DE19836522A1 - Method to correction course-indicating faults in electronic compasses produced by permanent vertical magnetism of vehicle for vehicle inclination after compensating for course-indicating faults produced by horizontal magnetism - Google Patents

Abstract

The method is performed after compensation for course-indicating faults produced by the horizontal magnetism with the aid of the constancy of the vertical, horizontal or overall Earth's magnetic field strength . Several measurements of the magnetometer , as well as from possible measurement of the inclination of the ship, are made. The vertical magnetism (Rs) of the ship is determined for different inclinations, to correct the course reckoning.

Description

State of the art

Magnetic compasses on ships - even if the following considerations are explicit for Ships are formulated, they also apply to aircraft and land vehicles - have the function of measuring the field of terrestrial magnetism and from that the misleading course (the course related to Earth's magnetic north pole) determine. Classic compasses have a magnetic needle that points towards the aligns magnetic meridians. However, more and more are coming lately electronic magnetic compasses on the strength of the magnetic field in longitudinal and Measure in the transverse direction or in the longitudinal, transverse and vertical directions of the ship and from these measurements with the help of electronic data processing systems Determine course. This is e.g. B. then of importance if because of less favorable magnetic conditions the magnetic compass cannot be set up there, where it is needed for navigation, or if it is missing or failed Gyro compass the magnetic compass as an alternative course reference for the self tax should be used.

Ships generally have a permanent ship-fixed magnetic field that Magnetic compass distracts. In addition, the magnetic field induces the earth in the soft iron a volatile magnetic field that also deflects the compass. With classic compasses, the deflection is caused by the permanent magnet mus compensated by permanent magnets near the compass be brought; the volatile magnetism is caused by near the compass soft iron parts compensated.

Electronic magnetic compasses can, just like the classic compasses such permanent magnets and soft iron parts can be compensated. Sit down but more and more procedures in which the measurement data only after the measurement be corrected arithmetically with the help of a process computer.

For the compensation of the horizontal magnetism (both of the permanent as well as the volatile) a number of procedures already exist, the largest of which Part of the assumption that the ship is at least once through 360 ° on a level keel is rotated. With this rotation (Rundschwojung) certain measurement data determined from which the parameters necessary for the compensation are calculated can.

However, these methods do not take into account the vertical fixed magnetism of the Ship. However, this affects the compass when the ship is heeling (lateral inclination) or stamps (longitudinal inclination). The error that occurs is called Heeling error, its correction is called K compensation. Below is described a method as from several measured values of the probe magnetometer with different positions of the ship the strength of the vertical Ship magnetism determined and then to correct the reading error can be used.  

Presentation of the innovation General

In the following presentation of the inventive concept, the term should continue world of the ship - but it goes without saying that the Results can also be applied to land and aircraft.

The probes of electronic magnetic compasses consist of several magnetometers elements that are oriented in different directions. They are common Probes that are arranged at right angles to each other in the horizontal plane (preferably in the longitudinal and transverse directions of the ship) magnetometer elements have. Also common are probes with three magnetometers, each in one Angles of 120 ° to each other are arranged. If more than two magnetometers in the horizontal plane or the two magnetometers are not in longitudinal and Transversal direction of the ship can be arranged as the compass one Process computer should have, using known methods from their measured values Components of the magnetic field to be measured in the longitudinal and transverse directions of the Calculate ship. The inventive concept further requires that the probe has a magnetometer in the vertical direction. This magnetometer is not exact oriented vertically or is not - as assumed below - down but oriented upwards, the required measurement value can also be easily found to calculate.

A distinction must also be made as to whether the magnetic probe is attached to the vehicle or gimbaled. The gimbal offers the advantage that the Magnetometer in the horizontal plane directly needed for the course calculation Deliver values. On the other hand, the vehicle-fixed attachment has the advantage that none dynamic errors can occur. For example, when cornering centrifugal force from a car is suspended by a gimbaled probe the horizontal position and thereby cause a reading error.

Finally, the invention requires that the ship have at least two Inclination measuring devices has the inclination of the ship in longitudinal and Determine the transverse direction. Again, if more than two inclinometers are present or the inclinometers are not exactly longitudinal and transverse measure, the required values are calculated from these measured values.

Fig. 1 to 3 show the coordinate systems and designations used for the mathematical formulation:

• - The top view is shown in Fig. 1. The vehicle, in this case a ship, is not inclined. The vector of the ship's fixed longitudinal magnetic field receives the designation P _S (positive ahead), the vector of the ship's fixed transverse magnetic field the designation Q _S (positive to starboard). The vector of the ship-fixed vertical magnetic field runs away from the viewer from the plane of the drawing.
• - Fig. 2 shows the side view of the ship. j indicates the longitudinal angle of inclination around the transverse axis and is calculated positively if the bow of the ship points upwards. The vector of the vertical field fixed to the ship is designated R _S ; it is counted positively downwards (thus P _S , Q _S , R _{S result in} a legal system). The vector P _{S of} the ship's fixed longitudinal field can also be seen here, while Q _{S runs} from the plane of the drawing towards the viewer. The components P ' _S and R' _S represent the projections on the horizontal plane and on the vertical, that is, on the original directions in the uninclined state.
• - In Fig. 3 one looks in the longitudinal direction of the ship. i indicates the transverse angle of inclination around the longitudinal axis and is calculated positively when heeling to starboard. Q _S and R _S are in turn the transept and vertical components of the ship's fixed field, Q ' _S and R' _S the projections on the horizontal plane and vertical.

In addition to the ship's fixed magnetic field, the vector of the previously performed compensation of the horizontal field, the measured field at the probe location and the earth's magnetic field, which is ultimately to be reconstructed and from which the missed course (the course in the direction of the magnetic meridian) is to be calculated. So there are:

• - F _S = (P _S , Q _S , R _S ) ^T the permanent magnetic field of the ship at the probe location,
• F _K = (P _K , Q _K , R _K ) ^T the vector of the compensation of the horizontal field,
• F _D = (P _D , Q _D , R _D ) ^T the measurement of the detector,
• - F _E = (P _E , Q _E , R _E ) ^T the earth's magnetic field at the probe location.

Terms without quotation marks refer to the fixed coordinate system tem, designations with inverted commas on the horizontal system in the longitudinal direction of the Ship. Attached indices 1 or 2 refer to two measurements at under different inclination of the ship.

With these names applies:

F _D = F _S + F _K + F _E
F ' _D = F' _S + F ' _K + F' _E (1)

If heeling i and trim j are known, the following applies for the transformation matrix T from the fixed coordinate system F = (P, Q, R) ^T to the horizontal system F '(P', Q ', R') ^T :

F '= TF (2)

With:

The transformation matrix T, which describes a rotation, is "orthogonal", ie the following applies:

This property simplifies some of the following calculations.  

It is always assumed that transept and longitudinal aisle interference fields have been compensated in advance on a flat keel. It therefore applies in all cases:

P _K = -P _S , since the longitudinal component of the ship's field was compensated,
Q _K = -Q _S , since the transverse component of the ship's field was compensated,
R _K = 0 since no K compensation has been carried out. (4)

In the following, nine cases are discussed in detail. These nine cases result from the fact that a distinction is made between three options, how the probe is attached or how the compensation of the horizontal magnetism takes place. On the other hand, three options for K compensation are described. Here are the cases in detail:

• a) The probe is gimbaled, the compensation is fixed to the ship. (This situation exists, for example, if the gimbal-mounted probe is the same as for the Classic magnetic compass with fixed ships nearby Permanent magnet is compensated.)
• b) The probe is mounted fixed to the ship, the compensation is fixed to the ship. (A compensation other than a fixed one would be used for a fixed one Probe make little sense.)
• c) The probe is gimbaled, the compensation acts horizontally. (This is the situation when the compensation is done arithmetically Measured values of the gimbal-mounted probe are always those on flat Keel measured values of longitudinal and transept magnetism subtra here.)

In all three cases, there are three ways to determine the size RS of the vertical ship magnetism:

• 1. The constancy of the vertical earth field is used.
• 2. The constancy of the horizontal earth field is used.
• 3. The constancy of the total earth field is used.

Case a: gimbal-mounted probe, off-board compensation

According to formulas (1) and (2):

Using equation (4):

P _K = -P _S
Q _K = -Q _S
R _K = 0

the first two links on the right side can be summarized:

or advertised:

P ' _D = a ₁₃ .R _S + P' _E ⇒ P ' _E = P' _D - a ₁₃ .R _S
Q ' _D = a ₂₃ .R _S + Q' _E ⇒ Q ' _E = Q' _D - a ₂₃ .R _S
R ' _D = a ₃₃ . R _S + R ' _E ⇒ R' _E = R ' _D - a ₃₃ .R _S (5)

Case a.1:

R ' _{E, 1} = R' _{E, 2}

The vertical component of the earth field is independent of Tilt condition of the ship.

The following applies:

R ' _{D, 1} - a _33.1 .R _S = R' _{D, 2} - a _33.2 .R _s
⇒ (a _33.2 - a _33.1 ) .R _s = R ' _{D, 2} - R' _{D, 1}
⇒ R _S = (R ' _{D, 2} - R' _{D, 1} ) / (a _33.2 - a _33.1 )
⇒ R _S = (R ' _{D, 2} - R' _{D, 1} ) / (cos i ₂ .cos j ₂ - cos j ₁ .cos j ₁ (6)

Case a.2:

P ' _{E, 1} ² + Q' _{E, 1} ² = P ' _{E, 2} ² + Q' _{E, 2} ²

The horizontal component of the earth's field is independent of Tilt condition of the ship.

So the following applies:

(P ' _{D, 1} - a _13.1. R _S ) ² + (Q' _{D, 1} - a _23.1. R _S ) = (P ' _{D, 2} - a _13.2. R _S ) ² + (Q ' _{D, 2} - a _23.2 .R _s ) ²
⇒ (a _13.1 ² + a _23.1 ² ) .R _s ² - 2. (P ' _{D, 1} .a _13.1 + Q' _{D, 1} .a _23.1 ) .R _s + (P ' _D1 ² + Q' _{D, 1} ² )
= (a _13.2 ² + a _23.2 ² ) .R _S ² - 2. (P ' _{D, 2} .a _13.2 + Q _{D, 2} .a _23.2 ) .R _s + (P' _{D, 2} ² + Q ' _{D, 2} ² )
or short:

A1.R _S ² - 2.B ₁ .R _S + C ₁ = A ₂ .R _s ² - 2.B ₂ .R _s + C ₂

With:

A _n = (a _{13, n} ² + a _{23, n} ² ) = (1 - cos ² i _n . Cos ² j _n )
B _n = (P ' _{D, n} .a _{13, n} + Q' _{D, n} .a _{23, n} ) = (-P ' _{D, n} .cos i _n .sin j _n - Q' _{D, n} .sin i _n )
C _n = (P ' _{D, n} ² + Q' _{D, n} ² ) (for n = 1, 2)

It follows:

By selecting the measurements in the various inclination states, the amount of solution can be narrowed so that R _{s is} clear.

Case a.3:

P ' _{E, 1} ² + Q' _E1 ² + R ' _{E, 1} ² = P _{E, 2} ² + Q' _{E, 2} ² + R ' _{E, 2} ²

The total field strength of the earth's field is independent of Tilt condition of the ship.

In this case:

(P ' _{D, 1} - a _13.1 .R _S ) ² + (Q' _{D, 1} - a _23.1 .R _S ) ² + (R ' _{D, 1} - a _33.1 .R _S ) ²
= (P ' _{D, 2} - a _13.2 .R _S ) ² + (Q' _{D, 2} - a _23.2 .R _S ) ² + (R ' _{D, 2} - a _33.2 .R _S ) ^2nd
⇒ A ₁ .R _S ² - 2.B ₁ .R _S + C1 = A ₂ .R _S ² - 2.B ₂ .R _S + C ₂

With:

A _n = (a _{13, n} ² + a _{23, n} ² + a _{33, n} ² ) = 1 (!)
B _n = (P ' _{D, n} .a _{13, n} + Q' _{D, n} .a _{23, n} + R ' _{D, n} .a _{33, n} )
= (-P ' _{D, n} .cos i _n .sin j _n - Q' _{D, n} .sin i _n + R ' _{D, n} .cos i _n . Cos j _n )
C _n = (P ' _{D, n} ² + Q' _{D, n} ² + R ' _{D, n} ² )
(for n = 1, 2)

It follows:

(A2 - A1) .R _s ² - 2. (B ₂ - B ₁ ) .R _s + (C ₂ - C ₁ ) = 0

or because of A ₂ - A ₁ = 1 - 1 = 0:

-2. (B ₂ -B ₁ ) .R _S + (C ₂ - C ₁ ) = 0
⇒ R _s = 1/2. (C ₂ -C ₁ ) / (B ₂ -B ₁ ) (8)

Case b: ship-proof probe, ship-proof compensation

According to formulas (1) and (2):

Using equation (4)

P _K = -P _S
Q _K = -Q _S
R _K = 0

the first two links on the right side can be summarized:

or advertised:

A: = a ₁₁ .P _D + a ₁₂ .Q _D + a ₁₃ .R _D = a ₁₃ .R _S + P ' _E ⇒ P' _E = A - a ₁₃ . R _S
B: = a ₂₁ .P _D + a ₂₂ .Q _D + a ₂₃ .R _D = a ₂₃ .R _S + Q ' _E ⇒ Q' _E = B - a ₂₃ .R _S
C: = a ₃₁ . P _D + a ₃₂ .Q _D + a ₃₃ .R _D = a ₃₃ .R _S + R ' _E ⇒ R' _E = C - a ₃₃ .R _S (9)

Case b.1:

R ' _{E, 1} = R' _{E, 2}

The vertical component of the earth field is independent of Tilt condition of the ship.

So:

C ₁ -a _33.1 .R _S = C ₂ - a _33.2 .R _S
⇒ (a _33.2 - a _33.1 ). R _S = C ₂ - C ₁
⇒R _S = (C ₂ - C ₁ ) / (a _33.2 - a _33.1 ) (10)

Case b.2:

P ' _{E, 1} ² + Q' _{E, 1} ² = P ' _{E, 2} ² + Q' _{E, 2} ²

The horizontal component of the earth's field is independent of Tilt condition of the ship.

The following applies:

(A ₁ - a _13.1 .R _S ) ² + (B ₁ - a _23.1 .R _S) ² = (A ₂ - a _13.2 .R _S ) ² + (B ₂ - a _23.2 .R _S ) ²
⇒ (a _13.1 ² + a _23.1 ² ) .Rs ² - 2. (A ₁ .a _13.1 + B ₁ .a _23.1 ) .R _S + (A ₁ ² + B ₁ ² )
= (a _13.2 ² + a _23.2 ² ) .R _s ² - 2. (A ₂ .a _13.2 + B ₂ .a _23.2 ) .R _S + (A ₂ ² + B ₂ ² )

or short:

D ₁ .R _S ² - 2.E ₁ .R _S + F ₁ = D ₂ .R _S ² - 2.E ₂ .R _S + F ₂

With:

D _n = (a _{13, n} ² + a _{23, n} ² )
E _n = (A _n .a _{13, n} + B _n .a _{23, n} )
F _n = (A _n ² + B _n ² )
(for n = 1, 2)

So:

By selecting the measurements in the different inclination states, the solution set of the quadratic equation can be narrowed down so that R _{s is} unique.

Case b.3:

P ' _{E, 1} ² + Q' _{E, 1} ² + R ' _{E, 1} ² = P' _{E, 2} ² + Q ' _{E, 2} ² + R' _{E, 2} ²

The total field strength of the earth's field is independent of Tilt condition of the ship.

In this case:

(A ₁ - a _13.1 .R _S ) ² + (B ₁ - a _23.1 .R _S ) ² + (C ₁ - a _33.1 .R _S ) ²
= (A ₂ - a _13.2 .R _S ) ² + (B ₂ - a _23.2 .R _S ) ² + (C ₂ - a _33.2 .R _S ) ²
⇒ D ₁ . R _S ² - 2.E ₁ .R _S + F ₁ = D ₂ .R _S ² - 2.E ₂ .R _S + F ₂

With:

D _n = (a _{13, n} ² + a _{23, n} ² + a _{33, n} ² = 1 (!)
E _n = (An.a _{13, n} + Bn.a _{23, n} + Cn.a _{33, n} = R _D (!)
F _n = (A _n ² + B _n ² + C _n ² ) = (P _{D, n} ² + Q _{D, n} ² + R _{D, n} ² ) (!)
(for n = 1, 2)

Because of D ₂ - D ₁ = 1-1 = 0:

-2. (E ₂ - E ₁ ) .R _S + (F ₂ - F ₁ ) = 0
⇒ R _S = 1/2. (F ₂ -F ₁ ) / (E ₂ -E ₁ )
⇒ R _S = 1/2. (P _{D, 2} ² + Q _{D, 2} ² + R _{D, 2} ² - P _{D, 1} ² - Q _{D, 1} ² - R _{D, 1} ² ) / (R _{D, 2} - R _{D, 1} ) (12)

In this case it is not necessary to measure the inclination angles i and j!  

This fact, which at first glance is astonishing, can be done in other ways demonstrate:

Fig. 4 shows the situation after the horizontal ship magnetism has been compensated. From the illustration you can see that the following applies:

(R _D - R _S ) ² + S _D ² = F _E ² = const.

respectively.:

(R _D - R _S ) ² + (P _D ² + Q _D ² ) = F _E ² = const.

With two measurements at different positions of the ship follows:

(R _{D, 1} - R _S ) ² + (P _{D, 1} ² + Q _{D, 1} ² ) = (R _{D, 2} - R _S ) ² + (P _{D, 2} ² + Q _{D, 2} ² )
⇒ R _{D, 1} ² + P _{D, 1} ² + Q _{D, 1} ² - 2.R _{D, 1.} R _S = R _{D, 2} ² + P _{D, 2} ² + Q _{D, 2} ² - 2.R _{D, 2} .R _S
⇒2. (R _{D, 2} - R _{D, 1} ) .R _S = R _{D, 2} ² + P _{D, 2} ² + Q _{D, 2} ² - R _{D, 1} ² - P _{D, 1} ² - Q _{D , 1} ²
⇒R _S = 1/2. (R _{D, 2} ² + P _{D, 2} ² + Q _{D, 2} ² - R _{D, 1} ² - P _{D, 1} ² - Q _{D, 1} ² ) / (R _{D, 2} - R _{D, 1} )

Again, this is equation (12).  

Case c: gimbal-mounted probe, horizontal compensation

The following applies:

As a prerequisite, the longitudinal and transverse fields are already compensated for on an even keel. The values obtained are also used when the ship is tilted. Since it is, according to the invention, a compass with a digital process computer, the components P _S and Q _{S are} known in terms of value and are stored in the system. The following therefore applies:

P ' _K = -P _S
Q ' _K = -Q _S
R ' _K = 0

It follows:

or advertised:

P ' _D = a ₁₁ .P _S + a ₁₂ .Q _S + a _13. R _S - P _S + P' _E ⇒ P ' _E = A - a ₁₃ .R _S
Q ' _D = a ₂₁ .P _S + a ₂₂ .Q _S + a ₂₃ .R _S - Q _S + Q' _E ⇒ Q ' _E = B - a ₂₃ .R _S
R ' _D = a ₃₁ .P _S + a ₃₂ .Q _S + a ₃₃ .R _S - R _S + R' _E ⇒ R _E = C - a ₃₃ .R _S (13)

With:

A = P ' _D - (a ₁₁ - 1) .P _S - a ₁₂ .Q _S
B = Q ' _D - a ₂₁ .P _S - (a ₂₂ -1) .Q _S
C = R ' _D - a ₃₁ .P _S - a ₃₂ .Q _S

Case c.1:

R ' _{E, 1} = R' _{E, 2}

The vertical component of the earth's field is independent of the ship's inclination.

So:

C ₁ - a _33.1 .R _S = C ₂ - a _33.2 .R _S
⇒ (a _33.2 - a _33.1 ). R _S = C ₂ - C ₁
⇒ R _S = (C ₂ - C ₁ ) / (a _33.2 - a _33.1 ) (14)

Case c.2:

P ' _{E, 1} ² + Q' _{E, 1} ² = P ' _{E, 2} ² + Q' _{E, 2} ²

The horizontal component of the earth's field is independent of Tilt condition of the ship.

The following applies:

(A ₁ - a _13.1 .R _S ) ² + (B ₁ - a _23.1 . R _S ) ² = (A ₂ - a _13.2 .R _S ) ² + (B ₂ - a _23.2 .R _S ) ²
⇒ D ₁ .R _S ² - 2.E ₁ .R _S + F ₁ = D ₂ .R _S ² - 2.E ₂ .R _S + F ₂

With:

D = (a _{13, n} ² + a _{23, n} ² )
E _n = (A _n .a _{13, n} + B _n .a _{23, n} )
F _n = A _n ² + B _n ² )
(for n = 1, 2)

The following applies:

The solution set of the quadratic equation can be narrowed down so that R _{S is} unambiguous by selecting the measurements in the different inclination states.

Case c.3:

P ' _{E, 1} ² + Q' _{E, 1} ² + R ' _{E, 1} ² = P' _{E, 2} ² + Q ' _{E, 2} ² + R' _{E, 2} ²

The total field strength of the earth's field is independent of Tilt condition of the ship.

In this case:

(A ₁ - a _13.1 .R _S ) ² + (B ₁ - a _23.1 .R _S ) ² + (C ₁ - a _33.1 .R _S ) ²
= (A ₂ - a _13.2 .R _S ) ² + (B ₂ - a _23.2 .R _S ) ² + (C ₂ - a _33.2 .R _S ) ²
⇒ D ₁ .R _S ² - 2.E ₁ .R _S + F ₁ = D ₂ .R _S ² - 2.E ₂ .R _S + F ₂

With:

D _n = (a _{13, n} ² + a _{23, n} ^2. + a _{33, n} ² ) = 1 (!)
E _n = (A _n .a _{13, n} + B _n .a _{23, n} + C _n .a _{33, n} )
F _n = (A _n ² + B _n ² + C _n ² ) (for n = 1, 2)

Because of D ₂ - D ₁ = 1 - 1 = 0:

-2. (E ₂ - E ₁ ) .R _S + (F ₂ - F ₁ ) = 0
⇒ Rs = 1/2. (F ₂ - F ₁ ) / (E ₂ - E ₁ ) (16).

Practical procedure

The factor R _{S is} calculated during the K compensation. It is also possible to calculate the factor R _S several times in several measurements and then to average the values obtained. This allows measurement errors to be noticed, estimated and reduced.

The procedure shown is also suitable for automatic compensation:

After the process has been initialized by the user, the necessary data (magnetic field and angle of inclination) are measured without further action by the user and the vertical component R _{S of} the ship's field is calculated from them.

Are the horizontal component P 'and Q _{E' E} can then the earth's field are calculated according to the case under consideration.

• - In case a, P ' _E and Q' _{E are determined} from the first two equations of (5). The probe signals and the inclinations i and j are required, which are included in the coefficients a ₁₃ and a _{23 of} the transformation matrix T.
• - In case b, the horizontal components of the earth's field become the first two Equations from (9) determined.
• - In case c, the first two equations of (13) apply.

In all cases, the negative course z 'results from:

z = arctan (Q ' _E / P' _E ) (17)

When determining the arctangent, however, the quadrant in which z 'lies must be observed. To find this quadrant, the signs of P ' _E and Q' _E can be used.

The method shown is also suitable for permanent compensation: the vertical component R _{S of} the ship's fixed magnetic field is determined periodically and compared with the currently valid one. A difference can either replace the old value with the new one. However, an alarm can also be triggered if a set differential limit is exceeded, which informs the user of the error situation.

Claims (22)

1. A method for correcting the course display errors in electronic magnetic compasses caused by the permanent vertical magnetism of the vehicle when the vehicle is tilted, characterized in that after completion of the compensation of the course display errors caused by horizontal magnetism using the constancy of the vertical, horizontal or total strength of the earth's magnetic field The strength of the vertical magnetism R _{S of} the vehicle is determined from several measurements of the magnetometers forming the probe and from possible measurements of the inclination of the vehicle in the case of a different inclination state of the ship and is then used to correct the course calculation. 2. The method according to claim 1, characterized in that the probe consists of three Magnetometers exist in the longitudinal, transverse and vertical directions of the vehicle are aligned. 3. The method according to claim 1, characterized in that three magnetometers are not aligned in the longitudinal, transverse and vertical directions of the vehicle or that more than three magnetometers are used, from whose measured values the Strength of the magnetic field in the longitudinal, transverse and vertical directions of the vehicle can be calculated. 4. The method according to claim 1 to 3, characterized in that the probe is mounted fixed to the vehicle. (In this case, the measured values in the longitudinal, transverse or vertical direction of the vehicle are denoted by P _D , Q _D and R _D. ) 5. The method according to claim 1 to 3, characterized in that the probe is gimbaled. (In this case, the measured values in the longitudinal, transverse or vertical direction of the vehicle are denoted by P ' _D , Q' _D and R ' _D. ) 6. The method according to claim 1 to 5, characterized in that two inclination measuring devices are used which measure the longitudinal or transverse inclination of the vehicle. (In this case, the lateral and longitudinal inclinations of the vehicle are denoted by i and j respectively. Furthermore:
the transformation matrix from the vehicle-fixed to the horizontal coordinate system.) 7. The method according to claim 1 to 5, characterized in that two Inclinometers do not measure the transverse and longitudinal inclinations or that there are more than two inclination measuring devices, of which longitudinal and Bank can be calculated.   8. The method according to claim 1 to 3 and 5 to 7, characterized in that, according to case a, the representation of the innovation, the probe is gimbal-mounted, the compensation of the horizontal field is fixed to the vehicle and the values P ' _E and Q' _E des required for course calculation Earth's magnetism in the longitudinal or transverse direction of the vehicle are determined according to formula (5):
P ' _E = P' _D - a ₁₃ .R _S
Q ' _E = Q' _D - a ₂₃ .R _S 9. The method according to claim 1 to 3 and 5 to 8, characterized in that according to case a1 of the presentation of the innovation for compensation, the constancy of the vertical portion of the earth's magnetism is used in two measurements and the vertical component R _{S of} the vehicle-fixed magnetic field is calculated according to the formula ( 6):
R _S = (R ' _{D, 2} - R' _{D, 1} ) / (a _33.2 - a _33.1 ) 10. The method according to claim 1 to 3 and 5 to 8, characterized in that according to case a2 of the presentation of the innovation for compensation, the constancy of the horizontal portion of the earth's magnetism is used in two measurements and the vertical component RS of the vehicle-fixed magnetic field is calculated according to formula (7 ):
R _{S1 / 2} = [(B₂-B₁) ± √ (B₂ - B₁) ² - (A₂- A₁). (C₂-C₁)] / (A₂- A₁)
With:
A _n = (a _{13, n} ² + a _{23, n} ² )
B _n = (P ' _{D, n} .a _{13, n} + Q' _{D, n} .a _{23, n} )
C _n = (P ' _{D, n} ² + Q' _{D, n} ² )
(for n = 1, 2) 11. The method according to claim 1 to 3 and 5 to 8, characterized in that according to case a3 of the presentation of the innovation for compensation, the constancy of the total field of geomagnetic is used in two measurements and the vertical component R _{S of} the vehicle-fixed magnetic field is calculated according to formula ( 8th):
R _S = 1/2. (C ₂ - C ₁ ) / (B ₂ - B ₁ )
With:
B _n = (P ' _{D, n} .a _{13, n} + Q' _{D, n} .a _{23, n} + R ' _{D, n} .a _{33, n} )
C _n = (P ' _{D, n} ² + Q' _{D, n} ² + R'D, n ² )
(for n = 1, 2) 12. The method according to claim 1 to 4 and 6 to 7, characterized in that according to case b of the presentation of the innovation, the probe is mounted fixed to the vehicle, the compensation of the horizontal field is fixed to the vehicle and the values P ' _E and Q' _E des required for course calculation Earth's magnetism in the longitudinal or transverse direction of the vehicle are determined according to formula (9):
P ' _E = A - a ₁₃ .R _S
Q ' _E = B - a ₂₃ .R _S
With:
A = a ₁₁ .P _D + a ₁₂ .Q _D + a ₁₃ .R _D
B = a ₂₁ .P _D + a ₂₂ .Q _D + a ₂₃ .R _D 13. The method according to claim 1 to 4, 6 to 7 and 12, characterized in that according to case b1 the representation of the innovation for compensation, the constancy of the vertical portion of the earth's magnetism is used in two measurements and the vertical component Rs of the vehicle-fixed magnetic field is calculated according to the formula (10):
R _S = (C ₂ - C ₁ ) / (a _33.2 - a _33.1 )
With:
C _n = a _{31, n} .P _{D, n} + a _{32, n} .Q _{D, n} + a _{33, n} .R _{D, n} (for n = 1, 2) 14. The method according to claim 1 to 4, 6 to 7 and 12, characterized in that according to case b2 the representation of the innovation for compensation, the constancy of the horizontal portion of the earth's magnetism is used in two measurements and the vertical component R _{S of} the vehicle-fixed magnetic field is calculated according to Formula (11):
R _{S1 / 2} = [(E ₂ - E ₁ ) ± √ (E₂ - E₁) ² - (D₂ - D₁). (F₂ - F₁)] / (D₂ - D₁)
With:
A _n = a _{11, n} .P _{D, n} + a _{12, n} .Q _{D, n} + a _{13, n} .R _{D, n}
B _n = a _{21, n} .P _{D, n} + a _{22, n} .Q _{D, n} + a _{23, n} .R _{D, n}
D _n = (a _{13, n} ² + a _{23, n} ² )
E _n = (A _n .a _{13, n} + B _n. A _{23, n} )
F _n = (A _n ² + B _n ² )
(for n = 1, 2) 15. The method according to claim 1 to 4, 6 to 7 and 12, characterized in that according to case b3 the representation of the innovation for compensation, the constancy of the total field of geomagnetic is used in two measurements and the vertical component R _{S of} the vehicle-fixed magnetic field is calculated according to Formula (12):
R _S = 1/2. (R _{D, 2} ² + P _{D, 2} ² + Q _{D, 2} ² - R _{D, 1} ² - P _{D, 1} ² - Q _{D, 1} ² ) / (R _{D, 2} - R _{D, 1} ) 16. The method according to claim 1 to 3 and 5 to 7, characterized in that according to case c the representation of the innovation, the probe is gimbal mounted, the compensation of the horizontal field acts horizontally, the values P _S determined in the compensation of the horizontal magnetism of the vehicle and Q _{S of} the magnetism in the longitudinal or transverse direction of the vehicle have been stored and the values P ' _E and Q' _{E of} the earth magnetism in the longitudinal or transverse direction of the vehicle required for course calculation are determined according to formula (13):
P ' _E = A - a ₁₃ .R _S
Q ' _E = B - a ₂₃ .R _S
With:
A = P ' _D - (a ₁₁ - 1) .P _S - a ₁₂ .Q _S
B = Q ' _D - a ₂₁ .P _S - (a ₂₂ -1) .Q _S
C = R ' _D - a ₃₁ .P _S - a ₃₂ .Q _S 17. The method according to claim 1 to 3, 5 to 7 and 16, characterized in that according to case c1 the representation of the innovation for compensation, the constancy of the vertical portion of the earth's magnetism is used in two measurements and the vertical component R _{S of} the vehicle-fixed magnetic field is calculated according to Formula (14):
R _S (C ₂ - C ₁ ) / (a _33.2 - a _33.1
With:
C _n - R ' _{D, n} - a31, nP _S - a _{32, n} .Q _S (for n = 1, 2) 18. The method according to claim 1 to 3, 5 to 7 and 16, characterized in that according to FaN c2 the representation of the innovation for compensation, the constancy of the horizontal portion of the earth's magnetism is used in two measurements and the vertical component R _{S of} the vehicle-fixed magnetic field is calculated according to Formula (15):
R _{S1 / 2} = [(E ₂ - E ₁ ) ± √ (E₂ - E₁) ² - (D₂ - D₁). (F₂ - F₁)] / (D ₂ - D ₁ )
With:
A _n = P ' _{D, n} - (a _{11, n} - 1) .P _S - a _{12, n} .Q _S
B _n = Q ' _{D, n} - a _{21, n} .P _S - (a _{22, n} - 1) .Q _S
D _n = (a _{13, n} ² + a _{23, n} ² )
E _n = (A _n .a _{13, n} + B _n .a _{23, n} )
F _n = (A _n ² + B _n ² )
(for n = 1, 2) 19. The method according to claim 1 to 3, 5 to 7 and 16, characterized in that according to case c3 the representation of the innovation for compensation, the constancy of the total field of geomagnetic is used in two measurements and the vertical component R _{S of} the vehicle-fixed magnetic field is calculated according to Formula (16):
R _S = ½. (F ₂ - F ₁ ) / (E ₂ - E ₁ )
With:
A _n = P ' _{D, n} - (a _{11, n} - 1) .P _S - a _{12, n} .Q _S
B _n = Q ' _{D, n} - a _{21, n} .P _S - (a _{22, n} - 1) .Q _S
C _n = R ' _{D, n} - a _{31, n} .P _S - a _{32, n} .Q _S
E _n = (A _n .a _{13, n} + B _n .a _{23, n} + C _n .a _{33, n} )
F _n = (A _n ² + B _n ² + C _n ² )
(for n = 1, 2) 20. The method according to claim 1 to 19, characterized in that the vertical component R _{S of} the vehicle-fixed magnetic field is determined several times from a larger number of measurements and then by forming the average of these variables or another statistical method, the value of R used for compensation _{S is} calculated. 21. The method according to claim 1 to 20, characterized in that the method runs automatically, i.e. without user intervention, after the process has been completed the user has been initialized. 22. The method according to claim 1 to 21, characterized in that the calculation of the vertical component R _{S of} the vehicle-fixed field is carried out alternately with the course calculation and that new values of the vertical component R _S differing from the old values replace the old values or to an alarm message to the Guide users.