CN108717177A - A kind of dual station TDOA-AOA two-step methods passive location method - Google Patents
A kind of dual station TDOA-AOA two-step methods passive location method Download PDFInfo
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- CN108717177A CN108717177A CN201810641932.2A CN201810641932A CN108717177A CN 108717177 A CN108717177 A CN 108717177A CN 201810641932 A CN201810641932 A CN 201810641932A CN 108717177 A CN108717177 A CN 108717177A
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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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- Radar, Positioning & Navigation (AREA)
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- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The invention discloses a kind of dual station TDOA-AOA two-step methods passive location methods, belong to electronic information technical field.The method of the invention includes the following steps：Matrixing processing observation data, the initial closed solutions for solving radiation source positions, the final estimation for solving position vector.Passive location problem is described as the optimization problem of two constraints of a band by the present invention, then by the constrained optimization problem equivalent abbreviation is two convex optimization subproblems that are simple, there are optimal closed solutions, it solves to sequential relay the two convex optimization subproblems and obtains final optimal solution, the three-dimensional position estimation for providing radiation source, realizes the passive location of radiation source.
Description
Technical field
The invention belongs to electronic information technical fields, are related to a kind of Passive Location of Emitter method, and in particular to Yi Zhongli
With reaching time-difference (TDOA) observed quantity and a pair of of two dimensional arrival angles (2D-AOA) observed quantity two-step method passive location method.
Background technology
Currently, the high values radiation source such as phased-array radar is passed through frequently with beam-forming technology and/or power control strategy, tool
There is very low intercept probability.In the prior art, Multi-Station passive location system and system it is difficult to ensure that receive above-mentioned low intercepting and capturing simultaneously
The website number of probability radiation source electromagnetic wave signal reaches the least stations number of system requirement, cannot establish effective location observation
Equation cannot achieve target positioning.In face of low probability of intercept radiation source, the Single passive location system and system of the prior art are also
It collects less than sufficiently long observation data, it is difficult to establish effective position observational equation, equally cannot achieve target positioning.
Invention content
The purpose of the present invention is overcoming the deficiencies of existing technologies, a kind of dual station TDOA-AOA two-step methods passive location side is provided
Method.
Technical problem proposed by the invention solves in this way：
A kind of dual station TDOA-AOA two-step methods passive location method, includes the following steps：
Step 1. matrixing processing observation data：Matrix is write out using the observation measured value of two observation stationsAnd vector
Wherein, to provide coordinate origin of the observation station as right hand rectangular coordinate system of two-dimentional angle estimation, a is another sight
The position vector of survey station,For radiation source to the measured value of two observation station spacing deviations, I3For the unit matrix of 3 × 3 ranks,To measure azimuth,To measure the elevation angle, subscript T indicates transposition, | | | |
Vectorial 2- norms are sought in expression；
Step 2. solves the initial closed solutions of radiation source positions：Using convex optimization strong dual theory and KKT optimal solution conditions,
Solve the least square solution of following convex optimization problems：
s.t.2fTx≤0
Wherein, x is location variable to be solved, f=[0,0,0, -0.5]T；
Solution obtains the initial closed solutions of xWhereinFor the object space in initial closed solutions
Position vector,For the 4th element of initial closed solutions, the distance of expression radiation source to coordinate origin；
Step 3. solves the final estimation of position vector u：Based on broad sense invariant criterion and Taylor series expansion technical office
Manage following optimization problems：
s.t.xTBx=0
Obtain the final estimation of position vector uWherein, Taylor series expansion one
Order derivative matrixTaylor series expansion error vector03×1For 3 × 1 zero moment
Battle array.
In step 2, initial closed solutionsMeet following KKT (Karush-Kuhn-Tucher) optimal solution conditions：
μ*≥0
Wherein μ*For the optimal variable of antithesis；4th element of initial closed solutionsIndicate radiation source to coordinate origin away from
From, typically much deeper than zero, therefore byPush away to obtain μ*=0, to obtain the optimal solution of step 2 convexity optimization problem
In step 3, the convex optimization problem obtained based on broad sense invariant criterion and Taylor series expansion technology is；
To sum up, the method for the invention has acquired the estimation of the optimization problem of following belt restrainings：
s.t.xTBx=0,2fTx≤0
The method of the present invention solves the optimization problem that this is complicated above using two-step method strategy, and the first step is temporarily ignored above
Quadratic equation constraint in Constrained Optimization, obtains a convex optimization subproblem, is easy to get related with radiation source positions
Initial closed solutions.Second step rethinks the convex optimization subproblem of a weighting, based on the initial closed solutions that the first step solves,
It is constrained using the quadratic equation in broad sense invariant criterion and the original optimization problem of Taylor series expansion technical finesse, it is final to obtain
The estimation of radiation source positions.
The method of the invention provides the reaching time-difference estimation of radiation source merely with two observation websites, then by wherein one
A website provides two dimensional arrival angles (the azimuth and pitch angle) estimation of radiation source, and passive location problem is thus described as one
The optimization problem constrained with two, then by the constrained optimization problem equivalent abbreviation is simple for two, there is optimal close
The convex optimization subproblem of formula solution solves to sequential relay the two convex optimization subproblems and obtains final optimal solution, provides radiation
The three-dimensional position in source is estimated, realizes the passive location of (low probability of intercept) radiation source.
The beneficial effects of the invention are as follows：
The method of the invention based on the step-out time observed quantity and a pair of of two dimension only provided by two observation stations to
Up to angle observation amount, passive location problem is described as the optimization problem of two constraints of a band, this point is fixed with traditional passive
Position Maximum Likelihood Estimation and based on pseudo- system of linear equations establish linearisation method of estimation it is entirely different.By using
Two-step method strategy solves this complicated optimum problem, the final estimation for obtaining radiation source positions.The present invention has required observation station
It counts out less, the spies such as low probability of intercept radiation source, positioning result are insensitive to measurement noise and computation complexity is low can be positioned
Point.
Description of the drawings
Fig. 1 is positioning scene geometric representation；
Fig. 2 is the statistic curve figure that position root-mean-square error changes with angular error standard deviation.
Specific implementation mode
The present invention is further detailed with reference to the accompanying drawings and examples.
The present embodiment provides a kind of dual station TDOA-AOA two-step methods passive location methods, are u=with radiation source positions
[1000,1000,1000]TFor 600 meters, the error to standard deviation for reaching range difference is fixed as 10 meters for rice, two observation stations, and two
The error to standard deviation of dimension angle of arrival changes to 2.5 degree from 0.5 degree.For the error to standard deviation of each two dimensional arrival angles, make 1000
Secondary Monte-Carlo experiments, calculate position root-mean-square error；Positioning scene schematic diagram is as shown in Figure 1, include the following steps：
Step 1. matrixing processing observation data：In the two dimensional arrival angles error to standard deviation investigated, from 0.5 degree of mistake
Poor standard deviation starts, and generates one and reaches range difference observed quantity and a pair of of two dimensional arrival angles observed quantity, utilizes two observation stations
Observation measured value writes out matrixAnd vector
Wherein, to provide coordinate origin of the observation station as right hand rectangular coordinate system of two-dimentional angle estimation, a is another sight
The position vector of survey station,For radiation source to the measured value of two observation station spacing deviations, I3For the unit matrix of 3 × 3 ranks,To measure azimuth,To measure the elevation angle, subscript T indicates transposition, | | | |
Vectorial 2- norms are sought in expression；
Step 2. solves the initial closed solutions of radiation source positions：Using convex optimization strong dual theory and KKT optimal solution conditions,
Solve the least square solution of following convex optimization problems：
s.t.2fTx≤0
Wherein, x is location variable to be solved, f=[0,0,0, -0.5]T；
Solution obtains the initial closed solutions of xWhereinFor the target empty meta position in initial closed solutions
Vector is set,For the 4th element of initial closed solutions, the distance of expression radiation source to coordinate origin；
Step 3. solves the final estimation of position vector u：Based on broad sense invariant criterion and Taylor series expansion technical office
Manage following optimization problems：
s.t.xTBx=0
Obtain the final estimation of position vector uWherein, Taylor series expansion one
Order derivative matrixTaylor series expansion error vector03×1For 3 × 1 zero moment
Battle array.
Fig. 2 is that the positioning using specific example mode of the present invention under the conditions of different two dimensional arrival angles error to standard deviation is square
For root error statistics as a result, ordinate is position root-mean-square value, unit is rice, and abscissa is two dimensional arrival angles error to standard deviation, single
Position is degree；In figure as it can be seen that the emulation experiment set by the present invention, radiation source positions estimate root-mean-square error in hundred meters of magnitudes.
Claims (3)
1. a kind of dual station TDOA-AOA two-step methods passive location method, which is characterized in that include the following steps：
Step 1. matrixing processing observation data：Matrix is write out using the observation measured value of two observation stationsAnd vector
Wherein, to provide coordinate origin of the observation station as right hand rectangular coordinate system of two-dimentional angle estimation, a is another observation station
Position vector,For radiation source to the measured value of two observation station spacing deviations, I3For the unit matrix of 3 × 3 ranks, To measure azimuth,To measure the elevation angle, subscript T indicates transposition, | | | | table
Show and seeks vectorial 2- norms；
Step 2. solves the initial closed solutions of radiation source positions：Using convex optimization strong dual theory and KKT optimal solution conditions, solve
The least square solution of following convex optimization problems：
s.t.2fTx≤0
Wherein, x is location variable to be solved, f=[0,0,0, -0.5]T；
Solution obtains the initial closed solutions of xWhereinFor the Target space position in initial closed solutions to
Amount,For the 4th element of initial closed solutions, the distance of expression radiation source to coordinate origin；
Step 3. solves the final estimation of position vector u：Based under broad sense invariant criterion and Taylor series expansion technical finesse
State optimization problem：
s.t.xTBx=0
Obtain the final estimation of position vector uWherein, Taylor series expansion single order is led
Matrix numberTaylor series expansion error vector03×1For 3 × 1 null matrix.
2. dual station TDOA-AOA two-step methods passive location method according to claim 1, which is characterized in that in step 2, just
Beginning closed solutionsMeet following KKT optimal solution conditions：
μ*≥0
Wherein μ*For the optimal variable of antithesis；4th element of initial closed solutionsIndicate radiation source to the distance of coordinate origin, μ*
=0, the optimal solution of step 2 convexity optimization problem
3. dual station TDOA-AOA two-step methods passive location method according to claim 1, which is characterized in that in step 3, base
It is in the convex optimization problem that broad sense invariant criterion and Taylor series expansion technology obtain；
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109901106A (en) * | 2019-04-02 | 2019-06-18 | 北京理工大学 | A kind of TDOA/AOA hybrid locating method |
| CN110208741A (en) * | 2019-06-28 | 2019-09-06 | 电子科技大学 | A kind of direct localization method of over the horizon single goal for surveying phase based on more circle battle arrays |
| CN110208782A (en) * | 2019-04-01 | 2019-09-06 | 西安电子科技大学 | A kind of radar fix method, apparatus, system, computer equipment and storage medium |
| CN113238217A (en) * | 2021-06-03 | 2021-08-10 | 哈尔滨工业大学 | Distributed high-frequency ground wave radar combined positioning method based on interior point method |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110208782A (en) * | 2019-04-01 | 2019-09-06 | 西安电子科技大学 | A kind of radar fix method, apparatus, system, computer equipment and storage medium |
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| CN110208741A (en) * | 2019-06-28 | 2019-09-06 | 电子科技大学 | A kind of direct localization method of over the horizon single goal for surveying phase based on more circle battle arrays |
| CN110208741B (en) * | 2019-06-28 | 2022-12-02 | 电子科技大学 | Beyond-visual-range single target direct positioning method based on multi-circle array phase measurement |
| CN113238217A (en) * | 2021-06-03 | 2021-08-10 | 哈尔滨工业大学 | Distributed high-frequency ground wave radar combined positioning method based on interior point method |
| CN113238217B (en) * | 2021-06-03 | 2024-03-08 | 哈尔滨工业大学 | Distributed high-frequency ground wave radar joint positioning method based on interior point method |
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