CN104048605B - Laser scanning measurement target adjustment equation establishing method - Google Patents

Abstract

The invention provides a laser scanning measurement target adjustment equation establishing method. The method comprises the following steps that (1) a scanned area where orientation targets are distributed is scanned through a plurality of scanning stations, it is guaranteed that three or more targets are distributed at each scanning station, at least two public targets are located at every two adjacent scanning stations, and coordinates of an engineering measurement coordinate system of the center of each target are measured through a GNSS or a total station; (2) data are scanned, and the data of the engineering measurement coordinate systems of the targets are organized; (3) a regional network is established according to the targets and the scanning stations, and overall adjustment is carried out on the regional network; (4) an adjustment value equation with an unknown number of a single laser beam shot to the single target h by the scanning station i is established; (5) linearization is carried out on a single-target equation with unknown numbers and a condition adjustment value; (6) the scanning station i and the scanning station j point to the public target k, a constraint equation is established under the limiting condition that the coordinates of the scanning station i and the coordinates of the scanning station j are identical to the coordinates of the public target k after being converted, linearization is carried out on the equation of the public target k, orientation parameters are obtained, and point cloud coordinate conversion is achieved.

Description

Laser scanning measurement target adjustment Equations formula construction method

Technical field

The present invention relates to a kind of laser scanning measurement target adjustment Equations formula construction method, belong to engineering survey field.

Background technology

In the measurements, objective geographic object is to carry out expressing and studying under unified engineering survey coordinate system.Ground 3 D laser scanning (Terrestrial Laser Scanning, TLS) can obtain geographic object three-dimensional geometry letter rapidly Breath, but scanner is often stood, the coordinate system of scanning element cloud is scanning device coordinate system, the most just has all for works scope surveys Site cloud be transformed in engineering specified measurement coordinate system (engineering survey coordinate origin and coordinate axes have defined, be referred to as Specified coordinate system) problem, i.e. during scanning instrument in the location point of engineering survey coordinate system and attitude (referred to as some cloud orientation).Right The method that every site cloud individually orients is independent model, and current domestic exterior point cloud is oriented in while using independent model, also Use a small amount of constraints, as to big object run-down, produce closure condition (Zhang Jianqing etc.), neighbor stations laying connection target Improve splicing precision.(ICP method) precision is higher, target is reasonably distributed, easily grasp relative to continuously splicing for independent model orientation Make, its weak point have following some: 1. field process amount is big.2. its public Target Center calculated by adjacent each station parameter Coordinate is the most variant, is conflicting, imprecision in theory.Respectively station precision is uneven, differs greatly, during precision evaluation Lack overall cogency.

Summary of the invention

It is an object of the invention to provide a kind of can overcome drawbacks described above, eliminate independent model lance of coordinate on public target Shield, the laser scanning measurement target adjustment Equations formula construction method of raising point cloud orientation accuracy.Its technical scheme is:

A kind of laser scanning measurement target adjustment Equations formula construction method, it is characterised in that employing following steps:

1) carrying out the scanning of many scanning movements in the scanning area laying orientation target, each scanning movement ensures to lay more than 3 Target, a minimum of two the public targets of adjacent scanning movement, the engineering survey coordinate of each Target Center is measured with GNSS or total powerstation It it is coordinate；

2) scan data, arranges the engineering survey coordinate system data of target；

3) build regional network according to target and scanning movement, regional network is carried out overall adjustment；

4) single laser beam of the vertical i scanning movement directive list target h of row with unknown number adjusted value equation, wherein single target is The target of the laser beam directive of only one of which scanning movement, public target is the same target of many scanning laser beams directive, now, respectively The laser beam stood is referred to as light beam of the same name, and its derivation is: Target Center coordinate L under specified coordinate system₁=[X Y Z]^T、 Coordinate L under scan coordinate system₂=[x y z]^T, then have

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]+R\left[\begin{array}{c}x\\ y\\ z\end{array}\right]---\left(1\right)$

X in formula_S、Y_S、Z_SThe three-dimensional coordinate at expression scanner center is in the position of specified coordinate system, and R matrix reflects scanning Time some cloud in the attitude of specified coordinate system, by antisymmetric matrixConstituting, wherein a, b, c are orientation ginseng Number, the relation of R with S and unit matrix I is

$\begin{array}{c}\left(1\right)S^T=-S,R=(I+S){(I-S)}^{-1}\\ \left(2\right){(I-S)}^T=I+S,{(I+S)}^T=I-S\\ \left(3\right)R^T=R^{-1}={(I+S)}^{-1}(I-S)\\ \left(4\right){(I+S)}^{-1}=\frac{1}{2}(I+R^{-1}),S=2{(I+R^{-1})}^{-1}-I\end{array}---\left(2\right)$

According to formula (1), single laser beam of i scanning movement directive list target h with unknown number adjusted value equation be

$\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]-\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]=\hat{R}\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]---\left(3\right)$

To formula (3) both sides with being multiplied by?

${\hat{R}}^{-1}\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]={\hat{R}}^{-1}\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]-\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]=0---\left(4\right)$

To formula (4) both sides with being multiplied by?

$(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]=(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]+(I+{\hat{S}}_i)\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]---\left(5\right)$

Formula (5) is transplanted,

$(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]-(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]-(I+{\hat{S}}_i)\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]=0---\left(6\right)$

Formula (6) is single target adjustment of condition equation value equation with unknown number；

5) single target is with the linearisation of adjustment of condition equations with unknowns, particularly as follows:

According to (6) formula, lienarized equation is

$A_1{V}_1+A_2{V}_2+B\hat{t}+W=0---\left(7\right)$

Scanning movement location X_S、Y_S、Z_SWith orientation parameter a, b, c and the adjusted value of zooming parameter λ Parameter approximationParameter correction Target is at the coordinate corrective value V of specified coordinate system₁CoefficientTarget scan coordinate system Coordinate corrective value V₂CoefficientOrientation parameter correction coefficient

Mis-tie misclosureWherein,

6) i scanning movement and j scanning movement (j ≠ i) point to public target k, with target k's public after two scanning movement Coordinate Conversion Coordinate is equal for restrictive condition, the vertical constraint equation of row, public target equation is carried out linearisation, solves orientation parameter, it is achieved Point cloud Coordinate Conversion, particularly as follows:

According to formula (3), i station and j station (j ≠ i) point to public target k, and restrictive condition is public after two station coordinates are changed The coordinate of target k is equal, then has the constraint equation shown in formula (8)

$\left[\begin{array}{c}{\hat{X}}_k\\ {\hat{Y}}_k\\ {\hat{Z}}_k\end{array}\right]=\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]+{\hat{R}}_i\left[\begin{array}{c}{\hat{x}}_{ki}\\ {\hat{y}}_{ki}\\ {\hat{z}}_{ki}\end{array}\right]=\left[\begin{array}{c}{\hat{X}}_{Sj}\\ {\hat{Y}}_{Sj}\\ {\hat{Z}}_{Sj}\end{array}\right]+{\hat{R}}_j\left[\begin{array}{c}{\hat{x}}_{kj}\\ {\hat{y}}_{kj}\\ {\hat{z}}_{kj}\end{array}\right]---\left(8\right)$

The linearised form of formula (8) is

$A_i{V}_i+A_j{V}_j+C_i{\hat{t}}_i+C_j{\hat{t}}_j+W_{ij}=0---\left(9\right)$

A in formula_iAnd A_jFor i station and the coefficient V of j public target coordinate corrective value_iAnd V_jCoefficient It is respectively i, j station orientation parameterWithCorrection, its coefficient C_i=[I C_ia C_ib C_ic C_λ],And the coefficient of zooming parameterThe correction coefficient of a isThe correction coefficient of b is The correction coefficient of c isMis-tie misclosure Then orientation parameter is solved, it is achieved some cloud Coordinate Conversion.

The present invention compared with prior art, has an advantage in that: after the present invention is with neighbor stations public Target Center Coordinate Conversion Should be equal for retraining, make laser beam of the same name intersect two-by-two, with three-dimensional coordinate conversion formula based on Luo De matrix for public affairs of setting out Formula, constraint equation on public target of having derived.This class equation compensate for existing independent model orientation and splices (ICP continuously Method) etc. by the theoretical defects of adjustment Models, and formula is simple and direct, regular by force, is conducive to realizing in a computer, measurement result Precision is high.

Accompanying drawing explanation

Fig. 1 is orientation target distribution method schematic diagram in present example；

Fig. 2 is point cloud chart after the public target Coordinate Conversion using independent model to resolve；

Fig. 3 is to set up point cloud chart after the public target Coordinate Conversion that constraint equation resolves in present example.

Detailed description of the invention

1～3 embodiments of the present invention is further illustrated below in conjunction with the accompanying drawings.

Step 1) select hard 6 scanning movements of soil property, it is ensured that and often station can observe 5-7 spherical target, adjacent scanning movement Typically having 2 public targets, adjacent scanning movement is up to 3 public targets, and the regional network that spherical target is constituted, the most each The spherical target number scope that scanning movement is laid is at 5-7, and the coincidence spherical target number of adjacent scanning movement is 2-3.Spherical Target is placed on and can set up on target in ground control point on the tripod neutralizing leveling, measure spherical Target Center and arrive The distance of ground control point, i.e. measures target high, in order to elevation introduces spherical Target Center, measures technology with GNSS RTK and surveys Amount ground control point.

Step 2) scan data, intercept the some cloud of spherical target surface, and simulate spherical mark according to the normal equation of ball The target centre of sphere；As long as there being the point of more than 4 on spherical target surface, just can be detected, matching sphere centre coordinate；Spherical by simulate Target sphere centre coordinate is corresponding with corresponding geodetic coordinates.

Step 3) region-wide all scanning movements and the line of corresponding target constitute netted, as regional network, with every line For unit, list region-wide equation, regional network is carried out overall adjustment.

Step 4) arrange the error equation with unknown number founding single beam one by one, set up region-wide unified error equation Formula；According to three-dimensional coordinate conversion formula point cloud recursive model based on Rodrigo, derive single target adjustment Equations formula process such as Under:

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]+R\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$

X in formula_S、Y_S、Z_SThe three-dimensional coordinate at expression scanner center is in the position of specified coordinate system, and R matrix reflects scanning Time some cloud in the attitude of specified coordinate system, can be by antisymmetric matrixConstitute, R Yu S and unit matrix I Relation be

(1)S^T=-S, R=(I+S) (I-S)^-1

(2)(I-S)^T=I+S, (I+S)^T=I-S

(3)R^T=R^-1=(I+S)^-1(I-S)

$\left(4\right)---{(I+S)}^{-1}=\frac{1}{2}(I+R^{-1}),S=2{(I+R^{-1})}^{-1}-I$

The most single target of the target of the laser beam directive of only one of which scanning movement, the same target of many scanning laser beams directive, Now, the laser beam at each station is referred to as light beam of the same name, and this target is referred to as public target of standing.With reference to Fig. 1, i scanning movement directive list target h Single laser beam with unknown number adjusted value equation be

$\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]-\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]=\hat{R}\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]$

Both sides are with being multiplied by

${\hat{R}}^{-1}\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]={\hat{R}}^{-1}\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]-\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]=0$

Both sides are with being multiplied by?

$(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]=(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]+(I+{\hat{S}}_i)\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]$

After transposition, single target with unknown number and adjustment of condition equation value equation is

$(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]-(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]-(I+{\hat{S}}_i)\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]=0.$

Step 5) to step 4) single target of obtaining carries out linearisation, linearly with unknown number and adjustment of condition equation value equation Changing equation is

$A_1{V}_1+A_2{V}_2+B\hat{t}+W=0$

The adjusted value of scanning movement position and orientation parameterParameter approximationParameter correctionMark Pinwheel coordinate L under specified coordinate system₁=[X Y Z]^T, coordinate L under scan coordinate system₂=[x y z]^T, target is referring to The coordinate corrective value V of position fixing system₁CoefficientThe seat of target scan coordinate system Mark correction V₂CoefficientOrientation parameter correction coefficient

Mis-tie misclosureWherein,Then orientation ginseng is solved Number, it is achieved some cloud Coordinate Conversion.

Experimental data proves:

1, the inventive method is relative to traditional independent model, adds laser beam constraint side, each station on public target Journey.After making the conversion of public Target Center, coordinate difference is greatly reduced.If calculating orientation parameter with independent model, list of respectively standing Solely adjustment, after the public target surface scanning element conversion of calculating, coordinate is inconsistent, puts Yun Zhongyou after orientation and " misplaces " phenomenon, as Fig. 2, the constraint equation of the present invention can make to put after public target Coordinate Conversion cloud then without obvious inconsistent phenomenon, such as Fig. 3.

2, mode error coefficient matrix is not 0 unit have 7, constraint equation build rule be: constraint equation is not Know several coefficient matrixes be not 0 unit have 13.

Claims (1)

1. a laser scanning measurement target adjustment Equations formula construction method, it is characterised in that employing following steps:

1) carrying out the scanning of many scanning movements in the scanning area laying orientation target, each scanning movement ensures to lay more than 3 targets, A minimum of two the public targets of adjacent scanning movement, the engineering survey coordinate system measuring each Target Center with GNSS or total powerstation is sat Mark；

2) scan data, arranges the engineering survey coordinate system data of target；

3) build regional network according to target and scanning movement, regional network is carried out overall adjustment；

4) single laser beam of the vertical i scanning movement directive list target h of row with unknown number adjusted value equation, wherein single target is for only The target of the laser beam directive of one scanning movement, public target is the same target of many scanning laser beams directive, now, each station Laser beam is referred to as light beam of the same name, and its derivation is: Target Center coordinate L under specified coordinate system₁=[X Y Z]^T, scanning Coordinate L under coordinate system₂=[x y z]^T, then have

$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}{X}_S\\ Y_S\\ Z_S\end{array}\right]+R\left[\begin{array}{c}x\\ y\\ z\end{array}\right]---\left(1\right)$

X in formula_S、Y_S、Z_SRepresent the three-dimensional coordinate at scanner center in the position of specified coordinate system, time R matrix reflects scanning Point cloud is in the attitude of specified coordinate system, by antisymmetric matrixConstituting, wherein a, b, c are orientation parameter, R With the relation of S and unit matrix I it is

$\begin{array}{c}\left(1\right)S^T=-S,R=(I+S){(I-S)}^{-1}\\ \left(2\right){(I-S)}^T=I+S,{(I+S)}^T=I-S\\ \left(3\right)R^T=R^{-1}={(I+S)}^{-1}(I+S)\\ \left(4\right){(I+S)}^{-1}=\frac{1}{2}(I+R^{-1}),S=2{(I+R^{-1})}^{-1}-I\end{array}---\left(2\right)$

According to formula (1), single laser beam of i scanning movement directive list target h with unknown number adjusted value equation be

$\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]-\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]=\hat{R}\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]---\left(3\right)$

To formula (3) both sides with being multiplied by?

${\hat{R}}^{-1}\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]={\hat{R}}^{-1}\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]-\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]=0---\left(4\right)$

To formula (4) both sides with being multiplied by?

$(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]=(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]+(I+{\hat{S}}_i)\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]---\left(5\right)$

Formula (5) is transplanted,

$(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_h\\ {\hat{Y}}_h\\ {\hat{Z}}_h\end{array}\right]-(I-{\hat{S}}_i)\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]-(I+{\hat{S}}_i)\left[\begin{array}{c}{\hat{x}}_{ih}\\ {\hat{y}}_{ih}\\ {\hat{z}}_{ih}\end{array}\right]=0---\left(6\right)$

Formula (6) is single target adjustment of condition equation value equation with unknown number；

5) single target is with the linearisation of adjustment of condition equations with unknowns, particularly as follows:

According to (6) formula, lienarized equation is

$A_1{V}_1+A_2{V}_2+B\hat{t}+W=0---\left(7\right)$

Scanning movement location X_S、Y_S、Z_SWith orientation parameter a, b, c and the adjusted value of zooming parameter λ Parameter approximationParameter correctionTarget Coordinate corrective value V in specified coordinate system₁CoefficientThe seat of target scan coordinate system Mark correction V₂CoefficientOrientation parameter correction coefficientMis-tie misclosureWherein,

6) i scanning movement and j scanning movement (j ≠ i) point to public target k, with the coordinate of target k public after two scanning movement Coordinate Conversion Equal for restrictive condition, the vertical constraint equation of row, public target equation is carried out linearisation, solves orientation parameter, it is achieved some cloud Coordinate Conversion, particularly as follows:

According to formula (3), i station and j station (j ≠ i) point to public target k, and restrictive condition is public target k after two station coordinates conversions Coordinate equal, then have the constraint equation shown in formula (8)

$\left[\begin{array}{c}{\hat{X}}_k\\ {\hat{Y}}_k\\ {\hat{Z}}_k\end{array}\right]=\left[\begin{array}{c}{\hat{X}}_{Si}\\ {\hat{Y}}_{Si}\\ {\hat{Z}}_{Si}\end{array}\right]+{\hat{R}}_i\left[\begin{array}{c}{\hat{x}}_{ki}\\ {\hat{y}}_{ki}\\ {\hat{z}}_{ki}\end{array}\right]=\left[\begin{array}{c}{\hat{X}}_{Sj}\\ {\hat{Y}}_{Sj}\\ {\hat{Z}}_{Sj}\end{array}\right]+{\hat{R}}_j\left[\begin{array}{c}{\hat{x}}_{kj}\\ {\hat{y}}_{kj}\\ {\hat{z}}_{kj}\end{array}\right]---\left(8\right)$

The linearised form of formula (8) is

$A_i{V}_i+A_j{V}_j+C_i{\hat{t}}_i+C_j{\hat{t}}_j+W_{ij}=0---\left(9\right)$

A in formula_iAnd A_jFor i station and the coefficient V of j public target coordinate corrective value_iAnd V_jCoefficient It is respectively i, j station orientation parameterWithCorrection, its coefficient C_i=[I C_ia C_ib C_ic C_λ],And the coefficient of zooming parameterThe correction coefficient of a isThe correction coefficient of b is The correction coefficient of c isMis-tie misclosure Then orientation parameter is solved, it is achieved some cloud Coordinate Conversion.