RU2623192C1 - Method for calibrating electronic magnetic compass - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method for calibrating an electronic magnetic compass comprises the stages, at which the compass is mounted on the plane so that the magnetic field receivers of its orthogonal axes 0X and 0Y lie in this plane, the compass is rotated around the axis 0Z perpendicular to this plane, and is fixed into four, i=1÷4, orthogonal positions, the signals of the magnetic field receivers M_xi and M_yi are measured in each compass position by the axes 0X and 0Y, the static compass errors m_x and m_y are evaluated for each of the compass axes by determining the average values of the signals M_xi and M_yi in all the compass positions:

;

the k-ratio of the compass receiver sensitivities is determined by the axes 0X and 0Y, the axis 0X is combined with the movement direction when using the compass, the signals of the magnetic field receivers B_x and B_y are measured by the axes 0X and 0Y, and the true direction to the manetic pole in the plane X0Y is calculated by the formula: α=arctg[(B_y-m_y)/(k(B_x-m_x)], wherein the k-ratio of the compass receiver sensitivities is calculated by the axes 0X and 0Y as the ratio of the magnetic field vector modules

obtained by using all the measurements on the axis Y and the axis X:

.

EFFECT: increasing the accuracy of calibrating the magnetic compass.

6 dwg

Description

The inventive method of calibration of an electronic magnetic compass (MK) relates to methods for constructing devices used on moving objects. The method can be used mainly for calibrating a pedestrian’s autonomous navigation system, for example, with the aim of increasing the accuracy of determining the azimuth of an object’s movement according to MK data in the absence of signals from global navigation systems (GNS).

Earth's magnetic field can be used to solve navigation problems. However, this field is subject to the influence of numerous disturbing factors [1], including: global and local anomalies, instrumental errors of the equipment, etc.

A significant contribution to the errors of the magnetometers is made by the instrumental errors of the device itself. The measuring signal M coming from any channel of the magnetometer can be represented as

where k is the channel sensitivity coefficient, H is the projection of the magnetic field strength on the corresponding axis, m is the static error of the magnetometer along this axis (M value in the absence of a magnetic field). The problem of magnetometers is that the values of k and m along the axes differ from each other. As a result, when measuring a constant magnetic field and arbitrary rotation of a triaxial magnetometer, the signals M form the surface of an ellipsoid with a center not at the origin. For calibration (determination of unknown parameters of the magnetometer k and m), the obtained measurement results are approximated and the sought quantities are calculated using numerical methods, for example, the least squares method. This procedure is distinguished by high complexity. In many applications, satisfactory calibration accuracy can be achieved by breaking the three-dimensional calibration problem in 0XYZ coordinates into two two-dimensional problems: in the 0XY and 0YZ planes. In some cases, for example, when moving along the surface of the Earth, to determine the azimuth - the direction to the magnetic pole (MP), it is enough to perform a calibration in this plane. However, even for a flat problem, the algorithms known to the authors for calculating the magnetometer parameters are quite complicated.

A known method of calibration [2] of any vector measuring instruments (magnetometers, accelerometers, antenna arrays, etc.), which consists in rotating the instruments at different angles and measuring the corresponding values with the calculation of the required adjustments.

The disadvantage of this method is its high complexity.

A known method of calibrating an electronic magnetic compass [3], which consists in moving it along a specific path and comparing its readings with GNS data.

The disadvantage of this method is the low calibration accuracy due to GNS errors.

A known method of calibrating an electronic magnetic compass [4], which consists in measuring magnetic fields with a large number of magnetometers and the formation of a distorting matrix of the calibrated electronic magnetic compass.

The disadvantage of this method is the high complexity of the calibration.

Closest to the claimed is a method of calibrating an electronic magnetic compass [5], which consists in installing the compass on a plane so that the magnetic field receivers of its orthogonal axes 0X and 0Y lie in this plane, rotate the compass around the 0Z axis perpendicular to this plane and fix it in four, i = 1 ÷ 4, orthogonal positions, in each position of the compass measure the signals of the magnetic field receivers M _xi and M _yi along the axes 0X and 0Y, evaluate the static errors of the compass m _x and m _y along each of the compass axes by definitions the average values of the signals M and M _{yi xi} for all the provisions of the compass:

determine k - the ratio of the sensitivity of the compass receivers along the axes 0X and 0Y, using the ratio:

when using a compass, the 0X axis is combined with the direction of motion, the signals of the magnetic field receivers B _x and B _y are measured along the 0X and 0Y axes and the true direction is determined - α to the magnetic pole in the X0Y plane according to the formula:

The disadvantage of this method is the low accuracy of the calibration, and hence the determination of the true direction, α to the magnetic pole.

The problem solved by the claimed invention is to improve the accuracy of calibration.

, полученных с использованием всех измерений по оси Y и по оси X:To solve this problem, in the method of calibrating the electronic magnetic compass, which consists in installing the compass on a plane so that the magnetic field receivers of its orthogonal axes 0X and 0Y lie in this plane, rotate the compass around the 0Z axis perpendicular to this plane and fix it four, i = 1 ÷ 4 orthogonal positions, in each position of the compass are measured signals of the magnetic field detectors M _xi and M _yi axes 0X and 0Y, evaluate static compass errors m _x and m _y for each of the compass axes by determining the average value th signal M _xi and M _yi over all positions of the compass using, as in [5], the ratio of (2), define k - the ratio of the sensitivities of the compass receivers axis 0X and 0Y, using the compass combine 0X axis with the direction of movement, measure the signals of the magnetic field receivers B _x and B _y along the axes 0X and 0Y and calculate the true direction to the magnetic pole in the X0Y plane, just as in [5], by formula (4), k is the sensitivity ratio of the compass receivers along the 0X and 0Y, calculated as the ratio of the modules of the magnetic field vector

obtained using all measurements along the Y axis and along the X axis:

Thus, a significant difference of the proposed method in comparison with the prototype consists in another method for determining k - the ratio of the sensitivity of the compass receivers along the axes 0X and 0Y, which in the prototype is performed by the ratio (3), and in the claimed method - (5).

The technical result of using the proposed method is to increase the accuracy of calibration of the magnetic compass.

The inventive method is illustrated by the following graphic materials:

на оси координат базиса 0XYZ.FIG. 1. Projections of the magnetic field vector

on the coordinate axis of the basis 0XYZ.

FIG. 2. Calibration schemes for the magnetic compass.

при вычислении азимута α.FIG. 3. Projections of the magnetic field vector

when calculating the azimuth of α.

FIG. 4. Calculation schemes: A) - prototype, B) - of the proposed method.

FIG. 5. Errors in the measurements of the azimuth of the prototype - S1 and the proposed method - S2.

FIG. 6. The scheme of the device that implements the method, where:

1, 2 - field sensors;

3, 4, 5, 6 - integrators;

7 - computer.

Consider the possibility of implementing the proposed method for calibrating an electronic magnetic compass in solving the simplest problem: determining the azimuth of motion when moving along the Earth's surface.

направлен на магнитный полюс. Каждым из датчиков компаса принимают сигналы M_x, M_y и M_z, соответствующие проекциям H_X, H_Y и H_Z вектора

, однако каждый канал принимает их со свойственными именно ему коэффициентом передачи k и статической ошибкой m:The sensors of the triaxial electronic magnetic compass, FIG. 1 are arranged orthogonally in the 0XYZ basis, and the directions of the respective axes are displayed on the compass body. Magnetic field vector

aimed at the magnetic pole. Each of the compass sensors receives signals M _x , M _y and M _z corresponding to the projections H _X , H _Y and H _{Z of the} vector

however, each channel receives them with the transmission coefficient k characteristic of it and the static error m:

M _x = k _x H _x + m _x ,

M _y = k _y H _y + m _y ,

M _z = k _z H _z + m _z .

не меняются. Этот факт можно проверить путем многократного измерения и сравнения значений М_х, М_у и M_z. Будем также считать, что в рассматриваемом случае проекция H_Z не имеет существенного значения.We assume that during calibration the magnitude and direction of the vector

do not change. This fact can be verified by repeatedly measuring and comparing the values of M _x , M _y and M _z . We will also assume that in the case under consideration the projection H _{Z is} not significant.

Set the plane 0XY of the compass parallel to the surface of the Earth, FIG. 2a).

The compass sensors measure the average values of the magnetic field M _x1 and M _y1 in the first position. In the simplest case, the average value of the magnetic field can be obtained as a result of one measurement. However, a valid estimate of the average value allows one to get rid of fluctuations of the magnetic field, measurement errors, etc. To obtain the average value in the analog compass, the input signals M are integrated for a fixed time interval, and in the digital compass, a certain number of input samples are summed. As a result of the measurements, the averaged values are obtained:

Turn the compass 90 ° to the second position, FIG. 2b), and the average values of the magnetic field components are measured in a similar manner:

The next turn of the compass, FIG. 2, c), will give the third position and values:

Finally, the fourth position (90 ° rotation), FIG. 2d), will make it possible to obtain:

Simultaneously with measuring the average values of the magnetic field along the sensitivity axes 0X and 0Y in each of the positions of the compass, the average coordinate values of the field for all positions of the compass are measured. Why integrate the compass coordinate readings obtained from the four stages of calibration in the analog version, or summarize in digital. Adding relations (6), (8), (10) and (12), as well as (7), (9), (11) and (13) along each of the axes 0X and 0Y, it is easy to verify that the average values of the magnetic fields for all compass positions are static compass errors m _x and m _y on each axis, respectively, see relation (2).

на ось 0Х при указанных ее положениях:The sensitive axis of the 0X magnetometer in the first, FIG. 2a), and in the third, FIG. 2c), the provisions are directed in the opposite direction. Therefore, if we subtract (10) from (6) and average, we can eliminate the static error m _{x of the} compass along the 0X axis, and also obtain the projection of the vector

on the axis 0X at its indicated positions:

(M _x1 -M _x3 ) / 2 = k _x H _x .

на ось 0Х при ее ортогональном положении:If you subtract and average the even measurements along the 0X axis, FIG. 2 b) and d), we obtain the projection of the vector

on the axis 0X at its orthogonal position:

(M _x2 -M _x4 ) / 2 = -k _x H _y .

на ось 0Х при ее двух ортогональных положениях, по теореме Пифагора найдем модуль вектора

, полученный с использованием только оси чувствительности магнитометра - 0Х:Knowing the projection of the vector

on the 0X axis at its two orthogonal positions, by the Pythagorean theorem we find the modulus of the vector

obtained using only the sensitivity axis of the magnetometer - 0X:

, полученный с использованием только оси чувствительности магнитометра 0Y:Similarly, the vector modulus can be obtained

obtained using only the sensitivity axis of the 0Y magnetometer:

, полученный выражениями (14) и (15), один и тот же. Следовательно, разделив (15) на (14), получим соотношение (5), которое позволяет оценить k - отношение чувствительностей приемников компаса по осям 0Х и 0Y, причем сами значения коэффициентов чувствительности k_x и k_y не требуются.Module H of the vector

obtained by expressions (14) and (15) is the same. Therefore, dividing (15) by (14), we obtain relation (5), which allows us to estimate the k - ratio of the sensitivities of the compass receivers along the 0X and 0Y axes, and the values of the sensitivity coefficients k _x and k _y themselves are not required.

Calibration results are used as follows. If the axis 0X of the compass, FIG. 3, combine with the direction of motion (ND) of the object and measure the components of the magnetic field B _x and B _y , then the azimuth - the angle α between the 0X axis and the direction to the magnetic pole can be calculated by formula (4). The meaning of this formula is obvious, because involves the correction of the measurement results B _x and B _y by the values of the static error m _x and m _y , and then the normalization of the measurement results using k - the sensitivity ratio of the compass receivers along the 0Y and 0X axes.

Consider in more detail the advantages of the proposed method for calibrating an electronic magnetic compass in comparison with the prototype [5], understanding that any measurements are accompanied by instrumental, methodological and other errors ε, including measurements of the components of the magnetic field M (B) by a magnetometer along the sensitivity axes:

M = kH + m + ε.

As noted above, the main difference between the prototype method and the claimed one are different ratios (3) and (5), used in assessing the sensitivity ratio of the receivers of the magnetic compass k.

The advantages of the proposed method we consider at three levels:

- intuitive;

- mathematical;

- probabilistic-statistical.

Intuitively, the prototype calculation circuit, FIG. 4A), involves at the first stage the determination of the static errors m _x and m _y using relation (2), and at the second, an estimate of the sensitivity ratio of the channels of the magnetic compass k using (3). Thus, the errors in the measurements of the magnetic field M turn into errors of the static errors m _x and m _y , and as a result, the ratio of the sensitivity of the channels of the magnetic compass k is estimated with double errors.

In the inventive method, FIG. 4B), the indicated values using relations (2) and (5) are determined independently, which should reduce errors.

на эту плоскость) может привести к нулевому значению знаменателя в одной из дробей (3), что делает невозможным определить k - отношение чувствительностей приемников компаса по осям 0Х и 0Y.In mathematical terms, in the prototype [5] when calculating by relation (3) with the “unsuccessful” compass orientation during calibration (proximity of the axes 0X or 0Y with the projection of the magnetic field vector

on this plane) can lead to a zero value of the denominator in one of the fractions (3), which makes it impossible to determine k - the ratio of the sensitivities of the compass receivers along the 0X and 0Y axes.

In the claimed method there is no such problem.

From a probabilistic-statistical point of view, it is not possible to obtain confirmation of a higher accuracy of calibration of the proposed method compared to the prototype in the presence of random errors ε by analytical methods because of problems with evaluating the probability characteristics of complex mathematical relationships (2-5). In these conditions, to prove the advantages of the proposed method was used simulation by the Monte Carlo method. It was assumed that the measurements of the magnetic field M are accompanied by random errors ε with zero mathematical expectation, standard deviation σ and normal distribution law. The final result of the calibration is the true direction, α (4), to the magnetic pole in the X0Y plane, with respect to which the estimation was carried out. The simulation was carried out by generating 100,000 realizations of the M measurements with a standard deviation σ of a random measurement error ε relative to the value of M from σ = 0.01 to σ = 0.04 (corresponds to 1% -4% values typical of modern precision magnetic compasses), k _x = 1, k _y = 0.8-1.2 for a wide range of values of the compass installation angles in the horizontal plane during calibration and azimuth α of the compass carrier motion.

As a result of the simulation, it was found that the use of the proposed calibration method provides a uniformly higher accuracy in determining the azimuth α in comparison with the prototype. In FIG. 5, as an example, typical graphs are presented, averaged over 100,000 implementations of the mean square errors S ₁ and S _{2 of} determining the azimuth α using the prototype (S ₁ ) and the proposed method (S ₂ ). It can be seen that S _{2 is} uniformly less than S ₁ .

A diagram of a device implementing the inventive method is shown in FIG. 6. The signals from the sensors 1 (2) of the magnetic field along the X (Y) axes arrive at integrators 3 and 4 (5 and 6), respectively. Integrator 3 (5) determines the average field value at each position of the compass, and integrator 4 (6) determines all four dimensions. The start and end of integration is determined by the control signals from computer 7. The latter saves the values of M _xi , M _yi , m _x and m _y , and also calculates by formula (5) k the degree of instrumental asymmetry of the transmission coefficients k _x and k _{y of} the compass receivers along the X axes and Y. After calibration, the compass is ready to go. When solving navigation problems, FIG. 4, the compass axis X is directed in the direction of travel, the magnetic field components B _x and B _y are measured, and computer 7 calculates the azimuth α according to formula (4).

Thus, the inventive method allows you to calibrate the electronic magnetic compass in one plane by simple means: both by technical implementation and by calculation algorithms.

Information sources

1. Richard B. Langley. Magnetic compass and GPS system, http://www.travelling.lv/en/snarjaga/kompas/compas_gps//.

2. Patent WO 2013188776.

3. Patent RU 2503923.

4. Patent RU 2497139.

5. Patent RU 2572109.

Claims (6)

A method of calibrating an electronic magnetic compass, namely, that the compass is mounted on a plane so that the magnetic field receivers of its orthogonal axes 0X and 0Y lie in this plane, rotate the compass around the 0Z axis perpendicular to this plane, and fix it in four, i = 1 ÷ 4, in orthogonal positions, at each compass position, the signals of the magnetic field receivers M _xi and M _yi are measured along the axes 0X and 0Y, the static errors of the compass m _x and m _y are estimated for each of the compass axes by determining the average values of the signals M _xi and M _yi for all Assumption of the compass:

;

, determine k - the sensitivity ratio of the compass receivers along the 0X and 0Y axes, when using the compass, combine the 0X axis with the direction of motion, measure the signals of the magnetic field receivers B _x and B _y along the 0X and 0Y axes and calculate the true direction to the magnetic pole in the X0Y plane using the formula :

, characterized in that k is the ratio of the sensitivity of the compass receivers along the axes 0X and 0Y is calculated as the ratio of the modules of the magnetic field vector

obtained using all measurements along the Y axis and along the X axis:

.

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