CA2220346C - Method for determining the direction of the earth's magnetic field - Google Patents
Method for determining the direction of the earth's magnetic field Download PDFInfo
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- CA2220346C CA2220346C CA002220346A CA2220346A CA2220346C CA 2220346 C CA2220346 C CA 2220346C CA 002220346 A CA002220346 A CA 002220346A CA 2220346 A CA2220346 A CA 2220346A CA 2220346 C CA2220346 C CA 2220346C
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C17/00—Compasses; Devices for ascertaining true or magnetic north for navigation or surveying purposes
- G01C17/38—Testing, calibrating, or compensating of compasses
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
- G01V3/40—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation specially adapted for measuring magnetic field characteristics of the earth
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C17/00—Compasses; Devices for ascertaining true or magnetic north for navigation or surveying purposes
- G01C17/02—Magnetic compasses
- G01C17/28—Electromagnetic compasses
Abstract
The invention relates to a process for determining the direction of the earth's magnetic field, which may be subject to interference from magnetic materials in the device and electric currents in the device, by means of an electronic magnetic compass containing three magnetic field sensors and two inclination detecting devices. The electronic magnetic compass is arranged in N different spatial positions, where in each of these N positions the inclination and magnetic field sensor signals are measured and inclinations and magnetic fields determined on the basis of said signals. The value of the earth's magnetic field vector is determined on the basis of said inclinations and magnetic fields by means of the vector equation const - b g = b E sin(i) = g T b E = g T m(b gem-b o) in which b g is the magnetic field component parallel to the gravitation vector g; b E is the length of the magnetic field vector b E; b gem is the measured magnetic field vector; b E is the actual earth's magnetic field vector at the point of measurement; .DELTA.M
is the low-retentivity field distortion, i.e. the magnetism induced by the earth's magnetic field; M is I + .DELTA.M where I is the unit matrix; b o is the hard magnetic stray field vector, is the angle of inclination, where N
must be at least equal to the number of determinant parameters of the vectorial equation.
is the low-retentivity field distortion, i.e. the magnetism induced by the earth's magnetic field; M is I + .DELTA.M where I is the unit matrix; b o is the hard magnetic stray field vector, is the angle of inclination, where N
must be at least equal to the number of determinant parameters of the vectorial equation.
Description
Method for Determining the Direction of the Earth's Magnetic Field Field of the Invention The invention relates to a method for determining the direction of the earth's magnetic field, which may be subject to interference from equipment-related magnetic materials and from magnetic fields generated by electrical currents, said method using an electronic magnetic compass containing three magnetic field sensors and two tilt detection devices..
Related Art US Patent 4 686 772 describes an electronic magnetic compass with which, for example, the heading of a tank can be determined. The tank possesses two iron bodies, namely the turret and the vehicle body, which are relatively movable with respect to each other about a vertical axis. The magnetic compass is arranged in the vehicle body and consists of a non-pendulous triaxial magnetometer outputting electrical magnetic field signals representing the three magnetic field components at the location of the magnetometer. Two tilt sensors are provided outputting electrical signals which represent the pitch angle and roll angle of the vehicle body on which the tilt sensors are mounted. In addition, an angle measuring device is provided for outputting a signal representing the angle of rotation between the two iron bodies. In a memory are stored a plurality of pre-calibrated correction factors for correcting the effect of the magnetic field induced by the vehicle on the measurements of the magnetometer for a plurality of angles of rotation between the two iron bodies. With the help of, a computer, the heading of the tank is calculated in real time from the electrical magnetic field signals and the signals output by the tilt sensors, which are corrected by the stored correction factors for the respective angles of rotation. Before the described magnetic compass can be used, it is necessary to carry out calibration measurements. For this purpose, the vehicle is. located in at least two different planes Which are not parallel to each other. In these positions, while the vehicle body is oriented at different headings, but the turret retains'the same relative heading, the azimuth angle, pitch angle and roll angle are measured. A theodolite, for example, is needed to measure the last-mentioned angles. When performing the calibration, it is required that the geomagnetic field at the measurement location is known. For this purpose, the values for the magnetic inclination and declination of the earth's magnetic field for the respective measurement location are taken from maps.
US Patent 4 539 760 describes an electronic magnetic compass for vehicles, said compass being equipped with three magnetic sensors. These sensors respond to the three orthogonal components of a magnetic field which includes the earth's magnetic field and an additional disturbance field which is associated with the vehicle. The magnetic sensors generate electrical signals corresponding to these components. In addition, tilt sensors respond to the tilt of the vehicle with respect to the horizontal plane. A data processing device and a memory are used to store signals which are derived as calibration correction values from the measurement sensors when the vehicle is rotated through a circle to calibrate the magnetic cori~pass. In order to eliminate the influence of the spurious magnetic field, the data processing device calculates corrected values for the earth's magnetic field at the location of the vehicle once the calibration procedure is completed, taking into account the calibration correction values. Then, proceeding from these corrected values and using the values supplied by the tilt sensors, which are used to define the horizon, the azimuth bearing of the vehicle heading is calculated. When performing the calculations, it is assumed that the correction matrix is symmetrical. This is only very rarely, if at all, the case.
Summary of the Invention The task of the invention is to propose a method for determining the direction of the earth's magnetic field that can be carried out more simply, using an electronic magnetic compass.
A method for determining the direction of the Earth's magnetic field, which may be interfered with by magnetic materials built into equipment and by magnetic fields produced by electric currents, using an electronic magnetic compass which contains three magnetic field sensors and two devices for measuring inclination, the electronic magnetic compass being arranged in N different spatial positions, in each of these N positions, signals of the devices for measuring inclination and signals of the magnetic field sensors being measured and inclination values and magnetic field values being determined from these signals, and on the basis of these inclination values and magnetic field values, the magnitude of the Earth's magnetic field vector being calculated using the vector equation const = b9 = bE sin(i) = gTbE =gTm (bmea-bo) where bg = magnetic field component parallel to the gravitation vector g bE = length of the magnetic field vector bE
bmea measured magnetic field vector =
bE = actual Earth's magnetic field vector at the measuring site DM = magnetically soft field distortion due in part to magnetism induced by the Earth's magnetic field M = I + OM where I = unit matrix m = M-, bo = hard magnetic disturbance field vector i = inclination angle N having to be at least equal to the number of parameters to be determined in the vector equation.
Related Art US Patent 4 686 772 describes an electronic magnetic compass with which, for example, the heading of a tank can be determined. The tank possesses two iron bodies, namely the turret and the vehicle body, which are relatively movable with respect to each other about a vertical axis. The magnetic compass is arranged in the vehicle body and consists of a non-pendulous triaxial magnetometer outputting electrical magnetic field signals representing the three magnetic field components at the location of the magnetometer. Two tilt sensors are provided outputting electrical signals which represent the pitch angle and roll angle of the vehicle body on which the tilt sensors are mounted. In addition, an angle measuring device is provided for outputting a signal representing the angle of rotation between the two iron bodies. In a memory are stored a plurality of pre-calibrated correction factors for correcting the effect of the magnetic field induced by the vehicle on the measurements of the magnetometer for a plurality of angles of rotation between the two iron bodies. With the help of, a computer, the heading of the tank is calculated in real time from the electrical magnetic field signals and the signals output by the tilt sensors, which are corrected by the stored correction factors for the respective angles of rotation. Before the described magnetic compass can be used, it is necessary to carry out calibration measurements. For this purpose, the vehicle is. located in at least two different planes Which are not parallel to each other. In these positions, while the vehicle body is oriented at different headings, but the turret retains'the same relative heading, the azimuth angle, pitch angle and roll angle are measured. A theodolite, for example, is needed to measure the last-mentioned angles. When performing the calibration, it is required that the geomagnetic field at the measurement location is known. For this purpose, the values for the magnetic inclination and declination of the earth's magnetic field for the respective measurement location are taken from maps.
US Patent 4 539 760 describes an electronic magnetic compass for vehicles, said compass being equipped with three magnetic sensors. These sensors respond to the three orthogonal components of a magnetic field which includes the earth's magnetic field and an additional disturbance field which is associated with the vehicle. The magnetic sensors generate electrical signals corresponding to these components. In addition, tilt sensors respond to the tilt of the vehicle with respect to the horizontal plane. A data processing device and a memory are used to store signals which are derived as calibration correction values from the measurement sensors when the vehicle is rotated through a circle to calibrate the magnetic cori~pass. In order to eliminate the influence of the spurious magnetic field, the data processing device calculates corrected values for the earth's magnetic field at the location of the vehicle once the calibration procedure is completed, taking into account the calibration correction values. Then, proceeding from these corrected values and using the values supplied by the tilt sensors, which are used to define the horizon, the azimuth bearing of the vehicle heading is calculated. When performing the calculations, it is assumed that the correction matrix is symmetrical. This is only very rarely, if at all, the case.
Summary of the Invention The task of the invention is to propose a method for determining the direction of the earth's magnetic field that can be carried out more simply, using an electronic magnetic compass.
A method for determining the direction of the Earth's magnetic field, which may be interfered with by magnetic materials built into equipment and by magnetic fields produced by electric currents, using an electronic magnetic compass which contains three magnetic field sensors and two devices for measuring inclination, the electronic magnetic compass being arranged in N different spatial positions, in each of these N positions, signals of the devices for measuring inclination and signals of the magnetic field sensors being measured and inclination values and magnetic field values being determined from these signals, and on the basis of these inclination values and magnetic field values, the magnitude of the Earth's magnetic field vector being calculated using the vector equation const = b9 = bE sin(i) = gTbE =gTm (bmea-bo) where bg = magnetic field component parallel to the gravitation vector g bE = length of the magnetic field vector bE
bmea measured magnetic field vector =
bE = actual Earth's magnetic field vector at the measuring site DM = magnetically soft field distortion due in part to magnetism induced by the Earth's magnetic field M = I + OM where I = unit matrix m = M-, bo = hard magnetic disturbance field vector i = inclination angle N having to be at least equal to the number of parameters to be determined in the vector equation.
Advantageously, the method according to the invention does not require any specific calibration measurements using additional measuring devices. The inputting of special data is also not necessary to prepare the electronic magnetic compass for use. All that is required is to arrange the magnetic compass in various, arbitrarily selected spatial positions. In each of these positions, preferably three magnetic field components are determined. These magnetic field components may be orthogonal to each other if desired, but this is not essential. With the aid of the tilt parameters, i.e. the pitch and roll angles, additionally measured in each spatial position, it is possible to determine the direction of the actual magnetic field vector of the earth's field from the respective magnetic field components.
The method according to the invention does not require that the electronic magnetic compass should be calibrated before it is installed. By means of the method according to the invention not only spurious magnetic fields but also manufacturing tolerances, differences in sensitivity of the sensors, etc.
are taken into account. Thus it is not necessary to use a magnetic compass which has already been pre-calibrated by the manufacturer.
The method according to the invention makes use of the fact that the angle of inclination between the gravitational vector and the earth's magnetic field vector remain constant at the respective fixed location, regardless of the momentary position of the system.
Brief Description of the Drawings Figures are provided as follows to facilitate understanding of the invention.
Fig. 1 is a diagrammatic view of an arrangement of the electronic magnetic compass and of soft and hard magnetic spurious field generators, and Fig. 2 shows the relevant vectors for measuring the earth's magnetic field.
Detailed Description of the Preferred Embodiments As early as in the 19th century, Poisson had 'studied the problem of how to determine the actually existing magnetic field when a magnetometer is mounted in a system which itself possesses magnetic components.
The method according to the invention does not require that the electronic magnetic compass should be calibrated before it is installed. By means of the method according to the invention not only spurious magnetic fields but also manufacturing tolerances, differences in sensitivity of the sensors, etc.
are taken into account. Thus it is not necessary to use a magnetic compass which has already been pre-calibrated by the manufacturer.
The method according to the invention makes use of the fact that the angle of inclination between the gravitational vector and the earth's magnetic field vector remain constant at the respective fixed location, regardless of the momentary position of the system.
Brief Description of the Drawings Figures are provided as follows to facilitate understanding of the invention.
Fig. 1 is a diagrammatic view of an arrangement of the electronic magnetic compass and of soft and hard magnetic spurious field generators, and Fig. 2 shows the relevant vectors for measuring the earth's magnetic field.
Detailed Description of the Preferred Embodiments As early as in the 19th century, Poisson had 'studied the problem of how to determine the actually existing magnetic field when a magnetometer is mounted in a system which itself possesses magnetic components.
Poisson's formula, which describes this situation, states that in such a case the measured magnetic field is a linear function of the actually existing field, and is thus an affine presentation. In this connection, reference is made to the already mentioned US Patent 4 686 772, Column 2, lines 26 to 30.
For the general case, it can be stated that the measured magnetic field is made up of the soft-magnetically distorted magnetic field of the earth at the measurement location, and of a hard magnetic component. The soft magnetically distorted magnetic field of the earth is the magnetism induced by the earth's magnetic field. The hard magnetic component comprises, for example, magnetic fields which are constant at the site of the magnetometer and which are generated by permanent magnets or electrical currents in the system. The hard magnetic component cannot be influenced by a change in the external field.
Mathematically, the aforementioned Poisson formula can be written, in slightly modified form, as follows:
b9ert, = M bE + bo = bE + DM bE + bo ( 1 where b9em = measured magnetic field vector bE = actual earth's magnetic field vector at the measurement location DM = soft magnetic field distortion, i.e. magnetism induced by the earth's magnetic field, where M - I + DM; I = unity matrix bo - hard magnetic components In the foregoing designations and below, the vectors and matrices are shown in bold typeface. The vectors are usually related to a Cartesian system of coordinates. The matrices are in general 3 x 3 matrices.
Figure 1 shows in diagrammatic form that the magnetic compass DMC is mounted in an item of equipment in which the measurements provided by the DMC are influenced by the combined action of permanent magnets, as sources of hard magnetic interference, and of soft magnetic materials.
Figure 2 shows the relevant vectors for measuring the earth's magnetic field and the relevant projections in the horizontal plane. In the case of a magnetic compass fixedly mounted in a vehicle, the aiming direction corresponds to the heading of the vehicle.
The electronic magnetic compass possesses three magnetic field sensors and two tilt sensors; the magnetic field sensors determine three magnetic field components which do not have to be orthogonal to each other.
The permanent magnets and the electric currents generate a fixed field at the location of the magnetic field sensors, and said field is expressed as a shift in the zero point of the coordinate system formed by the magnetic field components.
From an existing field, the soft magnetic materials generate a weakened or strengthened field in the direction of the field and additionally they generate field components in the directions perpendicular thereto. This can be regarded as "interference" between the field directions x, y and z.
The same above equations are also obtained if a magnetometer is considered which possesses three non-orthogonal magnetic field sensors of different sensitivity and a shift in the zero point, for example like a "crude"
magnetometer which has not been calibrated by the manufacturer.
For the general case, it can be stated that the measured magnetic field is made up of the soft-magnetically distorted magnetic field of the earth at the measurement location, and of a hard magnetic component. The soft magnetically distorted magnetic field of the earth is the magnetism induced by the earth's magnetic field. The hard magnetic component comprises, for example, magnetic fields which are constant at the site of the magnetometer and which are generated by permanent magnets or electrical currents in the system. The hard magnetic component cannot be influenced by a change in the external field.
Mathematically, the aforementioned Poisson formula can be written, in slightly modified form, as follows:
b9ert, = M bE + bo = bE + DM bE + bo ( 1 where b9em = measured magnetic field vector bE = actual earth's magnetic field vector at the measurement location DM = soft magnetic field distortion, i.e. magnetism induced by the earth's magnetic field, where M - I + DM; I = unity matrix bo - hard magnetic components In the foregoing designations and below, the vectors and matrices are shown in bold typeface. The vectors are usually related to a Cartesian system of coordinates. The matrices are in general 3 x 3 matrices.
Figure 1 shows in diagrammatic form that the magnetic compass DMC is mounted in an item of equipment in which the measurements provided by the DMC are influenced by the combined action of permanent magnets, as sources of hard magnetic interference, and of soft magnetic materials.
Figure 2 shows the relevant vectors for measuring the earth's magnetic field and the relevant projections in the horizontal plane. In the case of a magnetic compass fixedly mounted in a vehicle, the aiming direction corresponds to the heading of the vehicle.
The electronic magnetic compass possesses three magnetic field sensors and two tilt sensors; the magnetic field sensors determine three magnetic field components which do not have to be orthogonal to each other.
The permanent magnets and the electric currents generate a fixed field at the location of the magnetic field sensors, and said field is expressed as a shift in the zero point of the coordinate system formed by the magnetic field components.
From an existing field, the soft magnetic materials generate a weakened or strengthened field in the direction of the field and additionally they generate field components in the directions perpendicular thereto. This can be regarded as "interference" between the field directions x, y and z.
The same above equations are also obtained if a magnetometer is considered which possesses three non-orthogonal magnetic field sensors of different sensitivity and a shift in the zero point, for example like a "crude"
magnetometer which has not been calibrated by the manufacturer.
The measurement of the magnetic field using such a "crude" magnetometer can be mathematically expressed as follows:
b9em,~ = f. e, bE, + o. % i = x, y, z where f; is the strengthening, e; is the measurement direction, i.e. the unity vector, and o; is the offset of the ith sensor.
If we write f; e; _ (M;,, M;2, M;3) and o; = bo;, we again obtain the above equation (1).
In order to determine the magnitude of the actual magnetic field of the earth, it is necessary to resolve the above vectorial equation ( 1 ) according to bE. By inversion and subtraction, we obtain bE = M' (bgem - bo) = m(bgem - bo) (2) where m = M-' In order to determine the unknown variables M or m = M-' and bo from equation (1 ) or (2), it is possible to use a solution of the type known from US Patent 4 686 772, to which reference has already been made. There it is assumed that, in addition to the measured magnetic field vector b9em, the earth's magnetic field vector bE is also explicitly known in each case. The vectorial equations ( 1 ) and (2) represent a linear equation system for the unknowns M;~ or m;~ and bo; respectively. By conducting measurements in at least four geometrically different positions, and when the earth's magnetic field is known, M;~ and bo; can be obtained directly with the aid of elementary methods to resolve the linear equation systems.
The solution proposed in the above-mentioned US Patent 4 539 760 proceeds from the fact that the value for the earth's magnetic field is independent of the position of the magnetometer. If the variables m;~ and bo have been correctly determined, an earth's magnetic field vector bE is obtained which has the same length whatever the position of the magnetometer. It thus follows that a constant (const) is:
const = b~2 = bETbE = (b9em - bo1'~mTm (b9em ' bo) _ (beam - bolTU (b9e", - bo) (3) where UT = U, which means that U is a symmetrical matrix.
It can immediately be seen that this equation (3y can only be used to calculate the product U = mTm of the sought after matrix m. The elements of this matrix can be calculated only if it is assumed that this matrix is symmetrical and if the diagonal is taken to be positive. The first of these_ assumptions applies, however, only in the rarest of cases, because it would mean a soft magnetic symmetry which is extremely unlikely to exist in technical equipment such as an aircraft or motor vehicle.
According to the invention, the approach employed to determine the parameter bE , i.e. to solve the vector equation, makes use of the fact that in each position of the measuring system at the same geographical location, the angle between the horizontal plane and the earth's magnetic field, i.e.
the inclination angle, remains constant. This obviously then also applies to the angle between the direction of the gravitational vector g and the earth's magnetic field vector bE. We can therefore write:
const =b9 = bESin(i) = grbE = gTm (b9em - bob- (4) where b9 = the magnetic field component parallel to the gravitational vector g b~ = the length of the magnetic field vector bE
and where i is the inclination angle.
_8_ This equation states that the component of the magnetic field vector in the direction of the earth's gravitational field, i.e. perpendicular to the horizontal plane, is the same in all positions of the system.
In this equation, the parameter m occurs linearly and not as a product. The gravitational vector g can be determined with the aid of the tilt sensors.
Therefore, this parameter m can be directly calculated without having to measure the field as is done in the aforementioned US Patent 4 686 772, or without having to presuppose special symmetry conditions as in the aforementioned US Patent 4 539 760.
The number of parameters that need to be determined are as follows:
m = 3x3 = 9 bo = 3 b9 = 1 This results in a total of 9 + 3 + 1 - 13 parameters and at least 13 equations are needed to determine them.
An arbitrary scaling factor can be selected, such as for example is known from the aforementioned US Patent 4 539 760 (column 4, lines 3 ff).
Possible scales could, for example, be selected from the following list:
b9 = const.
m" = const.
m~ ~ + m22 + m33 = const.
mi~2 + m22Z + m332 = const.
m~~2 + m~22 + ... + m332 = const.
det m = const.
Or another suitable scale could be selected in which the constant is also 1.
By selecting the scale, the number of parameters is reduced by 1, so that now only 12 parameters remain for which a corresponding number of _g_ equations are required. When initially calibrating the magnetic compass, 12 different geometrical positions j = 1, ...., 12 are adopted at which the three magnetic field components and the two tilt angles are measured.
A linear equation system is obtained:
b9 = gjTm (b9em,i - bo) = giTm bsem,i - giTUO (5) where uo = m bo and, for example, b9 = 1, which then explicitly gives:
1 = g;, bgem,, m, 1 + 9;. bgem,2 m12 + ...
... + g~~ uo~ + g~2 uo2 + g;3 uos If more than 12 equations are available, the best matching can be achieved here by using, for example, the least squares method, which is generally known.
Within the framework of the invention the possibility also exists to make use of the fact that the angle of inclination or b9 is constant at the same fixed location, together with the fact that the length of the magnetic field vector (bE = ~ bE ~ ) is constant. Expressed differently, this means that not only the above equation (5) but also the equation (3) can be used for the method. Then, the parameter bE must be additionally determined so that the number N of the parameters and thus the necessary measurements can be increased by 1 to N = 13.
Advantageously, by using equations (3) and (5) the available data are better utilized, because each measurement is used in two equations. The number of necessary measurements is thus halved as a result. To implement this method, it is necessary to use an observational calculus, which can be based, for example, on the least squares method.
In the method described below, the above-mentioned equations (3) and (5) are used in a statistically correct manner.
In the following, the relationship that exists between the magnetic field sensor signals,u;j; j = 1, 2, 3 and the earth's magnetic field vector bEj is described in more detail. This relationship can be described by the equation ,uj = ,uo + MbEj + sj ; j = 1, ... N (measurement positions) N1j uj = ,u2j measurements of the 3 magnetic field sensors at position j /U3j uo = ,uoz vector for offset and hard magnetic disturbance field ~03 M11M1zM13 M= M21M2zM23 matrix of the soft magnetic distortion bEj = earth's magnetic field vector Ej - random vector which represents the noise of the sensors < Ej > = 0; < Ej EjT > = Qu213; < Ej EkT > = 0 j ~ k;
< > = expected statistical value The components of the earth's magnetic field bEj are not known in the various positions of the magnetic compass. However, it is possible to demonstrate them partially with the aid of the tilt sensors. The two tilt sensors each measure one component of the vector of the gravitational field which is standardized to 1. This vector runs in the perpendicular direction.
bE~ = s g~ + cr~~
s = sin(i) ; c = cos (i) bE~ ~ = 1 strength of earth's magnetic field = 1 i - angle of inclination of the earth's magnetic field r7~ = cos(a~)e~ +sin(a~)f~ ;
where a~ is the azimuth angle, i.e. the angle of rotation of the sensor's own coordinate system compared with a spatially fixed coordinate system in the horizontal plane.
= gravitational vector ~ g~ ! - 1 9,; ~1-9zi; ~0 9 = gz; ~ e~ _ ( 1-g~~ z)-~r~ -9~;gz; : f; _ ( 1-g~; z) i2 -gs;
9s; -9,;ga; 9z;
g~~, gz~: tilt sensor measurements, g3~ _ ( 1-g,~z - 9z;2)'~Z
The values of the parameters M ~ ~ ... M33, No, ~ Noz~ Nos~ a, ~ ~ ~ arv and i can be determined using a known optimization calculation where, for example, the minimum is required for the statistical sum N
L(M. Not ai ... aN, i) - F (~~ - /ao - MbE~)z j = 1 Various other solutions are possible within the framework of the invention, e.g. using Kalman filters, fuzzy procedures or neuronal networks.
Thus it is apparent that a substantial mathematical simplification can be achieved if the parameter DM = 0. This is the case when no soft magnetic disturbance field needs to be taken into account. M then corresponds to the unity matrix.
In the description given above, reference was made to tilt sensors. Instead of these, two orthogonally mounted encoders can also be used. These would measure angles relative to a reference point. However, in the practical embodiment, it would then be necessary to provide a firmly mounted bracket in relation to which the magnetic compass and the disrupting system would rotate.
It would also be possible to determine the desired tilt angles by means of two rate of rotation sensors, i.e. gyros, attached to the system. The angles of rotation can be derived through integration of the rate of rotation information.
b9em,~ = f. e, bE, + o. % i = x, y, z where f; is the strengthening, e; is the measurement direction, i.e. the unity vector, and o; is the offset of the ith sensor.
If we write f; e; _ (M;,, M;2, M;3) and o; = bo;, we again obtain the above equation (1).
In order to determine the magnitude of the actual magnetic field of the earth, it is necessary to resolve the above vectorial equation ( 1 ) according to bE. By inversion and subtraction, we obtain bE = M' (bgem - bo) = m(bgem - bo) (2) where m = M-' In order to determine the unknown variables M or m = M-' and bo from equation (1 ) or (2), it is possible to use a solution of the type known from US Patent 4 686 772, to which reference has already been made. There it is assumed that, in addition to the measured magnetic field vector b9em, the earth's magnetic field vector bE is also explicitly known in each case. The vectorial equations ( 1 ) and (2) represent a linear equation system for the unknowns M;~ or m;~ and bo; respectively. By conducting measurements in at least four geometrically different positions, and when the earth's magnetic field is known, M;~ and bo; can be obtained directly with the aid of elementary methods to resolve the linear equation systems.
The solution proposed in the above-mentioned US Patent 4 539 760 proceeds from the fact that the value for the earth's magnetic field is independent of the position of the magnetometer. If the variables m;~ and bo have been correctly determined, an earth's magnetic field vector bE is obtained which has the same length whatever the position of the magnetometer. It thus follows that a constant (const) is:
const = b~2 = bETbE = (b9em - bo1'~mTm (b9em ' bo) _ (beam - bolTU (b9e", - bo) (3) where UT = U, which means that U is a symmetrical matrix.
It can immediately be seen that this equation (3y can only be used to calculate the product U = mTm of the sought after matrix m. The elements of this matrix can be calculated only if it is assumed that this matrix is symmetrical and if the diagonal is taken to be positive. The first of these_ assumptions applies, however, only in the rarest of cases, because it would mean a soft magnetic symmetry which is extremely unlikely to exist in technical equipment such as an aircraft or motor vehicle.
According to the invention, the approach employed to determine the parameter bE , i.e. to solve the vector equation, makes use of the fact that in each position of the measuring system at the same geographical location, the angle between the horizontal plane and the earth's magnetic field, i.e.
the inclination angle, remains constant. This obviously then also applies to the angle between the direction of the gravitational vector g and the earth's magnetic field vector bE. We can therefore write:
const =b9 = bESin(i) = grbE = gTm (b9em - bob- (4) where b9 = the magnetic field component parallel to the gravitational vector g b~ = the length of the magnetic field vector bE
and where i is the inclination angle.
_8_ This equation states that the component of the magnetic field vector in the direction of the earth's gravitational field, i.e. perpendicular to the horizontal plane, is the same in all positions of the system.
In this equation, the parameter m occurs linearly and not as a product. The gravitational vector g can be determined with the aid of the tilt sensors.
Therefore, this parameter m can be directly calculated without having to measure the field as is done in the aforementioned US Patent 4 686 772, or without having to presuppose special symmetry conditions as in the aforementioned US Patent 4 539 760.
The number of parameters that need to be determined are as follows:
m = 3x3 = 9 bo = 3 b9 = 1 This results in a total of 9 + 3 + 1 - 13 parameters and at least 13 equations are needed to determine them.
An arbitrary scaling factor can be selected, such as for example is known from the aforementioned US Patent 4 539 760 (column 4, lines 3 ff).
Possible scales could, for example, be selected from the following list:
b9 = const.
m" = const.
m~ ~ + m22 + m33 = const.
mi~2 + m22Z + m332 = const.
m~~2 + m~22 + ... + m332 = const.
det m = const.
Or another suitable scale could be selected in which the constant is also 1.
By selecting the scale, the number of parameters is reduced by 1, so that now only 12 parameters remain for which a corresponding number of _g_ equations are required. When initially calibrating the magnetic compass, 12 different geometrical positions j = 1, ...., 12 are adopted at which the three magnetic field components and the two tilt angles are measured.
A linear equation system is obtained:
b9 = gjTm (b9em,i - bo) = giTm bsem,i - giTUO (5) where uo = m bo and, for example, b9 = 1, which then explicitly gives:
1 = g;, bgem,, m, 1 + 9;. bgem,2 m12 + ...
... + g~~ uo~ + g~2 uo2 + g;3 uos If more than 12 equations are available, the best matching can be achieved here by using, for example, the least squares method, which is generally known.
Within the framework of the invention the possibility also exists to make use of the fact that the angle of inclination or b9 is constant at the same fixed location, together with the fact that the length of the magnetic field vector (bE = ~ bE ~ ) is constant. Expressed differently, this means that not only the above equation (5) but also the equation (3) can be used for the method. Then, the parameter bE must be additionally determined so that the number N of the parameters and thus the necessary measurements can be increased by 1 to N = 13.
Advantageously, by using equations (3) and (5) the available data are better utilized, because each measurement is used in two equations. The number of necessary measurements is thus halved as a result. To implement this method, it is necessary to use an observational calculus, which can be based, for example, on the least squares method.
In the method described below, the above-mentioned equations (3) and (5) are used in a statistically correct manner.
In the following, the relationship that exists between the magnetic field sensor signals,u;j; j = 1, 2, 3 and the earth's magnetic field vector bEj is described in more detail. This relationship can be described by the equation ,uj = ,uo + MbEj + sj ; j = 1, ... N (measurement positions) N1j uj = ,u2j measurements of the 3 magnetic field sensors at position j /U3j uo = ,uoz vector for offset and hard magnetic disturbance field ~03 M11M1zM13 M= M21M2zM23 matrix of the soft magnetic distortion bEj = earth's magnetic field vector Ej - random vector which represents the noise of the sensors < Ej > = 0; < Ej EjT > = Qu213; < Ej EkT > = 0 j ~ k;
< > = expected statistical value The components of the earth's magnetic field bEj are not known in the various positions of the magnetic compass. However, it is possible to demonstrate them partially with the aid of the tilt sensors. The two tilt sensors each measure one component of the vector of the gravitational field which is standardized to 1. This vector runs in the perpendicular direction.
bE~ = s g~ + cr~~
s = sin(i) ; c = cos (i) bE~ ~ = 1 strength of earth's magnetic field = 1 i - angle of inclination of the earth's magnetic field r7~ = cos(a~)e~ +sin(a~)f~ ;
where a~ is the azimuth angle, i.e. the angle of rotation of the sensor's own coordinate system compared with a spatially fixed coordinate system in the horizontal plane.
= gravitational vector ~ g~ ! - 1 9,; ~1-9zi; ~0 9 = gz; ~ e~ _ ( 1-g~~ z)-~r~ -9~;gz; : f; _ ( 1-g~; z) i2 -gs;
9s; -9,;ga; 9z;
g~~, gz~: tilt sensor measurements, g3~ _ ( 1-g,~z - 9z;2)'~Z
The values of the parameters M ~ ~ ... M33, No, ~ Noz~ Nos~ a, ~ ~ ~ arv and i can be determined using a known optimization calculation where, for example, the minimum is required for the statistical sum N
L(M. Not ai ... aN, i) - F (~~ - /ao - MbE~)z j = 1 Various other solutions are possible within the framework of the invention, e.g. using Kalman filters, fuzzy procedures or neuronal networks.
Thus it is apparent that a substantial mathematical simplification can be achieved if the parameter DM = 0. This is the case when no soft magnetic disturbance field needs to be taken into account. M then corresponds to the unity matrix.
In the description given above, reference was made to tilt sensors. Instead of these, two orthogonally mounted encoders can also be used. These would measure angles relative to a reference point. However, in the practical embodiment, it would then be necessary to provide a firmly mounted bracket in relation to which the magnetic compass and the disrupting system would rotate.
It would also be possible to determine the desired tilt angles by means of two rate of rotation sensors, i.e. gyros, attached to the system. The angles of rotation can be derived through integration of the rate of rotation information.
Claims (8)
1. A method for determining the direction of the Earth's magnetic field, which may be interfered with by magnetic materials built into equipment and by magnetic fields produced by electric currents, using an electronic magnetic compass which contains three magnetic field sensors and two devices for measuring inclination, the electronic magnetic compass being arranged in N different spatial positions, in each of these N positions, signals of the devices for measuring inclination and signals of the magnetic field sensors being measured and inclination values and magnetic field values being determined from these signals, and on the basis of these inclination values and magnetic field values, the magnitude of the Earth's magnetic field vector being calculated using the vector equation const = b g = b E sin(i) = g T b E =g T m (b mea-b0) where b g = magnetic field component parallel to the gravitation vector g b E = length of the magnetic field vector b E
b mea = measured magnetic field vector b E = actual Earth's magnetic field vector at the measuring site .DELTA.M = magnetically soft field distortion due in part to magnetism induced by the Earth's magnetic field M = I + .DELTA.M where I = unit matrix m = M-1 b0 = hard magnetic disturbance field vector i = inclination angle N having to be at least equal to the number of parameters to be determined in the vector equation.
b mea = measured magnetic field vector b E = actual Earth's magnetic field vector at the measuring site .DELTA.M = magnetically soft field distortion due in part to magnetism induced by the Earth's magnetic field M = I + .DELTA.M where I = unit matrix m = M-1 b0 = hard magnetic disturbance field vector i = inclination angle N having to be at least equal to the number of parameters to be determined in the vector equation.
2. 'The method according to Claim 1, one of the following scale definitions b g = const.; m11= const.; m11 + m22 + m23 = const.;
m11 2 + m22 2 + m33 2 = const.;
m11 2 + m12 2 +...+ m33 2 = const.; det m = const.;
being selected.
m11 2 + m22 2 + m33 2 = const.;
m11 2 + m12 2 +...+ m33 2 = const.; det m = const.;
being selected.
3. The method according to Claim 1, .DELTA.M = 0 being set if no soft magnetic disturbance field is to be taken into account.
4. The method according to Claim 1, the magnetic field vector being determined with the aid of an optimization calculation if the number N of measurements in the various positions is greater than the number of available equations.
5. The method according to Claim 1, the magnitude of the Earth's magnetic field vector being determined using a statistical optimization method on the basis of the determined inclination values and magnetic field values with additional use of the equation const = b E2 = b E T b E = (b mea-b0) T m T (b mea-b0) b mea = measured magnetic field vector b E = actual Earth's magnetic field vector at the measuring site .DELTA.M = magnetically soft field distortion due in part to magnetism induced by the Earth's magnetic field M = I + .DELTA.M where I = unit matrix m = M-1 b0 = hard magnetic disturbance field vector
6. The method according to any of Claims 1 to 5, inclination sensors being used as devices for measuring inclination.
7. The method according to Claims 1 to 5, rotational speed sensors (gyros) being used for measuring inclination, and the inclination angle being derived by integrating the rotational speed information.
8. The method according to Claims 1 to 5, encoders with which angles are measured relative to a reference point being used as devices for measuring inclination.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DE19609762A DE19609762C1 (en) | 1996-03-13 | 1996-03-13 | Determination of direction of perturbed geomagnetic field by compass |
| DE19609762.2-52 | 1996-03-13 | ||
| PCT/EP1997/000583 WO1997034125A1 (en) | 1996-03-13 | 1997-02-10 | Process for determining the direction of the earth's magnetic field |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2220346A1 CA2220346A1 (en) | 1997-09-18 |
| CA2220346C true CA2220346C (en) | 2005-09-06 |
Family
ID=7788097
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002220346A Expired - Lifetime CA2220346C (en) | 1996-03-13 | 1997-02-10 | Method for determining the direction of the earth's magnetic field |
Country Status (11)
| Country | Link |
|---|---|
| US (1) | US6009629A (en) |
| EP (1) | EP0826137B1 (en) |
| JP (1) | JP3656095B2 (en) |
| KR (1) | KR100429931B1 (en) |
| CN (1) | CN1089433C (en) |
| AT (1) | ATE200571T1 (en) |
| AU (1) | AU703786B2 (en) |
| CA (1) | CA2220346C (en) |
| DE (2) | DE19609762C1 (en) |
| NO (1) | NO323891B1 (en) |
| WO (1) | WO1997034125A1 (en) |
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-
1996
- 1996-03-13 DE DE19609762A patent/DE19609762C1/en not_active Expired - Fee Related
-
1997
- 1997-02-10 AT AT97904399T patent/ATE200571T1/en active
- 1997-02-10 CN CN97190152A patent/CN1089433C/en not_active Expired - Lifetime
- 1997-02-10 JP JP53221997A patent/JP3656095B2/en not_active Expired - Lifetime
- 1997-02-10 CA CA002220346A patent/CA2220346C/en not_active Expired - Lifetime
- 1997-02-10 DE DE59703342T patent/DE59703342D1/en not_active Expired - Lifetime
- 1997-02-10 WO PCT/EP1997/000583 patent/WO1997034125A1/en active IP Right Grant
- 1997-02-10 US US08/945,797 patent/US6009629A/en not_active Expired - Lifetime
- 1997-02-10 AU AU17227/97A patent/AU703786B2/en not_active Expired
- 1997-02-10 EP EP97904399A patent/EP0826137B1/en not_active Expired - Lifetime
- 1997-02-10 KR KR1019970708077A patent/KR100429931B1/en not_active IP Right Cessation
- 1997-11-10 NO NO19975154A patent/NO323891B1/en not_active IP Right Cessation
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US10775450B1 (en) | 2020-03-28 | 2020-09-15 | QuSpin, Inc. | Zero field parametric resonance magnetometer with triaxial sensitivity |
Also Published As
| Publication number | Publication date |
|---|---|
| KR19990014735A (en) | 1999-02-25 |
| WO1997034125A1 (en) | 1997-09-18 |
| KR100429931B1 (en) | 2004-07-16 |
| CN1089433C (en) | 2002-08-21 |
| US6009629A (en) | 2000-01-04 |
| DE59703342D1 (en) | 2001-05-17 |
| JPH11505620A (en) | 1999-05-21 |
| EP0826137B1 (en) | 2001-04-11 |
| NO323891B1 (en) | 2007-07-16 |
| EP0826137A1 (en) | 1998-03-04 |
| NO975154D0 (en) | 1997-11-10 |
| AU703786B2 (en) | 1999-04-01 |
| NO975154L (en) | 1998-01-09 |
| CA2220346A1 (en) | 1997-09-18 |
| AU1722797A (en) | 1997-10-01 |
| CN1181808A (en) | 1998-05-13 |
| DE19609762C1 (en) | 1997-04-03 |
| ATE200571T1 (en) | 2001-04-15 |
| JP3656095B2 (en) | 2005-06-02 |
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