CN114415073B - Ground quick calibration method and system for aeromagnetic vector gradiometer error model - Google Patents
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Abstract
The invention is suitable for the technical field of unmanned aerial vehicle aeromagnetic measurement calibration, and provides a ground quick calibration method of an aeromagnetic vector gradiometer error model, which comprises the following steps: establishing a vector gradiometer coordinate system according to the unmanned aerial vehicle body information; establishing a linear independent error calibration model based on the coordinate system; performing learning training according to the shaking rule of the simulated unmanned aerial vehicle; and obtaining error calibration parameters based on a solving method of multiple linear regression. The invention correspondingly provides a system for realizing the method. Therefore, the method and the device can quickly solve the error calibration parameters, can better correct the structural error of the aeromagnetic vector gradient detection system, and has stronger adaptability to the change of the field measurement place for the model calibration parameters.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicle magnetic field gradient measurement calibration, in particular to a ground quick calibration method and a ground quick calibration system for an aeromagnetic vector gradiometer error model.
Background
The vector gradient detector carried on the unmanned platform can realize high-efficiency detection and positioning of target magnetic anomaly information such as underground pipelines, buried objects, geologic bodies, submarines, mines and the like, but the data quality is influenced due to process errors and installation errors among all axial directions of the vector magnetic detector, so that the detection precision is greatly reduced, and meanwhile, the errors can also bring great interference to detection data when the platform swings, and the detection operation cannot be finished.
In the existing actual error calibration work, there are the inconveniences that the dependence on high-precision measuring equipment is strong and the requirement on a uniform magnetic environment is high, so that the improvement is needed.
Disclosure of Invention
In view of the above-mentioned shortcomings, the present invention provides a ground fast calibration method and system for an error model of an aeromagnetic vector gradiometer, which can conveniently correct the error of an aeromagnetic vector gradient detection system in the field, get rid of the harsh laboratory condition limitation, and have strong adaptability to the change of the field measurement location for the model calibration parameters.
In order to achieve the purpose, the invention provides a ground quick calibration method for an error model of an aeromagnetic vector gradiometer, which is characterized by comprising the following steps:
establishing a coordinate system of the vector gradient magnetic detector according to the unmanned aerial vehicle body information;
establishing a linear independent error calibration model based on the coordinate system;
performing learning training according to the shaking rule of the simulated unmanned aerial vehicle;
and obtaining error calibration parameters based on a solving method of multiple linear regression.
According to the calibration method of the invention, the number of the vector gradient magnetic probes is 1.
According to the calibration method, the calibration model measures the structural error and the relative null shift error between the corresponding axial directions of the two triaxial fluxgate sensors.
According to the calibration method, the step of training learning according to the shaking rule of the simulated unmanned aerial vehicle comprises the following steps:
the ground shaking measurement system composed of the three-axis nonmagnetic turntable and the vector gradient magnetic detector is used for respectively combining the measurement data of the upper hemisphere space and the lower hemisphere space to serve as a training sample for full-attitude traversing shaking.
According to the calibration method of the present invention, the step of establishing a linear independent error calibration model based on the coordinate system comprises:
establishing a projection relation between two triaxial fluxgate sensors;
and establishing a corresponding mathematical expression according to a preset calculation formula.
The invention correspondingly provides a ground rapid calibration system of an error model of an aeromagnetic vector gradiometer, which comprises
The coordinate system generating unit is used for establishing a vector gradiometer coordinate system according to the unmanned aerial vehicle body information;
the model establishing unit is used for establishing a linear independent error calibration model according to the coordinate system;
the shaking setting unit is used for learning and training according to the shaking posture of the simulated unmanned aerial vehicle;
and the calculating unit is used for obtaining the error calibration parameters based on a solving method of multiple linear regression.
According to the system of the invention, the number of the vector gradient magnetic probes is 1.
According to the system, the calibration model measures the structural error and the relative null shift error between the corresponding axial directions of the two triaxial fluxgate sensors.
According to the system, the shake setting unit is used for combining the measurement data of the upper hemisphere space and the lower hemisphere space respectively through a ground shake measurement system consisting of the three-axis nonmagnetic turntable and the vector gradient magnetic detector to serve as a training sample for full-attitude traversing shake.
According to the system of the invention, the computing unit is further configured to establish a projection relationship between the two three-axis fluxgate sensors;
and establishing a corresponding mathematical expression according to a preset calculation formula.
The invention is suitable for the technical field of unmanned aerial vehicle aeromagnetic measurement calibration, and provides a ground quick calibration method of an aeromagnetic vector gradiometer error model, which comprises the following steps: establishing a vector gradient magnetic detector coordinate system according to the unmanned aerial vehicle body information; establishing a linear independent error calibration model based on the coordinate system; performing learning training according to the shaking rule of the simulated unmanned aerial vehicle; and obtaining error calibration parameters based on a solving method of multiple linear regression. The invention correspondingly provides a system for realizing the method. Therefore, the method can quickly solve error calibration parameters, can better correct the structural error of the aeromagnetic vector gradient detection system, and has stronger adaptability to the change of field measurement places.
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FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of the vector gradient magnetic probe of the present invention;
3(a) -3 (e) are graphs of vector gradient linear independent error calibration models of the present invention;
FIGS. 4(a) -4 (f) are pre-and post-error calibration contrast plots based on multiple linear regression;
5(a) -5 (f) comparison plots of error calibration based on multiple linear regression after a site change;
fig. 6(a) -6 (f) calibrate the sloshing error contrast map for site 2 with the calibration parameters for site 1.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, the invention provides a ground fast calibration method for an error model of an aeromagnetic vector gradiometer, which comprises the following steps:
and S101, establishing a vector gradiometer coordinate system according to the unmanned aerial vehicle body information.
With reference to fig. 2, the coordinate system of the unmanned aerial vehicle body is a front-right-lower right-hand sequence, three axial directions of two three-axis fluxgate sensors (hereinafter referred to as "Sensor-1" and "Sensor-2") are converged at respective central points, and the coordinate system is also constructed according to the front-right-lower right-hand sequence
And (c).
And S102, establishing a linear independent error calibration model based on the coordinate system.
In this step, a projection relationship is first established. Translating the Sensor-2 to the Sensor-1 to make the centers of the two vector magnetic detectors coincide, respectively taking Axis-11, Axis-12 and Axis-13 axes of the Sensor-1 as references as shown in FIG. 3(a), and respectively projecting three axes of the Sensor-2 on each axial direction of the Sensor-1 to obtain 9 projection parameters as shown in FIG. 3(b), FIG. 3(c) and FIG. 3 (d);
the notation is simplified. The actual output values of the magnetic fields of the Sensor-1 in three non-orthogonal axial directions are
、
And
the actual output value of the magnetic field of Sensor-2 is
、
And
as shown in fig. 3 (e).
Write the projection expression of Sensor-2 to Axis-11 Axis of Sensor-1
In the formula
For the estimate of the Sensor-2 projection,
、
and
the projection coefficients of Axis-11 of Sensor-1 in the three axial directions of Sensor-2 are shown respectively.
S102-1 writes a gradient expression in Axis-11 axial direction
In the formula
Showing the relative null shift of the Axis-11 up the two magnetic probes.
S102-2 deforms Axis-11 in an axial gradient expression mode
In the formula
，
，
。
Written in a compact form having
S102-3 writing out gradient expressions in other two axial directions
In the formula
Is the relative null shift on Axis-12,
，
，
。
in the formula
Is the relative null shift on Axis-13,
，
，
。
s102-4, establishing an error model of the vector gradient with linear independence between axial directions
S102-5 writing 9 projection parameters into a matrix form
Then (1)
、
、
、
、
、
、
、
、
) And (a)
、
、
) Together constituting linearly independent error calibration model parameters.
And S103, performing learning training according to the shaking rule of the simulated unmanned aerial vehicle.
According to the ground shaking measuring system, the three-axis nonmagnetic turntable and the vector gradient magnetic detector are used for combining the measuring data of the upper hemisphere space and the lower hemisphere space respectively to serve as training data of full-attitude traversing shaking, so that the resolving stability and the environmental adaptability of the calibration parameters are improved.
In one test embodiment of the invention, the three-axis non-magnetic turntable shaking test system is provided. And simulating the flight attitude of the unmanned aerial vehicle to perform a shaking test. The carbon fiber pipe forming the vector gradient magnetic detector is fixed in the center of the platform of the three-axis nonmagnetic turntable, the nonmagnetic turntable does not contain a motor, and the vector gradient magnetic detector can swing freely through manual operation to realize the swinging postures of the vector gradient magnetic detector in different directions.
The test procedure was as follows:
s103-1, selecting a measuring place 1. Regarding the geomagnetic field as a uniform constant field, and keeping Axis-13 and Axis-23 of the vector gradient magnetic detector in a fixed state (called a 'lying posture' for short) which is vertical to the ground downwards;
s103-2, traversing and shaking the upper hemisphere space. According to the sequence of east → south → west → north, the three degrees of freedom of yaw, pitch and roll are synthesized under each azimuth to carry out arbitrary shaking of 8-10 periods, the amplitude of each rotation angle is controlled within +/-20 degrees, and magnetic field data are collected;
s103-3, changing the fixed orientation of the gradient rod. Continuously acquiring data without power interruption, and adjusting Axis-13 and Axis-23 axes of the vector gradient magnetic detector pointing to the earth center to point to the sky (called 'lying posture' for short);
s103-4, traversing and shaking the lower hemisphere space. After the step of S103-2 shaking is repeated, stopping Data acquisition to obtain measurement Data-1 traversed in the global surface space of the measurement site 1;
substituting the output data of each axis of the measuring site 1 into an error calibration equation set to obtain 12 error calibration coefficients, calculating the error output after the calibration based on the multiple linear regression through the formula (4), and comparing the error output with the difference value of the original output value of the vector magnetic detector. FIG. 4(a), FIG. 4(c) and FIG. 4(e) are the difference values of the raw data measured in three axial directions; fig. 4(b), 4(d) and 4(f) are graphs showing the difference values between the three axes after calibration based on the multiple linear regression method, and the unit is nT.
In fig. 4(a) to 4(f), the interference of larger amplitude caused by changing the fixed state and the azimuth conversion is eliminated, and the peak-to-peak value of the actually measured shaking curve is counted as follows:
with reference to fig. 4(b), 4(d), 4(f) and table 1, the gradient data in the three axial directions after error calibration has a decrease in the shake error of 89% or more as compared to that before calibration.
S103-5, moving the measuring place. And (3) translating the three-axis nonmagnetic rotary table to the east by 5 meters to serve as a measurement place 2, repeating the processes from S103-1 to S103-4, recording output Data, and recording the Data as Data-2.
Comparing fig. 4(a) to fig. 4(f) and fig. 5(a) to fig. 5(f), it is found that the influence of the azimuth and attitude shake can be significantly eliminated after error calibration is performed again at different locations, and the error calibration effect of the peak-to-peak value of the shake interference before and after calibration at the location 2 can also reach more than 91%, see table 2.
And S103-6, solving parameters and analyzing performance. And substituting the error calibration parameters calculated by the Data-1 into the Data-2 so as to verify the applicability of the error calibration model to the position change. The new calibration results are shown in fig. 6(a) -6 (f).
The error correction data in each axial direction in fig. 6(a) to 6(f) are summarized as follows:
it can be seen from table 3 that, by using the calibration parameters of site 1 to correct the sway data of site 2, the calibration effect can still be maintained above 89%, and better calibration can be performed on the influence of changing the direction and the influence of sway attitude. The calibration effect is based on a calibration result randomly generated under a +/-20-degree large-angle shaking condition, and when the unmanned aerial vehicle carries out aeromagnetic detection, the unmanned aerial vehicle adopts flat flight (namely shaking in a small angle), which indicates that the calibration method can meet the small-angle shaking interference when the unmanned aerial vehicle carries out flat flight detection.
The above processes show that the error calibration parameters have good environmental adaptability, and show that the learning process of full-space posture traversal is adopted during learning training, so that the influence on the replacement place is certain in adaptability.
And step S104, obtaining error calibration parameters based on a solving method of multiple linear regression.
S104-1 constructs a cost function. Ideally, the calibrated error should be zero, and the left side of equation (4) is zero. Take the formula (1) as an example
The cost function is constructed such that it satisfies the minimum in the sense of a 2-norm sum of squares, i.e. it is
S104-2, the right side of the formula (6) is used for solving partial derivatives of the error parameters, and the partial derivatives are zero, so that
The equation set is simplified and written into a matrix form, and then
S104-3, obtaining an error calibration parameter solving matrix on the Axis-12 in the same way
S104-4, obtaining an error calibration parameter solving matrix on Axis-13 in the same way
And (S104-5) simultaneously establishing the formula (7), the formula (8), the formula (9) and the formula (5), and solving all calibration parameters of the linear independent error model between the Sensor-1 and the Sensor-2 of the magnetic field vector gradiometer.
Through the modeling and actual measurement calculation examples, the linear independent error calibration model constructed by the method has the following three advantages: on the premise of not considering the non-orthogonal calibration among three axial directions, the error calibration model is constructed with fewer parameters, is convenient to solve and is beneficial to fast learning; the learning training of random shaking can be carried out under the manual control, the mode gets rid of the limitation of higher rotation precision requirement on the instrument and equipment, and the operation threshold of carrying out precise calibration on the gradiometer in the field is reduced. Error calibration parameters after the place is changed still have good environmental adaptability, and a foundation is laid for the unmanned aerial vehicle carrying vector gradient magnetic detector to carry out ground rapid technology.
The invention also provides a system, which comprises:
and the coordinate system generating unit is used for establishing a vector gradiometer coordinate system according to the unmanned aerial vehicle body information.
And the model establishing unit is used for establishing a linear independent error calibration model according to the coordinate system.
The shaking setting unit is used for learning and training according to the shaking posture of the simulated unmanned aerial vehicle; the shaking setting unit is used for merging the measurement data of the upper hemisphere space and the lower hemisphere space respectively through a ground shaking measurement system consisting of a three-axis nonmagnetic turntable and a vector gradient magnetic detector, and the merged measurement data are used as training samples for full-attitude traversal shaking.
And the calculation unit is used for obtaining error calibration parameters based on a solving method of multiple linear regression, and can establish a projection relation between the two triaxial fluxgate sensors.
In the system, the number of the vector gradient magnetic detectors is 1, and the calibration model measures the structural error and the relative null shift error between the corresponding axial directions of the two triaxial fluxgate sensors.
In summary, the invention is applicable to the technical field of unmanned aerial vehicle aeromagnetic measurement calibration, and provides a ground rapid calibration method for an aeromagnetic vector gradiometer error model, which comprises the following steps: establishing a vector gradient magnetic detector coordinate system according to the unmanned aerial vehicle body information; establishing a linear independent error calibration model based on the coordinate system; performing learning training according to the shaking rule of the simulated unmanned aerial vehicle; and solving the error calibration parameters based on the multiple linear regression to obtain the calibration parameters. The invention correspondingly provides a system for realizing the method. Therefore, the method can quickly solve the error calibration parameters, can better correct the structural error and the relative null shift error of the aeromagnetic vector gradient detection system, and has stronger adaptability to the change of the field measurement place.
The present invention is capable of other embodiments, and various changes and modifications can be made by one skilled in the art without departing from the spirit and scope of the invention.
Claims (8)
1. A ground quick calibration method for an error model of an aeromagnetic vector gradiometer is characterized by comprising the following steps:
establishing a vector gradient magnetic detector coordinate system according to unmanned aerial vehicle body information: three axial directions of two three-axis fluxgate sensors Sensor-1 and Sensor-2 are preset to be intersected at respective central points,constructing a coordinate system according to a front-right-bottom right-hand order
And
；
establishing a linear independent error calibration model based on the coordinate system;
performing learning training according to the shaking rule of the simulated unmanned aerial vehicle;
obtaining error calibration parameters based on a solving method of multiple linear regression;
the step of establishing a linear independent error calibration model based on the coordinate system comprises the following steps:
firstly, establishing a projection relation, translating the Sensor-2 to the Sensor-1, enabling the centers of the two vector magnetic detectors to coincide, and respectively taking Axis-11, Axis-12 and Axis-13 axes of the Sensor-1 as references and respectively projecting three axes of the Sensor-2 in each axial direction of the Sensor-1 to obtain 9 projection parameters;
setting the actual output values of the magnetic fields in the three non-orthogonal axial directions of the Sensor-1 as
、
And
the actual output value of the magnetic field of Sensor-2 is
、
And
；
write the projection expression of Sensor-2 to Axis-11 Axis of Sensor-1
In the formula
For the estimate of the Sensor-2 projection,
、
and
the projection coefficients of the three axial directions of the Sensor-2 on the Axis-11 of the Sensor-1 are respectively;
writing an Axis-11 axial gradient expression
In the formula
Represents the relative zero drift of the Axis-11 two magnetic detectors upwards;
deforming the gradient expression of Axis-11 in the axial direction
In the formula
，
，
；
Written in a compact form, having
Writing out gradient expressions in two other axial directions
In the formula
Is the relative null shift on Axis-12,
，
，
；
in the formula
Is the relative null shift on Axis-13,
，
，
；
establishing an error model of vector gradients that is linearly independent between axial directions
Writing 9 projection parameters in matrix form
Then (a)
、
、
、
、
、
、
、
、
) And (a)
、
、
) Together, constitute the linearly independent error calibration model parameters.
2. The calibration method according to claim 1, wherein the number of the vector gradient magnetic probes is 1.
3. The calibration method according to claim 1, wherein the calibration model measures structural errors and relative null shift errors between corresponding axial directions of the two tri-axial fluxgate sensors.
4. The calibration method according to claim 1, wherein the step of training learning according to the law of shaking imitating the unmanned aerial vehicle comprises:
the ground shaking measurement system composed of the three-axis nonmagnetic turntable and the vector gradient magnetic detector is used for respectively combining the measurement data of the upper hemisphere space and the lower hemisphere space to serve as a training sample for full-attitude traversing shaking.
5. A ground rapid calibration system for an error model of an aeromagnetic vector gradiometer is characterized by comprising
A coordinate system generating unit for establishing a vector gradient magnetic detector coordinate system according to the unmanned aerial vehicle body information, and presetting three axial intersections of two triaxial fluxgate sensors Sensor-1 and Sensor-2 in eachA central point, constructing a coordinate system according to a front-right-lower right-hand order
And
；
the model establishing unit is used for establishing a linear independent error calibration model according to the coordinate system;
the shaking setting unit is used for learning and training according to the shaking rule of the simulated unmanned aerial vehicle;
the calculation unit is used for obtaining error calibration parameters based on a solving method of multiple linear regression;
the model building unit is specifically configured to:
firstly, establishing a projection relation, translating the Sensor-2 to the Sensor-1, enabling the centers of the two vector magnetic detectors to coincide, and respectively taking Axis-11, Axis-12 and Axis-13 axes of the Sensor-1 as references and respectively projecting three axes of the Sensor-2 in each axial direction of the Sensor-1 to obtain 9 projection parameters;
setting the actual output values of the magnetic fields in the three non-orthogonal axial directions of the Sensor-1 as
、
And
the actual output value of the magnetic field of Sensor-2 is
、
And
；
write the projection expression of Sensor-2 to Axis-11 Axis of Sensor-1
In the formula
For the estimate of the Sensor-2 projection,
、
and
the projection coefficients of the three axial directions of the Sensor-2 on the Axis-11 of the Sensor-1 are respectively;
writing an Axis-11 axial gradient expression
In the formula
Represents the relative zero drift of the Axis-11 two magnetic detectors upwards;
deforming the gradient expression of Axis-11 in the axial direction
In the formula
，
，
；
Written in a compact form, having
Writing out gradient expressions in two other axial directions
In the formula
Is the relative null shift on Axis-12,
，
，
；
in the formula
Is the relative null shift on Axis-13,
，
，
；
establishing an error model of vector gradients that is linearly independent between axial directions
Writing 9 projection parameters in matrix form
Then (1)
、
、
、
、
、
、
、
、
) And (a)
、
、
) Together, constitute the linearly independent error calibration model parameters.
6. The system of claim 5, wherein the number of vector gradient magnetometers is 1.
7. The system of claim 5, wherein the calibration model measures structural and relative null shift errors between corresponding axes of the two tri-axis fluxgate sensors.
8. The system according to claim 5, wherein the shake setting unit is configured to combine the measurement data of the upper hemispherical space and the lower hemispherical space, respectively, as a training sample for full-attitude traverse shake, by a ground shake measurement system composed of a three-axis nonmagnetic turntable and a vector gradient magnetic probe.
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