CN105069240A - Survey station layout intelligent optimization method of spatial measurement positioning system - Google Patents

Abstract

A survey station optimization deployment problem is one of important problems in use of a spatial measurement positioning system. The present invention provides a survey station layout intelligent optimization method of a spatial measurement positioning system, so that an optimized survey station layout can fully cover a tested area under certain costs and a requirement of measurement accuracy can be met. According to the present invention, a proper positioning error model is established from three aspects of constraint analysis, optimization objective, and optimization means, a multi-goal optimizing function is defined, and survey station layout optimization of the spatial measurement positioning system is implemented by using a practical intelligent optimization algorithm. According to the survey station layout intelligent optimization method of a spatial measurement positioning system, a survey station network optimization deployment problem of the spatial measurement positioning system in an engineering application is effectively resolved. As a quantity of survey stations increases, the method has good expansibility, provides a new method for a multi-station networking measurement layout optimization problem based on an angle intersection principle, and has important theoretical value and practical significance.

Description

A kind of space measurement positioning system survey station layout intelligent optimization method

Technical field

The invention belongs to industry spot large scale three-dimensional coordinate measurement technical field, particularly the survey station intelligent optimization dispositions method of multistation networking measuring system, be specifically related to a kind of space measurement positioning system survey station layout intelligent optimization method.

Background technology

In heavy construction is measured, measurand not only physical dimension is large, and relative accuracy requires high (being better than 10ppm), key point quantity to be measured is many, multiple measurement task is also deposited, and it is large to be affected by the external environment, and the measurer of therefore measuring method and use all has singularity.Network type multistation measuring system has balancing a survey scope, measuring accuracy and measure the great potential of contradiction between efficiency three, for the precision measurement in Large-Scale Equipment manufacture process provides strong technical support, be study hotspot and the important development direction in large-scale metrology field.

Space measurement positioning system (workspaceMeasuringandPositioningSystem, wMPS) be a kind of novel network type multistation measuring system, this systematic survey range can carry out unlimited expansion in theory, and can realize the measurement of detected space multiple spot real-time parallel.Abroad to this systematic study the earliest be Arcsecond company of the U.S. (being incorporated to Nikon), be referred to as indoor GPS or iGPS.Its composition mainly comprises transmitter, pick-up probe, engineer's scale, wireless receiving electronic devices and components and computer controlling center.Bath university of Britain and geodetic surveying research institute of German Karlsruhe university have carried out a large amount of Performance Evaluation experiment to iGPS and have dynamically followed the tracks of applied research.Some Domestic colleges and universities and research institution are also to the system have been a large amount of theoretical researches and prototype experiment.

Because space measurement positioning system realizes measurement of coordinates under the acting in conjunction of many survey stations, the synergy therefore between the performance of single survey station and each survey station is two critical aspects of influential system overall performance.The synergy of many survey stations not only depends on the measurement model of single survey station, the model that crosses of many survey stations, and has substantial connection with the distribution of survey station space geometry.In addition, along with increasing of survey station number, system use cost is also increasing gradually, in order to by cost control in rational scope, select suitable survey station number to be also problems faced in engineering practice.Research survey station layout, on the impact of system positioning error, optimizes survey station network structure, and for improving system accuracy, reducing costs and provide theory support, simultaneously for engineering practice provides cloth station to instruct, is the major issue that space measurement positioning system faces.

In the research of existing survey station network layout optimization, the people such as the ClaudiaDepenthal of German Ka Ersi Rule Institute of Technology are studied the layout of four cell site's compositions in iGPS system.Have employed Box layout and C layout in an experiment, devise 17 standard points, and the measurement result of experimental result and API laser tracker compared, experimental result shows to compare with Box type layout, and the error distribution of C type layout is more uneven.The people such as the Demeester of RobertSchmitthe and the Nikon-Metrology company of Aachen, Germany polytechnical university lathe and manufacturing engineering research institute have carried out simulation analysis to several representative configurations of iGPS when robot localization is followed the tracks of, result shows, the measurement effect of standard form is best.Also have scholar to start with from wMPS network topology and positioning error relation, have studied the impact of representative configuration on positioning error, experimental result shows that O_4 type layout overall measurement accuracy is the highest.All that minority station or specified arrangement are studied and contrast experiment to the research of survey station network topology above, when facing more survey station networkings and measuring, not there is general expansion, and the selection of layout is limited to representative configuration mode, lack dirigibility and versatility when measurement environment becomes complexity.

Also there is scholar to adopt standard genetic algorithm with wMPS system positioning error simultaneously, area coverage and use cost carry out layout optimization as objective function, but this method exists easily makes result be absorbed in local optimum, the problems such as speed of convergence is slow, cause survey station not reach optimal location, affect the raising of space measurement positioning system performance.

Summary of the invention

Technical matters to be solved by this invention overcomes the deficiencies in the prior art, for lacking the wider survey station layout optimization method of adaptability in engineering practice, and not by problems such as the parameters of influential system layout consider, a kind of office of portion intelligent optimization method of the space measurement positioning system survey station based on improved adaptive GA-IAGA is proposed.In space measurement positioning system, set up system positioning error, the multiple goal numerical relationship model of area coverage and use cost.When considering that different model dimension is different, using method for normalizing that the layout optimization problem of space measurement positioning system is converted into single objective programming problem, and using Revised genetic algorithum to carry out global optimizing, obtaining optimum survey station dispositions method.

The technical scheme that the present invention takes is a kind of space measurement positioning system survey station layout intelligent optimization method, it is characterized in that, in space measurement positioning system, in order to obtain optimum survey station layout, set up by survey station positioning error, the multiple goal numerical relationship model of coverage and use cost composition, i.e. survey station layout optimized mathematical model, use method for normalizing that the layout optimization problem of space measurement positioning system is converted into single-object problem, and utilize improved adaptive GA-IAGA to obtain optimum survey station layout.

Concrete steps are as follows:

Step 1), in space orientation measuring system, set up survey station layout optimized mathematical model, comprise system fixed

Position error model, system ovelay range model, cost model;

Step 2), use method for normalizing the layout multi-objective optimization question of space measurement positioning system is converted into single-object problem solves;

Step 3), use improved adaptive GA-IAGA survey station layout Optimized model is solved.

Described step 1) in,

The process of establishing of system Model of locating error is as follows:

In space orientation measuring system, mainly comprise cell site, receiver, engineer's scale, omnidirectional's vector rod, its direct observed quantity is that optical plane is from zero scan to the time of measured point.Under the local coordinate system of cell site, temporal information and horizontal angle and vertical angle can set up funtcional relationship one to one.Therefore for each measurement of cell site, following formula is all had to set up:

$\left\{\begin{array}{c}{\mathrm{\α}}_n=arctan\left(\frac{y_T-y_n}{x_T-x_n}\right)\\ {\mathrm{\β}}_n=\arctan \left(\frac{z_T-z_n}{R_n}\right)\\ R_n=\sqrt{{(x_T-x_n)}^2+(y_T-y_n)}\end{array}\right.$

T in formula _n=(x _n, y _n, z _n), n=1,2 ... N is expressed as n-th cell site's true origin coordinate, P=(x _t,y _t, z _t) represent tested point coordinate, R _nit is the distance of the horizontal projection range coordinate initial point of measured point under n-th cell site's coordinate system.

If m _nirepresent the i-th sub-level angle of the n-th cell site and the measurement of vertical angle, then have:

m _i＝f _i(T ₁,T ₂,...T _n,P)＝m _ni+ε _ni，n＝1,2…N

By f _ifunction is through Taylor series expansion and after removing all nonlinear components, obtain azimuth angle error propogator matrix H, be expressed as:

$H=\left[\begin{array}{c}{\left[\begin{array}{ccc}-\frac{(y_T-y_n)}{R_n^2}& \frac{(x_T-x_n)}{R_n^2}& 0\end{array}\right]}_{N\×3}\\ {\left[\begin{array}{ccc}-\frac{(x_T-x_n)(z_T-z_n)}{R_n{r}_n^2}& \frac{(y_T-y_n)(z_T-z_n)}{R_n{r}_n^2}& \frac{R_n}{r_n^2}\end{array}\right]}_{N\×3}\end{array}\right]$

In formula $r_n=\sqrt{{(x_T-x_n)}^2+{(y_T-y_n)}^2+{(z_T-z_n)}^2}$ For measured point is to n-th cell site's initial point distance, for measured point horizontal projection is to n-th cell site's initial point distance, now corresponding measuring error covariance matrix is Vm:

$Vm=\left[\begin{array}{cc}diag{\left({\mathrm{\σ}}_{\mathrm{\α}n}^2\right)}_{N\×N}& 0\\ 0& diag{\left({\mathrm{\σ}}_{\mathrm{\β}n}^2\right)}_{N\×N}\end{array}\right]$

In formula with represent that horizontal angle and vertical angle measure variance respectively.Be weighted process according to covariance matrix, now location estimation covariance matrix D is:

D＝(H ^TVm ^-1H) ^-1

According to matrix D, arrangement manner is for any point P spatially _kgDOP (precision geometry dilution gfactor) be expressed as:

${\mathrm{GDOP}}_{p_k}=\sqrt{tr\left(D_{p_k}\right)}$

Be the most high position precision in order to reach measured point to the layout optimization of all survey stations, then above formula can be derived as:

O ₁＝GDOP _pk。

Described step 1) in,

The process of establishing of system area coverage model is as follows:

Definition optical plane inclination angle, two, cell site is respectively φ ₁and φ ₂, make φ _max=max (φ ₁, φ ₂) be then axis of symmetry with Z axis, cone angle is 2 φ _maxtwo inverted cone be up and down the scan blind spot of cell site's laser plane.Receiver and cell site are apart from different, and the pulsewidth of light pulse will change, and therefore receiver will be operated in limited distance range.

The measured target P that horizontal surface areas β ≡ 0 dispenses at random _i, its coordinate is (x _i, y _i), for At any points T _j, measured target P _iwith At any points T _jbetween Euclidean distance be:

$d(P_i,T_j)=\sqrt{{\left(x_i-x_j\right)}^2+{\left(y_i-y_j\right)}^2}$

Therefore d (P is only needed _i, T _j) at the effective working distance [LR of receiver _min, LR _max] between.And for there being the plane domain of certain altitude H, the azimuth coverage that cell site can measure can be expressed as:

$\left\{\begin{array}{c}\mathrm{\α}\∈\[0,2\mathrm{\π}\]\\ \mathrm{\β}=\arctan \left(H/d\right)\end{array}\right.$

Wherein α is horizontal angle, and β is vertical angle.Then the area coverage model of survey station can be expressed as:

If measured target radial distance and vertical angle size can within survey scopes at survey station, think that the probability that survey station records this point is 1, can scope be surveyed if having one to exceed survey station in measured target radial distance or vertical angle size, then think that the probability recording this point is 0.

Described step 1) in,

The process of establishing of cost model is as follows:

The present invention only considers the cost of investment of survey station when completing measurement task, does not consider operating cost in measuring process.After all survey stations are all deployed, under often kind of layout, the cost consumption model of survey station can be expressed as:

O ₃＝C*N

In formula, C represents the cost of single survey station, and N represents the number of survey station.In measured zone, select suitable survey station quantity, make region maximal cover, use cost is few simultaneously to meet measuring system precision, can be exchanged into multi-objective optimization question and solves.

According to survey station positioning error D and coverage F and survey station cost C, obtain survey station layout Model for Multi-Objective Optimization:

MinO ₁＝GDOP _pk

MinO ₃＝C*N。

Described step 2) in, use method for normalizing that the layout multi-objective optimization question of space measurement positioning system is converted into single-object problem due to objective function dimension difference and solve, detailed process is as follows:

Wherein positioning error mathematical model can be expressed as:

In formula, PDOP _limit is the measuring accuracy requirement that user proposes.

Area coverage model:

Use cost model:

$\begin{array}{cc}{O}_3=1-\frac{N_{act}}{N_{\max }}& (O_3\∈\[0,1\])\end{array}$

In formula, N _actthe survey station number of actual use, N _maxit is spendable survey station number.

Therefore the layout optimization question variation of this space measurement positioning system is the single objective programming problem of following Weight coefficient:

$\begin{array}{cc}\max f\left(x\right)=K_1{O}_1+K_2{O}_2+K_3{O}_3& (\underset{i=1}{\overset{n}{\Σ}}{K}_i=1).\end{array}$

Described step 3) in,

Use improved adaptive GA-IAGA to solve survey station layout Optimized model, carry out as follows:

The parameter sets of objective function is encoded into chromosome, and the chromosome population of random initializtion certain scale, being encoded to of i-th survey station locus:

$\left[\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right]=\left[\begin{array}{c}a\\ a\\ a\end{array}\right]+\left[\begin{array}{c}b-a\\ b-a\\ b-a\end{array}\right]\·rand$

Wherein a and b represents coboundary and the lower boundary of measured zone respectively, and rand is [0,1] random number spatially;

According to the chromosome of coding, calculate corresponding fitness function FF:

FF＝K ₁O ₁+K ₂O ₂+K ₃O ₃

According to fitness function value, adopt roulette selection, namely based on the selection strategy of fitness ratio, individual i by the probability selected is:

$R=\frac{{\mathrm{FF}}_i}{\underset{i=1}{\overset{M}{\Σ}}{\mathrm{FF}}_i}$

In formula, FF _ibe i-th chromosomal adaptive value, M is colony's sum;

According to the chromosome that select probability obtains, carry out improvement self-adaptation and intersect, crossover probability is:

$P_C=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{c1}-\frac{(P_{c1}-P_{c2})(f-f_{avg})}{f_{max}-f_{avg}}\&rsqb;& f\&GreaterEqual;f_{avg}\\ P_{c1}& f<f_{avg}\end{array}\right.$

$P_m=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{m1}-\frac{(P_{m1}-P_{m2})(f_{\max }-f^{\&prime;})}{f_{max}-f_{avg}}\&rsqb;& f^{\&prime;}\&GreaterEqual;f_{avg}\\ P_{m1}& f^{\&prime;}<f_{avg}\end{array}\right.$

In formula, F (t) is evolution decay factor, t is current evolutionary generation; T is total evolutionary generation; F is the individuality that in the individuality that will intersect, fitness value is large; F' is the individual fitness value that will make a variation; f _avgfor colony's average fitness; f _maxfor colony's maximum adaptation degree.P _c1equal 0.9, P _c2equal 0.6, P _m1equal 0.1, P _m2equal 0.01.

Revised genetic algorithum is used to solve survey station layout Optimized model, make to have stronger ability of searching optimum at iteration initial stage algorithm, along with the increase of iterations, the ability of searching optimum of algorithm declines, local search ability strengthens, and is convenient to the globally optimal solution obtaining survey station layout.

Tool of the present invention has the following advantages:

(1) make full use of improved adaptive GA-IAGA to intersect and mutation probability according to ideal adaptation and evolutionary generation dynamic adjustments, thus improve global convergence and speed of convergence, this improved adaptive GA-IAGA is incorporated into solving of space measurement positioning system survey station layout optimization problem;

(2) advantage of algorithm in optimization problem, is incorporated into solving of space measurement positioning system survey station layout optimization problem by genetic algorithm;

(3) establish rational survey station layout optimization aim model, realize survey station and optimize distribution and to comprehensive covering in tested region under certain cost, and can meet the requirement of measuring accuracy;

(4) rational deployment that the present invention can be angled type Intersection Measuring System survey station provides effective theoretical direction and reference, can be used for the fields such as the precision measurement in Large-Scale Equipment manufacture process, has effect of optimization good, the features such as application is strong.

Accompanying drawing explanation

Fig. 1 is the space measurement positioning system survey station layout optimization method process flow diagram that the present invention is based on improved adaptive GA-IAGA; Fig. 2 adopts standard genetic algorithm to carry out optimizing with when adopting the improved adaptive GA-IAGA of the application to carry out optimizing, to optimal adaptation value iterative process emulation signal comparison diagram, Fig. 2 (a1) is the simulation result figure that two survey stations adopt the improved adaptive GA-IAGA of the application; Fig. 2 (a2) is the simulation result figure that two survey stations adopt standard genetic algorithm;

Fig. 2 (b1) is the simulation result figure that three survey stations adopt the improved adaptive GA-IAGA of the application; Fig. 2 (b2) is the simulation result figure that three survey stations adopt standard genetic algorithm;

Fig. 2 (c1) is the simulation result figure that four survey stations adopt the improved adaptive GA-IAGA of the application; Fig. 2 (c2) is the simulation result figure of four survey station standard genetic algorithm.

Specific embodiments

Core concept of the present invention is optimized modeling and solving based on improved adaptive GA-IAGA to space measurement positioning system survey station layout, therefore the present invention establishes the positioning error of survey station, area coverage, the mathematical function relationship of use cost, i.e. survey station layout optimization aim mathematical model, when considering that different model dimension is different, use method for normalizing that the layout optimization problem of space measurement positioning system is converted into single objective programming problem, finally use improved adaptive GA-IAGA to carry out global optimizing and obtain optimum solution.

With reference to Fig. 1 algorithm flow chart, the present invention is based on the space measurement positioning system survey station optimization method of improved adaptive GA-IAGA, implementation step is as follows:

1. set up survey station mathematical model:

1) system Model of locating error

Location estimation covariance matrix D determines primarily of azimuth angle error propogator matrix H and measuring error covariance matrix Vm, and its expression formula is:

D＝(H ^TVm ^-1H) ^-1(1)

According to matrix D, cloth station geometry is for any point P spatially _kgDOP (precision geometry dilution gfactor is expressed as:

${\mathrm{GDOP}}_{p_k}=\sqrt{tr\left(D_{p_k}\right)}---\left(2\right)$

Be the most high position precision in order to reach measured point to the layout optimization of all survey stations, then above formula can be derived as:

O ₁＝GDOP _pk(3)

2) system area coverage model

Definition optical plane inclination angle, two, cell site is respectively φ ₁and φ ₂, make φ _max=max (φ ₁, φ ₂), be then axis of symmetry with Z axis, cone angle is 2 φ _maxtwo inverted cone be up and down the scan blind spot of cell site's laser plane.Receiver and cell site are apart from different, and the pulsewidth of light pulse will change, and therefore receiver will be operated in limited distance range.

The measured target P that horizontal surface areas β ≡ 0 dispenses at random _i, its coordinate is (x _i, y _i), for At any points T _j, measured target P _iwith At any points T _jbetween Euclidean distance be:

$d(P_i,T_j)=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}---\left(4\right)$

Therefore d (P is only needed _i, T _j) at effective working distance of receiver ^from[LR _min, LR _max] between.And for there being the plane domain of certain altitude H, the azimuth coverage that cell site can measure can be expressed as:

$\left\{\begin{array}{c}\mathrm{\&alpha;}\&Element;\&lsqb;0,2\mathrm{\&pi;}\&rsqb;\\ \mathrm{\&beta;}=\arctan \left(H/d\right)\end{array}\right.---\left(5\right)$

Wherein α is horizontal angle, and β is vertical angle.Then the area coverage model of survey station can be expressed as:

3) system use cost model

Only considering the cost of investment of survey station when completing measurement task, not considering operating cost in measuring process.After all survey stations are all deployed, under often kind of layout, the cost consumption model of survey station can be expressed as:

O ₃＝C*N(7)

In formula, C represents the cost of single survey station, and N represents the number of survey station.In measured zone, select suitable survey station quantity, make region maximal cover, use cost is few simultaneously to meet measuring system precision.Can be exchanged into multi-objective optimization question to solve.

2. multiple objective function normalization

1) objective function

Objective function of the present invention mainly considers the positioning error of system, the coverage of system survey station and use cost, is meeting under measuring system accuracy requirement, and use cost is few simultaneously to make region maximal cover.For the ease of optimizing, this multiple goal need be converted into single-goal function, because the dimension of each target is different, first need each function normalization.

2) normalization

③ $O_3=1-\frac{N_{\mathrm{act}}}{N_{\max }}(O_3\&Element;[\mathrm{0,1}\left]\right)$

For multi-objective optimization question, if give its each sub-goal function f (x _i) (i=1,2 ..., n) give weight coefficient K _i(i=1,2 ..., n), wherein K _ifor corresponding f (x _i) significance level (Σ K in multi-objective optimization question _i=1), then each sub-goal function f (x _i) quadratic approach be expressed as:

$f\left(X\right)=\underset{i=1}{\overset{n}{\&Sigma;}}{K}_{i}f\left(x_i\right)---\left(11\right)$

Using the evaluation function of f (X) as multi-objective optimization question, then multi-objective optimization question just can be converted into single-object problem, can utilize the genetic algorithm for solving multi-objective optimization question of single object optimization.

Therefore the layout optimization question variation of this space measurement positioning system is the single objective programming problem of following Weight coefficient:

maxf(x)＝K ₁O ₁+K ₂O ₂+K ₃O ₃(12)

3. Revised genetic algorithum

1) crossover operator improved and mutation operator

Crossover probability P in genetic algorithm _cwith mutation probability P _mvital impact is had on the crossover and mutation operation in algorithm.But crossover probability and mutation probability normally remain unchanged in standard genetic algorithm calculating process, cause algorithm local convergence ability, there is the problems such as precocious.For the problems referred to above, the present invention proposes a kind of Revised genetic algorithum, and the thought of this innovatory algorithm is: in the initial stage of evolving and mid-term, decay is also not obvious, and the individuality being less than average fitness always gets larger crossover probability and mutation probability, is conducive to superseded poor individuality like this; Higher than the individuality of average fitness, its crossover probability and mutation probability can adjust according to the change of fitness dynamically.Along with the increase of evolutionary generation, crossover and mutation probability slowly reduces, and to later stage of evolution, crossover probability and mutation probability reduce rapidly under the effect of decay factor, thus ensures that optimum solution is not destroyed.

Improved adaptive GA-IAGA crossover and mutation probability, formula is as follows:

$P_C=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{c1}-\frac{(P_{c1}-P_{c2})(f-f_{avg})}{f_{max}-f_{avg}}\&rsqb;& f\&GreaterEqual;f_{avg}\\ P_{c1}& f<f_{avg}\end{array}\right.---\left(13\right)$

$P_m=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{m1}-\frac{(P_{m1}-P_{m2})(f_{\max }-f^{\&prime;})}{f_{max}-f_{avg}}\&rsqb;& f^{\&prime;}\&GreaterEqual;f_{avg}\\ P_{m1}& f^{\&prime;}<f_{avg}\end{array}\right.---\left(14\right)$

Wherein, F (t) is evolution decay factor, t is current evolutionary generation; T is total evolutionary generation; F is the individuality that in the individuality that will intersect, fitness value is large; F' is the individual fitness value that will make a variation; f _avgfor colony's average fitness; f _maxfor colony's maximum adaptation degree.P _c1equal 0.9, P _c2equal 0.6, P _m1equal 0.1, P _m2equal 0.01.

2) realization of improved adaptive GA-IAGA

1. system survey station is position encoded

This patent takes floating-point encoding form, and just the parameter sets of objective function is encoded into chromosome, and the chromosome population of random initializtion certain scale, being encoded to of i-th survey station locus:

$\left[\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right]=\left[\begin{array}{c}a\\ a\\ a\end{array}\right]+\left[\begin{array}{c}b-a\\ b-a\\ b-a\end{array}\right]\&CenterDot;rand---\left(15\right)$

Wherein a and b represents coboundary and the lower boundary of measured zone respectively, and rand is [0,1] random number spatially.

2. adaptive value calculates

According to the chromosome of coding, calculate corresponding fitness function F:

FF＝K ₁O ₁+K ₂O ₂+K ₃O ₃(16)

Wherein, Σ K _i=1.

3. selection opertor

According to fitness function value, adopt roulette selection, namely based on the selection strategy of fitness ratio, individual i by the probability selected is:

$p_i=\frac{{\mathrm{FF}}_i}{\underset{i=1}{\overset{M}{\&Sigma;}}{\mathrm{FF}}_i}---\left(17\right)$

FF in formula _ibe i-th chromosomal adaptive value, M is colony's sum.

4. intersect and variation

The genetic operator of the improvement that intersection and mutation operator adopt the present invention to propose.

5. iteration ends criterion

The present invention adopts the method for maximum termination algebraically to determine whether termination of iterations process, and termination algebraically of the present invention is 100.

According to the coding of survey station position, fitness function evaluation and selection opertor, crossover operator, the operation of mutation operator, through continuous iteration, obtains the globally optimal solution of survey station position, according to the globally optimal solution obtained, layout is carried out to space measurement positioning system survey station.

Advantage of the present invention can be further illustrated by following emulation experiment:

1. experiment condition is arranged

Assuming that deployment region is 16m*16m*8m, suppose that survey station is all operated in ideally simultaneously, the operating distance of every platform survey station is all 5m-20m, each survey station angle measurement accuracy is 1 "; during emulation, weight coefficient is all set to 1/3, is divided into 50 points by equally spaced for tested region simultaneously; simulate tested region by these points, claims these points for simulation measured point.The design parameter of propagation algorithm is arranged: the scale of population is 20, maximum iteration time G _maxbe 100.

2. experiment content and result

This patent adopts standard genetic algorithm and improved adaptive GA-IAGA to emulate different number survey station layout situation respectively, and simulation result is as follows:

In two survey station layout situations, one of them survey station position is at (1.8975m, 9.2343m, 3.9292m), and another survey station position is at (14.8413m, 4.1144m, 6.211m).

In three survey station layout situations, optimum survey station position is respectively (1.9438m, 1.5566m, 7.4284m), (8.1586m, 5.1908m, 3.6678m), (15.4011m, 5.8996m, 5.9677m).

In four survey station layout situations, optimum survey station position is respectively (0.3735m, 14.3828m, 2.8796m), (10.8328m, 12.9841m, 5.4793m), (8.3125m, 9.4336m, 7.9247m), (1.8155m, 3.0321m, 5.6189m).

As can be seen from the above results, the survey station being positioned at cloth station fringe region more easily covers measurement target, reaches the object at cloth station as required, and is optimal location.

Genetic algorithm and improved adaptive GA-IAGA emulation optimal-adaptive are worth the process of iteration situation, simulation result as shown in Figure 2, wherein Fig. 2 (a1) (a2) is the layout of 2 survey stations, Fig. 2 (b1) (b2) is the layout of 3 survey stations, and Fig. 2 (c1) (c2) is the layout of 4 survey stations.As can be seen from figure we, in two survey station situations, when adopting standard genetic algorithm to carry out optimizing, algorithm could close to optimum solution in 60 ~ 70 generations, corresponding objective function maximal value is 0.8092, when adopting the improved adaptive GA-IAGA of the application to carry out optimizing, algorithm reaches optimum solution in 10 ~ 20 generations, and corresponding objective function maximal value is 0.8227; In three survey station situations, when adopting standard genetic algorithm to carry out optimizing, algorithm could close to optimum solution in 60 ~ 70 generations, corresponding objective function maximal value is 0.7488, when adopting the improved adaptive GA-IAGA of the application to carry out optimizing, algorithm reaches optimum solution in 10 ~ 20 generations, and corresponding objective function maximal value is 0.7497; In four survey station situations, when adopting standard genetic algorithm to carry out optimizing, algorithm could close to optimum solution in 80 ~ 90 generations, corresponding objective function maximal value is 0.6662, when adopting the improved adaptive GA-IAGA of the application to carry out optimizing, algorithm reaches optimum solution in 10 ~ 20 generations, and corresponding objective function maximal value is 0.6666.As can be seen from above emulation, the improved adaptive GA-IAGA of this patent has fast convergence rate, low optimization accuracy high, makes optimal location can be found rapidly, reaches the object of survey station global optimum.

Claims (7)

1. a space measurement positioning system survey station layout intelligent optimization method, it is characterized in that: in space measurement positioning system, in order to obtain optimum survey station layout, set up by survey station positioning error, the multiple goal numerical relationship model of coverage and use cost composition, i.e. survey station layout optimized mathematical model, uses method for normalizing that the layout optimization problem of space measurement positioning system is converted into single-object problem, and utilizes improved adaptive GA-IAGA to obtain optimum survey station layout.

2. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 1, is characterized in that: concrete steps are as follows:

Step 1), in space orientation measuring system, set up survey station layout optimized mathematical model, comprise system Model of locating error, system ovelay range model, cost model;

Step 2), use method for normalizing the layout multi-objective optimization question of space measurement positioning system is converted into single-object problem solves;

Step 3), use improved adaptive GA-IAGA survey station layout Optimized model is solved.

3. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 2, is characterized in that: described step 1) in,

The process of establishing of system Model of locating error is as follows:

In space orientation measuring system, comprise cell site, receiver, engineer's scale, omnidirectional's vector rod, its direct observed quantity is that optical plane is from zero scan to the time of measured point, under the local coordinate system of cell site, temporal information and horizontal angle and vertical angle set up funtcional relationship one to one, therefore for each measurement of cell site, all have following formula to set up:

$\left\{\begin{array}{c}{\mathrm{\&alpha;}}_n=\arctan \left(\frac{y_T-y_n}{x_T-x_n}\right)\\ {\mathrm{\&beta;}}_n=\arctan \left(\frac{z_T-z_n}{R_n}\right)\\ R_n=\sqrt{{(x_T-x_n)}^2+(y_T-y_n)}\end{array}\right.$

T in formula _n=(x _n, y _n, z _n), n=1,2 ... N is expressed as n-th cell site's true origin coordinate, P=(x _t,y _t, z _t) represent tested point coordinate, R _nthe distance of the horizontal projection range coordinate initial point of measured point under n-th cell site's coordinate system, α _nrepresent the horizontal angle of the n-th cell site, β _nrepresent the vertical angle of the cell site of n-th;

If m _nirepresent the i-th sub-level angle of the n-th cell site and the measurement of vertical angle, m _irepresent measured value, ε _nirepresent that measuring error then has:

m _i＝f _i(T ₁,T ₂,...T _n,P)＝m _ni+ε _ni，n＝1,2…N

By f _ifunction is through Taylor series expansion and after removing all nonlinear components, obtain azimuth angle error propogator matrix H, be expressed as:

$H=\left[\begin{array}{c}{\left[\begin{array}{ccc}-\frac{(y_T-y_n)}{R_n^2}& \frac{(x_T-x_n)}{R_n^2}& 0\end{array}\right]}_{N\&times;3}\\ {\left[\begin{array}{ccc}-\frac{(x_T-x_n)(z_T-z_n)}{R_n{r}_n^2}& \frac{(y_T-y_n)(z_T-z_n)}{R_n{r}_n^2}& \frac{R_n}{r_n^2}\end{array}\right]}_{N\&times;3}\end{array}\right]$

In formula $r_n=\sqrt{{(x_T-x_n)}^2+{(y_T-y_n)}^2+{(z_T-z_n)}^2}$ For measured point is to n-th cell site's initial point distance, for measured point horizontal projection is to n-th cell site's initial point distance, now corresponding measuring error covariance matrix is Vm:

$Vm=\left[\begin{array}{cc}diag{\left({\mathrm{\&sigma;}}_{\mathrm{\&alpha;}n}^2\right)}_{N\&times;N}& 0\\ 0& diag{\left({\mathrm{\&sigma;}}_{\mathrm{\&beta;}n}^2\right)}_{N\&times;N}\end{array}\right]$

In formula with represent that horizontal angle and vertical angle measure variance respectively; Be weighted process according to covariance matrix, now location estimation covariance matrix D is:

D＝(H ^TVm ^-1H) ^-1

According to matrix D, cloth station geometry is for any point P spatially _kprecision geometry dilution gfactor GDOP be expressed as:

${\mathrm{GDOP}}_{p_k}=\sqrt{tr\left(D_{p_k}\right)}$

In formula, represent P _kthe location estimation covariance matrix of point;

Be the most high position precision in order to reach measured point to the layout optimization of all survey stations, then system Model of locating error is:

$O_1={\mathrm{GDOP}}_{p_k}.$

4. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 3, is characterized in that: described step 1) in,

The process of establishing of system ovelay range model is as follows:

Definition optical plane inclination angle, two, cell site is respectively φ ₁and φ ₂, make φ _max=max (φ ₁, φ ₂); Be then axis of symmetry with Z axis, cone angle is 2 φ _maxtwo inverted cone be up and down the scan blind spot of cell site's laser plane; Receiver and cell site are apart from different, and the pulsewidth of light pulse will change, and therefore receiver will be operated in limited distance range;

The measured target P that horizontal surface areas β ≡ 0 dispenses at random _i, its coordinate is (x _i, y _i), for At any points T _j, its coordinate is (x _j, y _j), then measured target P _iwith At any points T _jbetween Euclidean distance be:

$d(P_i,T_j)=\sqrt{{\left(x_i-x_j\right)}^2+{\left(y_i-y_j\right)}^2}$

Therefore d (P is only needed _i, T _j) at the effective working distance [LR of receiver _min, LR _max] between, wherein LR _min, LR _maxrepresent the minimum of receiver respectively, maximum range of receiving; And for the plane domain of height H, the azimuth coverage that cell site can measure is expressed as:

$\left\{\begin{array}{c}\mathrm{\&alpha;}\&Element;\&lsqb;0,2\mathrm{\&pi;}\&rsqb;\\ \mathrm{\&beta;}=\arctan \left(H/d\left(P_i,T_j\right)\right)\end{array}\right.$

Wherein α is horizontal angle, and β is vertical angle; Then the area coverage model representation of survey station is:

If measured target radial distance and vertical angle size can within survey scopes at survey station, think that the probability that survey station records this point is 1, can scope be surveyed if having one to exceed survey station in measured target radial distance or vertical angle size, then think that the probability recording this point is 0.

5. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 4, is characterized in that: described step 1) in,

The process of establishing of cost model is as follows:

After all survey stations are all deployed, under often kind of layout, the cost consumption model representation of survey station is:

O ₃＝C*N

In formula, C represents the cost of single survey station, and N represents the number of survey station; In measured zone, select survey station quantity, make region maximal cover, use cost is few simultaneously to meet measuring system precision, is converted to multi-objective optimization question and solves;

According to survey station positioning error D and coverage F and survey station cost C, obtain survey station layout Model for Multi-Objective Optimization:

$\begin{array}{cc}Min& O_1={\mathrm{GDOP}}_{p_k}\end{array}$

MinO ₃＝C*N。

6. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 5, it is characterized in that: described step 2) in, because objective function dimension is different, use method for normalizing that the layout multi-objective optimization question of space measurement positioning system is converted into single-object problem to solve, detailed process is as follows: positioning error mathematical model is expressed as:

Wherein, PDOP _limit is the measuring accuracy requirement that user proposes;

Area coverage model:

Use cost model:

$\begin{array}{cc}{O}_3=1-\frac{N_{act}}{N_{\max }}& (O_3\&Element;\&lsqb;0,1\&rsqb;)\end{array}$

In formula, N _actthe survey station number of actual use, N _maxit is spendable survey station number;

Therefore the layout optimization question variation of this space measurement positioning system is the single objective programming problem of following Weight coefficient:

maxf(x)＝K ₁O ₁+K ₂O ₂+K ₃O ₃

In formula, K ₁, K ₂, K ₃represent weight, and

7. a kind of space measurement positioning system survey station layout intelligent optimization method according to claim 6, is characterized in that: described step 3) in, use improved adaptive GA-IAGA to solve survey station layout Optimized model, carry out as follows:

The parameter sets of objective function is encoded into chromosome, and the chromosome population of random initializtion certain scale, being encoded to of i-th survey station locus:

$\left[\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right]=\left[\begin{array}{c}a\\ a\\ a\end{array}\right]+\left[\begin{array}{c}b-a\\ b-a\\ b-a\end{array}\right]\&CenterDot;rand$

Wherein a and b represents coboundary and the lower boundary of measured zone respectively, and rand is [0,1] random number spatially;

According to the chromosome of coding, calculate corresponding fitness function FF:

FF＝K ₁O ₁+K ₂O ₂+K ₃O ₃

According to fitness function value, adopt roulette selection, namely based on the selection strategy of fitness ratio, individual i by the probability selected is:

$p_i=\frac{{\mathrm{FF}}_i}{\underset{i=1}{\overset{M}{\&Sigma;}}{\mathrm{FF}}_i}$

In formula, FF _ibe i-th chromosomal adaptive value, M is colony's sum;

According to the chromosome that select probability obtains, carry out improvement self-adaptation and intersect, crossover probability is:

$P_C=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{c1}-\frac{(P_{c1}-P_{c2})(f-f_{avg})}{f_{max}-f_{avg}}\&rsqb;& f\&GreaterEqual;f_{avg}\\ P_{c1}& f<f_{avg}\end{array}\right.$

$P_m=\left\{\begin{array}{cc}F\left(t\right)\&CenterDot;\&lsqb;P_{m1}-\frac{(P_{m1}-P_{m2})(f_{\max }-f^{\&prime;})}{f_{max}-f_{avg}}\&rsqb;& f^{\&prime;}\&GreaterEqual;f_{avg}\\ P_{m1}& f^{\&prime;}<f_{avg}\end{array}\right.$

In formula, F (t) is evolution decay factor, t is current evolutionary generation; T is total evolutionary generation; F is the individuality that in the individuality that will intersect, fitness value is large; F' is the individual fitness value that will make a variation; f _avgfor colony's average fitness; f _maxfor colony's maximum adaptation degree.P _c1equal 0.9, P _c2equal 0.6, P _m1equal 0.1, P _m2equal 0.01.