CN117169980A - Accurate compensation method for gravity measurement acceleration eccentric effect error - Google Patents
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Abstract
The invention relates to the gravity measurement field, in particular to a gravity measurement acceleration eccentric effect error accurate compensation method which can effectively improve the dynamic measurement accuracy of a gravity meter by accurately and offline solving a space lever arm under the measurement condition of large-angle posture change carriers such as a fixed wing aircraft, an unmanned aerial vehicle, an AUV and the like.
Description
Technical Field
The invention relates to the field of gravity measurement, in particular to a gravity measurement acceleration eccentric effect error accurate compensation method which is used for realizing accurate off-line solving of an acceleration eccentric effect error through a space lever arm under the condition of measuring a carrier with large angle posture change such as a fixed wing aircraft, an unmanned aerial vehicle, an AUV and the like by a gravity meter and effectively improving the dynamic measurement precision of the gravity meter.
Background
The main body measuring part of the gravity meter comprises an inertial measuring unit and a triaxial inertial stabilization platform. The inertial measurement unit comprises three single-axis fiber optic gyroscopes and three quartz flexible accelerometers, wherein the vertical gravity measurement adopts a special gravity sensor, and the inertial measurement unit is arranged in three universal ring frames, thereby forming a triaxial inertial stabilization platform. The stable loop of the platform realizes the inertial system stability of two horizontal degrees of freedom by utilizing the stable loop technology based on the fiber-optic gyroscope, the horizontal correction loop utilizes the carrier acceleration output by the horizontal accelerometer, the azimuth correction loop utilizes the azimuth fiber-optic gyroscope to track the geographic north direction in real time, carries out navigation calculation and platform horizontal control, realizes the dynamic tracking of the input shaft of the gravity sensor to the direction of the geographic vertical line, and completes the direct measurement of the vertical acceleration, namely the original gravity measurement information. And in the later gravity data processing stage, carrying out carrier motion acceleration correction, standard ellipsoidal gravity correction and drift compensation on the original gravity measurement value by means of satellite navigation information such as differential GNSS and the like, and finally obtaining free space gravity anomaly information.
And the accelerometer on the stable platform measures the proportional component in the coordinate system of the output platform to obtain the output value of the accelerometer. And (3) taking the output value of the accelerometer, the external GNSS speed and the position as inputs, mechanically arranging according to a horizontal north-pointing semi-analytic inertial navigation system, carrying out GNSS information combination calculation and stable platform control, and calculating to obtain the instruction angular speed of the platform coordinate system for tracking the geographic coordinate system. Under the action of the instruction angular velocity, the inertial stabilization platform is controlled to track a local geographic coordinate system, so that the sensitive axis of the gravity sensor always points to the gravity plumb direction. The output of the gravity sensor on the stable platform is corrected and compensated to obtain the free space gravity abnormal value.
The measurement of gravity sensor contains both motion acceleration and gravitational acceleration information, no matter what carrier platform is measuring the gravitational information. In the water surface gravity measurement process, the influence of vertical acceleration can be filtered through simple low-pass filtering generally because the change frequency of sea waves and the change frequency of gravity signals have obvious differences. However, in the gravity measurement process of fixed wing aircraft, unmanned aerial vehicle and AUV, the carrier is subjected to the vertical acceleration caused by the factors of atmospheric turbulence, ocean current, sea water density change and the like, has a wider interference frequency spectrum, overlaps with the gravity signal frequency band, cannot be processed through simple low-pass filtering, and in this case, the vertical acceleration of the carrier needs to be separated through an external means. When the aviation gravity measurement is used for vertical acceleration compensation, accurate altitude information is obtained by means of a differential GNSS mode, and vertical acceleration is obtained by means of a carrier position difference method. The acquisition of the vertical acceleration of the underwater motion carrier is achieved by a secondary differential mode of carrier submergence data provided by a pressure depth sensor. Taking fixed wing airborne gravity measurement as an example, under most working conditions, the amplitude of vertical acceleration information in the output of the gravity sensor can reach more than 100000 mGlul, but the effective gravity information is basically in the order of tens of milligamma, and the amplitude of the effective gravity information is thousands of times of that of the effective gravity information. It can be said that the vertical acceleration correction is the most important data processing correction term for the gravity measurement of fixed wing aircraft, unmanned aerial vehicle and AUV, and is also a main factor for restricting the measurement accuracy and resolution of gravity anomaly in such high-dynamic application scenarios.
It is not difficult to obtain from the gravity measurement vertical acceleration correction processing method, and the accuracy of the vertical height or the diving depth information directly determines the accuracy level of the vertical acceleration correction. It should be noted that the effective vertical acceleration information sensed by the gravity sensor can be obtained from the position variation of the gravity sensor in the vertical direction. In general, the phase center of the differential GNSS antenna or the center of the depth gauge is not coincident with the installation position of the center of mass of the gravity sensor on the carrier, so that the vertical acceleration derived from the altitude and the submergence information output by the differential GNSS and the depth gauge cannot be directly used for the vertical acceleration compensation of the output information of the gravity sensor, and the error caused by the vertical acceleration compensation is the eccentric effect error. Under the condition that the precision level of the differential GNSS and the depth gauge is certain, the compensation precision of the eccentric effect error becomes one of important factors influencing the compensation precision of the vertical acceleration of the high dynamic gravity measurement.
From the above method for compensating the eccentric effect error, it can be derived that the compensation accuracy of the vertical acceleration eccentric effect error is related to the carrier posture matrix and the lever arm. The accuracy of the pose matrix is guaranteed by the design of the gravity meter and is negligible. Therefore, the distance between the center of mass of the gravity sensor and the center of the phase of the GNSS antenna or the center of the depth gauge, namely the precision of the lever arm coordinates, is the key of eccentric effect error compensation. Proved by demonstration and actual gravity measurement experiments, the precision of the lever arm coordinate under typical high dynamic measurement working conditions is required to be better than 5cm.
Currently, during gravity measurement operation, lever arm coordinates are obtained by manually measuring three-dimensional distances between a GNSS antenna phase center or a depth meter center and a gravity sensor centroid by using a tape measure, and the accuracy of the lever arm coordinates mainly depends on the standardization and the fineness of the operation of a measurer. The method has a plurality of defects, firstly, the standardization and the fineness of the operation of a measurer are difficult to quantify, and the precision of lever arm coordinates obtained by measurement cannot be evaluated; secondly, the installation environment of the gravity meter on carriers such as fixed wing aircrafts, unmanned aerial vehicles, AUVs and the like is complex, the shape in a carrier cabin is generally irregular, the top and the four walls are uneven, a GNSS antenna or a depth meter is generally installed outside the cabin, sectional measurement and repeated size transmission are inevitably needed in the measuring process of a tape measure, a plurality of adverse factors are brought to the accurate measurement by the tape measure, and the objective 5cm precision is difficult to realize, so that the precision of lever arm distance measurement is difficult to ensure by a method for manually measuring the three-dimensional distance between the center of the phase of the GNSS antenna or the center of the depth meter and the center of mass of a gravity sensor by the tape measure, the compensation error of the acceleration eccentric effect is brought under the dynamic condition, and the precision and the resolution of gravity measurement are reduced. In particular, in the case of aviation gravity measurement with high measurement resolution, the requirement on the compensation accuracy of the eccentric effect is higher because the filtering scale can be shorter, and no effective solution is available for the problem at present. Therefore, a method capable of accurately compensating the error of the eccentric effect of the acceleration is needed, and the problem of accurate compensation of the eccentric effect faced by the current high-dynamic gravity measurement is solved.
Disclosure of Invention
The present invention is directed to solving at least one of the technical problems existing in the related art. Therefore, the invention provides a gravity measurement acceleration eccentric effect error accurate compensation method, which comprises the following steps:
s1, setting a repeated measuring line in a gravity measuring area, completing measurement operation tasks of all measuring lines in the gravity measuring area, and collecting original gravity data;
s2, measuring the three-dimensional distance between the mass center of the gravity sensor and the phase center of the GNSS antenna or the center of the depth gauge to obtain an initial lever arm measurement value, and estimating the range of a horizontal X-direction lever arm and a horizontal Y-direction lever arm measurement value interval;
s3, in a plane corresponding to a horizontal X-direction lever arm value interval range and a Y-direction lever arm value interval range, four lever arm coordinate points are taken to obtain lever arm coordinates corresponding to the four lever arm coordinate points, carrier motion acceleration correction, standard ellipsoidal gravity correction, drift compensation and eccentric effect error compensation data processing are carried out on the original gravity data on the repeated measuring lines collected in the step S1 through the four lever arm coordinate points, the gravity abnormal values of the repeated measuring lines corresponding to the lever arm coordinate points are respectively obtained, and the coincidence precision in the repeated measuring lines corresponding to the lever arm coordinate points is obtained by utilizing a coincidence precision statistical formula in the repeated measuring lines;
s4, determining minimum values of coincidence precision in the four repeated measuring lines in the S3 through comparison, obtaining lever arm coordinate points corresponding to the minimum values of coincidence precision in the repeated measuring lines, and further reducing the range of the horizontal X-direction lever arm interval and the range of the horizontal Y-direction lever arm interval according to a golden section searching method;
s5, repeating the step S3 and the step S4 until the difference between the horizontal X-direction lever arm interval range and the horizontal Y-direction lever arm interval range meets the precision requirements of the corresponding horizontal X-direction lever arm interval range and horizontal Y-direction lever arm interval range;
s6, respectively solving the midpoint of the horizontal X-direction lever arm interval range and the midpoint of the horizontal Y-direction lever arm interval range obtained in the step S5 to obtain a corresponding horizontal X-direction lever arm accurate value and a horizontal Y-direction lever arm accurate value, carrying out carrier motion acceleration correction, standard ellipsoidal gravity correction, drift compensation and eccentric effect error compensation on the original gravity data of the gravity measurement area collected in the step S1, processing to obtain accurate gravity abnormal values of all measuring lines, and finally realizing accurate compensation on the gravity measurement acceleration eccentric effect error.
Further, in step S1, the number of repetitions of the repeated line is not less than 3.
Further in step S1, the one-way measurement time of the repeated line is not less than 1 hour.
Further, in step S3, the range of the horizontal X-direction and Y-direction lever arm value interval is respectively recorded as，Four lever arm coordinate points are taken and are respectively +.>，/>，/>And->Satisfies the following conditionsThe coincidence precision in the repeated measuring lines of four points is respectively recorded as，/>，/>And->。
Further in the step S3, the repetition corresponding to each lever arm coordinate point is completed by a formulaWithin-line coincidence accuracyThe calculation is performed such that,
the repeated measuring line accords with an accuracy statistical formula:
wherein:
for the coincidence precision in the repeated measuring line, namely +.>；
The difference between the gravity anomaly value of the ith measuring point on the jth repeated measuring line and the average value of the gravity anomaly values of the repeated measuring lines at the jth measuring point is obtained;
the number of repeated measuring points on the repeated measuring line;
the number of the repeated line-measuring is repeated,
wherein the method comprises the steps ofThe calculation formula of (2) is as follows:
=/>,/>，
，
wherein:
the gravity anomaly value of the ith measuring point on the jth repeated measuring line;
the average of the gravity anomaly values was measured for each repeat line for that point.
Further in step S6, the X-direction lever arm optimization solution and the Y-direction lever arm optimization solution obtain accurate values of respectively、/>Satisfy->，/>Wherein->，/>Obtained by step S5.
Compared with the prior art, the invention has the advantages that: the accurate compensation method for the gravity measurement eccentric effect error can accurately compensate the acceleration eccentric effect error of the fixed wing, the unmanned aerial vehicle, the AUV and other high dynamic gravity measurement scenes based on the designed repeated measuring lines in the post-processing stage of gravity measurement data, and solves the problem that the acceleration eccentric effect error in the output of the gravity meter cannot be completely eliminated due to the fact that the coordinates of a measuring rod arm are not accurately measured by manually using a measuring tape.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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In order to more clearly illustrate the invention or the technical solutions of the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the invention, and other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a diagram of an X-direction and Y-direction lever arm optimization solving process provided by the invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. The following examples are illustrative of the invention but are not intended to limit the scope of the invention.
In the description of the embodiments of the present invention, it should be noted that the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are merely for convenience in describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the apparatus or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the embodiments of the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In describing embodiments of the present invention, it should be noted that, unless explicitly stated and limited otherwise, the terms "coupled," "coupled," and "connected" should be construed broadly, and may be either a fixed connection, a removable connection, or an integral connection, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium. The specific meaning of the above terms in embodiments of the present invention will be understood in detail by those of ordinary skill in the art.
In embodiments of the invention, unless expressly specified and limited otherwise, a first feature "up" or "down" on a second feature may be that the first and second features are in direct contact, or that the first and second features are in indirect contact via an intervening medium. Moreover, a first feature being "above," "over" and "on" a second feature may be a first feature being directly above or obliquely above the second feature, or simply indicating that the first feature is level higher than the second feature. The first feature being "under", "below" and "beneath" the second feature may be the first feature being directly under or obliquely below the second feature, or simply indicating that the first feature is less level than the second feature.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the embodiments of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
Referring to fig. 1, an embodiment of the present invention provides a method for precisely compensating for an error of an eccentric effect in a high dynamic gravity measurement. The method can accurately compensate the acceleration eccentric effect errors of the fixed wing, the unmanned aerial vehicle, the AUV and other high dynamic gravity measurement scenes, and improves the accuracy level of gravity anomaly measurement.
Under the high dynamic gravity measurement scene of fixed wing aircraft, unmanned aerial vehicle and AUV, at first design a repeated survey line in the gravity measurement district, repetition number is not less than 3, survey line length satisfies single pass measurement time not less than 1 hour. And then after the task of measuring the whole survey line of the measuring area is completed, measuring the three-dimensional distance between the GNSS antenna phase center or the depth meter center and the mass center of the gravity sensor by using a tape measure to obtain an initial measuring value of the lever arm, and estimating the measuring value range of the lever arm. Then, carrying out optimization solution on lever arm coordinates in two horizontal directions (X direction and Y direction) based on a golden section method, wherein the objective of the solution is to enable the coincidence precision in a designed repeated measuring line to be the highest; and finally, compensating the eccentric effect error of the whole measuring line in the measuring area based on the lever arm parameter information obtained by the optimization solution, and processing to obtain the gravity abnormal result of all the measuring lines in the measuring area.
Under the high dynamic gravity measurement scenes of the fixed wings, the unmanned aerial vehicle, the AUV and the like, a repeated measuring line is designed in a gravity measurement area, the repetition times are not lower than 3 times, and the length of the measuring line meets the requirement that the single-pass measurement time is not less than 1 hour, so that the original data are obtained.
After the task of measuring all survey lines in a measuring area is completed, measuring the three-dimensional distance between the center of the GNSS antenna phase or the center of the depth gauge and the center of mass of the gravity sensor by using a tape measure to obtain an initial measuring value of the lever arm. Based on the initial lever arm measurement value obtained by measuring the tape measure and the experience of measuring the lever arm error range by the tape measure, estimating the proper value interval range of lever arm coordinate points in two horizontal directions (X direction and Y direction) respectively recorded as，/>。
Marking the coincidence precision in the designed repeated measuring line asFunction->Is a horizontal lever arm->The function of (2) is the objective function of the eccentric effect error compensation, and the calculation of the coincidence precision in the repeated measuring line is shown in the formula (1). According to the estimated range of the proper value interval of the lever arm coordinates in the two horizontal directions (X direction and Y direction), the objective function +.>The point at which the minimum is taken is +.>。
The repeated measuring line accords with an accuracy statistical formula:
……(1)
wherein:
-the coincidence precision in repeated line is the objective function +.>；
The difference between the gravity anomaly value of the ith measuring point on the jth repeated measuring line and the average value of the gravity anomaly values of the repeated measuring lines at the jth measuring point is obtained;
the number of repeated measuring points on the repeated measuring line;
the number of the repeated line-measuring is repeated,
wherein the method comprises the steps ofThe calculation formula of (2) is as follows:
=/>,/>，
，
wherein:
the gravity anomaly value of the ith measuring point on the jth repeated measuring line;
the average of the gravity anomaly values was measured for each repeat line for that point.
Selecting a probing point in the range of the X-direction and Y-direction lever arm values，/>，/>，/>（) Satisfy formula (2), in formula (2)>Is the golden section number, thereby obtaining four lever arm coordinate pointsLet alone->，/>，/>And->。
…(2)
Carrying out carrier motion acceleration correction, standard ellipsoidal gravity correction, drift compensation and eccentric effect error compensation data processing on the gravity measurement raw data on the repeated measuring lines to respectively obtain gravity abnormal values of the repeated measuring lines corresponding to four lever arm coordinate points,
and the coincidence precision in the repeated measuring line corresponding to each point is obtained by utilizing a coincidence precision statistical formula in the repeated measuring line. Determination by comparison，/>，/>And->The minimum of the four function values, and further the inclusion of the objective function +.>Interval range of minimum lever arm coordinate point +.>，/>. Then selecting the probe point again in the new lever arm value interval range and further narrowing the interval range +.>，/>. The process is iterated until +.>And is also provided with（/>、/>The precision requirements of the range of the lever arm interval in the X direction and the Y direction respectively), the iterative search process is ended. The coordinates of the minimum point of the objective function obtained at this time are: />，/>Namely, the accurate values obtained by the optimization solution of the X-direction lever arm and the Y-direction lever arm are respectively +.>、/>. The process of the optimization solution of the X-direction lever arm and the Y-direction lever arm is shown in figure 1.
According to the obtained accurate value of the X-direction lever arm and the Y-direction lever arm、/>And carrying out carrier motion acceleration correction, standard ellipsoidal gravity correction, drift compensation and eccentric effect error compensation on the collected raw gravity data of the gravity measurement area, processing to obtain accurate gravity abnormal values of all the measuring lines, and finally realizing accurate compensation on the eccentric effect error of the gravity measurement acceleration.
The accurate compensation method for the gravity measurement eccentric effect error can accurately compensate the acceleration eccentric effect error of the fixed wing, the unmanned aerial vehicle, the AUV and other high dynamic gravity measurement scenes based on the designed repeated measuring lines in the post-processing stage of gravity measurement data, and solves the problem that the acceleration eccentric effect error in the output of the gravity meter cannot be completely eliminated due to the fact that the coordinates of a measuring rod arm are not accurately measured by manually using a measuring tape.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. The accurate compensation method for the gravity measurement acceleration eccentric effect error is characterized by comprising the following steps of:
s1, setting a repeated measuring line in a gravity measuring area, completing measurement operation tasks of all measuring lines in the gravity measuring area, and collecting original gravity data;
s2, measuring the three-dimensional distance between the mass center of the gravity sensor and the phase center of the GNSS antenna or the center of the depth gauge to obtain an initial lever arm measurement value, and estimating the range of a horizontal X-direction lever arm and a horizontal Y-direction lever arm measurement value interval;
s3, in a plane corresponding to a horizontal X-direction lever arm value interval range and a Y-direction lever arm value interval range, four lever arm coordinate points are taken to obtain lever arm coordinates corresponding to the four lever arm coordinate points, carrier motion acceleration correction, standard ellipsoidal gravity correction, drift compensation and eccentric effect error compensation data processing are carried out on the original gravity data on the repeated measuring lines collected in the step S1 through the four lever arm coordinate points, the gravity abnormal values of the repeated measuring lines corresponding to the lever arm coordinate points are respectively obtained, and the coincidence precision in the repeated measuring lines corresponding to the lever arm coordinate points is obtained by utilizing a coincidence precision statistical formula in the repeated measuring lines;
s4, determining minimum values of coincidence precision in the four repeated measuring lines in the S3 through comparison, obtaining lever arm coordinate points corresponding to the minimum values of coincidence precision in the repeated measuring lines, and further reducing the range of the horizontal X-direction lever arm interval and the range of the horizontal Y-direction lever arm interval according to a golden section searching method;
s5, repeating the step S3 and the step S4 until the difference between the horizontal X-direction lever arm interval range and the horizontal Y-direction lever arm interval range meets the precision requirements of the corresponding horizontal X-direction lever arm interval range and horizontal Y-direction lever arm interval range;
s6, respectively solving the midpoint of the horizontal X-direction lever arm interval range and the midpoint of the horizontal Y-direction lever arm interval range obtained in the step S5 to obtain a corresponding horizontal X-direction lever arm accurate value and a horizontal Y-direction lever arm accurate value, carrying out carrier motion acceleration correction, standard ellipsoidal gravity correction, drift compensation and eccentric effect error compensation on the original gravity data of the gravity measurement area collected in the step S1, processing to obtain accurate gravity abnormal values of all measuring lines, and finally realizing accurate compensation on the gravity measurement acceleration eccentric effect error.
2. The method for precisely compensating for the error of the gravity measurement acceleration eccentricity effect according to claim 1, wherein in step S1, the number of repetitions of the repeated line is not less than 3.
3. The method for precisely compensating for the error of the gravity measurement acceleration eccentricity effect according to claim 1, wherein in step S1, the one-way measurement time of the repeated measuring line is not less than 1 hour.
4. The method for precisely compensating for error in gravity measurement acceleration eccentricity effect according to claim 1, wherein in step S3, ranges of horizontal X-direction and Y-direction lever arm values are respectively recorded as，/>Four lever arm coordinate points are taken and are respectively +.>，/>，/>And->Satisfies the following conditionsThe coincidence precision in the repeated measuring lines of four points is respectively recorded as，/>，/>And->。
5. The method for precisely compensating for the error of the gravity measurement acceleration eccentricity effect according to claim 4, wherein in said step S3, the coincidence precision in the repeated measuring line corresponding to each lever arm coordinate point is accomplished by a formulaThe calculation is performed such that,
the repeated measuring line accords with an accuracy statistical formula:
wherein:
for the coincidence precision in the repeated measuring line, namely +.>；
The difference between the gravity anomaly value of the ith measuring point on the jth repeated measuring line and the average value of the gravity anomaly values of the repeated measuring lines at the jth measuring point is obtained;
the number of repeated measuring points on the repeated measuring line;
the number of the repeated line-measuring is repeated,
wherein the method comprises the steps ofThe calculation formula of (2) is as follows:
=/>,/>，
，
wherein:
the gravity anomaly value of the ith measuring point on the jth repeated measuring line;
the average of the gravity anomaly values was measured for each repeat line for that point.
6. The method for precisely compensating for error in gravity measurement acceleration eccentricity effect according to claim 4, wherein in step S6, the precise values obtained by the optimization solution of the X-direction lever arm and the optimization solution of the Y-direction lever arm are respectively、/>Satisfies the following conditions，/>Wherein->，/>Obtained by step S5.
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