CN108761399A - A kind of passive radar object localization method and device - Google Patents
A kind of passive radar object localization method and device Download PDFInfo
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- CN108761399A CN108761399A CN201810556996.2A CN201810556996A CN108761399A CN 108761399 A CN108761399 A CN 108761399A CN 201810556996 A CN201810556996 A CN 201810556996A CN 108761399 A CN108761399 A CN 108761399A
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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
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
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Abstract
The present invention relates to a kind of passive radar object localization method and devices, the observational equation of angle and the time difference are linearized, obtain one group of linear equation, and obtain the rough estimate of target location using least square, by observation error and external sort algorithm site error simultaneously in view of in linear equation, it obtains constraint total least square model and the accurate estimation of target location is obtained using Newton iteration using obtained least square solution as initial solution.The present invention considers angular observation error, the site error of time difference observation error and external sort algorithm, positioning result is that there are optimal estimation results when error for external sort algorithm, by nonlinear angle and time difference observational equation linearization process, least square algebraic solution is obtained, and as the initial solution of Newton iteration, it ensure that convergence.
Description
Technical field
The invention belongs to Technology for Target Location of Passive Radar fields, and in particular to a kind of passive radar object localization method with
Device.
Background technology
Passive radar is as a kind of special bistatic radar, non-radiating source and electromagnetic wave itself, but by receiving and locating
Target is managed to the reflection of existing external sort algorithm or scattered signal in environment, to detect and position target.This special work is former
Reason makes it compared to conventional active radar, and having good four to resist, (electronic interferences, anti-radiation weapon attack, Stealthy Target are attacked
Hit, low latitude ultra-low altitude penetration) characteristic.Therefore, for many years, passive radar technology has been a concern in international field of radar.
The location information of external sort algorithm is the required argument of passive radar target positioning.But for some radiation sources,
Such as the military radiation source of enemy, position often can not accurately obtain, and be only capable of the outer spoke estimated by ESM systems, obtained
It is containing large error to penetrate source position.Such as author is that Zhao Yongjun is published in in September, 2016《Electronics and information journal》The
The paper of the phase of volume 38 the 9th《Single station DOA-TDOA passive localization algorithms based on regularization constraint total least square》, due to depositing
In outer radiation source positions error, which reduces the positioning accuracy of Passive Radar System, therefore, it is necessary to consider external sort algorithm
Influence of the site error to positioning accuracy, and design targetedly target location algorithm.
The positioning of joint angle and the time difference are a kind of passive radar commonly location methods, have better than merely with angle or
The positioning accuracy of the positioning system of the time difference.But in existing localization method, the site error of external sort algorithm is not examined
Consider.Therefore, there is an urgent need for a kind of more base passive radar object localization methods considering external sort algorithm site error, in external radiation
When the inaccuracy of source position, the optimal estimation to target location is realized.
Invention content
The object of the present invention is to provide a kind of passive radar object localization method and devices, for solving existing passive radar
Object localization method estimates the low problem of target positioning error.
In order to solve the above technical problems, the present invention proposes a kind of passive radar object localization method, include the following steps：
1) observational equation of angle and the time difference is built, and the observational equation of angle and the time difference are subjected to linearization process, is obtained
To linear equation, solves the linear equation and obtain the initial estimate of target location；
2) angle measurement is indicated to the difference for being at an angle of actual value and angular observation error, when time difference measurement value is expressed as
The difference of poor actual value and time difference observation error, by the measurement positional value of external sort algorithm be expressed as the actual position value of external sort algorithm with
The measured value of angle, the measured value of the time difference are substituted into the linear equation, respectively obtain angle by the difference of errors in position measurement respectively
First function, time difference actual value second function as to be asked amount of the actual value as amount to be asked；By the measurement position of external sort algorithm
It sets value and substitutes into the linear equation as new variables, obtain third function of the actual position value as amount to be asked of external sort algorithm；
3) least square model is built according to first function, second function, third function, by the model in the target position
Taylor expansion at the initial estimate set, solution obtain newton iteration formula, using the target location initial estimate and
Newton iteration formula is iterated, and iteration obtains the fine estimation of target location to number is set.
The present invention linearizes the observational equation of angle and the time difference, obtains one group of linear equation, and obtain using least square
To the rough estimate of target location, by observation error and external sort algorithm site error simultaneously in view of in linear equation, being constrained
Total least square model obtains the accurate of target location using obtained least square solution as initial solution using Newton iteration
Estimation.The present invention considers angular observation error, the site error of time difference observation error and external sort algorithm, and positioning result is outer spoke
Penetrating source, there are optimal estimation results when error；The present invention obtains nonlinear angle and time difference observational equation linearization process
Least square algebraic solution has been arrived, and as the initial solution of Newton iteration, ensure that convergence.
As further limiting for least square model, step 3) further includes the sub-step of following structure least square model
Suddenly：
It (1) will be in the angular observation error in first function, the time difference observation error and third function in second function
Errors in position measurement carries out whitening processing, and white noise vector is obtained after processing and is missed respectively with angular observation error, time difference observation
The functional relation of difference, errors in position measurement；
(2) according to the functional relation and first function, second function and third function, constraints is established, with
The minimum object function of norm squared of the white noise vector.
Further, further comprising the steps of：Object function under the constraints is transformed into without constraint item
The minimization object function of part, as final least square model.
In order to solve the above technical problems, the present invention also proposes a kind of passive radar target locating set, including calculation processing
Module, the calculation processing module is for realizing following steps：
1) observational equation of angle and the time difference is built, and the observational equation of angle and the time difference are subjected to linearization process, is obtained
To linear equation, solves the linear equation and obtain the initial estimate of target location；
2) angle measurement is indicated to the difference for being at an angle of actual value and angular observation error, when time difference measurement value is expressed as
The difference of poor actual value and time difference observation error, by the measurement positional value of external sort algorithm be expressed as the actual position value of external sort algorithm with
The measured value of angle, the measured value of the time difference are substituted into the linear equation, respectively obtain angle by the difference of errors in position measurement respectively
First function, time difference actual value second function as to be asked amount of the actual value as amount to be asked；By the measurement position of external sort algorithm
It sets value and substitutes into the linear equation as new variables, obtain third function of the actual position value as amount to be asked of external sort algorithm；
3) least square model is built according to first function, second function, third function, by the model in the target position
Taylor expansion at the initial estimate set, solution obtain newton iteration formula, using the target location initial estimate and
Newton iteration formula is iterated, and iteration obtains the fine estimation of target location to number is set.
Further, step 3) further includes the sub-step of following structure least square model：
It (1) will be in the angular observation error in first function, the time difference observation error and third function in second function
Errors in position measurement carries out whitening processing, and white noise vector is obtained after processing and is missed respectively with angular observation error, time difference observation
The functional relation of difference, errors in position measurement；
(2) according to the functional relation and first function, second function and third function, constraints is established, with
The minimum object function of norm squared of the white noise vector.
Further, further comprising the steps of：Object function under the constraints is transformed into without constraint item
The minimization object function of part, as final least square model.
Description of the drawings
Fig. 1 is the flow diagram of present invention estimation target location；
Fig. 2 is external sort algorithm and observation station geometric position schematic diagram in experiment simulation of the present invention；
Fig. 3 is simulation comparison figure of the target location evaluated error of the present invention with time difference measurement error change；
Fig. 4 is the simulation comparison figure that target location evaluated error of the present invention changes with angle measurement error；
Fig. 5 is the simulation comparison figure that target location evaluated error of the present invention changes with external sort algorithm site error.
Specific implementation mode
The specific implementation mode of the present invention is further described below in conjunction with the accompanying drawings.
The present invention provides a kind of passive radar object localization method, includes the following steps：
1) observational equation of angle and the time difference is built, and the observational equation of angle and the time difference are subjected to linearization process, is obtained
To linear equation, solves the linear equation and obtain the initial estimate of target location.
2) angle measurement is indicated to the difference for being at an angle of actual value and angular observation error, when time difference measurement value is expressed as
The difference of poor actual value and time difference observation error, by the measurement positional value of external sort algorithm be expressed as the actual position value of external sort algorithm with
The measured value of angle, the measured value of the time difference are substituted into above-mentioned linear equation, respectively obtain angle by the difference of errors in position measurement respectively
First function, time difference actual value second function as to be asked amount of the actual value as amount to be asked；By the measurement position of external sort algorithm
It sets value and substitutes into above-mentioned linear equation as new variables, obtain third function of the actual position value as amount to be asked of external sort algorithm.
3) least square model is built according to first function, second function, third function, by the model in target location
Taylor expansion at initial estimate, solution obtain newton iteration formula, utilize the initial estimate and Newton iteration of target location
Formula is iterated, and iteration obtains the fine estimation of target location to number is set.
The present invention linearizes the observational equation of angle and the time difference, obtains one group of linear equation, and obtain using least square
To the rough estimate of target location, by observation error and external sort algorithm site error simultaneously in view of in linear equation, being constrained
Total least square model obtains the accurate of target location using obtained least square solution as initial solution using Newton iteration
Estimation.The present invention considers angular observation error, the site error of time difference observation error and external sort algorithm, and positioning result is outer spoke
Penetrating source, there are optimal estimation results when error；The present invention obtains nonlinear angle and time difference observational equation linearization process
Least square algebraic solution has been arrived, and as the initial solution of Newton iteration, ensure that convergence.
Specifically, the present invention is directed to external sort algorithm position there are the Passive Radar System under error condition, propose that one kind is examined
The more base passive radar object localization methods for considering the joint angle and the time difference of external sort algorithm site error, as shown in Figure 1, step
It is as follows：
First, the observational equation of angle and the time difference are linearized, obtains one group of linear equation, and obtain using least square
The rough estimate of target location.Specific method for solving is as follows：
Assuming that have N number of external sort algorithm in scene, and 1 target, 1 observation station.Two slave antennas are laid on observation station, are respectively used to
Receive direct signal and target echo signal from external sort algorithm.Using observation station as origin, rectangular coordinate system in space is established.Assuming that
Target location X=[x to be estimatedo,yo,zo]T.The actual position of external sort algorithmNot
Know, can only obtain its measured value s for containing errork=[xk,yk,zk]T(k=1,2 ..., N), i.e.,
Wherein, Δ skFor corresponding measurement error vector.The position of N number of external sort algorithm is expressed as matrix form, is obtained
The matrix of following 3N × 1：
S=so+Δs
In formula,
The actual distance of target to observation station isActual distance of the target to radiation source kThe actual distance of radiation source k to observation station is
Assuming that signal velocity is c, then the direct signal of external sort algorithm k and its echo-signal after target reflects are to taking things philosophically
The time difference of survey station is：
If target to the azimuth of observation station and pitch angle be respectively θoWithThen closed according to the geometry of target and observation station
System：
By a series of transformation, linear forms that the observational equation of angle and the time difference can be expressed as：
The system of linear equations, which is expressed as matrix form, is：
HoX=bo
Wherein,
Using weighted least square method, the rough estimate for obtaining target location is calculated as：
Secondly, by observation error and external sort algorithm site error simultaneously in view of in linear equation, obtaining least square mould
Type, steps are as follows：
It (1) will be in the angular observation error in first function, the time difference observation error and third function in second function
Errors in position measurement carries out whitening processing, and white noise vector is obtained after processing and is missed respectively with angular observation error, time difference observation
The functional relation of difference, errors in position measurement.
(2) according to functional relation and first function, second function and third function, constraints is established, with albefaction
The minimum object function of norm squared of noise vector.
Further, above-mentioned least square model can also be converted, the object function under constraints is become
The minimization object function for changing unconfined condition into, as final least square model.
Detailed process is：
If observation vector actual valueIts measured value isIt surveys
Measure errorThen have：
θ=θo+Δθ
S and θ are merged into the column vector α=[θ of one (4N+2) × 1T,sT]T, as total observed quantity, corresponding observation
Error is n=[Δ θT,ΔsT]T.Consider angle, time difference observation error Δ θ and external sort algorithm site error Δ s to matrix simultaneously
HoAnd boInfluence, then HoX=boIt can be expressed as the function of observed quantity α：
Ho(α-n)=bo(α-n)
By Ho(α-n) and bo(α-n) Taylor expansion at measured value α, and ignore second order and the above error term, it obtains as follows
Formula：
Ho=H- Δs H, bo=b- Δs b
Then Ho(α-n)=bo(α-n) can be expressed as：
(H- Δ H) X=b- Δs b
In formula,
Δ H=[F1n,F2n,F3N], Δ b=F4n
Fl, l=1,2,3,4 can be calculated according to the following formula：
It is calculated according to above formula, obtains matrix Fl, l=1,2,3,4 is respectively：
Wherein, Σ1,Σ2,Σ4,Σ5For N × 3N, Σ3For the matrix of N × 2, element is as follows：
If every error, need to be by its whitening processing with correlation or with different variances in n.Enable Q=E [nnT], it is right
Q makees Cholesky decomposition (triangle decomposition) and obtains Q=PPT, obtain the noise vector u=P of albefaction-1N, then, it enablesThen
FlPu=Glu
Enable WX=xG1+yG2+zG3-G4, then (H- Δ H) X=b- Δs b can be expressed as：
HX-b=WXu
The CTLS solutions for solving target location, that is, meeting constraints HX-b=WXUnder u, a suitable solution vector is determined
X so that object function | | u | |2It is minimum.Its mathematical notation is：
Above formula is the minimization problem of a Quadratic Function Optimization under the constraint of quadratic form constraint equation, can be transformed into one
A unconstrained minimization problem to minimizer X：
In formulaRepresenting matrix WXMoore-Penrose it is inverse.It will
It substitutes into the object function of CTLS models (least square model), then the CTLS solutions (least square solution) of target location are to meet
Therefore the variable X of following objective functions minimization is considered measurement error and external sort algorithm site error in equation, structure
The constraint total least square model for building out target location is：
Finally, using obtained least square solution as initial solution, the accurate estimation of target location is obtained using Newton iteration.
Detailed process is：
Using least square solution obtained above as initial solutionBy J (X) in X0Locate Taylor expansion, and ignores
Three ranks and the above error term, obtain：
In formula,And Wherein,
It enablesIt obtains：
A+B(X-X0)=0
Above formula is solved, obtaining newton iteration formula is：
X=X0-B-1A
Obtain the accurate estimation of target location using newton iteration formula, it is only necessary to iteration can converge to for 2-3 times it is global most
Excellent solution.
Using the geometric position schematic diagram of Fig. 2 Passive Radar Systems and target, simulated experiment emulation is carried out to the present invention.Figure
3, Fig. 4, Fig. 5 respectively show target location evaluated error of the present invention with time difference measurement error, angle measurement error, external sort algorithm
The simulation comparison of site error variation, it can be seen that under conditions of there are external sort algorithm site error, the present invention estimates performance
It is substantially better than the location algorithm for ignoring external sort algorithm site error, evaluated error is closest to Cramér-Rao lower bound.
The present invention also proposes a kind of passive radar target locating set, including calculation processing module, the calculation processing module
For realizing following steps：
1) observational equation of angle and the time difference is built, and the observational equation of angle and the time difference are subjected to linearization process, is obtained
To linear equation, solves the linear equation and obtain the initial estimate of target location.
2) angle measurement is indicated to the difference for being at an angle of actual value and angular observation error, when time difference measurement value is expressed as
The difference of poor actual value and time difference observation error, by the measurement positional value of external sort algorithm be expressed as the actual position value of external sort algorithm with
The measured value of angle, the measured value of the time difference are substituted into above-mentioned linear equation, respectively obtain angle by the difference of errors in position measurement respectively
First function, time difference actual value second function as to be asked amount of the actual value as amount to be asked；By the measurement position of external sort algorithm
It sets value and substitutes into above-mentioned linear equation as new variables, obtain third function of the actual position value as amount to be asked of external sort algorithm.
3) least square model is built according to first function, second function, third function, by the model in target location
Taylor expansion at initial estimate, solution obtain newton iteration formula, utilize the initial estimate and Newton iteration of target location
Formula is iterated, and iteration obtains the fine estimation of target location to number is set.
Signified passive radar target locating set, is actually based on the one of the method for the present invention flow in above-described embodiment
Kind computer solution, i.e., a kind of software architecture can be applied in computer, and above-mentioned apparatus is opposite with method flow
The treatment progress answered.Since sufficiently clear is complete for the introduction to the above method, therefore no longer it is described in detail.
The foregoing is merely the preferred embodiment of the present invention, are not intended to restrict the invention, for those skilled in the art
For member, the invention may be variously modified and varied.Any modification made by all within the spirits and principles of the present invention,
Equivalent replacement, improvement etc., should be included within scope of the presently claimed invention.
Claims (6)
1. a kind of passive radar object localization method, which is characterized in that include the following steps：
1) observational equation of angle and the time difference is built, and the observational equation of angle and the time difference are subjected to linearization process, obtains line
Property equation, solves the linear equation and obtains the initial estimate of target location；
2) angle measurement is indicated to the difference for being at an angle of actual value and angular observation error, it is true that time difference measurement value is expressed as the time difference
The measurement positional value of external sort algorithm is expressed as actual position value and the position of external sort algorithm by the difference of real value and time difference observation error
The measured value of angle, the measured value of the time difference are substituted into the linear equation, it is true to respectively obtain angle by the difference of measurement error respectively
First function, time difference actual value second function as to be asked amount of the value as amount to be asked；By the measurement positional value of external sort algorithm
The linear equation is substituted into as new variables, obtains third function of the actual position value as amount to be asked of external sort algorithm；
3) least square model is built according to first function, second function, third function, by the model in the target location
Taylor expansion at initial estimate, solution obtain newton iteration formula, utilize the initial estimate and newton of the target location
Iterative formula is iterated, and iteration obtains the fine estimation of target location to number is set.
2. passive radar object localization method according to claim 1, which is characterized in that step 3) further includes following structure
The sub-step of least square model：
(1) by the angular observation error in first function, the position in the time difference observation error and third function in second function
Measurement error carry out whitening processing, obtained after processing white noise vector respectively with angular observation error, time difference observation error, position
Set the functional relation of measurement error；
(2) according to the functional relation and first function, second function and third function, constraints is established, with described
The minimum object function of norm squared of white noise vector.
3. passive radar object localization method according to claim 2, which is characterized in that further comprising the steps of：By institute
It states the object function under constraints and carries out the minimization object function for being transformed into unconfined condition, as final least square
Model.
4. a kind of passive radar target locating set, which is characterized in that including calculation processing module, which is used for
Realize following steps：
1) observational equation of angle and the time difference is built, and the observational equation of angle and the time difference are subjected to linearization process, obtains line
Property equation, solves the linear equation and obtains the initial estimate of target location；
2) angle measurement is indicated to the difference for being at an angle of actual value and angular observation error, it is true that time difference measurement value is expressed as the time difference
The measurement positional value of external sort algorithm is expressed as actual position value and the position of external sort algorithm by the difference of real value and time difference observation error
The measured value of angle, the measured value of the time difference are substituted into the linear equation, it is true to respectively obtain angle by the difference of measurement error respectively
First function, time difference actual value second function as to be asked amount of the value as amount to be asked；By the measurement positional value of external sort algorithm
The linear equation is substituted into as new variables, obtains third function of the actual position value as amount to be asked of external sort algorithm；
3) least square model is built according to first function, second function, third function, by the model in the target location
Taylor expansion at initial estimate, solution obtain newton iteration formula, utilize the initial estimate and newton of the target location
Iterative formula is iterated, and iteration obtains the fine estimation of target location to number is set.
5. passive radar target locating set according to claim 4, which is characterized in that step 3) further includes following structure
The sub-step of least square model：
(1) by the angular observation error in first function, the position in the time difference observation error and third function in second function
Measurement error carry out whitening processing, obtained after processing white noise vector respectively with angular observation error, time difference observation error, position
Set the functional relation of measurement error；
(2) according to the functional relation and first function, second function and third function, constraints is established, with described
The minimum object function of norm squared of white noise vector.
6. passive radar target locating set according to claim 5, which is characterized in that further comprising the steps of：By institute
It states the object function under constraints and carries out the minimization object function for being transformed into unconfined condition, as final least square
Model.
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