CN110389327A - The more external illuminators-based radars of multistation are biradical away from localization method under receiving station's location error - Google Patents
The more external illuminators-based radars of multistation are biradical away from localization method under receiving station's location error 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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/411—Identification of targets based on measurements of radar reflectivity
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Abstract
The invention discloses the more external illuminators-based radars of multistation under a kind of receiving station's location error are biradical away from localization method.The metric data of the more external radiation source radar systems of multistation is grouped by the present invention according to receiving station, and the distance of selection target to receiving station is auxiliary variable, biradical away from the linearisation of non-linear measurement equation puppet by every group.Receiving station position is measured into noise and biradical incorporate in target location algorithm away from measurement noise statistics designs weight, establishes the cost function based on weighted least-squares.On this basis, being associated with as constraint condition, building constraint weighted least-squares location model using auxiliary variable and target position, and optimized by method of Lagrange multipliers.Various estimated result Weighted Fusions are finally obtained target position finally to estimate.The present invention reduces the complexity of positioning under the premise of guaranteeing to estimate performance, reduces influence of the error to target positioning performance.
Description
Technical field
The invention belongs to radar data process fields, and in particular to the more external sort algorithms of multistation under a kind of receiving station's location error
Radar is biradical away from localization method.
Background technique
External illuminators-based radar utilizes third party non-co-operation signal source (such as mobile communication signal, television broadcasting signal and enemy
Radar information etc.) detection target, signal and direct wave from target scattering third party's radiation emission are received by receiving station
Signal obtains the time delay and Doppler frequency difference of signal using Coherent processing.Time delay observation corresponds directly to signal from external sort algorithm
After target reflects reach receiving station propagation distance and, it is also known as biradical away from (Bistatic Range, BR).In multiple-input multiple-output body
It makes in lower external illuminators-based radar positioning system, biradical under multiple external sort algorithms-reception source (T/R) can be obtained away from fusion treatment
To the positioning realized to static target.
Currently, being widely studied using time delay/Doppler frequency difference target radiation source orientation problem.However, utilizing
The research of the non-cooperative location problem of BR/BRR is then relatively fewer.Godrich, H. team propose a kind of based on maximum likelihood
The direct localization method of estimation, the likelihood function of direct construction target position and speed obtain mesh by multi-dimensional grid search
Cursor position parameter Estimation.Noroozi etc. proposes one kind for the moving target orientation problem in distributed MIMO radar system
Two step weighted least square algorithms.Zhao Yongsheng etc. proposes a kind of three step weighted least square algorithms in succession.Most based on multistep weighting
Small two multiply estimation method when measurement noise is smaller, and positioning accuracy can reach a carat Metro lower bound, but when noise increases to one
When determining degree, position error be increased dramatically, and threshold effect occurs.
Above-mentioned estimation method assumes that the accurately known of the position of receiving station.And receiving station is normal in practical non-cooperative location
It is often installed on the motion platforms such as satellite, aircraft, naval vessels or surface car, position often can not accurately obtain, receiving station
There are certain errors for position.Receiving station's location error is very big on target location accuracy influence, and therefore, external illuminators-based radar positioning is asked
Receiving station's location error must be considered when topic research.Patent 201910048330.0 proposes a kind of receiving station's location error and places an order station
More external illuminators-based radars are biradical away from orientation problem, and it is biradical away from positioning that the present invention designs the more external illuminators-based radars of multistation under a kind of error
Algorithm.
Summary of the invention
The present invention is directed to the more external illuminators-based radars of multistation, considers influence of receiving station's location error to positioning performance, proposes
The more external illuminators-based radars of multistation are biradical away from positioning under receiving station's location error of the one kind based on constraint weighted least-squares (CWLS)
Method.The distance of the algorithms selection target to receiving station is auxiliary variable, is linearized biradical away from non-linear measurement equation puppet, will
Receiving station's position noise and biradical incorporate in target location algorithm away from measurement noise statistics design weight, establish based on weighting
The cost function of least square.On this basis, being associated with as constraint condition, building using auxiliary variable and target position
CWLS location model, and optimized by method of Lagrange multipliers.
Specific steps of the method for the invention are:
Each receiving station n, which is received, in the more external illuminators-based radar nets of step 1. multistation (M external sort algorithm and N number of receiving station) comes
From target scattering third side emitter m emit signal, obtain target away from external sort algorithm m and away from radar receiving station n it is biradical away from
Measurement information dm,n。
Measurement is divided into N group according to different receiving stations by step 2., and corresponding one group of each receiving station n (n=1 ..., N) double
Cardinal distance measures dm,n(m=1,2 ..., M).The distance of selection target to receiving station n are auxiliary variable Rn, will be non-linear biradical away from amount
Pseudo- linearisation is surveyed, estimation equation is obtained
Step 3. selects least-square residuals quadratic sum for cost function, will measure noise statistics and incorporates location algorithm
Middle design weight constructs cost functionWeightConsider auxiliary
Variable RnWith the correlation of target position, structure constraint condition θn TΩθn=0, the constraint weighted least-squares for constructing quadratic form are estimated
Meter problem.
Step 4. utilizes Lagrange relaxation, converts unconfined optimization problem for constrained optimization problemOptimization Solution
Step 5. utilizes minimum mean square error criterion, and each group of receiving station is measured the target position estimated value obtained and is melted
It closes, obtains globally optimal solution.
Beneficial effects of the present invention:
1. by introduce auxiliary variable, rationally by it is non-linear it is biradical be converted into pseudo square-free function model away from measurement model, obtain
Obtain the enclosed analytic solutions of target position estimation.
2. according to receiving station's location error and it is biradical away from measure Noise Design optimizing index weight, to reduce error to mesh
The influence of positioning performance is marked, target position estimated accuracy is improved.
3. consider the relevance between auxiliary variable and unknown variable, structure constraint condition, design constraint weighting minimum two
Multiplication algorithm further decreases evaluated error.
Specific embodiment
It is biradical away from localization method, the party that the present invention devises the more external illuminators-based radars of multistation under a kind of receiving station's location error
Method the following steps are included:
Step 1: in the more external illuminators-based radar nets of multistation, it is assumed that the transmitting station You Ge M, m emit station locationN number of receiving station, the actual position of n-th of receiving stationActually due to depositing
It is disturbing, the actual position of receiving station is unable to get, and be can only obtain the position comprising noise and isAnd For the position error vector of receiving station n, and assume to be independent Gauss zero-mean white noise,
Covariance isTarget position to be estimated is Starget=[x, y, z]T, then target away from external sort algorithm m and away from
The biradical of receiving station n be away from measurement information
In formula, dm,nFor the biradical measured value away from measurement；| | | | it is Euclidean distance, the distance of target to receiving station n areDistance of the target to external sort algorithm mem,nTo be biradical away from error in measurement, obey
Zero-mean gaussian distribution；
Measurement is divided into N group according to different receiving stations by step 2., and corresponding one group of each receiving station n biradical away from measurement dm,n；
Formula (1) is subjected to pseudo- linearisation
In formula, Measurement distance for target away from receiving station n, For corresponding gradient,
Write formula (2) as matrix form
In formula,en=[e1,n e2,n … eM,n]T
Step 3. establishes constraint weighted least square model；
Step 3.1. selects least-square residuals quadratic sum for cost function J (θn)
Noise statistics will be measured and incorporate design weight W in location algorithmn
In formula, n-th group is biradical away from error in measurement covarianceReceiving station n location error covariance
Step 3.2. considers auxiliary variableWith the correlation of target position, constraint condition between the two is established
Then have
θn TΩθn=0 (7)
In formula,Ω=diag [1 1 1-1]；
The constraint weighted least square problem that step 3.3. constructs quadratic form is as follows
Step 4. utilizes Lagrange relaxation, and Optimization Solution constrains weighted least square problem；
Step 4.1. introduces Lagrange multiplier λn, unconstrained optimization problem is converted by constrained optimization problem, that is, formula (8),
Establish Lagrangian
Step 4.2. solves parameter θ to be estimated using Lagrangian Relaxation Algorithmn；
To LagrangianL (θn,λn) local derviation is sought, enable partial derivativeIt is zero, can obtains
Due to λnIt is unknown, formula (10) are substituted into formula (7), can be obtained
It, will be in formula (11) using Eigenvalues Decomposition methodDiagonalization
In formula, Λn=diag { γ1,…,γ4, and γi(i=1 ..., 4) is characteristic value, UnFor corresponding eigenvalue composition
Feature vector；
Formula (12) are substituted into formula (11), can be obtained
In formula,
By convolution and polynomial rooting operation, λ is acquirednMultiple；Choose the λ of real rootnSubstitution formula (10), can be in the hope of
Several θ outn, by θnValue substitutes into cost function formula (4), selects cost function J (θn) the smallest θnValue
Step 4.3. is worth available target locator value according to optimal estimation are as follows:
In formula,For based on n-th group target position estimated value,For estimated valueFirst three items；
Step 5. utilizes minimum mean square error criterion, and the target position estimated value obtained is measured to each group of receiving stationWeighted Fusion obtains the globally optimal solution of target position；
Step 5.1. calculates n-th group and measures lower estimated valueCovariance；
By HnH is decomposed by columnn=[Hn,1:3,Hn,4], wherein Hn,1:3And Hn,4Respectively indicate Hn1~3 column of matrix and the 4th
Column；Therefore cost function formula (4) indicates again are as follows:
In formula, gn=Hn,1:3vn+Hn,4(vn Tvn)1/2-Zn,
To gnThe small noise disturbance analysis of single order is carried out, can be obtained
In formula, Gn=Hn,1:3vn+Hn,4vn T(vn Tvn)-1/2；
N-th group can be obtained as a result, measures lower estimated valueCovariance be
Step 5.2. hypothesis is biradical uncorrelated away from the estimation for measuring lower target position according to N group, according to unbiased lowest mean square
Poor criterion obtains final global optimization value to N group target state estimator value Weighted Fusion
Claims (1)
1. the more external illuminators-based radars of multistation are biradical away from localization method under receiving station's location error, it is characterised in that: this method includes
Following steps:
Step 1: in the more external illuminators-based radar nets of multistation, it is assumed that the transmitting station You Ge M, m-th of transmitting station locationN number of receiving station, the actual position of n-th of receiving stationActually due to depositing
It is disturbing, the actual position of receiving station is unable to get, and be can only obtain the position comprising noise and isAnd For the position error vector of receiving station n, and assume to be independent Gauss zero-mean white noise,
Covariance isTarget position to be estimated is Starget=[x, y, z]T, then target away from external sort algorithm m and away from
The biradical of receiving station n be away from measurement information
In formula, dm,nFor the biradical measured value away from measurement；| | | | it is Euclidean distance, the distance of target to receiving station n areDistance of the target to external sort algorithm mem,nTo be biradical away from error in measurement, obey
Zero-mean gaussian distribution；
Measurement is divided into N group according to different receiving stations by step 2., and corresponding one group of each receiving station n biradical away from measurement dm,n；By formula
(1) pseudo- linearisation is carried out
In formula, Measurement distance for target away from receiving station n, For corresponding gradient,
Write formula (2) as matrix form
In formula,en=[e1,n e2,n … eM,n]T
Step 3. establishes constraint weighted least square model；
Step 3.1. selects least-square residuals quadratic sum for cost function J (θn)
Noise statistics will be measured and incorporate design weight W in location algorithmn
In formula, n-th group is biradical away from error in measurement covarianceReceiving station n location error covariance
Step 3.2. considers auxiliary variableWith the correlation of target position, constraint condition between the two is established
Then have
θn TΩθn=0 (7)
In formula,Ω=diag [1 1 1-1]；
The constraint weighted least square problem that step 3.3. constructs quadratic form is as follows
Step 4. utilizes Lagrange relaxation, and Optimization Solution constrains weighted least square problem；
Step 4.1. introduces Lagrange multiplier λn, unconstrained optimization problem is converted by constrained optimization problem, that is, formula (8), is established
Lagrangian
L(θn,λn)=(Zn-Hnθn)TWn -1(Zn-Hnθn)+λnθn TΩθn (9)
Step 4.2. solves parameter θ to be estimated using Lagrangian Relaxation Algorithmn；
To LagrangianL (θn,λn) local derviation is sought, enable partial derivativeIt is zero, can obtains
Due to λnIt is unknown, formula (10) are substituted into formula (7), can be obtained
It, will be in formula (11) using Eigenvalues Decomposition methodDiagonalization
In formula, Λn=diag { γ1,…,γ4, and γi(i=1 ..., 4) is characteristic value, UnFor the spy of corresponding eigenvalue composition
Levy vector；
Formula (12) are substituted into formula (11), can be obtained
In formula,
By convolution and polynomial rooting operation, λ is acquirednMultiple；Choose the λ of real rootnSubstitution formula (10), if can find out
Dry θn, by θnValue substitutes into cost function formula (4), selects cost function J (θn) the smallest θnValue
Step 4.3. is worth available target locator value according to optimal estimation are as follows:
In formula,For based on n-th group target position estimated value,For estimated valueFirst three items；
Step 5. utilizes minimum mean square error criterion, and the target position estimated value obtained is measured to each group of receiving stationWeighting
Fusion, obtains the globally optimal solution of target position；
Step 5.1. calculates n-th group and measures lower estimated valueCovariance；
By HnH is decomposed by columnn=[Hn,1:3,Hn,4], wherein Hn,1:3And Hn,4Respectively indicate Hn1~3 column and the 4th column of matrix；Cause
This cost function formula (4) indicates again are as follows:
In formula, gn=Hn,1:3vn+Hn,4(vn Tvn)1/2-Zn,
To gnThe small noise disturbance analysis of single order is carried out, can be obtained
In formula, Gn=Hn,1:3vn+Hn,4vn T(vn Tvn)-1/2；
N-th group can be obtained as a result, measures lower estimated valueCovariance be
Step 5.2. hypothesis is biradical uncorrelated away from the estimation for measuring lower target position according to N group, quasi- according to unbiased Minimum Mean Square Error
Then, final global optimization value is obtained to N group target state estimator value Weighted Fusion
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| CN111123197A (en) * | 2019-12-21 | 2020-05-08 | 杭州电子科技大学 | TDOA-based target radiation source positioning method |
| CN111308530A (en) * | 2020-02-17 | 2020-06-19 | 中国人民解放军战略支援部队信息工程大学 | Short wave multi-station and single-satellite cooperative direct positioning method based on two-dimensional direction of arrival |
| CN111371432A (en) * | 2020-03-24 | 2020-07-03 | 宁波飞拓电器有限公司 | Noise-related nonlinear observability degree analysis method |
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| CN112526449A (en) * | 2020-11-27 | 2021-03-19 | 中国人民解放军海军工程大学 | Method for calibrating position information of receiving station by utilizing moving target |
| CN112683265A (en) * | 2021-01-20 | 2021-04-20 | 中国人民解放***箭军工程大学 | MIMU/GPS integrated navigation method based on rapid ISS collective filtering |
| CN115508774A (en) * | 2022-10-12 | 2022-12-23 | 中国电子科技集团公司信息科学研究院 | Time difference positioning method and device based on two-step weighted least square and storage medium |
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| CN112526449B (en) * | 2020-11-27 | 2022-12-27 | 中国人民解放军海军工程大学 | Method for calibrating position information of receiving station by utilizing moving target |
| CN112683265A (en) * | 2021-01-20 | 2021-04-20 | 中国人民解放***箭军工程大学 | MIMU/GPS integrated navigation method based on rapid ISS collective filtering |
| CN115508774A (en) * | 2022-10-12 | 2022-12-23 | 中国电子科技集团公司信息科学研究院 | Time difference positioning method and device based on two-step weighted least square and storage medium |
| CN115508774B (en) * | 2022-10-12 | 2023-07-28 | 中国电子科技集团公司信息科学研究院 | Time difference positioning method and device based on two-step weighted least square and storage medium |
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Application publication date: 20191029 |