CN110389326A - The more external illuminators-based radar moving target localization methods of multistation under a kind of reception station error - Google Patents
The more external illuminators-based radar moving target localization methods of multistation under a kind of reception station error Download PDFInfo
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- CN110389326A CN110389326A CN201910688686.0A CN201910688686A CN110389326A CN 110389326 A CN110389326 A CN 110389326A CN 201910688686 A CN201910688686 A CN 201910688686A CN 110389326 A CN110389326 A CN 110389326A
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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
- G01S7/415—Identification of targets based on measurements of movement associated with the target
Abstract
The invention discloses the more external illuminators-based radar moving target localization methods of multistation under a kind of reception station error.For the present invention according to the biradical away from measuring with biradical away from change rate of acquisition, the Range And Range Rate of introducing target to receiving station, by the linearisation of strong nonlinearity equation puppet, establishes the estimation model of target position and speed as auxiliary variable.Observation station position and speed error in measurement statistical property is incorporated in location algorithm and designs weight, using the relevance between auxiliary variable and target position and speed as constraint condition, building constraint weighted least-squares location model.And it is optimized by method of Lagrange multipliers.Present invention introduces auxiliary variables, are that puppet is linear by non-linear measurement model conversation, the complexity of the more non-cooperative locations of multistation is reduced under the premise of guaranteeing to estimate performance；And weighted least square is constrained according to intermediate variable and Contingent negative variation, to reduce influence of the observation station error to target positioning performance.
Description
Technical field
The invention belongs to radar data process fields, and in particular to the more external illuminators-based radars of multistation under a kind of reception station error
Moving target 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.It may be implemented using time delay and Doppler frequency difference to fortune
The positioning of moving-target.Time delay observation corresponds directly to the propagation distance that signal reaches receiving station from external sort algorithm after target reflects
With, it is also known as biradical away from (Bistatic Range, BR), Doppler frequency difference then correspond to it is biradical away from change rate (Bistatic
Range Rate,BRR).Under multiple-input multiple-output system in external illuminators-based radar positioning system, by multiple external sort algorithms-reception source
(T/R) the biradical positioning away from the available realization of fusion treatment to moving target under.
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 etc. proposes a kind of based on maximal possibility estimation
Direct localization method, the algorithm is computationally intensive, big by initial value affecting.Noroozi etc. is in distributed MIMO radar system
Moving target orientation problem propose a kind of two step weighted least square algorithms.Then, Zhao Yongsheng etc. proposes one kind three in succession
Walk weighted least square algorithm.
The above-mentioned non-cooperative location problem based on BR/BRR assumes that receiving station's position and speed is accurately known, and practical outer
Observation station is usually installed on the motion platforms such as satellite, aircraft, naval vessels or surface car in radiation source radar fix system, to the greatest extent
Pipe can be obtained the position of receiving station by the navigation system on locating platform, but still inevitably contain random error.Ignore
The influence for receiving station error will lead to target location estimation performance degradation, or even generate false target.Therefore, external sort algorithm
It must consider to receive station error when radar fix Study on Problems.Patent 201910048341.9 proposes a kind of receiving station's location error
Place an order more external illuminators-based radar BR/BRR orientation problems of standing, and the present invention is directed to the more external illuminators-based radars of multistation, proposes one kind and connects
Receive BR/BRR alignment by union algorithm under station error.
Summary of the invention
The present invention is directed to the more external illuminators-based radars of multistation, considers receiving station's position and speed error to the shadow of positioning performance
It rings, it is a kind of fixed based on the more external illuminators-based radar BR/BRR of multistation under the reception station error for constraining weighted least-squares (CWLS) to propose
Position method.The algorithm introduces suitable auxiliary variable, and non-linear measurement equation puppet is linearized.By receiving station's position and speed amount
It surveys noise and biradical incorporate in target location algorithm away from measurement noise statistics designs weight, establish and be based on weighted least-squares
Cost function.On this basis, using being associated with as constraint condition, building between auxiliary variable and target position and speed
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
The signal emitted from target scattering third side emitter m obtains BR of the target away from external sort algorithm m and away from radar receiving station n and measures
Information dm,nIt is measured with BRR
Measurement is divided into N group, the corresponding one group of BR of each receiving station n (n=1 ..., N) according to different receiving stations by step 2.
Measure dm,nIt is measured with BRRDistance R of the selection target to receiving station nnWith the change rate of distanceFor
BR is measured and BRR measures pseudo- linearisation, obtains Linear Estimation equation ε by auxiliary variablen=Zn-Hnθn=AnΔen+BnΔqn。
Step 3. selects least-square residuals quadratic sum for cost function, will measure noise statistics and incorporates location algorithm
Middle design weight constructs cost functionWeightQs,n=E [(Δ qn)TΔqn].Consider auxiliary
Variable RnWithWith the correlation of target position and speed, structure constraint condition θn TΩθn=0, construct the constraint weighting of quadratic form
Least-squares estimation problem.
Step 4. utilizes Lagrange relaxation, converts unconfined optimization problem for constrained optimization problemOptimization SolutionObtain moving target position and speed
Estimated valueWith
Step 5. utilizes minimum mean square error criterion, and each group of receiving station n is measured to the target position estimated value obtainedWith velocity estimation valueFusion obtains globally optimal solution.
Beneficial effects of the present invention:
1., rationally will be non-linear biradical away from being converted into pseudo-wire away from change rate measurement model with biradical by introducing auxiliary variable
Property estimation model, obtain target position estimation enclosed analytic solutions.
2. considering to receive influence of the station error to target positioning performance, noise is measured according to receiving station's position and speed error
Statistical property incorporate optimizing index weight design, receive influence of the station error to target positioning performance to reduce, improve mesh
Mark positioning accuracy.
3. consider the relevance between auxiliary variable and unknown variable, structure constraint condition, design constraint weighting minimum two
Multiplication algorithm improves the noise immunity of location algorithm.
Specific embodiment
The present invention devises the more external illuminators-based radar moving target localization methods of multistation under a kind of reception station error, this method
The following steps are included:
1:M external sort algorithm of step and N number of receiving station composition more external illuminators-based radar nets of multistation position moving target；The
M external sort algorithm positionN number of receiving station is deployed in airborne platform, the actual position of n-th of receiving station and
Speed is respectivelyWithActually due to exist disturb, receiving station it is true
Position and speed is unable to get, and be can only obtain the position and speed measuring value comprising noise and is respectively
WithAnd meetWithRespectively receiving station n's
Position error vector and velocity error vector, and assume to be independent Gauss zero-mean white noise, covariance is respectivelyWithMoving target position to be estimated and speed are respectively Starget=[x, y, z]T
WithThen BR and BRR of the target away from external sort algorithm m and away from radar receiving station n, which are measured, is respectively
In formula, dm,nWithThe measuring value of respectively BR and BRR；| | | | be Euclidean distance, target to receiving station n away from
It is respectively from range rateWithTarget is to external radiation
The Range And Range Rate of source m is respectivelyWithΔ
dm,nWithRespectively BR error in measurement and BRR error in measurement obey zero-mean gaussian distribution, and
Measurement is divided into N group according to different receiving stations by step 2., and the corresponding one group of BR of each receiving station n measures dm,n；By formula
(1) pseudo- linearisation is carried out
In formula,
By formula (3) both members simultaneously to time derivation, obtain
In formula,
Write formula (3) and formula (4) as matrix form
εn=Zn-Hnθn=AnΔen+BnΔsn (5)
In formula,
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 BR/BRR error in measurement covarianceReceiving station n
Location/velocity 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 (10)
In formula,
Ω1=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, convert constrained optimization problem, that is, formula (11) to unconstrained optimization and ask
Topic, establishes 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 (13) are substituted into formula (10), can be obtained
It, will be in formula (14) using Eigenvalues Decomposition methodDiagonalization
In formula, Λn=diag { γ1,…,γ8, and γiIt is characteristic value, i=1 ..., 8, UnFor corresponding eigenvalue composition
Feature vector；
Formula (15) are substituted into formula (14), can be obtained
In formula,
By convolution and polynomial rooting operation, λ is acquirednMultiple；Choose the λ of real rootnSubstitution formula (13), can be in the hope of
Several θ outn, by θnValue substitutes into cost function formula (6), selects cost function J (θn) the smallest θnValue
Step 4.3. is worth the position and speed estimated value of available moving target according to optimal estimation
In formula,WithThe target position obtained and target velocity estimated value are respectively measured based on n-th group,For estimated valueThe 1st~3 value,For estimated valueThe 5th~7 value；；
Step 5. utilizes minimum mean square error criterion, and the target position estimated value obtained is measured to each group of receiving station
Weighted 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,13,Hn,4,Hn,57,Hn,8], wherein Hn,13Hn,4Hn,57Hn,8Respectively indicate HnMatrix
1~3 column, the 4th column, the 5th~7 column and the 8th train value；Therefore cost function can indicate again are as follows:
In formula,
To gnThe small noise disturbance analysis of single order is carried out, can be obtained
In formula, Gn=[G1,n G2,n],G2n=
Hn,57+Hn,8vn T(vn Tvn)-1/2；
N-th group can be obtained as a result, measures lower position and velocity estimation valueCovariance be
cov(θn')=(Gn TW-1Gn)-1 (20)
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 is weighted fusion to N group target position and velocity estimation value, obtains final global optimization value
Claims (1)
1. the more external illuminators-based radar moving target localization methods of multistation under a kind of reception station error, which is characterized in that this method packet
Include following steps:
1:M external sort algorithm of step and N number of receiving station composition more external illuminators-based radar nets of multistation position moving target；Outside m
Radiation source positionsN number of receiving station is deployed in airborne platform, the actual position and speed of n-th of receiving station
RespectivelyWithIt is actually disturbed due to existing, the actual position of receiving station
It is unable to get with speed, can only obtain the position and speed measuring value comprising noise is respectivelyWithAnd meet WithThe respectively position of receiving station n
Error vector and velocity error vector are set, and assumes to be independent Gauss zero-mean white noise, covariance is respectivelyWithMoving target position to be estimated and speed are respectively Starget=[x, y, z]T
WithThen BR and BRR of the target away from external sort algorithm m and away from radar receiving station n, which are measured, is respectively
In formula, dm,nWithThe measuring value of respectively BR and BRR；| | | | be Euclidean distance, the distance of target to receiving station n with
Range rate is respectivelyWithTarget is to external sort algorithm m's
Range And Range Rate is respectivelyWithΔdm,nWithRespectively BR error in measurement and BRR error in measurement obey zero-mean gaussian distribution, and
Measurement is divided into N group according to different receiving stations by step 2., and the corresponding one group of BR of each receiving station n measures dm,n；By formula (1)
Carry out pseudo- linearisation
In formula,
By formula (3) both members simultaneously to time derivation, obtain
In formula,
Write formula (3) and formula (4) as matrix form
εn=Zn-Hnθn=AnΔen+BnΔsn (5)
In formula,
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 BR/BRR error in measurement covarianceThe position receiving station n/
Velocity 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 (10)
In formula,
Ω1=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 (11), is established
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 (13) are substituted into formula (10), can be obtained
It, will be in formula (14) using Eigenvalues Decomposition methodDiagonalization
In formula, Λn=diag { γ1,…,γ8, and γiIt is characteristic value, i=1 ..., 8, UnFor the feature of corresponding eigenvalue composition
Vector；
Formula (15) are substituted into formula (14), can be obtained
In formula,
By convolution and polynomial rooting operation, λ is acquirednMultiple；Choose the λ of real rootnSubstitution formula (13), if can find out
Dry θn, by θnValue substitutes into cost function formula (6), selects cost function J (θn) the smallest θnValue
Step 4.3. is worth the position and speed estimated value of available moving target according to optimal estimation
In formula,WithThe target position obtained and target velocity estimated value are respectively measured based on n-th group,
For estimated valueThe 1st~3 value,For estimated valueThe 5th~7 value；；
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,13,Hn,4,Hn,57,Hn,8], wherein Hn,13 Hn,4 Hn,57 Hn,8Respectively indicate HnThe 1 of matrix
~3 column, the 4th column, the 5th~7 column and the 8th train value；Therefore cost function can indicate again are as follows:
In formula,
To gnThe small noise disturbance analysis of single order is carried out, can be obtained
In formula, Gn=[G1,n G2,n],G2n=Hn,57+
Hn,8vn T(vn Tvn)-1/2；
N-th group can be obtained as a result, measures lower position and velocity estimation valueCovariance be
cov(θn')=(Gn TW-1Gn)-1 (20)
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, fusion is weighted to N group target position and velocity estimation value, obtains final global optimization value
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