CN112629438A - Three-dimensional laser scanner calibration algorithm - Google Patents

Three-dimensional laser scanner calibration algorithm Download PDF

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CN112629438A
CN112629438A CN202011383679.9A CN202011383679A CN112629438A CN 112629438 A CN112629438 A CN 112629438A CN 202011383679 A CN202011383679 A CN 202011383679A CN 112629438 A CN112629438 A CN 112629438A
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horizontal
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CN112629438B (en
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文述生
庄所增
李宁
周光海
肖浩威
丁永祥
闫少霞
张德先
赵瑞东
陈奕均
黄海锋
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South GNSS Navigation Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The application discloses three-dimensional laser scanner calibration algorithm constructs a three-dimensional laser scanner calibration model after calculating the deviation value, substitutes an initial observation value into the three-dimensional laser scanner calibration model to obtain a calibration parameter result, calibrates the deviation of a laser incident beam in the projection of a reflecting prism and the eccentricity difference of a calibration horizontal dial according to the calibration parameter result, and accordingly completes the parallel calibration of a horizontal axis and a horizontal rotating axis formed by the laser beam incident reflecting prism.

Description

Three-dimensional laser scanner calibration algorithm
Technical Field
The application relates to the technical field of three-dimensional laser scanners, in particular to a three-dimensional laser scanner calibration algorithm.
Background
Three-dimensional laser scanning is a novel spatial data acquisition technology, and compared with an electronic theodolite, the three-dimensional laser scanning has the advantages of small precision difference, high data density, high acquisition speed and the like; and if compared with a visual sensor, the device has the advantages of high measurement precision, low possibility of being influenced by the environment, all-weather working, high stability and the like.
The working principle of the three-dimensional laser scanner is similar to that of an electronic theodolite, but the structure is complex. In general, the distance measuring and transmitting device of the electronic theodolite is fixedly arranged in a lens barrel rotating at a low speed, and the calibration can be completed only by considering the sighting axis error, the horizontal axis error and the vertical disc index difference of the lens barrel. The distance measuring and transmitting device of the three-dimensional laser scanner is fixed on one side of the host, the 45-degree reflecting prism rotates around the horizontal shaft at a high speed, and whether laser emitted from the distance measuring and transmitting device can be accurately projected to the center of the 45-degree reflecting prism at the moment is an important problem for subsequent spatial data acquisition. However, in the three-dimensional laser scanner calibration algorithm documents disclosed at present, the possible deviation of the incident light beam projected on the 45 ° reflection prism is not considered, which affects the calibration accuracy of the three-dimensional laser scanner.
The reason why the deviation is affected is whether or not the rotation axis of the 45 ° reflection prism and the horizontal axis formed by the incident beam are parallel to each other, and therefore, before the three-dimensional laser scanner is used, it is necessary to calibrate both the rotation axis of the 45 ° reflection prism and the horizontal axis formed by the incident beam. In addition, a problem that the center of the horizontal scale of the three-dimensional laser scanner may not be completely horizontally overlapped with the center of the 45 ° reflection prism is also considered.
Disclosure of Invention
The application provides a three-dimensional laser scanner calibration algorithm which is used for solving the technical problems that incident light beams are projected on a 45-degree reflecting prism to have deviation and the centers of a horizontal scale and the 45-degree reflecting prism cannot be completely horizontally superposed.
In view of the above, a first aspect of the present application provides a calibration algorithm for a three-dimensional laser scanner, which is applied to a three-dimensional laser scanner, the three-dimensional laser scanner includes a reflection prism and a distance measurement emission device, the reflection prism is provided with a horizontal rotation shaft, the horizontal rotation shaft is provided with a horizontal scale for measuring a horizontal axis angle and a vertical axis angle of the horizontal rotation shaft, the distance measurement emission device emits a laser beam to be projected into the reflection prism, and the calibration algorithm specifically includes the following steps:
s100: establishing a three-dimensional body coordinate system in the space where the reflecting prism and the horizontal rotating shaft are located, wherein the central point of the reflecting prism is set as an O point of the three-dimensional body coordinate system, the horizontal axis is set as an X axis, the collimation axis is set as a Y axis, and the vertical axis is set as a Z axis;
s200: a standing center coordinate system of the three-dimensional laser scanner is established by taking the central point of the reflecting prism as an original point, and the three-dimensional body coordinate system can be coincided with the standing center coordinate system through rotation;
s300: analyzing the deviation amount of the incident beam according to the three-dimensional body coordinate system and the station center coordinate system, and establishing an incident beam deviation model according to the deviation amount of the incident beam and a pre-obtained original observed quantity;
s400: projecting the center-of-gravity coordinate system onto the three-dimensional body coordinate system so as to establish a horizontal scale eccentricity difference model;
s500: substituting the incident beam deviation model into the horizontal scale eccentricity difference model to obtain a three-dimensional laser scanner calibration model, wherein the three-dimensional laser scanner calibration model comprises calibration parameters to be solved;
s600: constructing an instrument precision error model and a collimation error model according to a pre-obtained angle measurement error, wherein the pre-obtained angle measurement error comprises a horizontal angle error, a vertical angle error and a distance measurement error, constructing an observation error equation according to the instrument precision error model and the collimation error model, analyzing the observation error equation to obtain an X-axis coordinate error, a Y-axis coordinate error and a Z-axis coordinate error, and taking the X-axis coordinate error, the Y-axis coordinate error and the Z-axis coordinate error as a basis for weighting the calibration parameters to be solved;
s700: calculating partial derivatives of the incident beam deviation model and the horizontal scale eccentricity difference model to obtain a coefficient matrix of a differential equation, establishing an iterative weighted least square equation according to the basis for weighting and pre-obtained observation data of the same-name point, and solving the three-dimensional laser scanner calibration model by using the iterative weighted least square equation to obtain a solution result of the calibration parameter to be solved;
s800: and calibrating the deviation of the laser incident beam in the projection of the reflecting prism and the eccentricity difference of the calibration horizontal scale according to the solving result of the calibration parameter to be solved, thereby completing the parallel calibration of the horizontal axis formed by the laser beam incident on the reflecting prism and the horizontal rotating shaft.
According to the technical scheme, the embodiment of the application has the following advantages:
according to the three-dimensional laser scanner calibration algorithm, a three-dimensional laser scanner calibration model is constructed after the deviation value is calculated, the initial observation value is substituted into the three-dimensional laser scanner calibration model to obtain a calibration parameter result, the deviation of a laser incident beam projected on a reflecting prism and the eccentricity difference of a calibration horizontal dial are calibrated according to the calibration parameter result, and therefore the parallel calibration of a horizontal shaft and a horizontal rotating shaft formed by the laser beam incident reflecting prism is completed.
Drawings
Fig. 1 is a flowchart of a three-dimensional laser scanner calibration algorithm provided in an embodiment of the present application;
FIG. 2 is a schematic diagram of a coordinate system provided in an embodiment of the present application;
fig. 3 is a schematic view of another coordinate system provided in the embodiment of the present application.
Detailed Description
In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The application provides a pair of three-dimensional laser scanner calibration algorithm is applied to three-dimensional laser scanner, and three-dimensional laser scanner includes reflecting prism and range finding emitter, and reflecting prism is equipped with horizontal rotation axis, and horizontal rotation axis is equipped with the horizontal scale that is used for measuring its horizontal axis angle and vertical axis angle, and the projection is in reflecting prism after range finding emitter launches the laser beam.
Referring to fig. 1, the calibration algorithm specifically includes the following steps:
s100: establishing a three-dimensional coordinate system in a space where the reflecting prism and the horizontal rotating shaft are located, wherein the central point of the reflecting prism is set as an O point of the three-dimensional coordinate system, the horizontal axis is set as an X axis, the collimation axis is set as a Y axis, and the vertical axis is set as a Z axis;
s200: a three-dimensional body coordinate system can be superposed with the standing center coordinate system through rotation by taking the central point of the reflecting prism as an original point;
note that, by establishing a three-dimensional body coordinate system in which the reflecting prism and the horizontal rotation axis are located and a center-of-gravity coordinate system established with the center point of the reflecting prism as the origin, since the three-dimensional laser scanner can rotate 360 °, the three-dimensional body coordinate system is used as the coordinate system in which the three-dimensional laser scanner rotates, and the center-of-gravity coordinate system and the three-dimensional body coordinate system coincide at the initial rotation angle.
S300: analyzing the deviation amount of the incident beam according to the three-dimensional body coordinate system and the station center coordinate system, and establishing an incident beam deviation model according to the deviation amount of the incident beam and a pre-obtained original observed quantity;
it should be noted that, the deviation amount of the incident light beam can be calculated through the comparison between the three-dimensional body coordinate system and the center-of-gravity coordinate system, so as to establish an incident light beam deviation model according to the deviation amount of the incident light beam and the original observed amount, where the original observed amount is an observed amount which can be given by the three-dimensional laser scanner in advance and has a certain error, and the original observed amount is corrected through the deviation amount of the incident light beam, so as to obtain the incident light beam deviation model.
S400: projecting the center of gravity coordinate system to a three-dimensional body coordinate system so as to establish a horizontal scale eccentricity difference model;
s500: substituting the incident beam deviation model into a horizontal scale eccentricity difference model to obtain a three-dimensional laser scanner calibration model, wherein the three-dimensional laser scanner calibration model comprises calibration parameters to be solved;
s600: constructing an instrument precision error model and a collimation error model according to a pre-obtained angle measurement error, wherein the pre-obtained angle measurement error comprises a horizontal angle error, a vertical angle error and a distance measurement error, constructing an observation error equation according to the instrument precision error model and the collimation error model, analyzing the observation error equation to obtain an X-axis coordinate error, a Y-axis coordinate error and a Z-axis coordinate error, and taking the X-axis coordinate error, the Y-axis coordinate error and the Z-axis coordinate error as a basis for weighting a calibration parameter to be solved;
it should be noted that, in this embodiment, the influence of the error generated by the accuracy of the instrument itself and the collimation error on the estimation result of the calibration parameter is considered, and the horizontal angle error, the vertical angle error and the ranging error can be obtained from a user manual in the angle measurement device, after the instrument accuracy error model and the collimation error model are established according to the angle measurement error, the observation error equation is constructed according to the instrument accuracy error model and the collimation error model, so as to obtain the basis for weighting the calibration parameter, and thus the weight of each error can be given according to the basis for weighting, so as to improve the estimation accuracy.
S700: calculating partial derivatives of the incident beam deviation model and the horizontal scale eccentricity difference model to obtain a coefficient matrix of a differential equation, establishing an iterative weighted least square equation according to a fixed weight basis and pre-obtained homonymy point observation data, and solving the iterative weighted least square equation into a three-dimensional laser scanner calibration model so as to obtain a solution result of a calibration parameter to be solved;
it should be noted that after the three-dimensional laser scanner calibration model is constructed, the original observation value is substituted into the three-dimensional laser scanner calibration model, and the calibration parameter result can be obtained through iteration.
S800: and calibrating the deviation of the laser incident beam in the projection of the reflecting prism and the eccentricity difference of the calibration horizontal scale according to the solving result of the calibration parameter to be solved, thereby completing the parallel calibration of the horizontal axis formed by the laser incident reflecting prism and the horizontal rotating shaft.
In the embodiment, the three-dimensional laser scanner calibration model is constructed after the deviation value is calculated, the initial observation value is substituted into the three-dimensional laser scanner calibration model to obtain the calibration parameter result, and the deviation of the laser beam incident on the reflecting prism and the eccentricity difference of the calibration horizontal disc are calibrated according to the calibration parameter result, so that the parallel calibration of the horizontal axis and the horizontal rotating axis formed by the laser beam incident reflecting prism is completed.
The following is a detailed description of the present embodiment:
step S100 specifically includes: a three-dimensional body coordinate system O-XYZ is established in the space where the reflection prism and the horizontal rotation axis are located, as shown in the schematic diagram of the coordinate system shown in fig. 2, wherein the central point of the reflection prism is set as the O point of the three-dimensional body coordinate system, the horizontal axis is set as the X axis, the collimation axis is set as the Y axis, the vertical axis is set as the Z axis, the angle that the three-dimensional body coordinate system passes when rotating around the Z axis is the horizontal angle Φ, the angle that the three-dimensional body coordinate system passes when rotating around the Y axis is the vertical angle θ, and when there is no deviation and the reflection vector is in the same direction with the Z axis.
Step S200 specifically includes: as shown in fig. 2, with three-dimensional laser scanningStanding center coordinate system O-X of three-dimensional laser scanner established by taking central point of scanner as original pointsYsZsAnd the station center coordinate system does not change along with the horizontal angle phi and the vertical angle theta, and when the horizontal angle phi is 0, the station center coordinate system is superposed with the three-dimensional body coordinate system, wherein the distance from the original point O to the target point B is defined as r, and the target point is a reflection point of the incident light beam hitting on the reflection prism.
Step S300 specifically includes: as shown in the schematic diagram of the coordinate system shown in fig. 3, the distance measuring and transmitting device 100 transmits the incident beam 110 to generate the reflected beam 120 after being reflected by the 45 ° reflective prism 200, and the reflection point hit by the 45 ° reflective prism 200 is B;
the 45-degree reflecting prism rotates around the Y axis, and the three-dimensional body coordinate system O-XYZ does not change along with the vertical angle theta but changes along with the horizontal angle phi (around the Z axis);
in plane XOZ, if there is no aberration in incident beam 110, then incident beam 110 is incident along the Y-axis and reflected along the Z-axis; in the plane X 'OZ', if the incident light beam 110 is deviated, the incident light beam 110 is incident along AO 'and reflected along OB'.
The incident beam deviation model comprises a horizontal angle correction observed quantity phi 'and a vertical angle correction observed quantity theta';
wherein the horizontal angle correction observed quantity phi' is expressed by formula 1 as:
φ'＝φ+co/sinθ+io cotθ+φoequation 1
In equation 1, phi is the original observed quantity of the horizontal angle, C0As the boresight error constant term, ioIs a constant term of error in the horizontal axis, phioIs the index difference constant term of the horizontal angle.
At the same time, horizontal axis error ioIs caused by the fact that the horizontal rotation axis of the 45 deg. reflecting prism 200 cannot be kept horizontal, i.e. due to the incident deviation deltaz of the incident beam 100 with respect to the Z axis, and does not vary with the vertical angle, while the horizontal axis error is generally a small angle, when the horizontal axis error i is smalloAt small angles, this can be expressed in terms of the deviation Δ z of incidence, which is:
s3011: according to the z-axis direction deviation Delta z of the incident beamThe distance delta y from the light source of the distance measurement transmitting device to the reflecting point of the reflecting prism represents a horizontal axis error constant term ioExpressed as:
Figure BDA0002810404240000061
in the formula, Δ y is a unit distance 1;
s3012: the distance Δ y from the light source of the ranging transmitter to the reflection point of the reflection prism according to the deviation Δ x of the incident beam in the x-axis direction represents a horizontal-axis error constant term φ o, expressed as:
Figure BDA0002810404240000062
in the formula, Δ y is a unit distance 1;
s3013: substituting equation 2 and equation 3 into equation 1, the horizontal angle correction observation φ' is converted to:
φ'＝φ+co[ theta ] - Δ zcot- Δ x equation 4
Further, the vertical angle correction observation amount θ' is expressed by equation 5 as:
θ' ═ θ + ξ (θ) equation 5
In formula 5, θ is the original vertical angle observation, and ξ (θ) is the vertical angle index difference.
Meanwhile, the vertical angle index difference ξ (θ) is caused by the incident deviations Δ x and Δ z, which can be represented by Δ x and Δ z, then there are:
s3001: constructing a transpose matrix of an incident vector a of the incident ray as:
a＝[Δx Δy Δz]Twherein, Δ x is the deviation of the incident beam in the x-axis direction, Δ y is the distance from the light source of the distance measuring and transmitting device to the reflection point of the reflection prism, Δ y is the unit distance 1, and Δ z is the deviation of the incident beam in the z-axis direction;
s3002: calculating a reflection vector b of the incident light reflected by the reflecting prism through a formula 6 according to the incident vector a and a unit normal vector n of the reflecting surface of the reflecting prism, wherein the formula 6 is as follows:
b-a-2 (a · n) n formula 6
In the formula, the unit normal vector n is calculated by formula 7, where formula 7 is:
Figure BDA0002810404240000071
then a · n in equation 6 is:
Figure BDA0002810404240000072
s3003: constructing a transpose matrix of the reflection vector b as follows:
b＝[bx by bz]Twherein b isxIs the X-axis component of the reflection vector b, byIs the y-axis direction component of the reflection vector b; bzIs the z-axis direction component of the reflection vector b;
s3004: the component vector in each axis direction according to the reflection vector b in step S3002 is expressed as:
Figure BDA0002810404240000073
s3005: and projecting the reflection vector to a plane XOZ belonging to the three-dimensional body coordinate system, and then rotating the reflection vector by an angle theta by taking the Y axis as a rotating axis to obtain a vector u, wherein u is expressed as:
u＝[ux uy uz]Tt is a matrix transpose,
the components of the vector u are then:
Figure BDA0002810404240000074
s3006: and calculating a vertical angle index difference xi (theta) according to the included angle between the vector u and the Z axis as follows:
Figure BDA0002810404240000081
in the formula, xioIs a vertical angular scale difference constant;
s3007: substituting equation 10 into equation 5, the vertical angle correction observation θ' is converted to:
Figure BDA0002810404240000082
further, step S400 specifically includes:
s4001: defining the center of gravity coordinate system as O-XsYsZsThen belongs to the horizontal plane X in the center-of-gravity coordinate systemsOYsEstablishing a polar coordinate with the horizontal angle phi as a variable as follows:
Figure BDA0002810404240000083
in the formula, δ X is the deviation of the X-axis direction of the horizontal scale, δ Y is the deviation of the Y-axis direction of the horizontal scale;
s4002: defining the three-dimensional body coordinate system as O-XYZ, substituting formula 12 into the polar coordinates of the three-dimensional body coordinate system O-XYZ to obtain a horizontal scale eccentricity difference corrected station center coordinate system, namely obtaining a horizontal scale eccentricity difference model, wherein the horizontal scale eccentricity difference model is as follows:
Figure BDA0002810404240000084
further, step S500 specifically includes:
s5001: substituting formula 4 and formula 11 into formula 13 to obtain a three-dimensional laser scanner calibration model, where the three-dimensional laser scanner calibration model is:
Figure BDA0002810404240000085
wherein r is an original distance measurement observed quantity, phi is an original horizontal angle observed quantity, theta is an original vertical angle observed quantity, m is a distance correction addition constant, lambda is a distance correction multiplication constant, coIs the collimation axis error constant term, xioThe constant term of the vertical angle scale difference is adopted, wherein delta X is the deviation of an incident beam in the X-axis direction, delta Z is the deviation of an incident beam in the Z-axis direction, delta X is the deviation of the horizontal scale in the X-axis direction, and delta Y is the deviation of the horizontal scale in the Y-axis direction;
it should be noted that the original distance measurement observed quantity r, the original horizontal angle observed quantity phi and the original vertical angle observed quantity theta are parameters that can be observed in the three-dimensional laser scanner in advance; and distance correction adding constant m, distance correction multiplying constant lambda and collimation axis error constant item coVertical angle scale difference constant term xioThe X-axis direction deviation delta X of the incident light beam, the Z-axis direction deviation delta Z of the incident light beam, the X-axis direction deviation delta X of the horizontal scale and the Y-axis direction deviation delta Y of the horizontal scale are calibration parameters to be solved.
Because the three-dimensional laser scanner needs distance measurement and angle measurement to obtain point cloud data, but before calibration, the distance measurement and the angle measurement have errors, the calibration scanner needs observation data of the same-name point, and when the same-name point is selected, a collimation error exists. Therefore, the effect of observation errors on the calibration parameter estimation should be taken into account when estimating the scanner calibration parameters.
Before considering the influence of the observation error on the estimation result of the calibration parameter, it is also required to verify whether the error before establishing the calibration model of the three-dimensional laser scanner is consistent with the error after establishing the calibration model of the three-dimensional laser scanner, so that the following steps are performed:
if the horizontal angle error is δ Φ and the vertical angle error is δ θ, then:
Figure BDA0002810404240000091
the horizontal angle error and the vertical angle error can be obtained in a user manual of the angle measuring device, since the vertical angle error δ θ is a small angle and can be ignored, so a second-order term is ignored, according to a trigonometric function formula, cot δ θ → ∞, sin δ θ ═ 0, cos δ θ ═ 1, then the formula 15 can be simplified as follows:
Figure BDA0002810404240000092
since the above approximation and the right angle error are neglected, it can be seen that δ θ does not affect δ Φ', so there are:
δ Φ ═ δ Φ equation 17
The same reason is also that
θ '+ δ θ' ═ θ + δ θ + ξ (θ) formula 18
δ θ ═ δ θ equation 19
From the above formula, it is known that δ Φ 'is δ Φ and δ θ' is δ θ, and there are:
sin (phi ' + delta phi) ═ cos delta phi sin phi ' + cos phi ' sin delta phi ═ sin phi ' + delta phi cos phi ' equation 20
cos (phi ' + delta phi) ═ cos delta phi cos phi ' -sin phi ' sin delta phi ═ cos phi ' -delta phi sin phi ' equation 21
The same principle is as follows:
sin (θ ' + δ θ) ═ sin θ ' + δ θ cos θ ' equation 22
cos (θ ' + δ θ) ═ cos θ ' - δ θ sin θ ' equation 23
Substituting equations 22 and 23 into the three-dimensional laser scanner calibration model, the high order quantity is truncated as follows:
cos(φ'+δφ)sin(θ'+δθ)＝(cosφ'-δφsinφ')(sinθ'+δφsinθ')
the equation 24 is expressed by cos phi 'sin theta' + δ phi cos phi 'cos theta' - δ phi sin phi 'sin theta' + o (n)
sin(φ'+δφ)sin(θ'+δθ)＝(sinφ'+δφcosφ')(sinθ'+δφcosθ')
Sin phi 'sin theta' + δ phi sin phi 'cos theta' + δ phi cos phi 'sin theta' + o (n) formula 25
Therefore, the error before the three-dimensional laser scanner calibration model is established is consistent with the error after the three-dimensional laser scanner calibration model is established.
Further, step S600 specifically includes:
s6001: recording the corrected distance measurement observed value r' ═ r + m + λ r, and after eliminating the high-order quantity from formula 14, obtaining an instrument precision error model as follows:
Figure BDA0002810404240000101
Figure BDA0002810404240000102
Figure BDA0002810404240000103
s6002: because three-dimensional laser scanner aims a homonymy point and shines, then must produce the error, can divide into horizontal component and vertical component with the error that produces, register to aim at the horizontal component of error for delta alpha, aim at the vertical component of error for delta beta, then aim at the error model and be:
Figure BDA0002810404240000111
s6003: because δ Φ, δ θ, δ r are independent of each other, only the square value of each term needs to be taken, and then the high-order error is eliminated according to the formula 26, the formula 27, the formula 28, and the formula 29, and the observation error equation is obtained as follows:
Figure BDA0002810404240000112
in the formula (I), the compound is shown in the specification,
Figure BDA0002810404240000113
as a basis for weighting the calibration parameters to be solved.
Further, step S700 specifically includes:
s7001: for equation 14, distance correction adding constant m, distance correction multiplying constant lambda and collimation axis error constant item coVertical angle scale difference constant term xioSolving partial derivatives of X-axis direction deviation delta X of the incident light beams, Z-axis direction deviation delta Z of the incident light beams, X-axis direction deviation delta X of the horizontal scale and Y-axis direction deviation delta Y of the horizontal scale;
specifically, the partial derivatives of the calibration parameters are:
the distance correction plus the partial derivative of the constant m is:
Figure BDA0002810404240000114
the partial derivative of the distance correction times the constant λ is:
Figure BDA0002810404240000115
quasi-axis error constant term coThe partial derivatives of (a) are:
Figure BDA0002810404240000116
Figure BDA0002810404240000117
vertical angle scale difference constant term xioThe partial derivatives of (a) are:
Figure BDA0002810404240000121
the partial derivative of the X-axis directional deviation Δ X of the incident beam is:
Figure BDA0002810404240000122
the partial derivative of the Z-axis direction deviation Δ Z of the incident beam is:
Figure BDA0002810404240000123
the partial derivative of the X-axis deviation deltax on the horizontal scale is:
Figure BDA0002810404240000124
the partial derivative of the horizontal scale Y-axis direction deviation δ Y is:
Figure BDA0002810404240000125
s7002: and (3) constructing a full differential equation of the three-dimensional laser scanner calibration model according to the partial derivatives of the items in the step S7001, wherein the full differential equation is as follows:
Figure BDA0002810404240000126
in the formula (I), the compound is shown in the specification,
Figure BDA0002810404240000127
the partial derivative of the constant m is added for the distance correction,
Figure BDA0002810404240000128
to correct the distance by the partial derivative of the constant lambda,
Figure BDA0002810404240000129
multiplying constant c for distance correctionoThe partial derivative of (a) of (b),
Figure BDA00028104042400001210
is the vertical angle scale difference constant term xioThe partial derivative of (a) of (b),
Figure BDA00028104042400001211
to enterThe partial derivative of the X-axis directional deviation deltax of the beam,
Figure BDA00028104042400001212
as a partial derivative of the Z-axis directional deviation az of the incident light beam,
Figure BDA0002810404240000131
is the partial derivative of the deviation deltax in the X-axis direction of the horizontal scale,
Figure BDA0002810404240000132
the partial derivative of the deviation deltay of the Y-axis direction of the horizontal scale;
solving the three-dimensional laser scanner calibration model by the iterative weighted least square equation comprises an inner coincidence calibration parameter solving process and/or an outer coincidence calibration parameter solving process:
the solving process of the internal coincidence calibration parameters specifically comprises the following steps:
s7011: the three-dimensional laser scanner is driven by a horizontal rotating shaft to carry out 360-degree scanning work, and n homonymous points are collected and recorded as BiN, and the horizontal angle corresponding to n homonymous points is phioiHorizontal angle phioiA point measured in a range of 0 to 180 DEG of the rotation angle is defined as [ phi ]oi，θoi，roi]The corresponding three-dimensional coordinate system result is defined as [ x ]oi，yoi，zoi]Substituting the original observation results corresponding to n homonymous points within the range of 0-180 degrees of the rotation angle into a formula 14 to obtain
Figure BDA0002810404240000137
S7012: recording horizontal angle phioiThe point measured in the range of 180-360 DEG of rotation angle is defined as [ phi ]1i，θ1i，r1i]The corresponding three-dimensional coordinate system result is defined as [ x ]1i，y1i，z1i]Substituting the original observation results corresponding to n homonymous points within the range of the rotation angle of 180-360 degrees into the formula 14 to obtain
Figure BDA0002810404240000133
S7013: noting the true coordinate of the same name point as FrefFor F in equation 14sBy performing taylor expansion, one can obtain:
Figure BDA0002810404240000134
subtracting simultaneous formula 41, the true coordinate of the same-name point is FrefEliminated to obtain an observation equation internally conforming to the estimation of the calibration parameters, wherein the weight P array of the observed values is determined by the error equation of the observed quantity, and the vector of the calibration parameters is recorded as
Figure BDA0002810404240000135
The system of equations for the least squares solution can be found as:
Figure BDA0002810404240000136
s7014: since the calibration parameter to be estimated is a small numerical error, an initial value is given according to equation 42
Figure BDA0002810404240000141
Iterating by using Gauss-Newton iteration method
Figure BDA0002810404240000142
The result of the calibration parameter can be obtained
Figure BDA0002810404240000143
The solving process of the external coincidence calibration parameters specifically comprises the following steps:
s7021: providing a reference point and external orientation parameters by a total station through setting relative to the outside of the three-dimensional laser scanner, wherein the external orientation parameters comprise a three-dimensional body coordinate system of the three-dimensional laser scanner and conversion parameters of an external coordinate system, and specifically comprise an X-axis rotation angle, a Y-axis rotation angle, a Z-axis rotation angle, an X-axis translation amount, a Y-axis translation amount and a Z-axis translation amount;
s7022: rotating and translating the three-dimensional laser scanner calibration model through external orientation parameters to obtain an observation equation with external coincidence estimation as follows:
Figure BDA0002810404240000144
in the formula, R is a rotating cosine matrix;
s7023: solving the full differential equation for equation 43 as:
Figure BDA0002810404240000145
s7024: for n homonyms BiAnd i is 1,2, and n, and the observed quantity of the spherical coordinate system measured by the three-dimensional laser scanner is recorded as
Figure BDA0002810404240000146
Figure BDA0002810404240000147
The observed quantity in the Z-axis direction is obtained by substituting the observed quantity in the formula 43
Figure BDA0002810404240000148
Recording the reference observed quantity of a space rectangular coordinate system given by the total station as
Figure BDA0002810404240000149
Taylor expansion of equation 43 yields:
Figure BDA00028104042400001410
then the system of equations for the least squares solution is obtained according to equation 45 as:
Figure BDA00028104042400001411
s7025: to ensure
Figure BDA0002810404240000151
And the accuracy of the final convergence result, wherein the external orientation parameter needs to be given an initial value, the external orientation parameter is given an initial value according to a formula 47, and the formula 47 is expressed as follows:
Figure BDA0002810404240000152
wherein svd is singular value decomposition, and MEAN is column averaging; after obtaining the fixed initial value of the external orientation parameter, setting the initial values of the other parameters as 0, and iterating
Figure BDA0002810404240000153
All calibration parameter results can be obtained
Figure BDA0002810404240000154
The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.

Claims (10)

1. A three-dimensional laser scanner calibration algorithm is applied to a three-dimensional laser scanner, the three-dimensional laser scanner comprises a reflecting prism and a distance measurement transmitting device, the reflecting prism is provided with a horizontal rotating shaft, the horizontal rotating shaft is provided with a horizontal dial for measuring the horizontal shaft angle and the vertical shaft angle of the reflecting prism, the distance measurement transmitting device transmits laser beams and then projects the laser beams into the reflecting prism, and the calibration algorithm is characterized by specifically comprising the following steps:
s100: establishing a three-dimensional body coordinate system in the space where the reflecting prism and the horizontal rotating shaft are located, wherein the central point of the reflecting prism is set as an O point of the three-dimensional body coordinate system, the horizontal axis is set as an X axis, the collimation axis is set as a Y axis, and the vertical axis is set as a Z axis;
s200: a standing center coordinate system of the three-dimensional laser scanner is established by taking the central point of the reflecting prism as an original point, and the three-dimensional body coordinate system can be coincided with the standing center coordinate system through rotation;
s300: analyzing the deviation amount of the incident beam according to the three-dimensional body coordinate system and the station center coordinate system, and establishing an incident beam deviation model according to the deviation amount of the incident beam and a pre-obtained original observed quantity;
s400: projecting the center-of-gravity coordinate system onto the three-dimensional body coordinate system so as to establish a horizontal scale eccentricity difference model;
s500: substituting the incident beam deviation model into the horizontal scale eccentricity difference model to obtain a three-dimensional laser scanner calibration model, wherein the three-dimensional laser scanner calibration model comprises calibration parameters to be solved;
s600: constructing an instrument precision error model and a collimation error model according to a pre-obtained angle measurement error, wherein the pre-obtained angle measurement error comprises a horizontal angle error, a vertical angle error and a distance measurement error, constructing an observation error equation according to the instrument precision error model and the collimation error model, analyzing the observation error equation to obtain an X-axis coordinate error, a Y-axis coordinate error and a Z-axis coordinate error, and taking the X-axis coordinate error, the Y-axis coordinate error and the Z-axis coordinate error as a basis for weighting the calibration parameters to be solved;
s700: calculating partial derivatives of the incident beam deviation model and the horizontal scale eccentricity difference model to obtain a coefficient matrix of a differential equation, establishing an iterative weighted least square equation according to the basis for weighting and pre-obtained observation data of the same-name point, and solving the three-dimensional laser scanner calibration model by using the iterative weighted least square equation to obtain a solution result of the calibration parameter to be solved;
s800: and calibrating the deviation of the laser incident beam in the projection of the reflecting prism and the eccentricity difference of the calibration horizontal scale according to the solving result of the calibration parameter to be solved, thereby completing the parallel calibration of the horizontal axis formed by the laser beam incident on the reflecting prism and the horizontal rotating shaft.
2. The three-dimensional laser scanner calibration algorithm according to claim 1, wherein the step S100 specifically comprises: and establishing a three-dimensional body coordinate system in a space where the reflecting prism and the horizontal rotating shaft are located, wherein a central point of the reflecting prism is set as an O point of the three-dimensional body coordinate system, a horizontal axis is set as an X axis, a collimation axis is set as a Y axis, a vertical axis is set as a Z axis, an angle which the three-dimensional body coordinate system passes when rotating around the Z axis is a horizontal angle phi, an angle which the three-dimensional body coordinate system passes when rotating around the Y axis is a vertical angle theta, and when no deviation exists and a reflecting vector is in the same direction with the Z axis, the theta is 0.
3. The three-dimensional laser scanner calibration algorithm according to claim 2, wherein the step S200 specifically comprises: and establishing a station center coordinate system of the three-dimensional laser scanner by taking a central point of the three-dimensional laser scanner as an origin, wherein the station center coordinate system does not change along with the horizontal angle phi and the vertical angle theta, and when the horizontal angle phi is 0, the station center coordinate system is superposed with the three-dimensional body coordinate system.
4. The three-dimensional laser scanner calibration algorithm according to claim 1, wherein the incident beam deviation model in step S300 comprises a horizontal angle correction observation Φ 'and a vertical angle correction observation θ';
wherein the horizontal angle correction observed quantity phi' is expressed by formula 1 as:
φ'＝φ+co/sinθ+iocotθ+φoequation 1
In equation 1, phi is the original observed quantity of the horizontal angle, C0As the boresight error constant term, ioIs a constant term of error in the horizontal axis, phioIs a horizontal angle index difference constant term;
meanwhile, the vertical angle correction observed quantity θ' is expressed by equation 2 as:
θ' ═ θ + ξ (θ) equation 2
In formula 2, θ is the original observed quantity of the vertical angle, and ξ (θ) is the vertical angle index difference.
5. The three-dimensional laser scanner calibration algorithm according to claim 4, wherein the step S300 further comprises:
s3001: constructing a transpose matrix of the incident vector a of the incident ray as follows:
a＝[Δx Δy Δz]Twherein, Δ x is the x-axis direction deviation of the incident beam, Δ y is the distance from the light source of the distance measuring and transmitting device to the reflection point of the reflection prism, Δ y is the unit distance 1, and Δ z is the z-axis direction deviation of the incident beam;
s3002: calculating a reflection vector b of the incident light after being reflected by the reflection prism according to the incident vector a and a unit normal vector n of a reflection surface of the reflection prism through a formula 3, wherein the formula 3 is as follows:
b-a-2 (a · n) n formula 3
In the formula, the unit normal vector n is calculated by formula 4, where formula 4 is:
Figure RE-FDA0002959851930000031
then a · n in equation 3 is:
Figure RE-FDA0002959851930000032
s3003: constructing a transpose matrix of the reflection vector b as follows:
b＝[bx by bz]Twherein b isxIs the X-axis component of the reflection vector b, byIs the y-axis direction component of the reflection vector b; bzIs the z-axis direction component of the reflection vector b;
s3004: according to the axial component vector of the reflection vector b in the step S3002, it is expressed as:
Figure RE-FDA0002959851930000033
s3005: projecting the reflection vector to a plane XOZ belonging to the three-dimensional body coordinate system, and then rotating the plane by an angle theta by taking a Y axis as a rotating axis to obtain a vector u, wherein u is expressed as:
u＝[ux uy uz]Tt is a matrix transpose,
the components of the vector u are then:
Figure RE-FDA0002959851930000034
s3006: calculating the vertical angle index difference xi (theta) according to the included angle between the vector u and the Z axis as follows:
Figure RE-FDA0002959851930000035
in the formula, xioIs a vertical angular scale difference constant;
s3007: substituting equation 7 into equation 2, the vertical angle correction observation θ' is converted to:
Figure RE-FDA0002959851930000041
6. the three-dimensional laser scanner calibration algorithm according to claim 5, wherein the step S300 further comprises:
s3011: the error constant term i of the horizontal axis is expressed according to the deviation Delta z of the z-axis direction of the incident beam and the distance Delta y from the light source of the distance measurement transmitting device to the reflecting point of the reflecting prismoExpressed as:
Figure RE-FDA0002959851930000042
in the formula, Δ y is a unit distance 1;
s3012: and the distance delta y between the light source of the distance measuring and transmitting device and the reflecting point of the reflecting prism represents the error constant term phi o of the horizontal axis according to the deviation delta x of the incident beam in the x-axis direction and is expressed as:
Figure RE-FDA0002959851930000043
in the formula, Δ y is a unit distance 1;
s3013: substituting equation 9 and equation 10 into equation 1, the horizontal angle correction observation φ' is converted to:
φ'＝φ+cothe/sin θ - Δ zcot θ - Δ x equation 11.
7. The three-dimensional laser scanner calibration algorithm according to claim 6, wherein the step S400 specifically comprises:
s4001: defining the station center coordinate system as O-XsYsZsThen in the horizontal plane X of said center-of-gravity coordinate systemsOYsEstablishing a polar coordinate with the horizontal angle phi as a variable as follows:
Figure RE-FDA0002959851930000044
in the formula, δ X is the deviation of the X-axis direction of the horizontal scale, δ Y is the deviation of the Y-axis direction of the horizontal scale;
s4002: defining the three-dimensional body coordinate system as O-XYZ, and substituting formula 12 into the polar coordinates of the three-dimensional body coordinate system O-XYZ to obtain a horizontal scale eccentricity difference corrected station center coordinate system, that is, to obtain the horizontal scale eccentricity difference model, where the horizontal scale eccentricity difference model is:
Figure RE-FDA0002959851930000051
8. the three-dimensional laser scanner calibration algorithm according to claim 7, wherein the step S500 specifically comprises:
s5001: substituting formula 8 and formula 11 into formula 13 to obtain a three-dimensional laser scanner calibration model, where the three-dimensional laser scanner calibration model is:
Figure RE-FDA0002959851930000052
wherein r is an original distance measurement observed quantity, phi is an original horizontal angle observed quantity, theta is an original vertical angle observed quantity, m is a distance correction addition constant, lambda is a distance correction multiplication constant, coIs the collimation axis error constant term, xioIn the term of the vertical angle scale difference constant, Δ X is the deviation of the incident beam in the X-axis direction, Δ Z is the deviation of the incident beam in the Z-axis direction, δ X is the deviation of the horizontal scale in the X-axis direction, and δ Y is the deviation of the horizontal scale in the Y-axis direction.
9. The three-dimensional laser scanner calibration algorithm according to claim 8, wherein the step S600 specifically comprises:
s6001: recording the corrected distance measurement observed value r' ═ r + m + λ r, and after eliminating the high-order quantity from formula 14, obtaining an instrument precision error model as follows:
Figure RE-FDA0002959851930000053
Figure RE-FDA0002959851930000054
Figure RE-FDA0002959851930000055
s6002: and recording the horizontal component of the collimation error as delta alpha, and the vertical component of the collimation error as delta beta, wherein the collimation error model is as follows:
Figure RE-FDA0002959851930000061
s6003: because the delta phi, the delta theta and the delta r are mutually independent, high-order errors are eliminated according to a formula 15, a formula 16, a formula 17 and a formula 18, and an observation error equation is obtained
Figure RE-FDA0002959851930000062
In the formula (I), the compound is shown in the specification,
Figure RE-FDA0002959851930000063
as the basis for weighting the calibration parameters to be solved.
10. The three-dimensional laser scanner calibration algorithm according to claim 9, wherein the step S700 specifically comprises:
s7001: the distance correction in equation 14 is added with constant m, distance correction multiplied by constant lambda, collimation axis error constant term coVertical angle scale difference constant term xioX-axis direction deviation Deltax of incident light beam, Z-axis direction deviation Deltax of incident light beam, X-axis direction deviation Deltax of horizontal scale and horizontal scaleSolving a partial derivative by the deviation deltay in the Y-axis direction;
s7002: constructing a full differential equation of the three-dimensional laser scanner calibration model according to the partial derivatives of the items in the step S7001, wherein the full differential equation is as follows:
Figure RE-FDA0002959851930000064
Figure RE-FDA0002959851930000065
in the formula (I), the compound is shown in the specification,
Figure RE-FDA0002959851930000066
the partial derivative of the constant m is added for the distance correction,
Figure RE-FDA0002959851930000067
to correct the distance by the partial derivative of the constant lambda,
Figure RE-FDA0002959851930000068
multiplying constant c for distance correctionoThe partial derivative of (a) of (b),
Figure RE-FDA0002959851930000069
is the vertical angle scale difference constant term xioThe partial derivative of (a) of (b),
Figure RE-FDA00029598519300000610
as a partial derivative of the X-axis directional deviation deltax of the incident beam,
Figure RE-FDA00029598519300000611
as a partial derivative of the Z-axis directional deviation az of the incident light beam,
Figure RE-FDA00029598519300000612
is the partial derivative of the deviation deltax in the X-axis direction of the horizontal scale,
Figure RE-FDA00029598519300000613
the partial derivative of the deviation deltay of the Y-axis direction of the horizontal scale;
the step of solving the three-dimensional laser scanner calibration model by the iterative weighted least square equation comprises an inner coincidence calibration parameter solving process and/or an outer coincidence calibration parameter solving process;
the solving process of the internal coincidence calibration parameters specifically comprises the following steps:
s7011: the three-dimensional laser scanner is driven by the horizontal rotating shaft to carry out 360-degree scanning work, and n homonymous points are collected and recorded as Bi1,2, and n, wherein the horizontal angle corresponding to the n homonymous points is phioiSaid horizontal angle phioiA point measured in a range of 0 to 180 DEG of the rotation angle is defined as [ phi ]oi，θoi，roi]The corresponding three-dimensional coordinate system result is defined as [ x ]oi，yoi，zoi]Substituting the original observation results corresponding to the n homonyms within the range of the rotation angle of 0-180 degrees into a formula 14 to obtain
Figure RE-FDA0002959851930000077
S7012: recording horizontal angle phioiThe point measured in the range of 180-360 DEG of rotation angle is defined as [ phi ]1i，θ1i，r1i]The corresponding three-dimensional coordinate system result is defined as [ x ]1i，y1i，z1i]Substituting the original observation results corresponding to the n homonymous points within the range of the rotation angle of 180-360 degrees into a formula 14 to obtain
Figure RE-FDA0002959851930000078
S7013: noting the true coordinate of the same name point as FrefFor F in equation 14sTaylor expansion was performed to obtain:
Figure RE-FDA0002959851930000071
subtracting simultaneous formula 21, the true coordinate of the same-name point is FrefEliminated to obtain an observation equation internally conforming to the estimation of the calibration parameters, wherein the weight P array of the observed values is determined by the error equation of the observed quantity, and the vector of the calibration parameters is recorded as
Figure RE-FDA0002959851930000072
The system of equations for the least squares solution can be found as:
Figure RE-FDA0002959851930000073
s7014: according to equation 22, an initial value is given
Figure RE-FDA0002959851930000074
Iterating by using Gauss-Newton iteration method
Figure RE-FDA0002959851930000075
The result of the calibration parameter can be obtained
Figure RE-FDA0002959851930000076
The solving process of the external coincidence calibration parameters specifically comprises the following steps:
s7021: providing a reference point and external orientation parameters by a total station instrument arranged relative to the outside of the three-dimensional laser scanner, wherein the external orientation parameters comprise a three-dimensional body coordinate system of the three-dimensional laser scanner and conversion parameters of an external coordinate system, and specifically comprise an X-axis rotation angle, a Y-axis rotation angle, a Z-axis rotation angle, an X-axis translation amount, a Y-axis translation amount and a Z-axis translation amount;
s7022: and performing rotational translation on the three-dimensional laser scanner calibration model through the external orientation parameters to obtain an observation equation with external coincidence estimation as follows:
Figure RE-FDA0002959851930000081
in the formula, R is a rotating cosine matrix;
s7013: solving the full differential equation for equation 23 as:
Figure RE-FDA0002959851930000082
s7023: for n homonyms BiAnd i is 1,2, and n, and the observed quantity of the spherical coordinate system measured by the three-dimensional laser scanner is recorded as
Figure RE-FDA0002959851930000083
Figure RE-FDA0002959851930000084
The observed quantity in the Z-axis direction is obtained by substituting the observed quantity in the formula 23
Figure RE-FDA0002959851930000085
Recording the reference observed quantity of a space rectangular coordinate system given by the total station as
Figure RE-FDA0002959851930000086
Taylor expansion of equation 23 yields:
Figure RE-FDA0002959851930000087
then the system of equations for the least squares solution is obtained from equation 25 as:
Figure RE-FDA0002959851930000088
s7024: the initial value of the external orientation parameter is given according to the formula 27, and the formula 27 is expressed as follows:
Figure RE-FDA0002959851930000089
wherein svd is singular value decomposition, and MEAN is column averaging; after obtaining the fixed initial value of the external orientation parameter, setting the initial values of the other parameters as 0, and iterating
Figure RE-FDA0002959851930000091
The result of the calibration parameter can be obtained
Figure RE-FDA0002959851930000092
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