RU2577806C1 - Method of calibrating accelerometric three-axis inclinometer - Google Patents

Abstract

FIELD: test and measurement equipment.

SUBSTANCE: invention relates to metrological equipment - calibrated inclinometers based on three-axis accelerometer. Method suggests measurement of gravity acceleration vector projections $$\overline{\text{G}}$$

on the axis of the accelerometer during its rotation around two axes, each time in four orthogonal positions. Static error is determined based on measurement results of each axis and the ratio of coefficients of sensitivity along two pairs of axes. When using inclinometer the accelerometer is set on investigated object, gravity acceleration vector projections are measured $$\overline{\text{G}}$$

on the axis of the accelerometer, compensating for their static error, normalizing differences in sensitivity axes of accelerometer and calculating object inclination angles by simple relationships relative to gravity acceleration vector $$\overline{\text{G}}$$

.

EFFECT: technical result consists in simplification of the method of calibrating accelerometric three-axis inclinometer.

1 cl, 3 dwg

Description

The invention relates to metrological support - the calibration of inclinometers made on the basis of a three-axis accelerometer. Such inclinometers can be used in geophysical works, autonomous navigation devices and other tasks. A distinctive feature of the claimed invention is the simplicity and low cost of implementation.

Accelerometer measurements along the sensitivity axes can be represented as:

Where:

A is the result of measuring acceleration by an accelerometer along the sensitivity axis;

на ось чувствительности;G is the actual value of the projection of the gravitational acceleration vector $$\overline{\text{G}}$$

on the axis of sensitivity;

k - axis sensitivity coefficient of the accelerometer;

m is the static error of the accelerometer along the axis (readings of the accelerometer in the absence of gravity).

также изменяется в зависимости от места, высоты измерений и других факторов. Указанные обстоятельства не позволяют достоверно оценить и использовать результаты измерений акселерометра. У трехосевого акселерометра величины k и m по осям различны, что еще более усложняет задачу инклинометра - определение углов наклона объекта исследования. В заявляемом изобретении предлагается простой способ решения этой задачи, применимый в любых условиях.The values of k and m are generally unknown, but can be determined during calibration in the factory or laboratory conditions. However, these characteristics change over time and depend on the conditions of use. The magnitude of the gravitational acceleration vector $$\overline{\text{G}}$$

also varies depending on location, measurement height and other factors. These circumstances do not allow to reliably evaluate and use the results of measurements of the accelerometer. For a three-axis accelerometer, the values of k and m along the axes are different, which further complicates the task of the inclinometer - determining the angle of inclination of the object of study. The claimed invention provides a simple way to solve this problem, applicable in any conditions.

Known methods for calibrating inclinometers [1], [2] and many others, consisting in the fact that calibrated inclinometers are installed in special manual or automated installations that provide rotation of the tested device at certain angles. Results are compared with reference measurements. If necessary, the inclinometer is calibrated by taking measurements while rotating the device with the selected step.

The disadvantages of such methods are the high cost of the equipment and the complexity.

A known method for determining the scale factor of the accelerometer [3], which consists in the fact that the accelerometer is rotated around the axis by positive and negative angles and evaluate the difference of the received signals. This technique eliminates the static measurement error m.

известна не точно.The disadvantage of this method is the difficulty of determining the sensitivity coefficient, since the magnitude of the gravitational acceleration vector $$\overline{\text{G}}$$

not exactly known.

, предпочтительно под углом 90°, калибруют вторую ось акселерометра, для чего вращают его вокруг первой оси, фиксируют в четырех, i=1÷4, ортогональных положениях, в каждом из которых измеряют проекции A_2i вектора гравитационного ускорения $$\overline{\text{G}}$$

на вторую ось акселерометра, вычисляют статическую ошибку акселерометра по второй оси m₂ путем усреднения измерений проекций вектора гравитации на эту ось:Closest to the claimed method is a method for determining the angle of inclination by a three-axis, j = 1 ÷ 3, accelerometer [4], which consists in the fact that the accelerometer is set so that its first axis, selected as the axis of rotation, intersects with the gravitational acceleration vector $$\overline{\text{G}}$$

, preferably at an angle of 90 °, calibrate the second axis of the accelerometer, for which they rotate it around the first axis, fix in four, i = 1 ÷ 4, orthogonal positions, in each of which projections A _2i of the gravitational acceleration vector are measured $$\overline{\text{G}}$$

on the second axis of the accelerometer, calculate the static error of the accelerometer along the second axis m ₂ by averaging the measurements of the projections of the gravity vector on this axis:

Method [4] involves the following calibration procedure.

, ось 2 имеет угол α с вектором гравитационного ускорения $$\overline{\text{G}}$$

, а его проекция на эту ось G₂₁=Gcos(α). Тогда в соответствии с (1) в этом положении акселерометр измерит величину:In FIG. 1 shows the axes 1, 2 and 3 of a three-axis accelerometer. The axis of rotation 1 is perpendicular to the plane of the figure and the gravitational acceleration vector $$\overline{\text{G}}$$

axis 2 has an angle α with a gravitational acceleration vector $$\overline{\text{G}}$$

, and its projection on this axis is G ₂₁ = Gcos (α). Then, in accordance with (1) in this position, the accelerometer will measure:

When the axes of the accelerometer 2 and 3 are rotated around axis 1 by 180 °, FIG. 1C, the second axis accelerometer will measure:

Since G ₂₃ = -G ₂₁ , (see Fig. 1A and C), we obtain:

Similar results will be obtained with rotations of ± 90 ° relative to the initial position, FIG. 1B and D:

It is taken into account that G ₂₄ = -G ₂₂ .

The addition of the measurement results A _2i for all four, i = 1 ÷ 4, the positions of the axes allows you to get the average value of the static error of the second axis:

. В противном случае в качестве вектора $$\overline{\text{G}}$$

следует использовать его проекцию на плоскость 23 с ухудшением точности.It is important to note that the measurement results are most accurate for values of the angle α close to 45 °. In addition, as shown in [4], the most accurate result will be obtained if axis 1 is perpendicular to the vector of gravitational acceleration $$\overline{\text{G}}$$

. Otherwise, as a vector $$\overline{\text{G}}$$

should use its projection on the plane 23 with a deterioration in accuracy.

In [4], it was proposed to calibrate the axes in turn, however, it is obvious that the calibration procedure described above can be carried out simultaneously for axes 2 and 3 to obtain a static error of the third axis m ₃ .

известна не точно, что не позволяет получить искомые коэффициенты.To determine the sensitivity coefficients k _j along the axes in [4], it is proposed to use relation (1), however, as noted above, the magnitude of the gravitational acceleration vector $$\overline{\text{G}}$$

not known exactly, which does not allow us to obtain the desired coefficients.

Thus, the disadvantage of the method [4] is the low accuracy of determining the sensitivity coefficients along the axes of the accelerometer, and therefore, the low accuracy of determining the angle of inclination of the object.

The problem solved by the claimed invention is the creation of a simple and cheap method of calibrating a three-axis accelerometer to determine the angle of inclination of the object with an inclinometer.

на все оси акселерометра, устраняют статические ошибки измерений по каждой оси, нормируют измерения по всем осям с использованием относительных коэффициентов чувствительности, вычисляя углы α_j между осями чувствительности акселерометра и вектором гравитационного ускорения $$\overline{\text{G}}$$

(углы наклона).To solve this problem, simultaneously with the second axis, the third axis of the accelerometer is similarly calibrated with its static error m ₃ calculated, the relative k ₃₂ is the sensitivity coefficient of the third k ₃ and second k ₂ axes of the accelerometer, then the accelerometer is set so that it is selected as its axis a second rotation axis, and acting similarly calculated static error m the first axis ₁ and the relative k ₃₁ - k coefficient of the sensitivity of the third ₃ and k ₁ of the first axes accelerometer mounted in practical measurements rebuemoe position measured projection vectors B _j gravitational acceleration $$\overline{\text{G}}$$

on all axes of the accelerometer, eliminate static measurement errors on each axis, normalize measurements on all axes using relative sensitivity coefficients, calculating the angles α _j between the sensitivity axes of the accelerometer and the gravitational acceleration vector $$\overline{\text{G}}$$

(tilt angles).

Significant differences of the proposed method in comparison with the prototype are:

Simultaneously with the calibration of the second axis of the accelerometer, the third axis of the accelerometer is similarly calibrated with the calculation of its static error m ₃ . This speeds up the calibration process.

In the prototype, the axes are calibrated in turn.

в этой плоскости.Calculation of the relative k ₃₂ = k ₃ / k ₂ sensitivity coefficient of the third and second axes of the accelerometer allows us to evaluate the degree of difference, subsequently align their sensitivity and, due to this, accurately determine the orientation of the gravity vector $$\overline{\text{G}}$$

in this plane.

Calibration of the accelerometer using the second axis as the axis of rotation allows you to determine the static error of the first axis m ₁ and the relative k ₃₁ = k ₃ / k ₁ sensitivity coefficient of the third and first axes. As a result, this allows you to calibrate the accelerometer in all axes with the receipt of static errors and relative sensitivities of all axes.

и его проекций на оси.The prototype makes an unsuccessful attempt to determine the sensitivity k of all axes separately, using inaccurate values of the gravitational acceleration vector $$\overline{\text{G}}$$

and its projections on the axis.

на все оси акселерометра устраняют статические ошибки измерений по каждой оси, нормируют измерения по всем осям и вычисляют углы наклона α_j осей чувствительности акселерометра к вектору гравитационного ускорения $$\overline{\text{G}}$$

.In practical measurements, after installing the accelerometer in the required position and measuring the projections B _j of the gravitational acceleration vector $$\overline{\text{G}}$$

on all axes of the accelerometer eliminate static measurement errors on each axis, normalize the measurements on all axes and calculate the tilt angles α _j of the sensitivity axes of the accelerometer to the gravitational acceleration vector $$\overline{\text{G}}$$

.

In the prototype, it is possible to compensate only for the static error of the accelerometer.

.Thus, the main difference of the proposed method in comparison with analogues known to the authors is that due to the obtained relations, there is no need to determine not only the k coefficients - sensitivity along the axes of the accelerometer, but also the gravity vector itself $$\overline{\text{G}}$$

.

The invention is illustrated by the following graphic materials.

на оси 2 и 3 акселерометра при вращении плоскости 23.FIG. 1 - projection of the gravitational acceleration vector $$\overline{\text{G}}$$

on the axis 2 and 3 of the accelerometer while rotating the plane 23.

на оси 1, 2 и 3 акселерометра при практических измерениях углов наклона.FIG. 2 - projections of the gravitational acceleration vector $$\overline{\text{G}}$$

on the axes 1, 2 and 3 of the accelerometer for practical measurements of tilt angles.

FIG. 3 - tilt angles of the object relative to the horizon plane.

Consider the possibility of implementing the proposed method.

, т.е. ось не должна совпадать с вектором $$\overline{\text{G}}$$

. На практике предпочтительно, чтобы первая ось была перпендикулярна вектору гравитационного ускорения $$\overline{\text{G}}$$

и лежала в плоскости местного горизонта. Данное требование не является категоричным. Если первая ось имеет угол наклона α₁, отличный от 90°, то проекция вектора гравитационного ускорения $$\overline{\text{G}}$$

на плоскость 23 составит Gsin(α₁). Строго математически результат калибровки не зависит от величины указанной проекции. Однако на практике при уменьшении угла α₁ от 90° до 0° реальная точность измерений снижается, а при α₁=0° калибровка по второй и третьей осям становится невозможной, поскольку проекция вектора $$\overline{\text{G}}$$

на плоскость 23 оказывается нулевой.For calibration, set the accelerometer so that its one axis (axis of rotation), which we arbitrarily call the "first", intersects with the gravitational acceleration vector $$\overline{\text{G}}$$

, i.e. the axis must not coincide with the vector $$\overline{\text{G}}$$

. In practice, it is preferable that the first axis is perpendicular to the gravitational acceleration vector $$\overline{\text{G}}$$

and lay in the plane of the local horizon. This requirement is not categorical. If the first axis has an inclination angle α ₁ other than 90 °, then the projection of the gravitational acceleration vector $$\overline{\text{G}}$$

on the plane 23 will be Gsin (α ₁ ). Strictly mathematically, the calibration result does not depend on the magnitude of the indicated projection. However, in practice, when the angle α ₁ decreases from 90 ° to 0 °, the actual measurement accuracy decreases, and when α ₁ = 0 °, calibration along the second and third axes becomes impossible, since the projection of the vector $$\overline{\text{G}}$$

on the plane 23 is zero.

. Это требование тоже не категорично, но улучшает точность калибровки.It is advisable to deploy the axes 2 and 3 of the accelerometer for calibration at an angle of 45 ° with respect to the gravitational acceleration vector $$\overline{\text{G}}$$

. This requirement is also not categorical, but improves calibration accuracy.

The second and third axes of the accelerometer are calibrated, for which they rotate it around the first axis, fixed in four, i = 1 ÷ 4, orthogonal positions, in each of which the projections A _2i and A _3i of the gravitational acceleration vector G are measured on the second and third axes of the accelerometer, respectively . The static error of the accelerometer is calculated along the second m ₂ and third m ₃ axes by averaging the measurements of the projections of the gravitational acceleration vector on this axis using a formula of the form (7).

At the second stage, the first and third axes of the accelerometer are calibrated, for which the second axis is selected as the axis of rotation and, acting in the same way as described above, A _3i and A _1i are measured and the static error of the first axis m _{1 is} calculated.

To calculate the relative sensitivity coefficient along the second and third axes of the accelerometer, we use the following considerations: we find the differences between (3) and (4), as well as between (5) and (6):

After squaring (8) and (9) and adding, we get:

For the third axis, acting in a similar way, we get:

If we divide (11) by (10) and extract the square root, we obtain an expression for calculating the relative sensitivity coefficient of the third and second axes of the accelerometer:

, т.е. достаточно тех же измерений, которые были необходимы для определения статических ошибок m.Thus, to calculate the relative sensitivity coefficient along the third and second axes, it is not necessary to know the sensitivity coefficients k for each of them, as well as the magnitude and orientation of the gravitational acceleration vector $$\overline{\text{G}}$$

, i.e. the same measurements that were necessary to determine the static errors m are sufficient.

Similarly, at the second calibration stage, the relative sensitivity coefficient is calculated along the third and first axes of the accelerometer:

на все оси акселерометра. Далее по ним определяют углы α_j между вектором гравитационного ускорения $$\overline{\text{G}}$$

и 1, 2 и 3 осями акселерометра, Фиг. 2, используя соотношения:In practical measurements - using a calibrated accelerometer - set the inclinometer on the object of study and measure the projection B _j of the gravitational acceleration vector $$\overline{\text{G}}$$

on all axes of the accelerometer. Then they determine the angles α _j between the vector of gravitational acceleration $$\overline{\text{G}}$$

and 1, 2 and 3 axes of the accelerometer, FIG. 2 using the ratios:

In these relations, in accordance with (1), expressions in parentheses (B _j -m _j ) compensate for static measurement errors along the axes of the accelerometer. The coefficients of relative sensitivity k ₃₂ and k ₃₁ normalize measurements along all axes, eliminating differences in their sensitivity. The validity of expressions (12) is easy to verify by substituting in them:

In a number of practical applications, it is convenient to use the angles β _j = (90 ° -α _j ) between the axes 1, 2 and 3 of the accelerometer and the horizon plane. These angles are calculated using formulas similar to (12), with the arcctg function replaced by arctg.

For example, FIG. 3, if the object is a stationary or uniformly moving car, then by combining the first axis of the accelerometer with the longitudinal axis of the car, the second axis of the accelerometer with the transverse axis, and the third should be directed orthogonally to the first two, in accordance with (12), angles β ₁ and β can be determined ₂ tilt of the car to the horizon plane N.

In the technical implementation, the three-axis accelerometer is connected to the computer through the appropriate controllers, which ensures the reception of measurements at the stages of the inclinometer calibration, the calculation of static errors and relative sensitivity coefficients, and in its practical use, the determination of the object's tilt angles.

Thus, the inventive method can be implemented and allows by simple measurements and calculations to calibrate the inclinometer and determine the orientation angles of the investigated object relative to the gravitational field of the Earth.

Information sources

1. Lobank V.M. Calibration of downhole geophysical equipment. Publisher: Ufa: Master Kopi 2011, 176 pp. Http://tinref.ru/000_uchebniki/05300tehnika/003_kalibrovka_geofizich_aparaturi/015.htm.

2. Patent RU 120215.

3. S.F. Konovalov and others. Automatic equipment for testing accelerometers. Collection of 4 St. Petersburg International Conference on Integrated Navigation Systems. May 1997, ISB No. 5-900780-13-9.

4. Determination of the angle of inclination of the accelerometer, http://bitaks.com/resources/inclinometer/ugol_naklona.pdf.

Claims (1)

A method for calibrating an accelerometer triaxial, j = 1 ÷ 3, inclinometer, namely, that the accelerometer is set so that its first axis, selected as the axis of rotation, intersects the gravitational acceleration vector

preferably, at an angle of 90 °, the second axis of the accelerometer is calibrated, for which it is rotated around the first axis, fixed in four, i = 1 ÷ 4, orthogonal positions, in each of which projections A _2i of the gravitational acceleration vector are measured

on the second axis of the accelerometer, calculate the static error of the accelerometer along the second axis m ₂ by averaging the measurements of the projections of the gravity vector on this axis:

characterized in that simultaneously with the second axis, the third axis of the accelerometer is calibrated in a similar manner with the calculation of its static error m ₃ , the relative k ₃₂ is calculated - the sensitivity coefficient of the third k ₃ and second k ₂ axes of the accelerometer:

then set the accelerometer so as to select the second axis as the axis of its rotation and, acting similarly, calculate the static error of the first axis m ₁ and relative k ₃₁ - sensitivity coefficient of the third k ₃ and first k ₁ axes:

in practical measurements, set the accelerometer to the desired position, measure the projection B _j of the gravitational acceleration vector

on all axes of the accelerometer, eliminate static measurement errors on each axis, normalize measurements on all axes using relative sensitivity coefficients, calculating the angles α _j between the sensitivity axes of the accelerometer and the gravitational acceleration vector

according to the formulas:

Images