CN102607506B - Free stationing transformation monitoring method of high-fill airport side slope unit set total station - Google Patents

Abstract

The invention relates to a free stationing transformation monitoring method of a high-fill airport side slope unit set total station, and is used for effectively solving the accurate monitoring problems that a high-fill airport side slope is long and narrow, is a strip shape and is linear extension, and the graph intensity is poor. The monitoring method comprises the following steps of: dividing the involved range into a first measuring region, a second measuring region and a third measuring region from large to small, and setting a control point, a monitoring point and a turning point in each measure region, wherein the position of a survey station is freely selected; establishing a control net of the whole monitoring region, carrying out substation measurement on the control points and the monitoring points in the measuring regions, establishing a posture and oriented relation between adjacent survey stations, meanwhile, realizing larger expansion in an instrument measurement range; and taking the acquired horizon angle, a vertical angle and slant distance as observed values, taking a survey station position parameter and a monitoring point coordinate as an adjustment parameter so as to carry out parameter adjustment, and obtaining the precision result of the survey station position parameter and the monitoring point coordinate. The monitoring method provided by the invention has the advantages of high measuring accuracy, flexibility and convenience, convenience for carrying and good portability.

Description

The Free Station deformation monitoring method of high embankment airport side slope separate unit total powerstation

Technical field

The present invention relates to the Aerodrome Construction engineering, particularly the Free Station deformation monitoring method of a kind of high embankment airport side slope separate unit total powerstation.

Background technology

Because aviation development, air resource is more and more nervous, certainly will cause airport addressing to a certain extent " the empty ground that determines ", because State owned land is tightly controlled policy, certainly will cause airport construction " to be climbed mountains and gone to sea ", airport construction has to be chosen on the geology unfavorable foundation thus, such as the soft soil foundation of southeastern coast, west-southwest Mountainous Region high fill foundation etc., is commonly referred to high embankment airport on the airport that this class ground is built.The southeastern coast soft soil foundation in order to satisfy the designing requirement of flood frequency flood control level, need to carry out embankment usually; The mountain area high fill foundation, because mistake, cheuch are in length and breadth between alpine terrain undulation, river, mound, must cut the mountain and fill out gully, carry out on the spot a cubic meter balance, form filling body, because the formation of filling body has destroyed original equilibrium state on natural ground, filling body itself also deforms owing to many factors simultaneously, the form of expression is: settlement of foundation, slope displacement etc.

Because the anisotropy of distortion genesis mechanism and the uncertainty that Deformation Theory is calculated, Stability Checking Calculation is analyzed, deformation monitoring is as the only resource of the substantial amount that obtains to deform, safety evaluatio for engineering seems particularly important, it also is important means information-based, scientific construction, can verify on the one hand the rationality of ground Treatment Design scheme, can be on the other hand the foundation that next step construction provides science.

Existing deformation monitoring method is divided into horizontal displacement monitoring, perpendicular displacement monitoring and three-dimensional monitoring by the observation purpose:

Horizontal displacement monitoring has following several method: method of tension wire alignment, and collimation line method, method of laser alignment, just, the reversed pendulum method, forward intersection and precise traverse method etc.The perpendicular displacement monitoring mainly contains geometric leveling method and hydrostatic levelling method (communicating pipe method).More than various monitoring methods be with the horizontal shift of deformation point and respectively testing of perpendicular displacement.Along with the development of surveying instrument and measuring technique, this problem has obtained solution basically.Developed at present the measuring system of the observation deformation point horizontal shift of energy real-time continuous and perpendicular displacement, because these systematic surveys is the three-D displacement value of deformation point, so be called " three-D displacement monitoring system ", can be divided into GPS method, Distance Intersection method, polar coordinates method of difference and forward intersection by its principle and observation procedure.Although static Relative Difference method is feasible, signal is affected seriously by high slope GPS (comprising " the many antennas of a machine " technology), and instrument is expensive simultaneously, and is excessive for unitem cost input, lays under the multiple spot condition in net, and observed efficiency is very low.Distance Intersection method and polar coordinates method of difference all need special measuring system to cooperate, and the whole system expense is higher.In the deformation monitoring of high embankment airport side slope, use most often forward intersection, the error source of the method has: angle error, the variation of intersection angle and graphic structure, base length, external condition etc.The method labour intensity is large in general, the measurements and calculations process is complicated, computational accuracy is undesirable.The reason of searching to the bottom is to have occurred the artificial error in many places in observation process, such as the error of centralization of instrument and reflecting prism, Setting error, instrument high measurement error, prism high measurement error etc.

Said method exists: observation condition institute is restricted greatly, the monitoring system Meteorological is higher, the accidental error source is many, the Measurement and Data Processing process complicated, and its Monitoring Result does not have real-time usually.

Simultaneously, the Free Station with Total Station electronic Thacheometer method of mentioning in the pertinent literature is only measured two reference mark, and there is following problem in composition control net not:

(1), the distribution method of control net lacks the assessment of the strength of figure factor;

(2), lack the robust estimation of control net in its initial observation adjustment result, control the anti-rough error capabilities of net;

(3), do not carry out deciding power in the Monitoring Data adjustment process, effect is bad, and measuring accuracy is poor, does not satisfy the actual needs of airport construction, and therefore, the improvement and bring new ideas on the monitoring method is imperative.

Summary of the invention

For above-mentioned situation, for overcoming the defective of prior art, the present invention's purpose just provides the Free Station deformation monitoring method of a kind of high embankment airport side slope separate unit total powerstation, it is poor effectively to solve measuring accuracy, can not satisfy high embankment airport side slope and be that long and narrow, ribbon, straight line extend, the poor monitoring problem of strength of figure.

The technical scheme that the present invention solves is may further comprise the steps:

1, high embankment airport side slope subregion

The scope that high embankment airport side slope is comprised is divided into from large to small first, second, third and establishes measured rectangular area, station, and the length of side of each rectangular area is 200-300m; Establish reference mark, monitoring point and turning point in each measured zone, the position of survey station can freely be selected, but is located at the centre of measured zone as far as possible, so that measuring error is regular even distribution;

2, measure

The resulting coordinate system of control survey is called control net coordinate system, and every station formed coordinate system of surveying instrument three axles is called the survey station coordinate system, measures in two steps:

(1) control survey: before deformation monitoring begins, should set up the control net of whole monitored area, the establishment of control net mode is GPS free net or classical triangulateration network, adopt rectangular space coordinate, shorter for the common length of side of deformation monitoring, do not carry out projection, with the error effect of avoiding distortion of projection to be produced;

(2) deformation monitoring: Free Station is measured, and substation is carried out in the reference mark in the measured zone and monitoring point measure, and method is, and the one, single station is measured, and instrument is motionless, measures all targets, the zone that suitable monitoring range is less; The 2nd, turn the station and measure (be commonly referred to and leapfrog), finishing the one-shot measurement task needs the repeatedly position of mobile instrument, can avoid the impact of external environment, improves sighting condition; By the orientation point more than 3 (being the common point of adjacent two station duplicate measurementss) is measured, set up attitude, directional relation between the adjacent survey station, realize simultaneously the larger expansion of apparatus measures scope, also can avoid measuring accuracy to increase and fast reducing with distance, be fit to measured zone in a big way;

3, data are processed

The horizontal angle, vertical angle and the oblique distance that measure to obtain as observed reading, are carried out parameter adjustment with survey station location parameter and monitoring point coordinate as adjustment parameter, obtain the precise results of survey station location parameter and monitoring point coordinate.

Monitoring method precision of the present invention is high, the measuring system that consists of is convenient, flexible, volume is little, lightweight, be convenient to move, have good portability, adapted to fully that slope monitoring place, airport is long and narrow, construction disturbs frequently, needs flexible, the motor-driven needs of establishing the station.

Description of drawings

Fig. 1 is Free Station deformation monitoring schematic diagram of the present invention.

Fig. 2 is that common point is measured sign picture between adjacent 2 survey station points of the present invention.

Fig. 3 is polar coordinate measurement sign picture of the present invention.

Fig. 4 is the transformational relation figure between survey station of the present invention and control net.

Fig. 5 is certain embodiment monitoring point, airport distribution plan of the present invention.

Fig. 6 is chopped-off head control net net type figure of the present invention.

Fig. 7 is encryption control net net type figure of the present invention.

Embodiment

Below in conjunction with drawings and Examples the specific embodiment of the present invention is elaborated.

The present invention is realized by following steps in implementation:

1, high embankment airport side slope subregion

As shown in Figure 1, be separate unit Free Station with Total Station electronic Thacheometer deformation monitoring method schematic diagram, its intermediate cam represents the reference mark, circle represents the monitoring point, square frame represents turning point, the instrument icon represents the survey station position, and the scope that high embankment airport side slope is comprised is divided into from large to small first, second, third and establishes measured rectangular area, station, and the length of side of each rectangular area is 200-300m; If monitoring range is large again, measure the measured zone of separating and continue to increase, each survey station is measured all reference mark, monitoring point and the turning point in its scope, and the position of survey station can freely be selected, but as far as possible in the centre of measured zone, can make like this measuring error be regular even distribution;

The total station survey precision is relevant with angle measurement and range error, the error of angle measurement and range finding is less on the positional accuracy impact in the time of closely, but along with distance increases, the range error impact obviously increases, the Free Station deformation monitoring method is divided into the zone that less, the suitable total powerstation of several scopes is monitored with larger monitored area, thereby effectively guaranteed measuring accuracy, fully adapted to high embankment airport side slope and be that long and narrow, ribbon, straight line extend, the poor situation of strength of figure;

2, measure

The resulting coordinate system of control survey is called control net coordinate system, and every station formed coordinate system of surveying instrument three axles is called the survey station coordinate system, measures in two steps:

(1) control survey: before deformation monitoring begins, set up first the control net of whole monitored area, the establishment of control net mode is GPS free net or classical triangulateration network, adopt rectangular space coordinate, shorter because of the length of side for deformation monitoring, do not carry out projection, with the error effect of avoiding distortion of projection to be produced;

(2) deformation monitoring, Free Station are measured, and substation is carried out in the reference mark in the measured zone and monitoring point measure, and method is, when measured zone is less, adopt single station to measure, and instrument is motionless, measures all targets, and measuring radius is in the 300m; When measured zone in a big way, employing turns the station and measures (be commonly referred to and leapfrog), finish the one-shot measurement task and need the repeatedly position of mobile instrument, can avoid the impact of external environment, improve sighting condition, by the orientation point more than 3 (being the common point of adjacent two station duplicate measurementss) is measured, set up attitude, directional relation between the adjacent survey station, realize simultaneously the larger expansion of apparatus measures scope, also can avoid measuring accuracy to increase and fast reducing with distance;

3, data are processed

The horizontal angle, vertical angle and the oblique distance that measure to obtain as observed reading, are carried out parameter adjustment with survey station location parameter and monitoring point coordinate as adjustment parameter, obtain the precise results of survey station location parameter and monitoring point coordinate; Said process is similar to the bundle adjustment in photogrammetric, each survey station parameter is similar to the inside and outside parameter in photogrammetric, the coordinate of monitoring point then is the unknown point coordinate in photogrammetric, the data processing method that the many survey stations data unification that therefore is referred to as to resolve based on bundle adjustment is resolved;

A, net adjustment

The net adjustment is after observation finishes, eliminate incongruent data, assess measuring accuracy, obtain the important means of coordinate, traditional net adjustment can be divided into the adjustment of condition equation, parameter adjustment two large classes, parameter adjustment (reaching the parameter adjustment with constraint condition) is convenient to computer aided calculation, specifically (as shown in Figure 2):

Two instruments are observed 1 point simultaneously, and 6 observed readings are arranged, if to the simultaneously observation of n point, 6n observed reading just arranged; There is 3n unknown number in n unknown point, two instrument relative orientations have other 7 unknown numbers (3 rotation parameters, 3 translation parameterss, 1 scale factor), if resolve the relative position of instrument, should be so that following condition establishment: 6n＞7+3n, be n＞2.5, for this reason during actual measurement, require adjacent survey station that common point more than 3 is arranged, in Practical Project, high-precision monitoring net can be laid 5～15 common points usually, increase excess observation component, and network point distribution has good geometry, to improve reliability, to reduce the impact of measuring error;

Process by excess observation being carried out least square during adjustment, try to achieve best instrument position and the best coordinates of spatial attitude and spatial point, so that the quadratic sum of observed reading correction is minimum, its error equation is nonlinear, need to carry out repeatedly iteration and just can reach final requirement;

B, data processing method

(1) coordinate Calculation (as shown in Figure 3) under the survey station coordinate system

Survey station i comprises horizontal angle H to the observed reading of arbitrfary point P _I-p, vertical angle V _I-pWith oblique distance D _I-p, then put the coordinate of P under survey station i and be denoted as (X _I-P, Y _I-P, Z _I-P), computing formula is as follows:

$\left\{\begin{array}{c}{X}_{i-P}=D_{i-P}\·\cos \left(V_{i-P}\right)\·\cos \left(H_{i-P}\right)\\ Y_{i-P}=D_{i-P}\·\cos \left(V_{i-P}\right)\·\sin \left(H_{i-P}\right)\\ Z_{i-P}=D_{i-P}\·\sin \left(V_{i-P}\right)\end{array}\right.---\left(1\right)$

(2) the conversion parameter summary between survey station 1 coordinate system and all the other survey stations calculates

Can calculate the conversion parameter between two adjacent survey station i and i+1, i.e. translation parameters according to boolean Sha seven parameter models (realizing by 3 basic rotations of coordinate system, 3 translations and 1 yardstick convergent-divergent)

Rotation parameter With scale factor k:

$(X_i,Y_i,Z_i)=N_{\mathrm{ii}+1}\·(X_{i+1},Y_{i+1},Z_{i+1})+(X_0^{\mathrm{ii}+1},Y_0^{\mathrm{ii}+1},Z_0^{\mathrm{ii}+1})---\left(2\right)$

(X _i, Y _i, Z _i) be the coordinate of survey station i, (X _I+1, Y _I+1, Z _I+1) be survey station i+1 coordinate,

Be the angle of rotating around X, Y, Z axis successively, N _Ii+1It is rotation parameter Corresponding rotation matrix;

The transformational relation that can be got between survey station 1 and survey station i by (2) formula is:

$(X_1,Y_1,Z_1)=\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}{N}_{\mathrm{jj}+1}\·(X_i,Y_i,Z_i)+\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}(X_0^{\mathrm{jj}+1},Y_0^{\mathrm{jj}+1},Z_0^{\mathrm{jj}+1})$

Be denoted as:

$(X_1,Y_1,Z_1)=N_{1i}\·(X_i,Y_i,Z_i)+(X_0^{1i},Y_0^{1i},Z_0^{1i})---\left(3\right)$

Wherein:

$\left\{\begin{array}{c}{N}_{1i}=\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}{N}_{\mathrm{jj}+1};\\ (X_0^{1i},Y_0^{1i},Z_0^{1i})=\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}(X_0^{\mathrm{jj}+1},Y_0^{\mathrm{jj}+1},Z_0^{\mathrm{jj}+1})\end{array}\right.$

Scale factor k mainly is because two coordinate systems adopt different length standards to cause, perhaps the testee factor such as expand with heat and contract with cold causes, if the length standard of two coordinate systems is identical, scale factor k is fixed as 1, otherwise can be calculated by following formula the summary value of k:

$\left\{\begin{array}{c}k=(S_{12}+S_{13}+S_{23})/(S_{12}^{\′\′}+S_{13}^{\′\′}+S_{23}^{\′\′})\\ S_{\mathrm{ij}}=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2+{(z_i-z_j)}^2}\\ S_{\mathrm{ij}}^{\′\′}=\sqrt{{(x_i^{\′\′}-x_j^{\′\′})}^2+{(y_i^{\′\′}-y_j^{\′\′})}^2+{(z_i^{\′\′}-z_j^{\′\′})}^2}\end{array}\right.---\left(4\right)$

Wherein: (x _i, y _i, z _i) be the coordinate under the survey station coordinate system, (x " _i, y " _i, z " _i) for controlling the coordinate under the net coordinate system;

(3) transformational relation calculates between each survey station coordinate system and control net coordinate system

By (3) formula, can with all measurement point coordinate conversion under survey station 1 coordinate system, to measure at least 3 not reference mark of conllinear during monitoring, obtain the summary conversion parameter between control net coordinate system and survey station 1 coordinate system, i.e. translation parameters

And rotation parameter

Then have:

$(X_c,Y_c,Z_c)=N_{c1}\·(X_1,Y_1,Z_1)+(X_0^{c1},Y_0^{c1},Z_0^{c1})---\left(5\right)$

Wherein: (X _c, Y _c, Z _c) coordinate under the expression control net coordinate system, (X ₁, Y ₁, Z ₁) be the coordinate under survey station 1 coordinate system, N _C1It is rotation parameter Corresponding rotation matrix is namely controlled the net coordinate and is tied to survey station 1;

By the transformational relation between (3) and (5) Shi Kede control net coordinate system and At any points i:

$(X_c,Y_c,Z_c)=N_{c1}\·N_{1i}\·(X_i,Y_i,Z_i)+N_{c1}\·(X_0^{1i},Y_0^{1i},Z_0^{1i})+(X_0^{c1},Y_0^{c1},Z_0^{c1})---\left(6\right);$

Wherein: (X _i, Y _i, Z _i) coordinate under the expression survey station i coordinate system, Be the translation parameters of survey station 1 to survey station i, N _1iIt is rotation parameter

Corresponding rotation matrix, namely survey station 1 to survey station i;

(4) accurately resolve position relationship and monitoring point coordinate between survey station

For survey station i, can be calculated the summary value of the conversion parameter between control net coordinate system and survey station coordinate system by (6) formula

In the actual measurement process, the reference field of control net coordinate system and the reference field of survey station coordinate system are geoid surface, so the conversion parameter between two coordinate systems will only have the rotation angle around Z axis As shown in Figure 4, O wherein _C-X _CY _CZ _CBe control net coordinate system, O _i-X _iY _iZ _iBe survey station i coordinate system, O ' _C-X ' _CY ' _CZ ' _CCoordinate system is by coordinate system O _C-X _CY _CZ _CMove to O _i, plane O _C-X _CY _C, O ' _C-X ' _CY ' _CAnd O _i-X _iY _iAll parallel with surface level, O then _i-X _iY _iZ _iBy coordinate system O ' _C-X ' _CY ' _CZ ' _CRotation obtains the rotation angle around Z axis

The measured point is divided into reference mark and monitoring point, and the coordinate of monitoring point j under control net coordinate system is denoted as (X _C-j, Y _C-j, Z _C-j), for whole monitoring net, the unknown number that find the solution comprises the conversion parameter between survey station and control net coordinate system

And the unknown number coordinate (X of monitoring point _C-k, Y _C-k, Z _C-k); Survey station i comprises horizontal angle Hi-p, vertical angle Vi-p and oblique distance Di-p to the observed reading of measurement point P, and following relational expression is arranged:

Then can get following error equation by parameter adjustment:

Order:

$\left\{\begin{array}{c}{S}_{i-p}^0=\sqrt{{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}^2+{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}^2}\\ D_{i-p}^0=\sqrt{{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}^2+{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}^2+{(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)}^2}\end{array}\right.$

Wherein: X _C-k| ₀,

Y _C-k| ₀, Z _C-k| ₀,

Be X _C-k,

Y _C-k,

Z _C-k,

Corresponding approximate value, and the unit of angle adopts second, and the unit of length adopts millimeter, can avoid like this error equation coefficient difference larger, and following relational expression is arranged:

$\left\{\begin{array}{c}\sin \left(H_{i-p}{|}_0\right)=\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{S_{i-p}^0}\\ \cos \left(H_{i-p}{|}_0\right)=\frac{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}{S_{i-p}^0}\end{array}\right.$

Wherein: H _I-p| ₀Be H _I-pCorresponding approximate value, then:

$a_1^{i-p}=\frac{\sin \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000},$ $a_2^{i-p}=-\frac{\cos \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000}$

$a_3^{i-p}=-\frac{\sin \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000},$ $a_4^{i-p}=\frac{\cos \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000}$

$b_1^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_2^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_3^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(\frac{-1}{D_{i-p}^0}+\frac{{(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)}^2}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_4^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_5^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_6^{i-p}=\frac{1}{\sin \left(V_{i-p}{|}_0\right)}\·(\frac{-1}{D_{i-p}^0}+\frac{{(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)}^2}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$c_1^{i-p}=\frac{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0},$ $c_2^{i-p}=\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}$

$c_3^{i-p}=\frac{Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0},$ $c_4^{i-p}=-\frac{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}$

$c_5^{i-p}=-\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0},$ $c_6^{i-p}=-\frac{Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}$

$L_1^{i-p}=2\mathrm{\π}-H_{i-p}-{\tan }^{-1}\left(\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}\right)$

$L_2^{i-p}={\cos }^{-1}\left(\frac{Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}\right)-V_{i-p}$

$L_3^{i-p}=D_{i-p}^0-D_{i-p}$

If observation station be the reference mark then $a_3^{i-p}=a_4^{i-p}=b_4^{i-p}=b_5^{i-p}=b_6^{i-p}=c_4^{i-p}=c_5^{i-p}=c_6^{i-p}=0;$

For all survey stations, can set up error equation V=AX+L, observed reading horizontal angle Hi-p, vertical angle Vi-p and oblique distance Di-p to decide the power expression formula as follows:

$\left\{\begin{array}{c}{P}_{H_{i-p}}=P_{V_{i-p}}=1\\ P_{D_{i-p}}=m_{\mathrm{\β}}/m_D\\ m_D=a+b*D_{i-p}\end{array}\right.---\left(9\right)$

Wherein: m _βBe the nominal accuracy of instrument angle measurement, unit is second; m _DBe distance accuracy, unit is millimeter; A, b are respectively fixed error and the proportional error coefficient of total powerstation nominal;

By least square method V ^TPV=is minimum, forms equation: $\left\{\begin{array}{c}\mathrm{NX}+W=0\\ X=-N^{-1}W\end{array}\right.,$ Wherein $\left\{\begin{array}{c}N=A^T\mathrm{PA}\\ W=A^T\mathrm{PL}\end{array}\right.,$ Thus, adjustment is resolved and can be obtained the survey station unknown number

With monitoring point coordinate (X _C-k, Y _C-k, Z _C-k) exact value;

(5) accuracy assessment

If n is the error equation number, t is the unknown number number, m _iIt is the precision valuation of i parameter; Q _IiBe the capable i column data of i on the inverse of weight matrix Q diagonal line; By adjustment result residual error V, but error in the unit of account power

Wherein

Unknown number inverse of weight matrix Q=(A ^TPA) ^-1, parameters precision is estimated

C, accuracy comparison test (being combined in the application in the specific embodiment, the reliability of sufficient proof the inventive method and accuracy)

(1) subregion is layouted

Certain airport is positioned at China the Northeast, belongs to Airport in Mountain Region, 22 meters of average height of embankments, 35 meters of maximum height of embankments, side slope is than 1: 0.75, more than 800 meters of whole length of slopes, as shown in Figure 5, monitoring section is laid 10 at reference mark altogether, is distributed in around the whole deformed slope, and period is K01-K10; Lay altogether 42 by the designing requirement monitoring point, minute side slope top, centre and bottom 3 rows, 14 row are laid, and period is B01-B42, and row are spaced apart 50 meters;

(2) control survey

Because the GPS technology has bearing accuracy height, good in economic efficiency, the easy and simple to handle and characteristics such as degree of freedom is large of arranging net, military affairs at home and abroad, the department such as civilian have obtained using very widely, especially in geodetic surveying and deformation monitoring field, publish from Chinese Geology Publishing House, Liu Ping write " newly organized mapping and measurement data quick checking disposal route checks in quick checking technical application handbook: the monitoring point horizontal direction precision that the 6hGPS Monitoring Data is resolved in the Geheyan Reservoir dam monitoring is ± 0.5mm, and the elevation directional precision is ± 1.0mm; The monitoring point horizontal direction precision that 1～2hGPS Monitoring Data is resolved is ± 1.0mm that the elevation directional precision is ± 1.5mm;

According to above-mentioned situation, adopt the GPS method, divided for three steps carried out: the high precision Fixed Initial Point is measured, measurement is netted in chopped-off head control and encrypt the measurement of control net, in the GPS processing procedure, be divided into high-precision GPS measurement, conventional GPS measurement, the subject matter of its solution is: the foundation of control net, the monitoring of control net absolute deformation, the monitoring of control net relative deformation;

High precision Fixed Initial Point and chopped-off head control net are measured:

Chopped-off head is controlled net net type as shown in Figure 6, and it is as follows that high precision Fixed Initial Point and chopped-off head control net are measured the employing scheme:

(a) according to actual conditions, form this project chopped-off head control net by K001, K005, K006, K010, selection K010 is reference point, K001, K005, K006 are point to be located;

(b) translocation BJFS (BeiJing, China), DAEJ (Taejon, Korea), the international tracking station of 3 IGS of SUWN (Suwon, Korea) adopt the final sophisticated product of IGS, the final sophisticated product of CODE;

(c) adopt Bernese 5.0 softwares to carry out data and process, calculation method is two poor phase place static solutions, short Baselines pattern;

(d) achievement adopts geocentric coordinate X, Y, Z;

(e) all the other observation technologies adopt the requirement of National GPS specifications of surveys C level network technology;

Encrypting the control net measures:

Detail network net type is encrypted the measurement of control net and is adopted conventional GPS to measure static Relative Difference method as shown in Figure 7, and scheme is as follows:

(a) resolve software and adopt Leica LGO 7.0;

(b) grid connect mode adopts Bian Lianshi;

(c) requirement of National GPS specifications of surveys D level network technology is adopted in all the other observations;

Flow process is resolved in control survey:

(a) the fixing calculating coordinate K010 of BJFS tracking station reference point coordinate;

(b) fixedly each point coordinate is netted in K010 calculating coordinate K001, K005, the control of K006 chopped-off head;

(c) adopt K010, K001, K005, K006 geocentric coordinate directly to retrain adjustment and resolve each point coordinate in the detail network;

(d) geocentric coordinate is transformed into the airport coordinate system;

Final calculation result is as shown in table 1:

Table 1 airport coordinate system calculation result

Call the roll	Type	X/m	Y/m	Z/m	RMS/mm
						K001	Adjusted value	2409.1665	3642.0733	45.3931	0.05
K002	Adjusted value	2412.8010	3515.4494	36.2717	Fixed value
						K003	Adjusted value	2408.1534	3315.6843	32.8461	0.06
K004	Adjusted value	2392.0331	3173.7755	35.9157	0.06
						K005	Adjusted value	2255.2726	3112.0514	33.8521	Fixed value
K006	Adjusted value	2292.3103	2910.9994	46.2114	Fixed value
						K007	Adjusted value	2518.8474	3084.7063	47.3788	0.06
K008	Adjusted value	2523.6450	3189.1383	48.4965	0.04
						K009	Adjusted value	2508.7601	3534.8179	49.5865	0.04
K010	Adjusted value	2517.5188	3735.8074	59.5505	Fixed value

(3) deformation monitoring

The deformation monitoring scheme adopts Leica company's T CA1800 type total powerstation (as shown in Figure 5), lay altogether 4 survey stations, the scope that different big or small square frames surround is respectively first, second, the 3rd, the 4th establishes measured rectangular area, station, the length of side is 200～300 meters, if monitoring range is large again, measuring the zone of separating continues to increase, each is established the station and measures all interior reference mark of its scope, monitoring point and interim turning point (can be laid interim turning point when the interval, monitoring point is larger, strengthen network structure), at least duplicate measurements two row points between adjacent two stations, i.e. at least 6 common points, the position of survey station can freely be selected, but as far as possible in the centre of measured zone, can make like this measuring error be regular even distribution, real-time Accurate Measurement temperature and air pressure before every station is measured, and correct in instrument;

(4) resolve

First measurement result is as shown in table 2, and Using such method can obtain the result of each issue observation;

The first monitoring point coordinate of table 2 and precision (fragment)

Simultaneously, in order to verify the correctness of the inventive method, also the result of total powerstation and GPS measurement contrasted, measurement result such as table 3, comparing result is as shown in table 4:

Table 3GPS and total station survey result

Table 4GPS and total station survey result are relatively poor

Period	dX/mm	dY/mm	dH/mm	Plane deviation/mm	The point biased poor/mm
						K02	1.3	2.0	1.9	2.4	3.0
K04	2.7	0.7	0.3	2.8	2.8
						K08	0.0	2.2	0.0	2.2	2.2
K09	2.8	0.7	1.9	2.9	3.5
						Mean value	1.7	1.4	1.0	2.6	2.9

Can find out from above result of calculation, use the Free Station method and be 2.9mm with the mean value of the biased difference of GPS method measurement point, the mean value of planimetric coordinates deviation is 2.6mm, comprehensively it seems, GPS method and Free Station deformation monitoring method measured result grid deviation in this paper are in 3.0mm, can satisfy the accuracy requirement of deformation measurement secondary in " building deformation measurement standard " (JGJ 8-2007) fully, namely satisfy the monitoring requirement of high embankment airport side slope.

Clearly show by above-mentioned situation, the present invention is directed to the deformation monitoring problem of high embankment airport side slope, on the basis of summing up classic method, Free Station deformation monitoring method based on the separate unit total powerstation has been proposed, the measuring system that the method forms, volume is little, lightweight, be convenient to move, have good portability, adapted to fully that slope monitoring place, airport is long and narrow, construction is disturbed frequent, need flexible, motor-driven characteristics of establishing the station, also carried out ratio of precision pair with the GPS method, proved absolutely the correctness of the inventive method, the inventive method has the following advantages:

(1) laying at reference mark requires lowly, and single survey station does not require the measurement number at reference mark, as long as whole survey stations can observe 4 reference mark altogether.

(2) Free Station, alignment error of instrument, amount high level error have been avoided, guarantee measurement of higher degree precision, the survey station position freely arranges, and namely instrument does not need to be centered on some fixing reference mark, has avoided the error of centralization of instrument, do not need to measure the antenna height of instrument in the measuring process, height can be any, is as the criterion with suitable observation, avoided height of instrument to measure error.

(3) three-dimensional measurement, make plane and the synchronization gain of measurement of higher degree data, improve observed efficiency, traditional airport Monitoring of Slope Deformation method is processed respectively by plane and elevation, because plane, dissimilar instruments is adopted in the measurement of higher degree, different working specifications and computing method, so that measuring process is more loaded down with trivial details, inefficiency, sometimes unavoidably measuring accuracy is caused damage, comparatively speaking, three-dimensional measurement then utilizes a kind of surveying instrument to obtain simultaneously three-dimensional coordinate, measurement data is synchronous, be the innovation on the slope monitoring method of high embankment airport, extend to highway, railway, use on the correlation engineering High Slope Monitoring such as dam, huge economic and social benefit is arranged.

Claims (1)

1. the Free Station deformation monitoring method of a high embankment airport side slope separate unit total powerstation is characterized in that, may further comprise the steps:

One, high embankment airport side slope subregion

The scope that high embankment airport side slope is comprised is divided into from large to small first, second, third and establishes measured rectangular area, station, and each regional length of side is 200-300m; If monitoring range is large again, measure the measured zone of separating and continue to increase, each survey station is measured all reference mark, monitoring point and the turning point in its scope, and the position of survey station can freely be selected, in the centre of measured zone, make measuring error be regular even distribution as far as possible;

Two, measure

The resulting coordinate system of control survey is called control net coordinate system, and every station formed coordinate system of surveying instrument three axles is called the survey station coordinate system, measures in two steps:

(1) control survey: before deformation monitoring begins, set up first the control net of whole monitored area, the establishment of control net mode is GPS free net or classical triangulateration network, adopt rectangular space coordinate, shorter because of the length of side for deformation monitoring, do not carry out projection, with the error effect of avoiding distortion of projection to be produced;

(2) deformation monitoring, Free Station are measured, and substation is carried out in the reference mark in the measured zone and monitoring point measure, and method is, when measured zone is less, adopt single station to measure, and instrument is motionless, measures all targets, and measuring radius is in the 300m; When measured zone in a big way, employing turns the station and measures, finish the one-shot measurement task and need the repeatedly position of mobile instrument, can avoid the impact of external environment, improve sighting condition, by the orientation point more than 3 is measured, set up attitude, directional relation between the adjacent survey station, realize simultaneously the larger expansion of apparatus measures scope, avoid measuring accuracy to increase and fast reducing with distance;

Three, data are processed

The horizontal angle, vertical angle and the oblique distance that measure to obtain as observed reading, are carried out parameter adjustment with survey station location parameter and monitoring point coordinate as adjustment parameter, obtain the precise results of survey station location parameter and monitoring point coordinate;

A, net adjustment

The net adjustment is after observation finishes, eliminates incongruent data, assesses measuring accuracy, obtains coordinate, specifically:

Two instruments are observed 1 point simultaneously, and 6 observed readings are arranged, if to the simultaneously observation of n point, 6n observed reading just arranged; There is 3n unknown number in n unknown point, and two instrument relative orientations have other 7 unknown numbers, 3 rotation parameters, 3 translation parameterss, 1 scale factor, according to 6n＞7+3n, n＞2.5, resolve the relative position of instrument, adjacent survey station has the common point more than 3, and high-precision monitoring net is laid 5～15 common points, increases excess observation component, and network point distribution has geometry, to improve reliability, to reduce the impact of measuring error;

By excess observation is carried out Least Square in Processing, try to achieve the coordinate of instrument position and spatial attitude and spatial point during adjustment, so that the quadratic sum of observed reading correction is minimum, its error equation is nonlinear, through repeatedly iteration realization;

B, data processing method

(1) coordinate Calculation under the survey station coordinate system

Survey station i comprises horizontal angle H to the observed reading of arbitrfary point P _I-p, vertical angle V _I-pWith oblique distance D _I-p, then put the coordinate of P under survey station i and be denoted as (X _I-P, Y _I-P, Z _I-P), computing formula is as follows:

$\left\{\begin{array}{c}{X}_{i-P}=D_{i-P}\·\cos \left(V_{i-P}\right)\·\cos \left(H_{i-P}\right)\\ Y_{i-P}=D_{i-P}\·\cos \left(V_{i-P}\right)\·\sin \left(H_{i-P}\right)\\ Z_{i-P}=D_{i-P}\·\sin \left(V_{i-P}\right)\end{array}\right.$

(2) the conversion parameter summary between survey station 1 coordinate system and all the other survey stations calculates

According to boolean Sha seven parameter models, by 3 basic rotations of coordinate system, 3 translations and 1 yardstick convergent-divergent, calculate the conversion parameter between two adjacent survey station i and i+1, comprise translation parameters

Rotation parameter

With scale factor k:

$(X_i,Y_i,Z_i)=N_{\mathrm{ii}+1}\·(X_{i+1},Y_{i+1},Z_{i+1})+(X_0^{\mathrm{ii}+1},Y_0^{\mathrm{ii}+1},Z_0^{\mathrm{ii}+1})$

(X _i, Y _i, Z _i) be the coordinate of survey station i, (X _I+1, Y _I+1, Z _I+1) be survey station i+1 coordinate,

Be the angle of rotating around X, Y, Z axis successively, N _Ii+1It is rotation parameter Corresponding rotation matrix;

Transformational relation between survey station 1 and survey station i is:

$(X_1,Y_1,Z_1)=\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}{N}_{\mathrm{jj}+1}\·(X_i,Y_i,Z_i)+\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}(X_0^{\mathrm{jj}+1},Y_0^{\mathrm{jj}+1},Z_0^{\mathrm{jj}+1})$

Be denoted as:

$(X_1,Y_1,Z_1)=N_{1i}\·(X_i,Y_i,Z_i)+(X_0^{1i},Y_0^{1i},Z_0^{1i})$

Wherein:

$\left\{\begin{array}{c}{N}_{1i}=\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}{N}_{\mathrm{jj}+1};\\ (X_0^{1i},Y_0^{1i},Z_0^{1i})=\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}(X_0^{\mathrm{jj}+1},Y_0^{\mathrm{jj}+1},Z_0^{\mathrm{jj}+1})\end{array}\right.$

Scale factor k mainly is because two coordinate systems adopt different length standards to cause, and perhaps the testee factor such as expand with heat and contract with cold causes, if the length standard of two coordinate systems is identical, scale factor k is fixed as 1, is calculated the summary value of k by following formula:

$\left\{\begin{array}{c}k=(S_{12}+S_{13}+S_{23})/(S_{12}^{\′\′}+S_{13}^{\′\′}+S_{23}^{\′\′})\\ S_{\mathrm{ij}}=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2+{(z_i-z_j)}^2}\\ S_{\mathrm{ij}}^{\′\′}=\sqrt{{(x_i^{\′\′}-x_j^{\′\′})}^2+{(y_i^{\′\′}-y_j^{\′\′})}^2+{(z_i^{\′\′}-z_j^{\′\′})}^2}\end{array}\right.$

Wherein: (x _i, y _i, z _i) be the coordinate under the survey station coordinate system, (x " _i, y " _i, z " _i) for controlling the coordinate under the net coordinate system;

(3) transformational relation calculates between each survey station coordinate system and control net coordinate system

By $(X_1,Y_1,Z_1)=N_{1i}\·(X_i,Y_i,Z_i)+(X_0^{1i},Y_0^{1i},Z_0^{1i})$ Formula under survey station 1 coordinate system, will measure at least 3 not reference mark of conllinear with all measurement point coordinate conversion during monitoring, obtain the summary conversion parameter between control net coordinate system and survey station 1 coordinate system, translation parameters

And rotation parameter Then have:

$(X_c,Y_c,Z_c)=N_{c1}\·(X_1,Y_1,Z_1)+(X_0^{c1},Y_0^{c1},Z_0^{c1})$

Wherein: (X _c, Y _c, Z _c) coordinate under the expression control net coordinate system, (X ₁, Y ₁, Z ₁) be the coordinate under survey station 1 coordinate system, N _C1It is rotation parameter

Corresponding rotation matrix is namely controlled the net coordinate and is tied to survey station 1;

By $(X_1,Y_1,Z_1)=N_{1i}\·(X_i,Y_i,Z_i)+(X_0^{1i},Y_0^{1i},Z_0^{1i})$ With $(X_c,Y_c,Z_c)=N_{c1}\·(X_1,Y_1,Z_1)+(X_0^{c1},Y_0^{c1},Z_0^{c1})$ Formula must be controlled the transformational relation between net coordinate system and At any points i:

$(X_c,Y_c,Z_c)=N_{c1}\·N_{1i}\·(X_i,Y_i,Z_i)+N_{c1}\·(X_0^{1i},Y_0^{1i},Z_0^{1i})+(X_0^{c1},Y_0^{c1},Z_0^{c1})$

Wherein: (X _i, Y _i, Z _i) coordinate under the expression survey station i coordinate system, Be the translation parameters of survey station 1 to survey station i, N _1iIt is rotation parameter Corresponding rotation matrix, namely survey station 1 to survey station i;

(4) accurately resolve position relationship and monitoring point coordinate between survey station

For survey station i, by $(X_c,Y_c,Z_c)=N_{c1}\·N_{1i}\·(X_i,Y_i,Z_i)+N_{c1}\·(X_0^{1i},Y_0^{1i},Z_0^{1i})+(X_0^{c1},Y_0^{c1},Z_0^{c1})$ Formula calculates the summary value of the conversion parameter between control net coordinate system and survey station coordinate system

In measurement, the reference field of control net coordinate system and the reference field of survey station coordinate system are geoid surface, so the conversion parameter between two coordinate systems will only have the rotation angle around Z axis

O wherein _C-X _CY _CZ _CBe control net coordinate system, O _i-X _iY _iZ _iBe survey station i coordinate system, O ' _C-X ' _CY ' _CZ ' _CCoordinate system is by coordinate system O _C-X _CY _CZ _CMove to O _i, plane O _C-X _CY _C, O ' _C-X ' _CY ' _CAnd O _i-X _iY _iAll parallel with surface level, O then _i-X _iY _iZ _iBy coordinate system O ' _C-X ' _CY ' _CZ ' _CRotation obtains the rotation angle around Z axis

The measured point is divided into reference mark and monitoring point, and the coordinate of monitoring point j under control net coordinate system is denoted as (X _C-j, Y _C-j, Z _C-j), for whole monitoring net, the unknown number that find the solution comprises the conversion parameter between survey station and control net coordinate system

And the unknown number coordinate (X of monitoring point _C-k, Y _C-k, Z _C-k); Survey station i comprises horizontal angle Hi-p, vertical angle Vi-p and oblique distance Di-p to the observed reading of measurement point P, and following relational expression is arranged:

Then can get following error equation by parameter adjustment:

Order:

$\left\{\begin{array}{c}{S}_{i-p}^0=\sqrt{{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}^2+{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}^2}\\ D_{i-p}^0=\sqrt{{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}^2+{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}^2+{(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)}^2}\end{array}\right.$

Wherein: X _C-k| ₀,

Y _C-k| ₀,

Z _C-k| ₀, Be X _C-k,

Y _C-k,

Z _C-k,

Corresponding approximate value, and the unit of angle adopts second, and the unit of length adopts millimeter, can avoid like this error equation coefficient difference larger, and following relational expression is arranged:

$\left\{\begin{array}{c}\sin \left(H_{i-p}{|}_0\right)=\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{S_{i-p}^0}\\ \cos \left(H_{i-p}{|}_0\right)=\frac{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}{S_{i-p}^0}\end{array}\right.$

Wherein: H _I-p| ₀Be H _I-pCorresponding approximate value, then:

$a_1^{i-p}=\frac{\sin \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000},$ $a_2^{i-p}=-\frac{\cos \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000}$

$a_3^{i-p}=-\frac{\sin \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000},$ $a_4^{i-p}=\frac{\cos \left(H_{i-p}{|}_0\right)}{S_{i-p}^0}\·\frac{\mathrm{\ρ}}{1000}$

$b_1^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_2^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_3^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(\frac{-1}{D_{i-p}^0}+\frac{{(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)}^2}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_4^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_5^{i-p}=\frac{-1}{\sin \left(V_{i-p}{|}_0\right)}\·(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)\·\frac{(Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0)}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$b_6^{i-p}=\frac{1}{\sin \left(V_{i-p}{|}_0\right)}\·(\frac{-1}{D_{i-p}^0}+\frac{{(Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0)}^2}{{\left(D_{i-p}^0\right)}^3}\·\frac{\mathrm{\ρ}}{1000}$

$c_1^{i-p}=\frac{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0},$ $c_2^{i-p}=\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}$

$c_3^{i-p}=\frac{Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0},$ $c_4^{i-p}=-\frac{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}$

$c_5^{i-p}=-\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0},$ $c_6^{i-p}=-\frac{Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}$

$L_1^{i-p}=2\mathrm{\π}-H_{i-p}-{\tan }^{-1}\left(\frac{Y_{c-k}{|}_0-Y_0^{\mathrm{ci}}{|}_0}{X_{c-k}{|}_0-X_0^{\mathrm{ci}}{|}_0}\right)$

$L_2^{i-p}={\cos }^{-1}\left(\frac{Z_{c-k}{|}_0-Z_0^{\mathrm{ci}}{|}_0}{D_{i-p}^0}\right)-V_{i-p}$

$L_3^{i-p}=D_{i-p}^0-D_{i-p}$

If observation station be the reference mark then $a_3^{i-p}=a_4^{i-p}=b_4^{i-p}=b_5^{i-p}=b_6^{i-p}=c_4^{i-p}=c_5^{i-p}=c_6^{i-p}=0;$

For all survey stations, can set up error equation V=AX+L, observed reading horizontal angle Hi-p, vertical angle Vi-p and oblique distance Di-p to decide the power expression formula as follows:

$\left\{\begin{array}{c}{P}_{H_{i-p}}=P_{V_{i-p}}=1\\ P_{D_{i-p}}=m_{\mathrm{\β}}/m_D\\ m_D=a+b*D_{i-p}\end{array}\right.$

Wherein: m _βBe the nominal accuracy of instrument angle measurement, unit is second; m _DBe distance accuracy, unit is millimeter; A, b are respectively fixed error and the proportional error coefficient of total powerstation nominal;

By least square method V ^TPV=is minimum, forms equation: $\left\{\begin{array}{c}\mathrm{NX}+W=0\\ X=-N^{-1}W\end{array}\right.,$ Wherein $\left\{\begin{array}{c}N=A^T\mathrm{PA}\\ W=A^T\mathrm{PL}\end{array}\right.,$ Thus, adjustment is resolved and can be obtained the survey station unknown number

With monitoring point coordinate (X _C-k, Y _C-k, Z _C-k) exact value;

(5) accuracy assessment

If n is the error equation number, t is the unknown number number, m _iIt is the precision valuation of i parameter; Q _IiBe the capable i column data of i on the inverse of weight matrix Q diagonal line; By adjustment result residual error V, but error in the unit of account power

Wherein

Unknown number inverse of weight matrix Q=(A ^TPA) ^-1, parameters precision is estimated

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