CN109541708B - method for measuring three-dimensional vector field by using double-shaft sensor - Google Patents
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Abstract
The invention discloses methods for measuring a three-dimensional vector field by adopting a double-shaft sensor, which comprises the steps of firstly obtaining accurate two-dimensional output by compensating self two-dimensional zero error, non-orthogonality error and sensitivity error of the double-shaft sensor, then obtaining a third three-dimensional vector field value of the three-dimensional vector field by using the constraint that local vector field strength is a fixed value, and then carrying out non-alignment error on the three-dimensional vector field to obtain a final three-dimensional vector field value.
Description
Technical Field
The invention relates to the technical field of sensors, in particular to methods for measuring a three-dimensional vector field by adopting a double-shaft sensor.
Background
However, due to factors such as manufacturing process and environmental changes, the accelerometer and magnetometer inevitably have errors including but not limited to zero offset of each axis, sensitivity (or scale coefficient) error, non-orthogonal error, inter-axis interference and the like, and the magnetometer further includes soft magnetic and hard magnetic interference caused by magnetic materials near the sensor, so that the measurement of the existing three-dimensional vector field has larger errors.
Disclosure of Invention
The invention aims to solve the problem that the existing three-dimensional vector field measurement has large errors, and provides methods for measuring the three-dimensional vector field by adopting a double-axis sensor.
In order to solve the problems, the invention is realized by the following technical scheme:
A method for measuring three-dimensional vector field by using a double-axis sensor, comprising the following steps:
step 1, placing a double-axis sensor in a measured three-dimensional vector field to obtain an output value v of the double-axis sensor; wherein:
step 2, subtracting a zero-position zero-deviation matrix from the output value v of the double-shaft sensor to obtain an output value v' after zero-position deviation compensation; wherein:
step 3, orthogonalizing the output value v 'after zero offset compensation to obtain an output value v' after non-orthogonal error compensation; wherein:
and 4, performing a normalization treatment on the output value v 'after the non-orthogonal error compensation, namely dividing the output value v' after the non-orthogonal error compensation by the modulus of the error coefficient of the row where the output value v 'is located respectively to obtain an output value u' after the sensitivity error compensation, namely the unit orthogonal components of the X axis and the Y axis of the double-axis sensor, wherein:
step 5, utilizing the vector field intensity u0Keeping the constraint relation of constant, calculating the unit orthogonal component u 'of the Z axis of the dual-axis sensor based on the unit orthogonal components of the X axis and the Y axis of the dual-axis sensor obtained in the step 4'3(ii) a Wherein:
step 6, constructing a three-dimensional vector u 'of the measured vector field based on the orthogonal components of the X axis, the Y axis and the Z axis of the double-axis sensor obtained in the steps 4 and 5, and performing non-alignment error compensation of a coordinate system on the three-dimensional vector u' of the measured vector field to obtain an accurate three-dimensional vector u of the measured vector field; wherein:
in each of the above formulae, v1Is the X-axis output value, v, of a two-axis sensor2Being dual-axis sensorsA Y-axis output value; v'1Is an X-axis output value v 'after zero offset compensation'2The Y-axis output value after zero offset compensation is obtained; b1Is X-axis null of a two-axis sensor, b2Is the Y-axis zero offset of the dual-axis sensor; v. of1"is the X-axis output value after non-orthogonal error compensation, v2"is the Y-axis output value after non-orthogonal error compensation; c is a coefficient of orthogonalization of the block,
u1' X-axis output value after sensitivity error compensation, i.e. unit orthogonal component of X-axis of used two-axis sensor, u2' is a sensitivity error compensated Y-axis output value, i.e., a unit quadrature component, u ', of the Y-axis of the two-axis sensor used '3The orthogonal component of the Z axis of the measured vector field is the unit orthogonal component of the Z axis of the used double-axis sensor; u. of0Is the strength of the measured vector field; and L is a non-alignment error coefficient matrix.
In the step 1, when the measured three-dimensional vector field is a gravity field, the double-shaft sensor is a double-shaft acceleration sensor; when the measured three-dimensional vector field is a geomagnetic field, the double-shaft sensor is a double-shaft magnetometer.
Compared with the prior art, the method has the advantages that the error model is built for the double-shaft sensor for measuring the three-dimensional vector field, the error compensation and calculation are carried out on the output value according to the constraint of the local vector field, the error model is solved, the three-dimensional vector of the three-dimensional vector field can be calculated, other auxiliary sensors are not needed, the error influence caused by objective reasons of the sensor can be eliminated and reduced, the cost is low, and the accuracy is high.
Drawings
FIG. 1 is a schematic diagram of kinds of devices for measuring three-dimensional vector field by using two-axis sensors.
Fig. 2 is a flow chart of methods for measuring a three-dimensional vector field by using a two-axis sensor.
FIG. 3 is a flowchart of the processing of the microprocessor.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to specific examples and the accompanying drawings.
In view of various objective problems of the sensor such as manufacturing process and using environment, and the like, inevitable errors exist, the invention firstly obtains accurate two-dimensional output for the two-dimensional output of the double-shaft sensor by compensating the self two-dimensional zero error, the non-orthogonality error and the sensitivity error; then, a third three-dimensional vector field value of the three-dimensional vector field is obtained by utilizing the constraint that the local vector field strength is a fixed value; and then carrying out non-alignment error on the three-dimensional vector field so as to obtain a final three-dimensional vector field value.
A device for measuring three-dimensional vector field by using a dual-axis sensor, as shown in fig. 1, is mainly composed of a power module, a dual-axis sensor, a signal conditioning module, an analog-to-digital conversion module and a microprocessor, wherein the power module is responsible for charging other units including the dual-axis sensor, the power module can be a direct current power supply or a storage battery module, so as to measure outdoor without power supply, the dual-axis sensor is responsible for measuring the measured vector field and obtaining signals, and sending the signals to the signal conditioning module, the signal conditioning module is responsible for processing the signals of the dual-axis sensor, and sending the processed signals to the analog-to-digital conversion module, the analog-to-digital conversion module is responsible for performing analog-to-digital conversion on the output values of the signal conditioning so as to be processed by the subsequent microprocessor, and the microprocessor is responsible for compensating and calculating the analog-to-converted signals, and outputting.
A method for measuring three-dimensional vector field by using a two-axis sensor, as shown in FIG. 2, specifically comprises the following steps:
step 1, placing a double-shaft sensor (a double-shaft acceleration sensor or a magnetometer) in a measured three-dimensional vector field to obtain measurement data, wherein the corresponding measurement data of an X shaft and a Y shaft are respectively X1And x2。
Step 2, sending the obtained measurement data to a signal conditioning module for corresponding signal conditioning to obtain x1' and x2′。
Step 3, will be passed throughSending the data after signal conditioning to an analog-to-digital conversion module for analog-to-digital conversion to obtain v1And v2。
The double-shaft sensor is placed in a measured three-dimensional vector field, at any time in the measuring process, the measured vector field is a gravity field or a geomagnetic field and has a three-dimensional component, and the sensor has a two-dimensional output v ═ v [ (v [ - ])1v2)TAnd the strength of the measured vector field is always kept as
Wherein u is0Is a known constant.
The two-axis sensor (gravity acceleration sensor or magnetometer) used has a linear error model v ═ ku + b, where the parameters of k, b and v are known and developed:
where v is the measurement data of the two-axis sensor, v1、v2The method comprises the steps of respectively obtaining two axis output values of a double-axis sensor, respectively referring two axes of the double-axis sensor to be an X axis and a Y axis, respectively, further referring a third axis perpendicular to two axis planes of the double-axis sensor to be a Z axis, wherein k is an error coefficient matrix, each element in the error coefficient matrix represents different error coefficients, and due to objective reasons of factors such as manufacturing process, environmental change and the like, sensitivity between the two axes of the double-axis sensor is incomplete , so that the sensitivity error is a sensitivity error and is also commonly referred to as a calibration factor error, wherein k is also called11，k22Sensitivity error coefficients of the double-shaft sensor in the horizontal direction and the vertical direction are respectively set; due to manufacturing process and other reasons, two axes of the double-axis sensor are not kept strictly orthogonal to each other, so that vector values of a measured vector field in other directions may exist in the two axes, and the situation becomes a non-orthogonal error; wherein k is12The non-orthogonal error coefficient of a horizontal axis and a vertical axis of the biaxial sensor; k is a radical of13Is a non-orthogonal error coefficient between a horizontal axis and a vertical axis of the dual-axis sensor; k is a radical of21Of vertical and horizontal axes of a two-axis sensorA non-quadrature error coefficient; k is a radical of23The vector field to be measured is zero, and when the output position of the sensor is zero, the error can be zero offset b ═ b1,b2)TTo illustrate, the null offset is a constant value.
In addition, because the sensor coordinate system and the carrier coordinate system can not be completely coincided, definite misalignment error exists, and at the moment, a three-dimensional square matrix L, namely a misalignment error coefficient matrix, is introduced to describe the error, wherein the element value of the misalignment error coefficient is LxyX, Y ∈ (1.3), where the subscript X denotes the sensor coordinate system, Y denotes the carrier coordinate system, 1 denotes the X-axis of the coordinate system, 2 denotes the Y-axis of the coordinate system, and 3 denotes the Z-axis. Such as: l is12Expressed as the misalignment error between the X-axis of the sensor coordinate system and the Y-axis of the carrier coordinate system.
In this embodiment, let u be the strength of the measured vector field0The two-axis sensor used had an error model of 9.8:
the measured vector field is then provided with the following 5 sets of real data, the third component u3The signs are all positive:
| group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
| u1 | 1.781 | 5.286 | -1.174 | 6.276 | 6.967 |
| u2 | 6.074 | 1.954 | 0.927 | -3.059 | -0.606 |
| u3 | 7.482 | 8.017 | 9.685 | 6.877 | 6.865 |
Step 4, converting the data v after analog-to-digital conversion1And v2And sending the error compensation data to a microprocessor for error compensation calculation and processing.
And the microprocessor calculates and compensates the error model, wherein the process comprises compensating zero offset, non-orthogonal error, sensitivity error and the like, and finally obtains a two-dimensional vector. Two-dimensional vector compensated by the compensation
And calculating the constraint of the local magnetic field to obtain a third-dimensional vectorAnd finally, compensating the non-alignment error of the sensor coordinate system to obtain the three-dimensional component of the measured vector field in the error model, and outputting the final result. See fig. 3.
, obtaining sensor output:
| group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
| v1 | 0.573 | 3.617 | -2.822 | 4.478 | 5.259 |
| v2 | 7.473 | 2.294 | 2.623 | -3.532 | -0.974 |
And secondly, compensating the zero offset.
Since the null offset is a constant value, the null error can be eliminated by subtracting the null zero offset matrix b, i.e., v '═ v-b, from the output value v of the biaxial sensor, and the compensated output value v'1And v'2The following were used:
| group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
| v′1 | 0.873 | 3.917 | -2.522 | 4.778 | 5.559 |
| v′2 | 7.073 | 1.894 | 2.223 | -3.932 | -1.374 |
And thirdly, compensating the non-orthogonal error.
Because the double-shaft sensor has possible double-shaft non-orthogonal condition, after eliminating zero-bit deviation, the two-dimensional output value is orthogonalized to obtain two orthogonalized vectors, the non-orthogonal error is compensated, and the compensated output values are v ″, respectively1And v ″)2，
Where c is the orthogonalization coefficient, which has the value:
the value v "after compensating for the non-orthogonal error1And v ″)2The following were used:
| group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
| v″1 | 0.873 | 3.917 | -2.522 | 4.778 | 5.559 |
| v″2 | 7.215 | 2.527 | 1.815 | -3.160 | -0.475 |
And fourthly, compensating sensitivity errors.
The processed v' is measured due to the different sensitivities of the two axes of the biaxial sensor1And v ″)2The quadrature component is normalized by dividing it by the matrix of the line error coefficient to compensate for the sensitivity error, and the compensated output value is u'1And u'2. Wherein the error coefficient v ″1And v ″)2The dies of (a) are respectively:
thus, an output value u 'with sensitivity error compensated is obtained'1And u'2The following were used:
| group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
| u′1 | 0.907 | 4.067 | -2.618 | 4.961 | 5.772 |
| u′2 | 6.490 | 2.274 | 1.633 | -2.842 | -0.427 |
And step five, solving a third component.
Calculating two orthogonal vectors after compensation of zero error, non-orthogonal error and sensitivity error in the second-fourth steps, calculating the third orthogonal component of the measured vector field by using the constraint of vector field strength keeping constant, namely subtracting the square sum of the two compensated orthogonal components from the square of the constraint constant value, namely the square of the third orthogonal component, and obtaining the third component by opening the root of the third orthogonal component, which is recorded as u'3Is provided with
The following were used:
| group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
| u′3 | 7.287 | 8.621 | 9.301 | 7.959 | 7.909 |
The third component of the solution is taken as the third element value, at this time, u'1，u′2，u′3 three-dimensional vectors are formed, and u 'represents (u'1u′2u′3)T。
And sixthly, compensating the non-alignment error of the sensor coordinate system.
The non-alignment error model of the coordinate system can be expressed as u ═ Lu ', and the original three-dimensional vector value u of the vector field can be obtained by only multiplying u' by L matrix and L is 3 x 3 matrix.
The matrix L of misalignment errors should be unit orthogonal matrices with a value of 1, and the coefficients in the L matrix can be obtained as follows:
1) representing the error coefficients of the X-axis and Y-axis of the sensor in the determinant K of the error coefficients of the sensor in the error modelThe th row elements are orthogonalized with the second row elements to eliminate the quadrature error.
Wherein the orthogonalization coefficient c is:
2) and respectively unitizing the th row elements and the second row elements in the k' to obtain th column elements and second column elements of the matrix L, and obtaining third column elements through unit orthogonality.
3) And (4) carrying out left multiplication on u' by an L matrix to obtain the original three-dimensional vector value u of the vector field, wherein the non-alignment error is eliminated.
Through calculation, a non-alignment error parameter matrix L of the sensor coordinate system and the carrier coordinate system is as follows:
the u' is subjected to left multiplication by an L matrix to obtain an original three-dimensional vector value u for eliminating the non-alignment error and obtaining a vector field1、u2And u3。
| Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
| u1 | 1.781 | 5.286 | -1.174 | 6.276 | 6.967 |
| u2 | 6.074 | 1.954 | 0.927 | -3.059 | -0.606 |
| u3 | 7.482 | 8.017 | 9.685 | 6.877 | 6.865 |
And 5, outputting three accurate vector values after final processing of the vector field by the microprocessor through final operation.
Full compensation of all error parameters in the linear error model, i.e. output by the sensor (v)1v2)TReversely deducing the three-dimensional component (u) of the measured vector field1u2u3)T。
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.
Claims (2)
1, method for measuring three-dimensional vector field by using double-axis sensor, which is characterized by comprising the following steps:
step 1, placing a double-axis sensor in a measured three-dimensional vector field to obtain an output value v of the double-axis sensor; wherein:
step 2, subtracting a zero-position zero-deviation matrix from the output value v of the double-shaft sensor to obtain an output value v' after zero-position deviation compensation; wherein:
step 3, orthogonalizing the output value v 'after zero offset compensation to obtain an output value v' after non-orthogonal error compensation; wherein:
and 4, performing a normalization treatment on the output value v ' after the non-orthogonal error compensation, namely dividing the output value v ' after the non-orthogonal error compensation by the modulus of the error coefficient of the row to obtain an output value u ' after the sensitivity error compensation, namely the unit orthogonal components of the used X axis and Y axis, wherein:
step 5, utilizing the vector field intensity u0Keeping the constraint relationship of constant, calculating the unit orthogonal component u 'of the used Z axis based on the unit orthogonal components of the used X axis and Y axis obtained in step 4'3(ii) a Wherein:
step 6, constructing a three-dimensional vector u 'of the measured vector field based on the unit orthogonal components of the X axis, the Y axis and the Z axis obtained in the steps 4 and 5, and performing non-alignment error compensation of a coordinate system on the three-dimensional vector u' of the measured vector field to obtain an accurate three-dimensional vector u of the measured vector field; wherein:
in each of the above formulae, v1Is the X-axis output value, v, of a two-axis sensor2Is the Y-axis output value of the dual-axis sensor; v. of1' is the X-axis output value, v, after compensation for zero offset2' is the Y-axis output value after zero offset compensation; b1Is X-axis null of a two-axis sensor, b2Is the Y-axis zero offset of the dual-axis sensor; v. of1"is the X-axis output value after non-orthogonal error compensation, v2"is the Y-axis output value after non-orthogonal error compensation; c is a coefficient of orthogonalization of the block,
u1' X-axis output value after sensitivity error compensation, i.e. unit orthogonal component of used X-axis, u2' is a sensitivity error compensated Y-axis output value, i.e., a unit quadrature component, u ' of the Y-axis used '3The orthogonal component of the Z axis of the measured vector field is the unit orthogonal component of the used Z axis; u. of0Is the strength of the measured vector field; and L is a non-alignment error coefficient matrix.
2. The method for measuring three-dimensional vector field according to claim 1, wherein in step 1, the two-axis sensor is a two-axis acceleration sensor when the measured three-dimensional vector field is gravity field, and the two-axis sensor is a two-axis magnetometer when the measured three-dimensional vector field is geomagnetic field.
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