0.062, investigated 0.065, 0.07 in and which 0.08.x It= is 0.05, found 0.055, that the 0.06, noise 0.062, is really 0.065, dependent 0.07 and 0.08.on It is found the compositionthat and the the noise noise is reallyreaches dependent the minimum on the when composition x = 0.06. andAt the the same noise time, reaches the the minimum magnetostrictionwhen is alsox = almost 0.06. At va thenishing. same On time, the the other magnetostriction hand, when x = is0.06, also the almost noise vanishing.does On the not depend onother the stress hand, anymore. when x It= means 0.06, the that noise this part does of not noise depend is strongly on the dependent stress anymore. on It means the magnetostriction.that this Based part of on noise the above is strongly results, dependent they propose on the that magnetostriction. when annealing, Based the on the above materials shouldresults, not be they bend propose and the that stress when shou annealing,ld be as thesmall materials as possible. should That not is bebecause bend and the stress the magnetostrictionshould beis dependent as small as on possible. the temperature. That is because Even the materials magnetostriction without obvious is dependent on the magnetostrictiontemperature. effects at room Even temperature, materials without may still obvious have magnetostriction strong magnetostriction effects at at room an- temperature, nealing temperature.may still have strong magnetostriction at annealing temperature. Song et al. triedSong to reduce et al. tried the noise to reduce of the the fluxgate noise of sensor the fluxgate system sensorby another system way. by As another way. As the noise is dependentthe noise on is dependent the input excitation on the input current, excitation they proposed current, they a method proposed to easily a method to easily find the most findproper the excitation most proper current excitation for a specific current fluxgate for a specific sensor fluxgate [24]. The sensor considered [24]. The considered parameters ofparameters the excitation of thecurrent excitation include current IAC, IDC include and IAC, the frequency. IDC and the The frequency. excitation The excitation module whichmodule provides which the excitation provides thecurrent excitation mainly current includes mainly three includes parts: the three waveform parts: the waveform generator, thegenerator, signal conditioning the signal conditioningelectronics and electronics the voltage and controlled the voltage current controlled source, current source, as as shown in Figureshown 3. inWith Figure such3. Witha module, such ath module,e proper the parameters proper parameters of the excitation of the excitation current current with with the lowestthe noise lowest can noise be easily can be obtained. easily obtained. Finally, Finally, they tested they testedthe noise the noiseof the of corre- the corresponding sponding sensorsensor in practical in practical application. application.

Figure 3.FigureThe structure3. The structure of the excitation of the excitation module module which provides which pr theovides excitation the excitation current current in S.X. Song in S.X. et Song al.’s work. et al.’s work. Janosek et al. developed the lowest noise fundamental-mode, orthogonal fluxgate Janosek etmagnetometer al. developed published the lowest so nois fare [25 fundamental-mode,]. Low noise magnetometers orthogonal are fluxgate important in many magnetometerfields published such as so geomagnetic far [25]. Low observatories, noise magnetometers scientific experimentsare important in aerospace,in many nondestruc- fields such as geomagnetictive testing and observatories, evaluation, andscientific nanoparticle experiments detection in aerospace, [26–34]. Accordingnondestruc- to the structure, tive testing andfluxgate evaluation, magnetometers and nanoparticle can be de classifiedtection [26–34]. into the According parallel type to the and structure, orthogonal type. For fluxgate magnetometersthe parallel can type be fluxgate classified magnetometer, into the parallel the 1-pT type noise and orthogonal for 1 Hz can type. be only For obtained with the parallel typespecial fluxgate arrangements magnetometer, and cross the 1- correlationpT noise for measurements 1 Hz can be only [34 –obtained39]. On thewith other hand, for special arrangementsthe orthogonal and cross type, correlation low noise me canasurements be only obtained [34–39]. with On the the other fundamental-mode hand, for operated the orthogonalfluxgate. type, low Since noise the can discovery be only obtained of the orthogonal with the typefundamental-mode by Sasada in 2001 operated [40], the noise of this fluxgate. Sincekind the ofdiscovery magnetometer of the hasorthogonal been continuously type by Sasada improved. in 2001 However, [40], the a widelynoise of acknowledged this kind of magnetometerdisadvantage has of orthogonal been contin typeuously fluxgate improved. magnetometers However, isa theirwidely relatively acknowl- large offset drift. edged disadvantageAlthough of orthogon this offsetal drift type can fluxgate be reduced magnetometer in eithers digital is their or relatively analog domain, large in Janosek’s offset drift. Althoughwork, this this method offset drift is not can applied be reduced because in either it will digital cause anor increaseanalog domain,√ of the noise. in Janosek’s work, thisIn method Janosek’s is not work, applied the noise because for 1it Hzwill is cause 0.75 andan increase 1.5 pTrms of /theHz noise. for the open loop and closed loop, respectively. Additionally, benefitting from the annealing process of the In Janosek’s work, the noise for 1 Hz is 0.75 and 1.5 pTrms/√Hz for the open loop and closed loop, respectively.alloy core, the Addi offsettionally, drift benefitting is also very from small the (about annealing 2.5 nT/K). process With of the such alloy a good property, the developed fluxgate magnetometer has many promising applications. For example, core, the offset drift is also very small (about 2.5 nT/K). With such a good property, the compared to a low-noise observatory magnetometer, it is found that it has good perfor- mance at mHz frequency and is suitable for the measurement such as magnetotellurics. It can be also used in magnetocardiography (MCG) measurement. Benefitting from the low noise and offset drift, MCG measurements can be performed under room temperature and

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developed fluxgate magnetometer has many promising applications. For example, com- Sensors 2021, 21, 1500 pared to a low-noise observatory magnetometer, it is found that it has good performance5 of 18 at mHz frequency and is suitable for the measurement such as magnetotellurics. It can be also used in magnetocardiography (MCG) measurement. Benefitting from the low noise and offset drift, MCG measurements can be performed under room temperature and withoutwithout shielding shielding and and averaging. averaging. The The arrangement arrangement of of the the MCG MCG measurement measurement is is shown shown in in FigureFigure4[ 425 [25].].

FigureFigure 4. 4.The The schematic schematic diagram diagram of of MCG MCG measurements measurements based based on on fluxgate fluxgate magnetometers. magnetometers.

2.2.2.2. Errors Errors and and Calibration Calibration Methods Methods ForFor tri-axis tri-axis orthogonal orthogonal fluxgate fluxgate magnetometers, magnetometers, there there are are three three kinds kinds of of inevitable inevitable errorserrors because because of of the the limitation limitation of of manufacture manufacture technology: technology: zero zero position position error, error, sensitivity sensitivity errorerror and and orthogonal orthogonal error.error. ForFor the zero position error, error, it it means means the the output output of of the the magne- mag- netometertometer is isnot not zero zero under under a zero a zero magnetic magnetic field. field. If we If weonly only consider consider the theeffect effect of core of core rem- remanenceanence and and circuit circuit drift, drift, the therelationship relationship betw betweeneen the output the output of a ofreal a realmagnetometer, magnetometer, ideal idealmagnetometer magnetometer and andzero zeroposition position error error term term can be can written be written as: as:   𝐵  𝐵  𝐵  Bx1 Bx Bx0 𝐵 𝐵 𝐵  By1 ==By ++  By0, , (1)(1) 𝐵 𝐵 𝐵 Bz1 Bz Bz0

in the above equation, Bx1, By1 and Bz1 are real output. Bx, By, and Bz are ideal output. Bx0, in the above equation, Bx1, By1 and Bz1 are real output. Bx, By, and Bz are ideal output. Bx0, By0 and Bz0 are the zero position error terms and they can be obtained by the output of the By0 and Bz0 are the zero position error terms and they can be obtained by the output of the magnetometermagnetometer when when there there is is no no magnetic magnetic field. field. The The sensitivity sensitivity error error is is originated originated from from the the differencedifference between between the the sensitivity sensitivity of of the the three three coordinate coordinate axes. axes. The The relationship relationship between between thethe real real output, output, ideal ideal output output and and the the sensitivity sensitivity of of three three axes axes can can be be written written as: as: 𝐵 𝐾 00𝐵      B Kx 0 0 Bx x1 𝐵=0𝐾 0 𝐵, (2)  By1  =  0 Ky 0  By , (2) 𝐵 00𝐾 𝐵 Bz1 0 0 Kz Bz in the above equation, Bx1, By1 and Bz1 are the real output. Bx, By, and Bz are the ideal output. inKx the, Ky above, and K equation,z are the sensitivitiesBx1, By1 and of Bthez1 xare axis, the y realaxis output.and z axis,Bx ,respectively.By, and Bz are In theideal ideal case, output.Kx = Ky K=x K, Kz =y, 1. and TheK zorthogonalare the sensitivities error is originat of the xedaxis, fromy axisthe mismatch and z axis, between respectively. the ideal In idealcoordinate case, K xand= K yreal= K coordinatez = 1. The orthogonal or the relati erroronship is originated between fromthe real the mismatchcoordinates between are not theexactly ideal orthogonal. coordinate andAs above, real coordinate if the angle or betw theeen relationship the ideal betweencoordinate the and real real coordinates coordinate areis as not shown exactly in orthogonal.Figure 5 [41], As the above, relationship if the angle between between the real the output ideal coordinateand ideal output and real can coordinatebe written is as: as shown in Figure5[ 41], the relationship between the real output and ideal output can be written as: 𝐵 cos 𝛼 cos 𝛼 cos 𝛼 𝐵  𝐵  cos 𝛽 cos 𝛽 cos 𝛽 𝐵  Bx1 =cos αx cos αy cos αz Bx, (3) 𝐵 cos 𝛾 cos 𝛾 cos 𝛾 𝐵  By1  = cos βx cos βy cos βz  By , (3) B cos γx cos γy cos γz Bz in ideal case, αx = βy = zγ1z = 0, αy = αz = βx = βz = γx = γy = 90°. If we consider a fluxgate gradiometer which is composed of two identical fluxgate magnetometers,◦ an additional in ideal case, αx = βy = γz = 0, αy = αz = βx = βz = γx = γy = 90 . If we consider a fluxgate gradiometer which is composed of two identical fluxgate magnetometers, an additional error term will occur which is originated from the inconsistent placement of two fluxgate magnetometers. It is named the position error for the fluxgate gradiometer and the form of the expression is same to the orthogonal error. Sensors 2020, 20, x FOR PEER REVIEW 6 of 18

Sensors 2021, 21, 1500 error term will occur which is originated from the inconsistent placement of two fluxgate6 of 18 magnetometers. It is named the position error for the fluxgate gradiometer and the form of the expression is same to the orthogonal error.

FigureFigure 5.5.The The differencedifference betweenbetween idealideal coordinatecoordinate (a(a)) and and real real coordinate coordinate ( b(b)) about about the the orthogonal orthogonal error.error. TheThe a-b-ca-b-c coordinatecoordinate systemsystemis is the the reference reference coordinate. coordinate.Under Under ideal ideal condition, condition, the the output output coordinatecoordinate system system coincides coincides withwith thethe reference reference coordinate, coordinate, as as shown shown in in Figure Figure4 a.4a. However, However, under under real condition, there will be a deviation as shown in Figure 4b. For Equation (3), αx, βy and γz are the real condition, there will be a deviation as shown in Figure4b. For Equation (3), αx, βy and γz are the angle between x and x1, y and y1, z and z1, respectively. Accordingly, αy, αz, βx, βz, γx, and γy are the angle between x and x1, y and y1, z and z1, respectively. Accordingly, αy, αz, βx, βz, γx, and γy are the angle between x and y1, x and z1, y and x1, y and z1, z and x1, z and y1, respectively. angle between x and y1, x and z1, y and x1, y and z1, z and x1, z and y1, respectively. In Xu et al.’s work, the effect of sensitivity error, orthogonal error and position error In Xu et al.’s work, the effect of sensitivity error, orthogonal error and position error are considered together in one matrix A and the zero position error is considered in an- are considered together in one matrix A and the zero position error is considered in another other term B0. So, the total effect of these error terms can be written as: term B0. So, the total effect of these error terms can be written as: 𝑩𝟏 = 𝑨 ⋅𝑩+𝑩𝟎, (4) B1 = A · B + B0, (4) 𝐵 𝑎 𝑎 𝑎 𝐵 𝐵         where 𝑩𝟏 =𝐵Bx1, 𝑨=𝑎 a11𝑎 a12𝑎a,13 𝑩=𝐵, 𝑩B𝟎x=𝐵. Bx0 𝑎 𝑎 𝑎 where B1 =  𝐵By1 , A =  a21 a22 a23 , B𝐵=  By ,𝐵B0 =  By0 . Bz1 a31 a32 a33 Bz Bz0 With this method, the calibration is quick and accurate. The coefficients A and B0 can With this method, the calibration is quick and accurate. The coefficients A and B can be obtained by the method of undetermined coefficients after several measurements.0 At be obtained by the method of undetermined coefficients after several measurements. At the end of the paper, this calibration method is performed in experiments. For a single the end of the paper, this calibration method is performed in experiments. For a single three-component magnetometer, the maximum deviation can be reduced from 552.4 nT three-component magnetometer, the maximum deviation can be reduced from 552.4 nT to 15.0 nT with this calibration method. For the fluxgate gradiometer which is composed to 15.0 nT with this calibration method. For the fluxgate gradiometer which is composed ofof twotwo similarsimilar magnetometers,magnetometers, thethe maximummaximum deviation deviation can can be be reduced reduced from from 3891.5 3891.5 nT nT to to 37.237.2 nTnT withwith thisthis calibrationcalibration method. method. PanPan etet al.al. providedprovided aa newnew calibrationcalibration methodmethod forfor triaxialtriaxial fluxgate fluxgate magnetometers magnetometers (TFMs)(TFMs) which which combines combines a a magnetic magnetic shielding shielding room room (MSR) (MSR) and and a a triaxial triaxial uniform uniform magnetic magnetic fieldfield coilcoil (TUMC)(TUMC) [42[42].]. AsAs describeddescribed above,above, thethe TFMTFM hashas threethree intrinsicintrinsic errors.errors. ToTo date,date, twotwo kindskinds ofof calibrationcalibration methodsmethods areare proposed. proposed. TheThe vectorvector calibrationcalibration methodmethod usesuses aa knownknown vector vector magnetic magnetic field field as as the the reference referenc ande and its accuracyits accuracy is strongly is strongly dependent dependent on the on accuracythe accuracy of the of known the known magnetic magnetic field [field43]. However,[43]. However, the disturbance the disturbance of the environmentalof the environ- magneticmental magnetic field and field the inaccuracy and the inaccuracy of the turntable of the cannotturntable support cannot the support pursuit the of calibration pursuit of ofcalibration fluxgatemagnetometers, of fluxgate magnetometers, so another method, so another the scalarmethod, calibration the scalar method calibration is proposed, method whoseis proposed, accuracy whose is not accuracy dependent is not on dependent the attitude on information.the attitude information. The concept The of theconcept scalar of calibrationthe scalar calibration method was method proposed was as proposed early as the as early 1970s. as Under the 1970s. ideal Under conditions, ideal theconditions, form of thethe TFM form output of the TFM should output be a spherical should be surface. a spherical However, surface. due However, to the existence due to ofthe the existence above threeof the errors, above the three form errors, of the the TFM form output of the will TF changeM output from will a sphere change to from an ellipsoid. a sphere Based to an onellipsoid. the shape Based of the on ellipsoid,the shape the of the magnetometer ellipsoid, the can magnetometer be calibrated can [44]. be calibrated [44]. InIn practicalpractical calibration, calibration, the the accuracy accuracy may may be be affected affected by by the the environmental environmental magnetic magnetic fieldfield [ 45[45,46],46] and and the the intrinsic intrinsic magnetic magnetic impurities impurities in in the the turntable turntable [47 [47,48],48] if theif the turntable turntable is usedis used to tuneto tune the the attitude attitude of the of the magnetic magnetic field. field. The The problem problem of the of environmentalthe environmental magnetic mag- fieldnetic isfield more is more and moreand more serious serious with with the the widely widely used used electronic electronic devices. devices. To To solve solve this this problem,problem, in in this this work, work, the the MSR MSR is is used. used. On On thethe otherother hand,hand, in in somesomeearly early works, works, to to reduce reduce thethe magneticmagnetic fieldfield which which is is originated originated from from the the power power system system of of the the turntable, turntable, they they use use a a manual method to rotate the turntable, but in this way, another problem about the time evolution of the magnetic field emerges because it usually takes more time to tune the turntable manually. To solve this problem, a standard TUMC is used. In Pan’s work,

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Sensors 2021, 21, 1500 7 of 18 manual method to rotate the turntable, but in this way, another problem about the time manual method to rotate the turntable, but in this way, another problem about the time evolution of the magnetic field emerges because it usually takes more time to tune the evolution of the magnetic field emerges because it usually takes more time to tune the turntable manually. To solve this problem, a standard TUMC is used. In Pan’s work, turntable manually. To solve this problem, a standard TUMC is used. In Pan’s work, firstly,firstly, they they constructed constructed the the error error model model of of the the TUMC TUMC and and TFM. TFM. Secondly, Secondly, the the magnetic magnetic firstly, they constructed the error model of the TUMC and TFM. Secondly, the magnetic environmentalenvironmental noise noise model model of of MSR MSR is is added. added. The The most most important important part part of of this this work work is is the the environmental noise model of MSR is added. The most important part of this work is the analysisanalysis of of the the magnetic magnetic field field disturbance disturbance in in MSR MSR and and the the magnetic magnetic field field characteristics characteristics of of analysis of the magnetic field disturbance in MSR and the magnetic field characteristics of TUMCTUMC inin MSR. MSR. Finally, Finally, experiments experiments are are performed performed and and it it is is proved proved that that this this calibration calibration TUMC in MSR. Finally, experiments are performed and it is proved that this calibration methodmethod hashas highhigh sensitivity sensitivity andand accuracy. accuracy. The The schematic schematic diagram diagram and and the the experimental experimental method has high sensitivity and accuracy. The schematic diagram and the experimental picturepicture of of this this method method is is shown shown in in Figures Figures6 6and and7, respectively7, respectively [42 [42].]. picture of this method is shown in Figures 6 and 7, respectively [42].

Figure 6. Schematic diagram of the calibration method of TFMs based on MSR and TUMC. FigureFigure 6. 6. SchematicSchematic diagram diagram of of the the calibration calibration method method of of TFMs TFMs based on MSR and TUMC.

Figure 7. Experimental picture of the device for calibration of TFMs with MSR and TUMC: (a) Test platform; (b) Calibra- Figure 7. Experimental picture ofof thethe devicedevice forfor calibration calibration of of TFMs TFMs with with MSR MSR and and TUMC: TUMC: (a )(a Test) Test platform; platform; (b) ( Calibrationb) Calibra- tion of TUMC; (c) Calibration of TFM. tionof TUMC; of TUMC; (c) Calibration (c) Calibration of TFM. of TFM. 2.3. Sensitivity and Other Related Research Works 2.3.2.3. Sensitivity Sensitivity and and Other Other Related Related Research Research Works Works SensitivitySensitivity isis aa corecore property property of of sensors. sensors. ForFor fluxgatefluxgate magnetometers,magnetometers, itit isis usually usually Sensitivity is a core property of sensors. For fluxgate magnetometers, it is usually expressedexpressed as as the the change change ofof anan outputoutput suchsuch asas voltagevoltage oror timetime differencedifference perper ambientambient field.field. expressed as the change of an output such as voltage or time difference per ambient field. Szewczyk et al. tried to increase the sensitivity of fluxgate sensors produced by the printed circuit board method [15]. The printed circuit board method is proposed to solve the

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Szewczyk et al. tried to increase the sensitivity of fluxgate sensors produced by the printed circuit board method [15]. The printed circuit board method is proposed to solve the prob- problemlem of the of thehigh high cost cost of oftraditional traditional fluxgate fluxgate sensors. sensors. The The high high cost cost of traditional fluxgatefluxgate sensorssensors isis duedue toto thethe largelarge amountamount ofof manualmanual workwork involvedinvolved inin theirtheir production,production, soso thethe printedprinted circuitcircuit boardboard methodmethod cancan reducereduce thethe costcost ofof fluxgatefluxgate sensorssensors efficiently,efficiently,but butat atthe the samesame time,time, thethe sensitivitysensitivity ofof fluxgatefluxgate magnetometersmagnetometers basedbased onon printedprinted circuitcircuit boardsboards isis stronglystrongly reducedreduced [49]. [49]. In In [15], [15], the the authors authors investigated investigated the the feasibility feasibility of increasing of increasing the sen- the sensitivitysitivity by lengthening by lengthening the thecore core and andusing using a magnetic a magnetic flux fluxconcentrator concentrator based based on the on finite the finite element method and open-source software. The magnetic flux concentrator has element method and open-source software. The magnetic flux concentrator has been ap- been applied in many other magnetic sensors to increase the sensitivity [50,51]. Generally plied in many other magnetic sensors to increase the sensitivity [50,51]. Generally speak- speaking, it increases the sensitivity by decreasing the demagnetization field. However, the ing, it increases the sensitivity by decreasing the demagnetization field. However, the per- performance of magnetic flux concentrators based on thin layer fluxgate sensors has never formance of magnetic flux concentrators based on thin layer fluxgate sensors has never been discussed. In this work, it is found that a longer core will effectively increase the sensi- been discussed. In this work, it is found that a longer core will effectively increase the tivity but the effect of the magnetic flux concentrator is very weak, so it is not recommended sensitivity but the effect of the magnetic flux concentrator is very weak, so it is not recom- to use a magnetic flux concentrator in a printed circuit board-based fluxgate magnetometer. mended to use a magnetic flux concentrator in a printed circuit board-based fluxgate mag- To increase the sensitivity of a RTD fluxgate magnetometer, Chen et al. built a sen- netometer. sitivity model for RTD fluxgate magnetometers [16]. The model is clear and simple and To increase the sensitivity of a RTD fluxgate magnetometer, Chen et al. built a sensi- can discuss the sensitivity of the RTD fluxgate and the coercivity of the magnetic core tivity model for RTD fluxgate magnetometers [16]. The model is clear and simple and can separately. When the excitation current is sinusoidal, the sensitivity of the RTD fluxgate sensordiscuss can the be sensitivity written as of the the function RTD fluxgate of coercivity and the of the coercivity magnetic of core the asmagnetic well as amplitudecore sepa- andrately. frequency When the of excitation the driving current field, asis shownsinusoid inal, Equation the sensitivity (5) [52 ]:of the RTD fluxgate sensor can be written as the function of coercivity of the magnetic core as well as amplitude and frequency of the driving field, as shown in Equation (5) [52]:  1 1 ∂RTD 2 = =  Hem + Hem  S  r r , (5) ∂Hx ω  2  2  𝑆= = Hc+Hx + Hc−,H x (5) 1 − 1 − Hem Hem However, as as the the coercivity coercivity of of the the core core is isdependent dependent on on the the driving driving condition condition and and the therelationship relationship between between them them is unknown, is unknown, it is difficult it is difficult to calculate to calculate the sensitivity the sensitivity with Equa- with Equationtion (5). What’s (5). What’s more, more, the thesensitivity sensitivity is isalso also dependent dependent on on the the target target magnetic fieldfield asas shownshown inin FigureFigure8 [8 [16].16]. ItIt cancan bebe seen that only under low target magneticmagnetic fieldfield conditions,conditions, thethe sensitivitysensitivity isis nearlynearly uniformuniform (within(within ±± 1000 nT),nT), soso thethe sensorsensor cancan onlyonly accuratelyaccurately measuremeasure lowlow fieldsfields [[53].53]. InIn Szewczyk’sSzewczyk’s work,work, theythey deduceddeduced thethe expressionexpression ofof sensitivitysensitivity underunder sinusoidalsinusoidal excitationexcitation fromfrom thethe expressionexpression ofof sensitivitysensitivity underunder trilineartrilinear excitationexcitation andand triedtried toto calculatecalculate thethe differentialdifferential permeabilitypermeability µµdd moremore accurately.accurately. Finally,Finally, thethe modelmodel isis verifiedverified byby experiments.experiments. ThisThis workwork separatesseparates thethe investigationinvestigation ofof sensitivitysensitivity ofof RTDRTD fluxgatesfluxgatesand andcoercivity coercivity of of the themagnetic magnetic core. core.It It alsoalso offersoffers aa platformplatform toto furtherfurther investigateinvestigate thethe structurestructure ofof RTDRTD fluxgate fluxgate magnetic magnetic sensors. sensors.

FigureFigure 8.8. RelationshipRelationship betweenbetween sensitivitysensitivity ofof RTDRTD fluxgate fluxgate magnetometer magnetometer and and target target magnetic magnetic field. Becausefield. Because of this of relationship, this relationship, the RTD the fluxgate RTD fluxga magnetometerte magnetometer can only can be only applied be applied in detecting in detect- weak magneticing weak field.magnetic field.

Yang et al. proposed a time domain method to measure current [54]. It is a bidirec- tionally saturated fluxgate based on open-loop self-oscillating technology. The advantage

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Sensors 2021, 21, 1500 9 of 18 Yang et al. proposed a time domain method to measure current [54]. It is a bidirec- tionally saturated fluxgate based on open-loop self-oscillating technology. The advantage of this method is that there is no time delay because the current is estimated by the time ofdifference this method between is that the there first ishalf-cycle no time and delay the because second thehalf-cycle current of is the estimated excitation. by To the obtain time differencea better temperature between the stability, first half-cycle the authors and the used second a nanocrystalline half-cycle of the alloy excitation. core. Finally, To obtain the aperformance better temperature of the method stability, is theconfirmed authors by used experiments a nanocrystalline and the properties alloy core. such Finally, as line- the performancearity and sensitivity of the method are discussed. is confirmed Ramasamy by experiments et al. characterized and the properties the superconducting such as linearity andquantum sensitivity interfere are discussed. device (SQUID)-based Ramasamy et al.time characterized domain electromagnetic the superconducting (TDEM) quantum system interfere[55]. It is devicefound that (SQUID)-based the early time time of th domaine fluxgate electromagnetic magnetometer (TDEM) behaves system like a [combina-55]. It is foundtion of thatinduction the early coil timeand magnetic of the fluxgate field sensor. magnetometer However, behaves at later times, like a combinationit behaves like of a inductionpure magnetic coil and field magnetic sensor. field sensor. However, at later times, it behaves like a pure magnetic field sensor. 3. Applications 3. Applications Because of their high sensitivity and resolution, fluxgate magnetic sensors are widely Because of their high sensitivity and resolution, fluxgate magnetic sensors are widely used in geophysics and astro-observations. Recently, China’s first Mars mission Tianwen-1 used in geophysics and astro-observations. Recently, China’s first Mars mission Tianwen-1 and NASA’s spacecraft Juno both used fluxgate sensors to detect the magnetic field on Mars and NASA’s spacecraft Juno both used fluxgate sensors to detect the magnetic field on Marsand Jupiter. and Jupiter. The unmanned The unmanned aerial aerial vehicles vehicles are al areso used also usedas the as new the newcarrier carrier to perform to perform such suchdetections detections about about Earth’s Earth’s magnetic magnetic field apart field fr apartom the from traditional the traditional carriers carrierssuch as sucha helicop- as a helicopterter aeromagnetic aeromagnetic surveys surveys or a ground or a groundmagnetic magnetic surveys. surveys.

3.1.3.1. AstroAstro ObservationObservation Recently,Recently, China’sChina’s firstfirst MarsMars missionmission Tianwen-1Tianwen-1 waswas lunchedlunched andand MarsMars OrbiterOrbiter Magne- tometertometer (MOMAG)(MOMAG) is one one of of the the seven seven scientific scientific payloads payloads on on it. it. The The project project is isperformed performed by bya team a team from from Chinese Chinese Academy Academy of of Sciences Sciences Ke Keyy Laboratory Laboratory of GeospaceGeospace EnvironmentEnvironment ofof UniversityUniversity ofof ScienceScience andand TechnologyTechnology ofof ChinaChina [56[56].]. TheThe MOMAGMOMAG includesincludes twotwo separateseparate fluxgatefluxgate sensors which which are are fixed fixed on on a aboom boom as as shown shown in inFigure Figure 9 [56].9[ 56 The]. The dual dual magnetom- magne- tometereter structure structure is designed is designed to eliminate to eliminate the theinte interferencerference of the of themagnetic magnetic field field induced induced by the by theorbiter. orbiter. Considering Considering that thatthe distance the distance between between the two the magnetometers two magnetometers (about (about 0.9 m) 0.9 is much m) is muchsmaller smaller compared compared with the with size the of size Mars’s of Mars’s magnetosphere, magnetosphere, so the sodifference the difference of the results of the resultsbetween between the two the magnetometers two magnetometers can be can assumed be assumed to be tosolely be solely due dueto the to theorbiter orbiter and and the thecorresponding corresponding noise. noise. In this In thisway, way, the magnetic the magnetic field field from from the orbiter the orbiter can be can separated be separated from fromthe total the totalmagnetic magnetic field. field. This Thismethod method is firs istly firstly developed developed in the in theVenus Venus Express Express project project in in2006. 2006.

FigureFigure 9.9. The schematic diagram diagram of of Tianwen-1 Tianwen-1 Mars Mars or orbiterbiter and and the the dual-structure dual-structure Mars Mars Orbiter Orbiter MagnetometerMagnetometer onon it.it.

ItIt hashas beenbeen foundfound thatthat therethere isis nono globalglobal magneticmagnetic fieldfield onon MarsMars byby thethe MarsMars GlobalGlobal SurveyorSurveyor (MGS)(MGS) MissionMission inin 1998,1998, butbut twotwo otherother kindskinds ofof magneticmagnetic fieldfield stillstill exist.exist. TheyThey areare thethe magnetospheremagnetosphere producedproduced byby thethe solarsolar windwind andand thethe locallocal strongstrong magneticmagnetic crustalcrustal fieldfield near the southern highlands of Mars. The most important mission of MOMAG is to measure the vector magnetic field of the two sources and the interaction between them. The solar

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near the southern highlands of Mars. The most important mission of MOMAG is to measure the vector magnetic field of the two sources and the interaction between them. The solar wind is a cluster of plasmas running under supersonic speed. It carries the interplanetary magnetic field (IMF) with it. As it cannot pass through Mars, it leaves a magnetosphere around the Mars with the frozen-in IMF. The structure of the magnetosphere is shown in Figure 10 [56]. It mainly includes the bow shock, magnetosheath, magnetic pileup boundary Sensors 2021, 21, 1500 10 of 18 (MPB) and the ionosphere or photoelectron boundary (PEB). The bow shock is the outer- most part of magnetosphere. The solar wind transitions from supersonic to subsonic when it passes through the bow shock. The layer inside the bow shock is the hotter, denser, more windturbulent is acluster magnetosheath of plasmas and running the MPB under is the supersonic lower boundary speed. of It carriesmagnetosheath. the interplanetary The layer magneticinside thefield magnetosheath (IMF) with is it. the As PEB. it cannot It is the pass critical through part Mars, of magnetosphere it leaves a magnetosphere of Mars which aroundseparates the the Mars ions withmostly the from frozen-in the solar IMF. wind The and structure the ions of mostly the magnetosphere from Mars. On is the shown night inside, Figure there 10 is[ a56 magnetic]. It mainly tail. About includes the the magnet bowic shock, crustal magnetosheath, field near the southern magnetic highlands, pileup boundarywe know that (MPB) it is andmuch the stronger ionosphere than orthe photoelectron magnetic field boundary of the Earth. (PEB). It forms The a bow small shock local ismagnetosphere the outermost and part strongly of magnetosphere. affects the magnetic The solar field wind from transitions solar winds from at lower supersonic altitude. to subsonicOn one hand, when it itcan passes protect through the planet the bowsurface shock. from Thethe damage layer inside of electrically the bow shockcharged is par- the hotter,ticles in denser, universe. more On turbulentthe other hand, magnetosheath it can also shield and thethe MPBion escape is the flux lower near boundary the southern of magnetosheath.highlands. The layer inside the magnetosheath is the PEB. It is the critical part of magnetosphereAs the fluxgate of Mars magnetometers which separates do not the perfor ions mostlym absolute from measurement, the solar wind they and need the ionsto be mostlycalibrated from both Mars. on Earth On the and night in-flight. side, thereAfter isthe a measurement, magnetic tail. the About results the need magnetic to be crustalfurther fieldcorrected near theto exclude southern the highlands, various influencing we know thatfactors. it is To much save stronger the limited than power the magnetic of the space- field ofcraft, the the Earth. observation It forms aplan small is also local carefully magnetosphere designed. and Near strongly the periareon affects the and magnetic apoareon, field the frommagnetometer solar winds will at work lower at altitude. the sampling On one frequency hand, it canof 32 protect Hz. In theother planet positions, surface the from magne- the damagetometer ofwill electrically work at the charged sampling particles frequency in universe. of 1 Hz. On On the average, other hand, the magnetometer it can also shield will thedetect ion the escape magnetic flux near field the of Mars’s southern ma highlands.gnetosphere 1.89 kilobits per second.

FigureFigure 10.10. SchematicSchematic diagramdiagram ofof thethe magnetospheremagnetosphere producedproduced byby solar solar wind wind on on Mars. Mars.

AsKotsiaros the fluxgate et al. magnetometersreported the measurement do not perform of Jupiter’s absolute magnetic measurement, field by they the needfluxgate to bemagnetometer calibrated both installed on Earth on the and spinning in-flight. spacecraft After the Juno measurement, [57]. Similar theto Tianwen-1 results need′s design, to be furtherthe fluxgate corrected magnetometer to exclude on the Juno various also uses influencing two independent factors. Tomagnetometers save the limited placed power on a ofbar the of spacecraft,the spacecraft the to observation eliminate the plan effect is also of magnetic carefully field designed. induced Near by the the spacecraft periareon itself. and apoareon,Differently, the Juno magnetometer spins every 30 will s, or work about at two the samplingturns per minute. frequency According of 32 Hz. to Faraday’s In other positions,law of electromagnetic the magnetometer induction will or work Lenz’s at law, thesampling a spinning frequency conductor of in 1 magnetic Hz. On average,field will theinduce magnetometer an edge current will in detect the conductor the magnetic and th fielde edge of Mars’scurrent magnetosphere will in turn generate 1.89 kilobitsan addi- pertional second. magnetic field. This additional magnetic field can be seen as the background noise Kotsiaros et al. reported the measurement of Jupiter’s magnetic field by the fluxgate magnetometer installed on the spinning spacecraft Juno [57]. Similar to Tianwen-1’s design, the fluxgate magnetometer on Juno also uses two independent magnetometers placed on a bar of the spacecraft to eliminate the effect of magnetic field induced by the spacecraft

itself. Differently, Juno spins every 30 s, or about two turns per minute. According to Faraday’s law of electromagnetic induction or Lenz’s law, a spinning conductor in magnetic field will induce an edge current in the conductor and the edge current will in turn generate an additional magnetic field. This additional magnetic field can be seen as the background noise and it will affect the measurement of the Jupiter’s intrinsic magnetic field. According to author’s estimations, the additional magnetic field is about 0.001 Gauss Sensors 2020, 20, x FORSensors PEER 2020 REVIEW, 20, x FOR PEER REVIEW 11 of 18 11 of 18

Sensors 2021, 21, 1500 11 of 18 and it will affectand the measurementit will affect the of measurement the Jupiter’s intrinsic of the Jupite magneticr’s intrinsic field. According magnetic field. to au- According to au- thor’s estimations,thor’s the estimations,additional magnetic the additional field is magnetic about 0.001 field Gauss is about in an 0.001 intrinsic Gauss field in an of intrinsic field of about 3 Gauss. inForabout an fluxgate intrinsic 3 Gauss. sensors, field For offluxgate this about value 3sensors, Gauss. is pretty this For largevalue fluxgate and is pretty sensors,should large not this andbe value ignored. should is pretty not be large ignored. and The authors appliedshouldThe authorsthe not finite be applied ignored.element the method The finite authors element and the applied methodMaxwell the and equations finite the elementMaxwell to quantitatively methodequations and to thequantitatively Maxwell calculate the spinningequationscalculate induced the to quantitativelyspinning magnetic induced field. calculate Thmagneticey also the spinningputfield. up Th aey method induced also put to magnetic upeliminate a method field. this to They eliminate also put this additional field.up additionalThe a methodcorresponding field. to eliminateThe results corresponding this are additionalshown results in Figures field. are shown The 11 and corresponding in 12 Figures [57]. At 11 the and results end 12 [57]. are shownAt the end in of the paper, theyFiguresof alsothe paper, provide11 and they 12 another[57 also] . Atprovide method the end another which of the is method paper, similar they whichto the also is“thin provide similar shell” to another methodthe “thin method shell” which method is to evaluate the similarinducedto evaluate to field. the the “thin induced shell” field. method to evaluate the induced field.

Figure 11. The results of different times of the finite element method used in analyzing the mag- Figure 11. TheFigure results 11. The of different results of times different of the times finite of element the finite method element used method in analyzing used in analyzing the magnetic the fieldmag- caused by the netic field caused by the spinning space craft. spinning spacenetic craft. field caused by the spinning space craft.

Figure 12. Two differentFigureFigure 12. 12.casesTwo Two of different differentthe modulation cases cases of of theresult the modulation modulations. The blue results. oneresult is s.for The The the blue blue case one one with is is for afor the the case case with with a strongera stronger magneticmagneticstronger field in fieldzmagnetic direction in z directionfield while in thez whiledirection yellow the onewhile yellow is thefor one theyellow is case for one with the is case afor stronger withthe case a strongermagnetic with a strongermagnetic magnetic field in field in x-y direction. field in x-y direction.x-y direction.

3.2. Geophysics Observation3.2.3.2. GeophysicsGeophysics Observation Observation Le Maire et al. LeappliedLe MaireMaire a et etfluxgate al. al. applied applied sensor a a fluxgate fluxgatewhich is sensor sensormounted which which on is anis mounted mountedunmanned on on anaerial an unmanned unmanned aerial aerial vehicle (UAV) invehiclevehicle magnetic (UAV)(UAV) mapping in magnetic magnetic [58]. Co mapping mappingmpared with[58]. [58 ].Coother Comparedmpared geophysical with with other mapping other geophysical geophysical meth- mapping mapping meth- ods, magnetic mappingmethods,ods, magnetic has magnetic the mapping advantages mapping has ofthe has mapping advantages the advantages both of large mapping of scale mapping bothobjects large both and largescale small- scaleobjects objects and small- and scale objects withsmall-scalescale the objects same objects instrument.with withthe same the Traditionally, same instrument. instrument. magnetic Traditionally, Traditionally, mapping magnetic is magnetic usually mapping mappingper- is usually is usually per- formed by the performedgroundformed or by airborne by the the ground ground magnetic or or airborne airborne surveying. magnetic magnetic However, su surveying.rveying. there However,is However, a gap of ther there heighte is aa gapgap ofof height height between the groundbetweenbetween and the theairborne ground ground magnetic and and airborne airborne surveying magnetic magnetic because surveying surveying the fixed-wing because because the aircraftthe fixed-wing fixed-wing and aircraft aircraft and and helicopters cannot fly too low for safety reasons. For ground magnetic surveying, its result can be easily affected by the noise from the anthropogenic origin which will affect the

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Sensors 2021, 21, 1500 12 of 18 helicopters cannot fly too low for safety reasons. For ground magnetic surveying, its result can be easily affected by the noise from the anthropogenic origin which will affect the results of airborne magnetic surveying, so the results of ground and airborne magnetic surveying results of airborne magnetic surveying, so the results of ground and airborne magnetic are not easy to relate. However, the demand for continuously measuring the magnetic field surveying are not easy to relate. However, the demand for continuously measuring the of different heights is strong. It is well known that the map obtained by magnetic method magnetic field of different heights is strong. It is well known that the map obtained by can vary by several orders of magnitude according to different distances to the magnetic magnetic method can vary by several orders of magnitude according to different distances origin or different spacing between magnetic profiles. to the magnetic origin or different spacing between magnetic profiles. The recently emerging emerging UAV UAV is is an an ideal ideal solu solutiontion for for this this problem. problem. As As UAVs UAVs can can fly fly at atthe the height height between between ground ground and and 100 100 m, m,it effe it effectivelyctively fills fills the thegap gap of traditional of traditional ground ground and andairborne airborne magnetic magnetic surveying. surveying. Generally, Generally, the UAV the UAV can be can divided be divided into two into types: two types: fixed fixedwing wingand rotary and rotarywing. wing.The fixed The wing fixed UAVs wing have UAVs higher have speed higher and speed larger and range. larger But range. they need But theylarger need plate larger to take plate off and to take land. off On and the land. other On hand, the the other rotary hand, wing the UAVs rotary is wing a new UAVs member is a newof the member family of of UAVs the family used of for UAVs airborne used magnet for airborneism. It magnetism.is smaller and It ismore smaller maneuverable and more maneuverablecomparing with comparing the fixed wing with theUAVs. fixed It wingonly re UAVs.quires It a onlyvery requiressmall plate a very to take small off plate and toland. take But off at and the land. same Buttime, at the the spatial same time, range the of spatialrotary wing range UAV of rotary is also wing smaller UAV (several is also smallerkilometers) (several and the kilometers) speed is andlower the (typically speed is 10 lower m/s). (typically In this work, 10 m/s). as the In rotary this work, wing as UAV the rotaryis used, wing the smaller UAV is and used, lighter the smaller fluxgate and vector lighter magnetometer fluxgate vector is more magnetometer preferrable. is As more the preferrable.fluxgate vector As themagnetometer fluxgate vector does magnetometer not measure the does absolute not measure magnetic the field, absolute it needs magnetic to be field,calibrated it needs before to beusing. calibrated In this beforework, the using. noise In is this mainly work, from the noisethe intrinsic is mainly and from induced the intrinsicmagnetic and field induced of UAV. magnetic field of UAV. The workwork isis performedperformed inin thethe NorthernNorthern VosgesVosges Mountains.Mountains. TheThe geologicalgeological contextcontext isis complex and and many many anthropogenic anthropogenic objects, objects, such such as ashouses, houses, pipelines pipelines and and various various buried buried fer- ferrousrous objects, objects, may may affect affect the the local local magnetic magnetic field. field. This This place place has has been widely investigatedinvestigated because it is the deep drilling projectproject forfor geothermalgeothermal resourceresource prospecting.prospecting. InIn thisthis work,work, thethe magnetic anomaly map ofof groundground (0.8(0.8 m),m), 1.21.2 m,m, 3030 mm andand 100100 mm areare drawn.drawn. TheThe resultsresults ofof 100100 mm afterafter reductionreduction to the pole of ground surveysurvey in the south is shown in Figure 13[ [58].58]. ItIt is superimposed superimposed on on a asatellite satellite image. image. A Ma A Matricetrice 210 210RTK RTK quadcopter quadcopter designed designed by Da by Jiang Da JiangInnovation Innovation (DJI, Shenzhen, (DJI, Shenzhen, China) China) is used is as used shown as shownin Figure in Figure14 [58]. 14 The[58 results]. The resultsof ground of groundsurvey and survey UAVs and are UAVs compared are compared and the comparis and theon comparison with upward with continuation upward continuation is also per- isformed. also performed. It is found that It is both found the that wavelength both the and wavelength amplitude and of the amplitude magnetic of anomaly the magnetic maps anomalyare different maps for aredifferent different altitudes. for different The results altitudes. are consistent The results with are former consistent studies with both former in the studiescrustal scale both (e.g., in the identification crustal scale of (e.g., major identification faults or geological of major contacts) faults or geologicaland local scale contacts) (e.g., andidentification local scale of (e.g., anthropic identification pipes or ofarchaeological anthropic pipes remains). or archaeological remains).

Figure 13. TheThe magnetic magnetic map map obtained obtained by by the the fluxgate fluxgate magnetometer magnetometer on on a UAV a UAV at atthe the height height of of 100100 mm withwith aa satellitesatellite imageimage asas thethe background.background.

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Figure 14. (a) The Matrice 210 RTK quadcopter designed by Da Jiang Innovation (b) and the Bar- FigureFigure 14. (a(a) )The The Matrice Matrice 210 210 RTK RTK quadcopter quadcopter designed designed by Da by Jiang Da Jiang Innovation Innovation (b) and (b )the and Bar- the tington MAG03-MC fluxgate magnetometer (c). The overall weight of the magnetic equipment is tington MAG03-MC fluxgate magnetometer (c). The overall weight of the magnetic equipment is 484 g. Bartington MAG03-MC fluxgate magnetometer (c). The overall weight of the magnetic equipment is 484484 g.g.

3.3. Other Related3.3.3.3. Applications OtherOther RelatedRelated ApplicationsApplications Schoinas et al. SchoinasSchoinasfabricated etet and al.al. fabricated fabricatedcharacterized andand a characterizedcharacterized flexible fluxgate aa flexibleflexible sensor fluxgatefluxgate with pad-printed sensorsensor withwith pad-printedpad-printed solenoid coils [59].solenoidsolenoid Recently, coilscoils [wearable[59].59]. Recently,Recently, intellig wearablewearableent devices intelligentintellig areent a new devicesdevices trend areare in a aconsumer newnew trendtrend daily inin consumerconsumer dailydaily electronic devices.electronicelectronic In this devices.devices. trend, the InIn this thisflexib trend,trend,le sensor thethe flexibleflexib is thele sensorindispsensorensable isis the the indispensable indispcomponent.ensable The component.component. TheThe fluxgate magneticfluxgatefluxgate sensor magneticmagnetic is well sensorsensorknown is isfor wellwell its knownhighknown sensitivity forfor itsits highhigh and sensitivitysensitivity resolution andand for resolutiontheresolution low forfor thethe lowlow magnetic field.magneticmagnetic However, field.field. in consumer However,However, electronic inin consumerconsumer devices, electronicelectronic the high devices,devices, sensitivity thethe highhigh and sensitivitysensitivity resolution and andresolution resolution are not necessary,areare not notso it necessary,necessary, is replaced soso by itit is isother replacedreplaced kinds byby of other othermagnetic kindskinds sensors ofof magnetic magnetic such as sensorssensors anisotropic suchsuch as as anisotropicanisotropic magnetoresistancemagnetoresistancemagnetoresistance (AMR) sensors. (AMR) (AMR) The main sensors. sensors. obst acleThe The formain main wider obst obstacle applicationacle for for wider wider of fluxgateapplication application sen- of fluxgate of fluxgate sen- sor is their complexsensorsor is andtheir is theirexpensive complex complex andfabrication expensive and expensive me thod,fabrication fabricationso a method method, method, that so cana method easily so a method thatfabricate can that easily can fabricate easily fluxgate sensorsfabricatefluxgate in large sensors fluxgate numbers in sensors largeis urgently numbers in large needed, numbersis urgently even is though urgentlyneeded, in even needed,this processthough even inthe though this sensi- process in this the process sensi- tivity and resolutionthetivity sensitivity and may resolution be andlowered. resolution may In bethis lowered. may work, be a lowered.In pad-printing this work, In this a technique pad-printing work, a is pad-printing applied technique to techniqueis applied isto fabricate the solenoidappliedfabricate tocoil the fabricate ofsolenoid the thesensor coil solenoid [60–63].of the coil sensor The of the schematic [60–63]. sensor [The 60diagram– 63schematic]. The and schematic thediagram photo- diagram and the and photo- the graphic view photographicofgraphic the printed view view ofsensor the of printed theare printedshown sensor sensorin Figureare areshown 15 shown [59]. in Figure inThe Figure synthesis 15 15[59].[ 59 Theprocess]. The synthesis synthesis is process process is schematically shownisschematically schematically in Figure shown 16 shown [59]. in After inFigure Figure synt 16 16[59].hesis,[ 59 After ].the After performance synt synthesis,hesis, the of performance the the performance sensor is ofchar- the of sensor the sensor is char- is acterized. The characterized.correspondingacterized. The corresponding Theresults corresponding include resultsthe waveform results include include ofthe the waveform output the waveform voltage of the output of of the the sens- voltage output of voltage the sens- of ing coil, the magnitudetheing sensingcoil, the of the coil,magnitude sensor’s the magnitude ofsecond the sensor’s harmonic of the second sensor’s response harmonic second and th harmonicresponsee sensor andsensitivity. response the sensor and thesensitivity. sensor All the above sensitivity.resultsAll the areabove measured All results the above areunder measured results differe arent under measuredexcitation differe currents. undernt excitation different It is worthcurrents. excitation noting It is currents. worth noting It is that the noise ofworththat the the sensor noting noise is thatof at the a thehigh sensor noise level. is of atThis the a high is sensor due level. to is the atThis ashape highis due of level. tothe the bar This shape sensor is due of whichthe to bar the sensor shape ofwhich the bar sensor which is similar to the case of linear transformer. Additionally, the temperature is similar to theis case similar of linear to the transformer. case of linear Additionally, transformer. the Additionally, temperature the of temperature the sensor is ofalso the sensor is also of the sensor is also measured. It is found that the temperature is dependent on the measured. It ismeasured. found that It the is foundtemperature that the is temperature dependent on is dependentthe strength on and the frequency strength andof frequency of strength and frequency of the excitation current. The highest temperature is 67.2 ◦C which the excitation current.the excitation The hi current.ghest temperature The highest is temperature67.2 °C which is 67.2appears °C which near the appears excitation near the excitation appears near the excitation coils under a 700-mA p-p excitation current at 100 kHz and the coils under a 700-mAcoils under p-p excitationa 700-mA currentp-p excitation at 100 kHzcurrent and at the 100 temperature kHz and the of temperature the sensing of the sensing temperature of the sensing coil is 32.6 ◦C under the same condition. It can be concluded that coil is 32.6 °C undercoil is the32.6 same °C under condition. the same It ca condition.n be concluded It can thatbe concluded the printing that technique the printing is technique is the printing technique is imperfect because the temperature distribution is unsymmetric imperfect becauseimperfect the temperature because the distribution temperature is unsymmetricdistribution is under unsymmetric the same under current. the The same current. The under the same current. The corresponding results are shown in Figure 17[59]. correspondingcorresponding results are shown results in Figure are shown 17 [59]. in Figure 17 [59].

Figure 15. StructureFigure 15. of Structure the printed of fluxgatethe printed magnetometer fluxgate magnet on wearableometer on intelligent wearable device intelligent (a) and device the experimental (a) and picture Figure 15. Structure of the printed fluxgate magnetometer on wearable intelligent device (a) and the experimental picture (b). (b). the experimental picture (b).

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Figure 16. 16. TheThe producing producing process process of ofthe the pr printedprintedinted fluxgate fluxgatefluxgate magnetometer. magnetometer.magnetometer. (a) Printing (a) PrintingPrinting the bottom thethe bottombottom conductive layer;layer; ( b( b) )Printing Printing the the conductive conductive vias; vias; (c) (Printingc) Printing the thebottom bottombottom insulating insulatinginsulating layer; layer;layer; (d) The ((d)) TheThe mounting andand attachmentattachment of of magnetic magnetic core; core; (e )( ePrinting) Printing the the insulating insulatinginsulating walls; walls; (f) Printing (f) PrintingPrinting the top the toptop insulating layer; (g) Printing the top conductive layer. insulating layer; (g) Printing the top conductive layer.

Figure 17. The temperature distribution of the printed fluxgate magnetometer under a certain Figureworking 17. 17. condition. TheThe temperature temperature distribution distribution of ofthe the printe printedd fluxgate fluxgate magnetometer magnetometer under under a certain a certain working condition.

Apart from the fluxgate magnetometer which needs the AC or DC excitation current, Zhou et al. applied a fluxgate magnetometer based on weak magnetic detection technology

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Apart from the fluxgate magnetometer which needs the AC or DC excitation current, Zhou et al. applied a fluxgate magnetometer based on weak magnetic detection technology toto probeprobe the the defects defects of of arbitrary arbitrary orientations orientations in coiled in coiled tubing tubing (CT) (CT) [64]. [Traditionally,64]. Traditionally, mag- magneticnetic flux fluxleakage leakage (MFL) (MFL) testing testing is one is oneof th ofe non-destructive the non-destructive testing testing (NDT) (NDT) methods methods used usedfor detection for detection CT failures CT failures [65–67]. [65 However,–67]. However, it is only it is sensitive only sensitive to circumferentially to circumferentially distrib- distributeduted defects defects and cannot and cannot detect detectaxially axially distribu distributedted defects. defects. The method The method proposed proposed in this inwork this can work effectively can effectively detect the detect defects the in defects any direction. in any direction.It can also distinguish It can also between distinguish dif- betweenferent types different of defects types such of as defects axial, suchcircumfe as axial,rential circumferential and pore type defects. and pore Additionally, type defects. as Additionally,it does not require as it does thenot rotation require ofthe magnetic rotation fie oflds, magnetic the size fields, of the the equipment size of the is equipment relatively issmall. relatively small. TheThe workingworking mechanism of of the the weak weak magnetic magnetic field field detection detection technology technology in defect in defect de- detectiontection is isschematically schematically shown shown in Figure in Figure 18 18[64].[ 64 The]. The mechanism mechanism of the of thetechnology technology is that is that the permeabilities of the workpiece (µ) and the defect (µ0) are usually different. If the the permeabilities of the workpiece (µ) and the defect (µ′) are usually different. If the per- permeability of the defect is higher (µ0 > µ), the curve of magnetic induction intensity B will meability of the defect is higher (µ′ > µ), the curve of magnetic induction intensity B will be be concave as shown on the left bottom panel of Figure 18. If the permeability of the defect concave as shown on the left bottom panel of Figure 18. If the permeability of the defect is is lower (µ0 < µ), the curve of magnetic induction intensity B will be upward as shown on lower (µ′ < µ), the curve of magnetic induction intensity B will be upward as shown on the the right bottom panel of Figure 18. The magnetic induction intensity of every position right bottom panel of Figure 18. The magnetic induction intensity of every position around around the workpiece can be measured by passing a three-dimensional magnetic sensor the workpiece can be measured by passing a three-dimensional magnetic sensor above the above the workpiece. Then, the gradient of magnetic induction intensity with space can be workpiece. Then,∂B Bthe(x+ gradient∆x)−B(x) of magnetic induction∂B intensity with space can be obtained obtained by∆≈ . As ∆x is a constant, and B(x + ∆x) − B(x) should have by ∂x . As∆ x∆𝑥 is a constant, and 𝐵∂𝑥+∆𝑥x 𝐵𝑥 should have the same the same shape∆ but different amplitudes, so the interference between adjacent magnetic anomaliesshape but willdifferent be reduced amplitudes, and this so the is helpful interference to distinguish between theadjacent superimposed magnetic magneticanomalies anomalies.will be reduced In addition, and this comparing is helpful withto distin theguish gradient the ofsuperimposed magnetic induction magnetic intensity anomalies. of the In workpiece,addition, comparing the gradient with of the the gradient geomagnetic of magnet fieldic isinduction much smaller, intensity so of it the can workpiece, suppress the the localgradient background of the geomagnetic gradient field. field If is we much calculate smaller, the so gradient it can suppress of the three the componentslocal background of B (gradientBx, By, B zfield.) in three If we directions calculate (thex, y ,gradientz), then theof the magnetic three components gradient tensor of B G(Bcanx, By be, Bz obtained) in three asdirections Equation (x (6):, y, z), then the magnetic gradient tensor G can be obtained as Equation (6):  ∂2 ϕ ∂2 ϕ ∂2 ϕ   ∂Bx ⎡∂Bx ∂Bx  ⎤ ⎡ m m m ⎤ 2 𝐵 𝐵 𝐵  ∂x ∂y ∂z ⎢∂x ∂x∂y ∂x∂z ⎥ Bxx Bxy Bxz ⎢ ⎥ 2 2 2   ∂By ∂By ∂By  ∂⎢ ϕm ∂ ϕm ∂ ϕm ⎥ 𝐵 𝐵 𝐵 G =  𝐺=⎢  =⎥= == Byx Byy Byz, , (6)(6)  ∂x ∂y ∂z   ∂⎢y∂x ∂y2 ∂y∂z ⎥ B B B  2 2 2  𝐵 𝐵 𝐵 ∂ z ⎢∂z ∂z ⎥ ∂⎢ϕm ∂ ϕm ∂ ϕm⎥ Bzx Bzy Bzz ∂x ∂y ∂z ⎣ ⎦ ∂⎣z∂x ∂z∂y ∂z2 ⎦

wherewhereϕ φmm isis thethe magneticmagnetic scalarscalar potentialpotential andand itsits differentialdifferential withwith spacespace is is the the corresponding corresponding magneticmagnetic induction intensity intensity in in that that direction. direction. BijB (iji, (ji ,=j x=, yx,, zy), arez) are the the components components of the of thetensor tensor in the in thej directionj direction along along the i the axis.i axis. The magnetic The magnetic gradient gradient tensor tensor contains contains the infor- the informationmation of the of defects. the defects. In Zhou’s In Zhou’s work, work,three magnetometers three magnetometers which whichare responsible are responsible for one fordirection one direction (x, y and (x ,zy), andrespectively,z), respectively, are composed are composed orthog orthogonallyonally together together and form and the form tri- theaxial triaxial fluxgate fluxgate sensor. sensor. Similar Similar to Section to Section2.2 of this 2.2 review, of this they review, also theycalibrate also the calibrate zero error, the zeroscale error, error scaleand orthogonal error andorthogonal error of the error triaxial of thesystem. triaxial At system.last, they At applied last, they this appliedmethod thisin experiment method in experimentand found andthat found different that forms different and forms directions and directions of defects of defectscan be candistin- be distinguishedguished effectively. effectively.

Figure 18. The working principle of the weak magnetic detection technology.

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4. Summary and Outlook In the past two years, much progress has been made about lowering the noise, new calibration methods and increasing the sensitivity of fluxgate magnetometers. Fluxgate magnetic sensors have been applied in many new fields and many practical problems solved. In the future, we believe that the following research fields will be productive. Firstly, the work about lowering the noise should focus on the type of noise apart from the Barkhausen noise because after years of effort, the Barkhausen noise has been reduced to a low level. More attention should be paid to the quality of the alloy core because the remanent noise may be due to the magnetostrictive effect of the alloy core. Additionally, the offset drift is also dependent on it. Secondly, due to the lower noise and wider bandwidth, the fundamental mode is a more popular trend comparing with the second harmonic mode. Thirdly, time domain magnetometers such as residence time difference fluxgate magnetometers are a new trend of this field. Fourthly, the most important problem of fluxgate magnetometers in consumption applications is their high cost, so the main target of this field is to reduce the production cost, even though in this process, the sensitivity may be reduced and the noise may be increased to some extent.

Author Contributions: Conceptualization and methodology, Y.Z. and J.P.; writing—original draft preparation, S.W. and X.L.; writing—review and editing, Y.Z., J.P. and H.Z. All authors have read and agreed to the published version of the manuscript. Funding: Y.Z. acknowledged the support by Guangdong Special Support Project (2019BT02X030), Shenzhen Peacock Group Plan (Grant No. KQTD20180413181702403), Pearl River Recruitment Program of Talents (2017GC010293) and National Natural Science Foundation of China (Grant No. 11974298, 61961136006). This work is supported by National Natural Science Foundation of China (No. 61961136001); Innovation Team Project of Department of Education of Guangdong Province (No. 2018KCXTD026). Natural Science Basic Research Program of Shaanxi (No. 2020JQ-344); Fundamental Research Funds for the Central Universities, CHD (No. 300102129302). Data Availability Statement: No new data were created as it is a review paper. Conflicts of Interest: The authors declare no conflict of interest.

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