CN106842118A - For the time difference positioning method of Distributed Multi positioning monitoring system - Google Patents
For the time difference positioning method of Distributed Multi positioning monitoring system Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0278—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves involving statistical or probabilistic considerations
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/16—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using electromagnetic waves other than radio waves
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
- G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
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- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Probability & Statistics with Applications (AREA)
- Electromagnetism (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The invention belongs to the real time positioning technology field of Distributed Multi positioning monitoring system, more particularly to a kind of time difference positioning method for Distributed Multi positioning monitoring system.The present invention is according to GDOP TOA difference locating accuracy regioselective methods；Determine main website of receiving station according to localization method, set up observation model；The Localization Estimate Algorithm of TDOA relaxed using positive semidefinite calculates the positional information of target, and positioning result is presented into user by terminal display monitoring system, so as to improve airfield controller to airdrome scene aircraft and guide car monitoring control ability.All process of calculation analysis of the invention are all spontaneous, influence of the artificial factor to aircraft and guide car positioning result is reduced to greatest extent, and all of data handling procedure is all parallel, the efficiency of data processing is drastically increased, user is performed the result of acquisition analysis most fast during operation.Accurate positioning of the present invention, remains to preferably estimate the position of signal source when measurement error is larger.
Description
Technical field
It is more particularly to a kind of for dividing the invention belongs to the real time positioning technology field of Distributed Multi positioning monitoring system
The time difference positioning method of cloth multipoint positioning monitoring system.
Background technology
With developing rapidly for China's economy, flight amount commander to air traffic control system controller and sets also being skyrocketed through
Arrange standby maintenance and propose requirement higher, airport surface detection radar is primary radar, be mainly used in monitoring airdrome scene
Aircraft and vehicle, using target to electromagnetic wave itself radiation or reflection characteristic find target.Plant maintenance personnel are safeguarding
Include following three aspects problem during airport surface detection radar：Aircraft Targets divide, there is certain blind area, easily go out
Existing decoy.The presence of these problems has upset controller and has normally commanded work, therefore, Distributed Multi alignment system is drawn
Enter necessary and necessary, this technology is upgrading and the supplement of airport surface detection radar, and can be by increasing receiving station
Or the layout of change receiving station realizes the extension of system.
Traditional time difference positioning method carry out positioning precision resolve when, it is contemplated that each target destination error elements it
Between be related, reduce the efficiency of positioning precision resolving, improve positioning precision and resolve complexity, and usually using safe
Strangle Series Algorithm, Chan algorithms, MDS algorithm to determine the positional information of target, using Taylor series algorithm to iteration initial value
Selection require, it may appear that local convergence or the phenomenon of diverging；Chan algorithms and MDS algorithm are led when measurement error is larger
Cause is inaccurate to the position judgment of signal source, the problem of nonlinearity often occurs so as to cause time difference positioning method so that
Positioning is inaccurate.
The content of the invention
The present invention in order to overcome the above-mentioned deficiencies of the prior art, there is provided for Distributed Multi positioning monitoring system when
Difference localization method, this time difference positioning method significantly reduces the complexity of positioning precision calculation method, improves positioning precision
The efficiency of resolving, and selection to iteration initial value do not require, can converge to global minimum point, is not in local receipts
The phenomenon held back or dissipate；Remain to preferably estimate the position of signal source when measurement error is larger, accurate positioning.
To achieve the above object, present invention employs following technical measures：
For the time difference positioning method of Distributed Multi positioning monitoring system, comprise the following steps：
Target destination main website and extension station of receiving station obtain target response letter in S1, Distributed Multi positioning monitoring system
Number, to measurement parameter number of the target response signal after Distributed Multi positioning monitoring system treatment is parsed
According to；
S2, the measured parameter data is obtained according to the target destination main website and extension station of receiving station, to measurement parameter
Same target answer back code and the confidence level more than 50% carry out pairing treatment in data, obtain the survey that target sends in synchronization
Amount supplemental characteristic；
S3, to pairing process after measured parameter data carry out main website position selection, obtain the positioning accurate of area to be targeted
Degree；
The positioning precision of S4, the measured parameter data according to target and area to be targeted, the reception station owner of selection target
Stand, determine positioning using TDOA model；
S5, using main website of receiving station and extension station of receiving station positional information measured parameter data, by positive semidefinite relax when
Difference positioning algorithm calculates the positional information of target；
S6, the positional information of the target is delivered into terminal show.
Preferably, when the measured parameter data includes target response code, confidence level, target response mode, target response
Between, the range value of target.
Preferably, the specific steps of step S3 include：
S31, determine target main website of receiving station positional information；
The measurement data of the receiving station of the target after pairing treatment is obtained, one of receiving station's connecing as target is chosen
Station owner's station location is received, the GDOP values that observation model calculates positioning region under the conditions of the observation model are set up, realization connects to target
The positional information for receiving station owner station determines；By choosing receiving station main website of the different receiving stations as target, calculate respectively different
The GDOP of positioning region under the conditions of observation model；By choosing GDOP minimum values as positioning using TDOA under the conditions of different observation models
Precision minimum value, realizes the structure to Distributed Multi positioning monitoring system positioning using TDOA model；
S32, the positional information to area to be targeted are differentiated；
By the region overlay figure of the main website of receiving station of target, the region overlay figure of the extension station of receiving station of target, acquisition can
The positional information of positioning region, using it is described can positioning region positional information and reach target i-th extension station of receiving station
And the time difference between the main website of receiving station of target, by positioning using TDOA equation, the positional information to area to be targeted is differentiated：
c·Δti=c (ti-t0)=ri-r0(i=1,2)
Wherein, c is the light velocity, Δ tiDuring between i-th extension station of receiving station and the main website of receiving station of target that reach target
Between poor, tiTo reach i-th time of extension station of receiving station, t of target0To reach receiving station's main station time, the r of targetiTo reach
I-th distance of extension station of receiving station, r of target0It is main website of the receiving station distance for reaching target, the receiving station that i is arrival target
The numbering of extension station；
S33, the receiving station for obtaining main website of the receiving station position, target and target of target and target in the area to be targeted
The correlation matrix of extension station position；
By the main website of receiving station of each extension station of receiving station of target in the area to be targeted to target and target to target
Alternate position spike, draw the correlation matrix of target and site position in area to be targeted：
X, y are the positional information of target, x0, y0It is main website of receiving station positional information, the x of targeti、yiIt is target
I-th extension station of receiving station positional information, r0It is main website of receiving station distance, the r of target to targetiConnect for i-th for target to target
Shou Zhan extension stations distance,
S34, the error estimate that the area to be targeted is calculated using pseudoinverse technique；
Error locator equation formula is：
Wherein,For position error in the x direction positioning variances,For position error, positioning variances, i are in y-direction
I-th extension station of receiving station of target, j are j-th extension station of receiving station of target,Its
In, ηijIt is Δ tiWith Δ tjBetween coefficient correlation,It is the standard deviation of the time measurement error at the i-th station,It is jth station
The standard deviation of time measurement error, σsIt is the standard deviation of site measurement error；
S35, the positioning precision for obtaining area to be targeted；
Coefficient correlation η according to time measurement errorij, the standard deviation sigma of each site measurement errors, asked using linear combination
Go out σij, then try to achieve positioning variances on x directionsPositioning variances on y directionsPass throughFormula, meter
Calculation obtains the positioning precision GDOP of area to be targeted.
Preferably, the specific steps of step S5 include：
S51, structure positioning using TDOA equation；
Set up corresponding observation model using main website of receiving station positional information measured parameter data, it is determined that main website of receiving station
Site information, using the distance of target to main website of receiving station, target to extension station of receiving station range difference build location from range-difference measurements
Equation：
Wherein,To reach main website of receiving station and the measured value of extension station of receiving station time difference, c is the light velocity, ri,k-r1,kFor
The answer signal of signal source transmitting is from k-th target location ukTo receiving station siWith main website of receiving station s1Between actual time it is poor,
ni1,kIt is measurement error, i is the index of extension station of receiving station, and k is indexed for target；
S52, it is that target location to be positioned carries out maximal possibility estimation to source location；
Represented using the covariance matrix of target to main website of receiving station and i-th range difference measurement error of extension station of receiving station
The maximal possibility estimation of target location：
Wherein, J (u) is nonlinearity, the non-convex cost function of source location u,ForThe range difference for being constituted
Estimate the vector of composition, f (u) is the answer signal of signal source transmitting from k-th target location ukTo receiving station siWith reception station owner
Stand s1Between actual time difference composition vector, Q be measurement error ni1,kThe covariance matrix that average is zero is obeyed, T is matrix
Transposition,To cause the value of desired signal source position u during cost function J (u) minimum；
S53, introduce auxiliary vector, by location from range-difference measurements it is equations turned be constrained least-squares problem；
Introduce auxiliary vector and be position of the target with main website of receiving station and distance, be converted into constrained least-squares problem,
And convex semi definite programming problem is converted on this basis, former cost function is arranged the matrix for obtaining as follows：
Wherein,ηk=
Bknk, Bk=diag { r2,k,...,rN,k, k=1,2, R=[s2-s1,...,sN-s1]T, O(N-1)×3It is 0 matrix of (N-1) × 3,
0N-1It is 0 row vector of N-1,It is the vector for reaching main website of receiving station and extension station of receiving station range difference estimation composition of target 1,
It is the vector for reaching main website of receiving station and extension station of receiving station range difference estimation composition of target 2；
S54, the auxiliary vector is weighted least square solution；
The matrix for obtaining is arranged to former cost function and is weighted least square solution, the auxiliary vector estimate for obtaining is such as
Under：
Wherein, weighting matrix W=E [η ηT]-1=(BQBT)-1, B=diag { B1,B2Represent with B1And B2It is diagonal blocks
Matrix, Q=E [nnT] it is noise covariance matrix, n is to reach main website of receiving station and extension station of receiving station range difference measurement error
Matrix form, Gy-h=η；
S55, the lax equality constraint of auxiliary vector initial estimation calculated using weighted least-square solution, construct new cost letter
Number；
According to constraints, new cost function is constructed：
S.t y (6+k)=| | y (3 (k-1)+1:3k)||2, k=1,2
By (Gy-h)TW (Gy-h) is converted into
Wherein, Y=yyT,
It follows that Y (6+k, 6+k)=trace { Y (3k-2:3k,3k-2:3k) }, wherein, k=1,2；By Y=yyT,
Wherein y=[(u1-s1)T,(u2-s1)T,r1,1,r1,2]T, it is known that Y (7,8)=r1,1r1,2；
S56, using convex semi definite programming Optimization Solution auxiliary vector and the value of the variable of auxiliary vector transposition, and by spy
Value indicative decomposes the value for obtaining auxiliary vector；
When optimizing solution using the new cost function for having constructed, corresponding equality constraint is converted convex positive semidefinite rule
Draw optimization problem,
Formula to be solved is：Its constraints is：
S.t Y (6+k, 6+k)=trace { Y (3k-2:3k,3k-2:3k)}
The positional information of the Relation acquisition target between S57, the value according to the auxiliary vector tried to achieve and target location；
Carrying out Eigenvalues Decomposition to Y can obtain：
Wherein, λiFor the characteristic value of Y, i=1 ..., r, qiIt is corresponding characteristic vector, if i=1 ..., r have been pressed from big
To minispread, i.e. λ1≥λ2≥...≥λr＞ 0, the definition according to Y can obtain source locationIt is estimated as：
The beneficial effects of the present invention are：
1), the present invention is according to GDOP TOA difference locating accuracy regioselective methods；Determine main website of receiving station according to localization method,
Set up observation model；The Localization Estimate Algorithm of TDOA relaxed using positive semidefinite calculates the positional information of target, and positioning result is led to
Cross terminal display monitoring system and be presented to user, so as to improve airfield controller to airdrome scene aircraft and guide car monitoring control
Ability.All process of calculation analysis of the invention are all spontaneous, artificial factor is reduced to greatest extent to aircraft and is drawn
The influence of guide-car's positioning result, and all of data handling procedure is all parallel, drastically increases the effect of data processing
Rate, enables user to perform the result of acquisition analysis most fast during operation.
2) positioning precision for, determining area to be targeted is made an uproar using the positional information and inside of the receiving station of multiple targets
The quantizing noise information of sound, ambient noise and time measurement carries out positioning precision resolving to the location estimation value of target, by not
With combination and different arrangement manners, obtain measurement target region covering positioning precision GDOP, so as to from different cloth station sides
GDOP under formula is compared, and selects Optimal Station mode, for the structure that follow-up positioning using TDOA resolves model provides foundation.
3), the positioning using TDOA problem of nonlinearity is converted into constraint weighted least square problem by the present invention, so
Relaxed by positive semidefinite on this basis afterwards and be converted into convex semi definite programming problem, optimize solution, it is to avoid tradition changes
For the local convergence and the problem of solution diverging that occur in algorithm, the precision of positioning is greatly increased.
Brief description of the drawings
Fig. 1 is flow chart of the invention；
Fig. 2 is the workflow diagram of step S3 of the invention；
Fig. 3 is the workflow diagram of step S5 of the invention；
Fig. 4 is Y shape cloth station analogous diagram of the invention；
Fig. 5 is del cloth station analogous diagram of the invention；
Fig. 6 is rhombus cloth station analogous diagram of the invention；
Fig. 7 is to signal source u using this positive semidefinite lax time difference positioning method, Chan algorithms, Taylor series Method1And u2Position
Put estimation withThe statistics schematic diagram of root-mean-square error during change；
Fig. 8 is to signal source using this positive semidefinite lax time difference positioning method, Chan algorithms, MDS algorithm, Taylor series Method
u3Location estimation withThe statistics schematic diagram of root-mean-square error during change.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
As shown in figure 1, for the time difference positioning method of Distributed Multi positioning monitoring system, comprising the following steps：
Target destination main website and extension station of receiving station obtain target response letter in S1, Distributed Multi positioning monitoring system
Number, to measurement parameter number of the target response signal after Distributed Multi positioning monitoring system treatment is parsed
According to；
S2, the measured parameter data is obtained according to the target destination main website and extension station of receiving station, to measurement parameter
Same target answer back code and the confidence level more than 50% carry out pairing treatment in data, obtain the survey that target sends in synchronization
Amount supplemental characteristic；
S3, to pairing process after measured parameter data carry out main website position selection, obtain the positioning accurate of area to be targeted
Degree；
The positioning precision of S4, the measured parameter data according to target and area to be targeted, the reception station owner of selection target
Stand, determine positioning using TDOA model；
S5, using main website of receiving station and extension station of receiving station positional information measured parameter data, by positive semidefinite relax when
Difference positioning algorithm calculates the positional information of target；
S6, the positional information of the target is delivered into terminal show.
The target is target to be positioned.
The measured parameter data includes target response code, confidence level, target response mode, target response time, target
Range value.
As shown in Fig. 2 the measured parameter data after processing pairing carries out main website position selection, area to be targeted is obtained
The concrete operation step of positioning precision includes：
S31, determine target main website of receiving station positional information；
The measurement data of the receiving station of the target after pairing treatment is obtained, one of receiving station's connecing as target is chosen
Station owner's station location is received, the GDOP values that observation model calculates positioning region under the conditions of the observation model are set up, realization connects to target
The positional information for receiving station owner station determines；By choosing receiving station main website of the different receiving stations as target, calculate respectively different
The GDOP of positioning region under the conditions of observation model；By choosing GDOP minimum values as positioning using TDOA under the conditions of different observation models
Precision minimum value, realizes the structure to Distributed Multi positioning monitoring system positioning using TDOA model；
S32, the positional information to area to be targeted are differentiated；
By the region overlay figure of the main website of receiving station of target, the region overlay figure of the extension station of receiving station of target, acquisition can
The positional information of positioning region, using it is described can positioning region positional information and reach target i-th extension station of receiving station
And the time difference between the main website of receiving station of target, by positioning using TDOA equation, the positional information to area to be targeted is differentiated：
c·Δti=c (ti-t0)=ri-r0(i=1,2)
Wherein, c is the light velocity, Δ tiDuring between i-th extension station of receiving station and the main website of receiving station of target that reach target
Between poor, tiTo reach i-th time of extension station of receiving station, t of target0To reach receiving station's main station time, the r of targetiTo reach
I-th distance of extension station of receiving station, r of target0It is main website of the receiving station distance for reaching target, the receiving station that i is arrival target
The numbering of extension station；
S33, the receiving station for obtaining main website of the receiving station position, target and target of target and target in the area to be targeted
The correlation matrix of extension station position；
By the main website of receiving station of each extension station of receiving station of target in the area to be targeted to target and target to target
Alternate position spike, draw the correlation matrix of target and site position in area to be targeted：
X, y are the positional information of target, x0, y0It is main website of receiving station positional information, the x of targeti、yiIt is target
I-th extension station of receiving station positional information, r0It is main website of receiving station distance, the r of target to targetiConnect for i-th for target to target
Shou Zhan extension stations distance,
S34, the error estimate that the area to be targeted is calculated using pseudoinverse technique；
Error locator equation formula is：
Wherein,For position error in the x direction positioning variances,For position error, positioning variances, i are in y-direction
I-th extension station of receiving station of target, j are j-th extension station of receiving station of target,
Wherein, ηijIt is Δ tiWith Δ tjBetween coefficient correlation,It is the standard deviation of the time measurement error at the i-th station,It is jth
The standard deviation of the time measurement error stood, σsIt is the standard deviation of site measurement error；
S35, the positioning precision for obtaining area to be targeted；
Coefficient correlation η according to time measurement errorij, the standard deviation sigma of each site measurement errors, asked using linear combination
Go out σij, then try to achieve positioning variances on x directionsPositioning variances on y directionsPass throughFormula,
It is calculated the positioning precision GDOP of area to be targeted.
When the coordinate of main website takes (0,0), when three coordinates of extension station take different values respectively, as shown in table 1, formation
Analogous diagram is respectively Y shape cloth station, inverted triangle cloth station, rhombus cloth station.
Table 1：
Knowable to Fig. 4~Fig. 6, for the form of same cloth station, positioning precision GDOP is with target and receiving station
The increase of the distance between distributed areas and reduce, for different arrangement manners, comprehensive interior position error is different, use
In the positioning precision method of Distributed Multi positioning monitoring system, Y shape, del, rhombus cloth station method can be taken into full account
The selection of the main website of receiving station and extension station position of target is carried out to the difference of different zones positioning precision.Target is made every effort to not
In same region, Optimal Station scheme is selected, realize the high accuracy positioning of target.
As shown in figure 3, using main website of receiving station and extension station of receiving station positional information measured parameter data, by positive semidefinite pine
The concrete operation step that the Localization Estimate Algorithm of TDOA of relaxation calculates the positional information of target is：
S51, structure positioning using TDOA equation；
Set up corresponding observation model using main website of receiving station positional information measured parameter data, it is determined that main website of receiving station
Site information, using the distance of target to main website of receiving station, target to extension station of receiving station range difference build location from range-difference measurements
Equation：
Wherein,To reach main website of receiving station and the measured value of extension station of receiving station time difference, c is the light velocity, ri,k-r1,kFor
The answer signal of signal source transmitting is from k-th target location ukTo receiving station siWith main website of receiving station s1Between actual time it is poor,
ni1,kIt is measurement error, i is the index of extension station of receiving station, and k is indexed for target.
S52, it is that target location to be positioned carries out maximal possibility estimation to source location；
Represented using the covariance matrix of target to main website of receiving station and i-th range difference measurement error of extension station of receiving station
The maximal possibility estimation of target location：
Wherein, J (u) is nonlinearity, the non-convex cost function of source location u,ForThe range difference for being constituted
Estimate the vector of composition, f (u) is the answer signal of signal source transmitting from k-th target location ukTo receiving station siWith reception station owner
Stand s1Between actual time difference composition vector, Q be measurement error ni1,kThe covariance matrix that average is zero is obeyed, T is matrix
Transposition,To cause the value of desired signal source position u during cost function J (u) minimum；
S53, introduce auxiliary vector, by location from range-difference measurements it is equations turned be constrained least-squares problem；
Introduce auxiliary vector and be position of the target with main website of receiving station and distance, be converted into constrained least-squares problem,
And convex semi definite programming problem is converted on this basis, former cost function is arranged the matrix for obtaining as follows：
Wherein,ηk=
Bknk, Bk=diag { r2,k,…,rN,k, k=1,2, R=[s2-s1,...,sN-s1]T, O(N-1)×3It is 0 matrix of (N-1) × 3,
0N-1It is 0 row vector of N-1,It is the vector for reaching main website of receiving station and extension station of receiving station range difference estimation composition of target 1,
It is the vector for reaching main website of receiving station and extension station of receiving station range difference estimation composition of target 2；
S54, the auxiliary vector is weighted least square solution；
The matrix for obtaining is arranged to former cost function and is weighted least square solution, the auxiliary vector estimate for obtaining is such as
Under：
Wherein, weighting matrix W=E [η ηT]-1=(BQBT)-1, B=diag { B1,B2Represent with B1And B2It is diagonal blocks
Matrix, Q=E [nnT] it is noise covariance matrix, n is to reach main website of receiving station and extension station of receiving station range difference measurement error
Matrix form, Gy-h=η, y are auxiliary vector；
S55, the lax equality constraint of auxiliary vector initial estimation calculated using weighted least-square solution, construct new cost letter
Number；
According to constraints, new cost function is constructed：
S.t y (6+k)=| | y (3 (k-1)+1:3k)||2, k=1,2
By (Gy-h)TW (Gy-h) is converted into
Wherein, Y=yyT,
It follows that Y (6+k, 6+k)=trace { Y (3k-2:3k,3k-2:3k) }, wherein, k=1,2；By Y=yyT,
Wherein y=[(u1-s1)T,(u2-s1)T,r1,1,r1,2]T, it is known that Y (7,8)=r1,1r1,2；
S56, using convex semi definite programming Optimization Solution auxiliary vector and the value of the variable of auxiliary vector transposition, and by spy
Value indicative decomposes the value for obtaining auxiliary vector；
When optimizing solution using the new cost function for having constructed, corresponding equality constraint is converted convex positive semidefinite rule
Draw optimization problem,
Formula to be solved is：Its constraints is：
S.t Y (6+k, 6+k)=trace { Y (3k-2:3k,3k-2:3k)}
The positional information of the Relation acquisition target between S57, the value according to the auxiliary vector tried to achieve and target location；
Carrying out Eigenvalues Decomposition to Y can obtain：
Wherein, λiFor the characteristic value of Y, i=1 ..., r, qiIt is corresponding characteristic vector, if i=1 ..., r have been pressed from big
To minispread, i.e. λ1≥λ2≥...≥λr＞ 0, the definition according to Y can obtain source locationIt is estimated as：
For the performance for checking the lax time difference positioning method of this positive semidefinite to estimate source location, we are by this positive semidefinite
Lax time difference positioning method is carried out with the simulation result of traditional Chan algorithms, Taylor series Method, MDS algorithm and Cramér-Rao lower bound
Compare, 5 receiving station's position coordinateses are respectively：s1=[300,100,150]T, s2=[400,150,100]T, s3=[300,
500,200]T, s4=[350,200,100]T, s5=[- 100, -100, -100]T, signal source coordinate unit is rice.Assuming that each
It is that zero, variance is that the TDOA measured values of individual signal source obey averageGaussian Profile, then QkMeeting diagonal entry is
Off diagonal element isFor the justice of contrast, it is weighted what least square was solved using to the auxiliary vector
Gained initial alignment result calculating in specific steps is lax etc. using the auxiliary vector initial estimation that weighted least-square solution is calculated
Formula is constrained, and constructs F and Chan algorithms in the specific steps of new cost function, the weights of MDS algorithm and as Taylor's level
The iteration initial value of number method.Three source location coordinates are respectively u1=[314,483,209]T, u2=[600,650,550]T
And u3=[285,325,275]T。
As shown in fig. 7, sets forth this positive semidefinite lax time difference positioning method, Chan algorithms and Taylor series Method to letter
Number source u1And u2Location estimation withThe statistics of root-mean-square error during change, relatively low suite line correspondence signal source
u1, one group of correspondence u higher2.As can be seen that when noise power is smaller, the estimation of three kinds of methods to two source locations is square
Root error is sufficiently close to Cramér-Rao lower bound.With the increase of measurement error, the root-mean-square error of each algorithm increased；Its
Middle Taylor series Method deviates Cramér-Rao lower bound at first, because when measurement error is larger, the initial value tried to achieve by step S4
Deviate actual value farther out, Taylor series Method is when solution is iterated, it is easy to be absorbed in local minimum point or diverging；And this is partly
The lax time difference positioning method of positive definite is significantly less than Chan algorithms to the estimation root-mean-square error of two source locations, with more
Accurate positioning performance.
As shown in figure 8, sets forth the lax time difference positioning method of this positive semidefinite, Chan algorithms, MDS algorithm and Taylor's level
Number method is to signal source u3Location estimation withThe statistics of root-mean-square error during change.As can be seen that in noise power
When smaller, several method is sufficiently close to Cramér-Rao lower bound to the root-mean-square error that source location is estimated.With noise power
Increase, the estimation root-mean-square error of each algorithm can all increased.When measurement error is larger, the estimation of Taylor series Method is equal
There is the phenomenon for sharply increasing in square error；MDS algorithm deviates Cramér-Rao lower bound will substantially be later than Chan algorithms, but in measurement
When error is larger, there is the phenomenon of the root-mean-square error more than Chan algorithms of MDS algorithm；And the lax positioning using TDOA side of this positive semidefinite
The estimation root-mean-square error of method is always maintained at minimum.
Positioning result is presented to user by the present invention by terminal display monitoring system, so as to improve airfield controller to machine
Field scene aircraft and guide car monitoring control ability.All process of calculation analysis of the invention be all it is spontaneous, to greatest extent
Influence of the artificial factor to aircraft and guide car positioning result is reduced, and all of data handling procedure is all parallel
, the efficiency of data processing is drastically increased, user is performed the result of acquisition analysis most fast during operation, the present invention is fixed
Level really, remains to preferably estimate the position of signal source when measurement error is larger.
Claims (4)
1. the time difference positioning method of Distributed Multi positioning monitoring system is used for, it is characterised in that comprised the following steps：
Target destination main website and extension station of receiving station obtain target response signal in S1, Distributed Multi positioning monitoring system, right
Measured parameter data of the target response signal after Distributed Multi positioning monitoring system treatment is parsed；
S2, the measured parameter data is obtained according to the target destination main website and extension station of receiving station, to measured parameter data
Middle same target answer back code and the confidence level more than 50% carry out pairing treatment, obtain the measurement ginseng that target sends in synchronization
Number data；
S3, to pairing process after measured parameter data carry out main website position selection, obtain the positioning precision of area to be targeted；
The positioning precision of S4, the measured parameter data according to target and area to be targeted, the main website of receiving station of selection target, really
Timing difference location model；
S5, using main website of receiving station and extension station of receiving station positional information measured parameter data, the time difference relaxed by positive semidefinite is determined
Position algorithm calculates the positional information of target；
S6, the positional information of the target is delivered into terminal show.
2. the time difference positioning method of Distributed Multi positioning monitoring system is used for as claimed in claim 1, it is characterised in that：Institute
Stating measured parameter data includes target response code, confidence level, target response mode, target response time, the range value of target.
3. the time difference positioning method of Distributed Multi positioning monitoring system is used for as claimed in claim 1, it is characterised in that step
The specific steps of rapid S3 include：
S31, determine target main website of receiving station positional information；
The measurement data of the receiving station of the target after pairing treatment is obtained, receiving station of one of receiving station as target is chosen
Main website position, sets up the GDOP values that observation model calculates positioning region under the conditions of the observation model, realizes the receiving station to target
The positional information of main website determines；By choosing receiving station main website of the different receiving stations as target, different observations are calculated respectively
The GDOP of positioning region under Model Condition；By choosing GDOP minimum values as TOA difference locating accuracy under the conditions of different observation models
Minimum value, realizes the structure to Distributed Multi positioning monitoring system positioning using TDOA model；
S32, the positional information to area to be targeted are differentiated；
By the region overlay figure of the main website of receiving station of target, the region overlay figure of the extension station of receiving station of target, acquisition can be positioned
The positional information in region, using it is described can positioning region positional information and reach target i-th extension station of receiving station and mesh
Time difference between main website of target receiving station, by positioning using TDOA equation, the positional information to area to be targeted is differentiated：
c·Δti=c (ti-t0)=ri-r0(i=1,2)
Wherein, c is the light velocity, Δ tiFor reach target i-th extension station of receiving station and the main website of receiving station of target between the time difference,
tiTo reach i-th time of extension station of receiving station, t of target0To reach receiving station's main station time, the r of targetiTo reach target
I-th distance of extension station of receiving station, r0It is main website of the receiving station distance for reaching target, the extension station of receiving station that i is arrival target
Numbering；
S33, the extension station of receiving station for obtaining main website of the receiving station position, target and target of target and target in the area to be targeted
The correlation matrix of position；
By each extension station of receiving station and target to the position of the main website of receiving station of target of target in the area to be targeted to target
Difference is put, the correlation matrix of target and site position in area to be targeted is drawn：
X, y are the positional information of target, x0, y0It is main website of receiving station positional information, the x of targeti、yiIt is the i-th of target
Individual extension station of receiving station positional information, r0It is main website of receiving station distance, the r of target to targetiIt is i-th reception of target to target
Stand extension station distance,
S34, the error estimate that the area to be targeted is calculated using pseudoinverse technique；
Error locator equation formula is：
Wherein,For position error in the x direction positioning variances,For position error, positioning variances, i are target in y-direction
I-th extension station of receiving station, j for target j-th extension station of receiving station,
Wherein, ηijIt is Δ tiWith Δ tjBetween coefficient correlation,It is the standard deviation of the time measurement error at the i-th station,It is jth
The standard deviation of the time measurement error stood, σsIt is the standard deviation of site measurement error；
S35, the positioning precision for obtaining area to be targeted；
Coefficient correlation η according to time measurement errorij, the standard deviation sigma of each site measurement errors, σ is obtained using linear combinationij,
Then positioning variances on x directions are tried to achievePositioning variances on y directionsPass throughFormula, calculates
To the positioning precision GDOP of area to be targeted.
4. the time difference positioning method of Distributed Multi positioning monitoring system is used for as claimed in claim 3, it is characterised in that step
The specific steps of rapid S5 include：
S51, structure positioning using TDOA equation；
Set up corresponding observation model using main website of receiving station positional information measured parameter data, it is determined that main website of receiving station station
Location information, location from range-difference measurements equation is built using the range difference of the distance of target to main website of receiving station, target to extension station of receiving station：
Wherein,To reach main website of receiving station and the measured value of extension station of receiving station time difference, c is the light velocity, ri,k-r1,kIt is signal
The answer signal of source transmitting is from k-th target location ukTo receiving station siWith main website of receiving station s1Between actual time it is poor, ni1,k
It is measurement error, i is the index of extension station of receiving station, and k is indexed for target；
S52, it is that target location to be positioned carries out maximal possibility estimation to source location；
Target is represented using the covariance matrix of target to main website of receiving station and i-th range difference measurement error of extension station of receiving station
The maximal possibility estimation of position：
Wherein, J (u) is nonlinearity, the non-convex cost function of source location u,ForThe range difference estimation group for being constituted
Into vector, f (u) is the answer signal of signal source transmitting from k-th target location ukTo receiving station siWith main website of receiving station s1It
Between actual time difference composition vector, Q be measurement error ni1,kThe covariance matrix that average is zero is obeyed, T turns for matrix
Put,To cause the value of desired signal source position u during cost function J (u) minimum；
S53, introduce auxiliary vector, by location from range-difference measurements it is equations turned be constrained least-squares problem；
Position and distance that auxiliary vector is target and main website of receiving station are introduced, constrained least-squares problem is converted into, and
Convex semi definite programming problem is converted on the basis of this, former cost function is arranged the matrix for obtaining as follows：
Wherein,ηk=Bknk, Bk
=diag { r2,k,...,rN,k, k=1,2, R=[s2-s1,...,sN-s1]T, O(N-1)×3It is 0 matrix of (N-1) × 3,0N-1For
0 row vector of N-1,It is the vector for reaching main website of receiving station and extension station of receiving station range difference estimation composition of target 1,It is mesh
The vector for reaching main website of receiving station and extension station of receiving station range difference estimation composition of mark 2；
S54, the auxiliary vector is weighted least square solution；
The matrix for obtaining is arranged to former cost function and is weighted least square solution, the auxiliary vector estimate for obtaining is as follows：
Wherein, weighting matrix W=E [η ηT]-1=(BQBT)-1, B=diag { B1,B2Represent with B1And B2It is the matrix of diagonal blocks, Q
=E [nnT] it is noise covariance matrix, n is the rectangular for reaching main website of receiving station and extension station of receiving station range difference measurement error
Formula, Gy-h=η；
S55, the lax equality constraint of auxiliary vector initial estimation calculated using weighted least-square solution, construct new cost function；
According to constraints, new cost function is constructed：
S.t y (6+k)=| | y (3 (k-1)+1:3k)||2, k=1,2
By (Gy-h)TW (Gy-h) is converted into
Wherein, Y=yyT,
It follows that Y (6+k, 6+k)=trace { Y (3k-2:3k,3k-2:3k) }, wherein, k=1,2；By Y=yyT, wherein y
=[(u1-s1)T,(u2-s1)T,r1,1,r1,2]T, it is known that Y (7,8)=r1,1r1,2；
S56, using convex semi definite programming Optimization Solution auxiliary vector and the value of the variable of auxiliary vector transposition, and by characteristic value
Decomposition obtains the value of auxiliary vector；
When optimizing solution using the new cost function for having constructed, corresponding equality constraint is converted convex semi definite programming excellent
Change problem,
Formula to be solved is：Its constraints is：
S.t Y (6+k, 6+k)=trace { Y (3k-2:3k,3k-2:3k)}
The positional information of the Relation acquisition target between S57, the value according to the auxiliary vector tried to achieve and target location；
Carrying out Eigenvalues Decomposition to Y can obtain：
Wherein, λiFor the characteristic value of Y, i=1 ..., r, qiIt is corresponding characteristic vector, if i=1 ..., r have been pressed from big to small
Arrangement, i.e. λ1≥λ2≥...≥λr＞ 0, the definition according to Y can obtain source locationIt is estimated as：
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