CN109975749A - A kind of shortwave list under calibration source existence condition, which is stood erectly, connects localization method - Google Patents
A kind of shortwave list under calibration source existence condition, which is stood erectly, connects localization method 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
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- 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
Abstract
The present invention relates to shortwave mono-station location technical fields, it discloses the shortwave list under a kind of calibration source existence condition and stands erectly and connect localization method, this method places shortwave calibration source known to several positions simultaneously first near shortwave target source, and short-wave signal data are received using the uniform circular array in single observation station, then determine the azimuth for receiving signal and the elevation angle about its longitude and latitude and the relationship of Ionospheric virtual height parameter, then it is constructed based on signal subspace fitting criterion about target source longitude and latitude and the cost function of Ionospheric virtual height parameter, Combined estimator is carried out to target source longitude and latitude and Ionospheric virtual height using Gauss-Newton iterative algorithm, so that it is determined that target position information.Due to the presence of calibration source, the present invention can effectively inhibit influence of the Ionospheric virtual height deviation for short-wave signal positioning accuracy.
Description
Technical field
Shortwave list station the present invention relates to shortwave mono-station location technical field, in particular under a kind of calibration source existence condition
Direct localization method.
Background technique
It is well known that wireless signal location technology is widely used in communication, radar, target monitoring, navigation telemetering, earthquake are surveyed
The fields such as survey, radio astronomy, Emergency Assistance, safety management all play an important role in industrial production and Military Application.
(i.e. position parameter Estimation) is positioned to target the active equipments such as radar, laser, sonar can be used and is completed, such technology
Referred to as active location technology, it has many advantages, such as round-the-clock, high-precision.However, active location system is usually required by transmitting
Great-power electromagnetic signal is easy to be found by other side come the position realized, therefore easily sticked one's chin out, thus dry by other side's electronics
The influence disturbed, causes positioning performance sharply to deteriorate, or even can jeopardize the safety and reliability of system itself.
Target, which positions, to be realized using the radio signal of target (active) radiation or (passive) scattering, such
Technology is known as passive location technology, it refers in the case where observation station not actively transmission of electromagnetic signals, by receiving target spoke
The radio signal penetrated or scattered estimates target position parameter.Compared with active location system, passive location system has
The advantages that actively transmission of electromagnetic signals, survival ability be not strong, reconnaissance range is remote, to obtain the extensive pass of domestic and foreign scholars
Note and further investigation.Passive location system can be divided into Single passive location system according to observation station number and multistation is passive fixed
Position system two major classes, wherein mono-station location system have flexibility height, mobility strong, system succinct and be not necessarily to interior communication and
The advantages that synchronous, the invention mainly relates to Single passive location systems.
For distant object, target emanation signal reaches observation station often through the mode of over-the-horizon propagation, most
A kind of common mode is that signal reaches surface-based observing station after ionospheric reflection, at this time to be positioned using single station,
Then need to know Ionospheric virtual height information, but the information is difficult accurately to know in practical applications, is only capable of obtaining its approximate evaluation
Value.Obviously, Ionospheric virtual height error can produce bigger effect the positioning accuracy of short-wave signal.
On the other hand, existing passive location process can be summarized as Two-step estimation station-keeping mode, i.e., first from signal
Positional parameter (such as orientation, delay inequality, Doppler etc.) is extracted in data, then calculates the position of target based on these parametric solutions again
Confidence breath.Although this two steps station-keeping mode has been widely used in modern positioning system, Israel scholar A.J.Weiss
The shortcomings in the presence of it are but indicated with A.Amar, and propose the thought that single step directly positions, and basic concept is
The location parameter of direct estimation target from the data field of signal acquisition, without estimating other interfix parameters again.Obviously,
This direct station-keeping mode of single step is also applied for shortwave mono-station location scene, and only direct localization method equally will receive ionosphere
The influence of virtual height error, to generate biggish deviations.
Summary of the invention
The present invention provides the shortwave list station under a kind of calibration source existence condition aiming at the problem that Ionospheric virtual height error influences
Direct localization method, to improve the mono-station location precision to shortwave radiation source.
To achieve the goals above, the invention adopts the following technical scheme:
A kind of shortwave list under calibration source existence condition, which is stood erectly, connects localization method, comprising:
Step 1: placing shortwave calibration source known to D longitude and latitude simultaneously on shortwave target source region periphery；
Step 2: target source signal and D correction source signal being received using M member uniform circular array in observation station, docked
The collection of letters number is sampled, and acquires K sample of signal altogether, and establish the corresponding array signal model of K sample of signal；
Step 3: determine target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude and
The relationship of Ionospheric virtual height；
Step 4: determining that d-th of correction source signal reaches the azimuth of M member uniform circular array and the elevation angle is corrected with d-th respectively
The relationship of source longitude and latitude and Ionospheric virtual height, 1≤d≤D；
Step 5: using the corresponding array signal Construction of A Model covariance matrix of the K sample of signal, and to covariance
Matrix carries out Eigenvalues Decomposition, to obtain signal subspace matrix and optimal weighting matrix；
Step 6: using the signal subspace matrix and optimal weighting matrix construction about target source longitude and latitude and ionization
The cost function of layer virtual height；
Step 7: according to target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude and
The relationship of Ionospheric virtual height, d-th of correction source signal reaches the azimuth of M member uniform circular array and the elevation angle is corrected with d-th respectively
The relationship and the cost function of source longitude and latitude and Ionospheric virtual height, using Gauss-Newton iterative algorithm to target source longitude and latitude
Degree and Ionospheric virtual height carry out Combined estimator, so that it is determined that target position information.
Further, array signal model in the step 2 are as follows:
Wherein, x (tk) it is k-th of array received signal；sc,d(tk) it is d-th of complex envelope for correcting source signal；st(tk)
For the complex envelope of target source signal；n(tk) it is array additive noise；For signal
Complex envelope vector；a(ωc,d,ρc,d, h) and it is the array manifold vector that source signal is corrected about d-th, ωc,dFor calibration source longitude,
ρc,dFor calibration source latitude, h is Ionospheric virtual height；a(ωt,ρt, h) and it is array manifold vector about target source signal, ωtFor mesh
Mark source longitude, ρtFor target source latitude；
For array manifold matrix.
Further, the step 3 includes:
Step 3.1: the latitude and longitude coordinates of target source are converted to the horizontal coordinate centered on observation station according to formula (2):
Wherein, (xt,g,yt,g,zt,g) it is coordinate of the target source under the observation station horizontal system of coordinates；ωoAnd ρoRespectively observe
The longitude and latitude stood；R is earth radius.
Step 3.2: azimuth angle theta is obtained according to formula (2)tWith longitude ωtAnd latitude ρtRelationship:
Wherein,
Step 3.3: obtaining and face upward using triangle sine by observation station, center point and ionization layer building triangle
Angle betatWith longitude ωt, latitude ρtAnd the relationship of Ionospheric virtual height h:
Wherein,It is the triangle using center point as the interior angle on vertex.
Further, the step 4 includes:
Step 4.1: the latitude and longitude coordinates of d-th of calibration source are converted to the Horizon centered on observation station according to formula (5)
Coordinate:
Wherein, (xd,g,yd,g,zd,g) it is coordinate of d-th of calibration source target source under the observation station horizontal system of coordinates；
Step 4.2: azimuth angle theta is obtained according to formula (5)c,dWith longitude ωc,dAnd latitude ρc,dRelationship:
Step 4.3: utilizing triangle sine, obtain elevation angle βc,dWith longitude ωc,d, latitude ρc,dAnd ionosphere is empty
The relationship of high h:
Wherein,
Further, the step 5 includes:
Step 5.1: utilizing the corresponding array signal model { x (t of K sample of signalk)}1≤k≤KConstruct covariance matrixAnd it is right according to formula (8)Carry out Eigenvalues Decomposition:
Wherein,For (D+1) × (D+1) rank diagonal matrix, diagonal element is matrixPreceding D+1 characteristic value；For (M-D-1) × (M-D-1) rank diagonal matrix, diagonal element is matrixRear M-D-1 characteristic value；For M ×
(D+1) rank signal subspace matrix, column vector correspond to the unit character vector of big characteristic value；For M × (M-D-1)
Rank noise subspace matrix, column vector correspond to the unit character vector of small characteristic value；
Step 5.2: utilizingParameter after Eigenvalues Decomposition constructs optimal weighting matrix according to formula (9)
Wherein,For matrixIn j-th of diagonal element, ID+1For (D+1) × (D+1) rank unit matrix.
Further, the step 6 includes:
Utilize signal subspace matrixWith optimal weighting matrixConstruction is empty about target source longitude and latitude and ionosphere
High cost function；The cost function are as follows:
Wherein,Π⊥[A(ωt,ρt, h)] it is orthogonal intersection cast shadow matrix；
Π⊥[A(ωt,ρt, h)]=IM-A(ωt,ρt,h)((A(ωt,ρt,h))HA(ωt,ρt,h))-1(A(ωt,ρt,h))H
Wherein, IMFor M × M rank unit matrix.
Further, the step 7 includes:
According to target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude and ionosphere
The relationship of virtual height, d-th correction source signal reach M member uniform circular array azimuth and the elevation angle respectively with d-th of calibration source longitude and latitude
Relationship and the cost function of degree and Ionospheric virtual height, using Gauss-Newton iterative algorithm according to formula (11) to target source
Longitude ωt, latitude ρtAnd Ionospheric virtual height h carries out Combined estimator:
Wherein, μ is step factor, 0 < μ < 1, μiFor i-th iteration step factor；And h(i)It is i-th
Secondary iteration result；And h(i+1)It is i+1 time iteration result；For gradient vector；For Hessian matrix；
Wherein the expression formula of each element is respectively
Wherein,
Wherein l is uniform circular array radius, and λ is signal wavelength,For unit matrix ID+1In the last one column vector.
Compared with prior art, the invention has the benefit that
The present invention places shortwave calibration source known to several positions simultaneously first near shortwave target source, and using individually
Uniform circular array in observation station receives short-wave signal data, then determines that receiving signal (while including target source signal and correction
Source signal) azimuth and the elevation angle about its longitude and latitude and the relationship of Ionospheric virtual height parameter, then be based on signal subspace
Fitting criterion construction is calculated about target source longitude and latitude and the cost function of Ionospheric virtual height parameter using Gauss-Newton iteration
Method carries out Combined estimator to target source longitude and latitude and Ionospheric virtual height, so that it is determined that target position information.The present invention utilizes longitude and latitude
Accurately known shortwave calibration source is spent, based on the basic thought directly positioned, shortwave target source is positioned, can effectively be disappeared
Except the deviations as caused by Ionospheric virtual height error, to improve shortwave mono-station location precision.
Detailed description of the invention
Fig. 1 stands erectly for the shortwave list under a kind of calibration source existence condition of the embodiment of the present invention and connects localization method flow chart.
Fig. 2 is coordinate system of embodiment of the present invention transition diagram.
Fig. 3 is the triangle schematic diagram that the embodiment of the present invention determines elevation angle expression formula.
Fig. 4 stands erectly for shortwave of embodiment of the present invention list and connects positioning result scatter diagram.
Fig. 5 is change curve of target source of the embodiment of the present invention position root-mean-square error with target source signal-to-noise ratio.
Fig. 6 is that Ionospheric virtual height of the embodiment of the present invention estimates root-mean-square error with the change curve of target source signal-to-noise ratio
Figure.
Fig. 7 is change curve of target source of the embodiment of the present invention position root-mean-square error with array antenna number.
Fig. 8 is that Ionospheric virtual height of the embodiment of the present invention estimates root-mean-square error with the change curve of array antenna number
Figure.
Fig. 9 is variation of target source of the embodiment of the present invention position root-mean-square error with Ionospheric virtual height prior estimate error
Curve graph.
Figure 10 is that Ionospheric virtual height of the embodiment of the present invention estimates root-mean-square error with Ionospheric virtual height prior estimate error
Change curve.
Specific embodiment
With reference to the accompanying drawing with specific embodiment the present invention will be further explained explanation:
Embodiment one:
As shown in Figure 1, the shortwave list under a kind of calibration source existence condition stands erectly and connects localization method, comprising the following steps:
Step S101: shortwave calibration source known to D longitude and latitude is placed simultaneously on shortwave target source region periphery；
Step S102: receiving target source signal and D correction source signal using M member uniform circular array in observation station,
It is sampled to signal is received, acquires K sample of signal altogether, and establish the corresponding array signal model of K sample of signal；
Step S103: determine target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude
The relationship of degree and Ionospheric virtual height；
Step S104: determine d-th correction source signal reach M member uniform circular array azimuth and the elevation angle respectively with d-th
The relationship of calibration source longitude and latitude and Ionospheric virtual height, 1≤d≤D；
Step S105: using the corresponding array signal Construction of A Model covariance matrix of the K sample of signal, and to association side
Poor matrix carries out Eigenvalues Decomposition, to obtain signal subspace matrix and optimal weighting matrix；
Step S106: using the signal subspace matrix and optimal weighting matrix construction about target source longitude and latitude and electricity
The cost function of absciss layer virtual height；
Step S107: according to target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude
Degree and Ionospheric virtual height relationship, d-th correction source signal reach M member uniform circular array azimuth and the elevation angle respectively with d-th
The relationship and the cost function of calibration source longitude and latitude and Ionospheric virtual height, using Gauss-Newton iterative algorithm to target source
Longitude and latitude and Ionospheric virtual height carry out Combined estimator, so that it is determined that target position information.
The present invention places shortwave calibration source known to several positions simultaneously first near shortwave target source, and using individually
Uniform circular array in observation station receives short-wave signal data, then determines that receiving signal (while including target source signal and correction
Source signal) azimuth and the elevation angle about its longitude and latitude and the relationship of Ionospheric virtual height parameter, then be based on signal subspace
Fitting criterion construction is calculated about target source longitude and latitude and the cost function of Ionospheric virtual height parameter using Gauss-Newton iteration
Method carries out Combined estimator to target source longitude and latitude and Ionospheric virtual height, so that it is determined that target position information.The present invention utilizes longitude and latitude
Accurately known shortwave calibration source is spent, based on the basic thought directly positioned, shortwave target source is positioned, can effectively be disappeared
Except the deviations as caused by Ionospheric virtual height error, to improve shortwave mono-station location precision.
Specifically, in step S101, it is accurately known that D longitude and latitude is placed simultaneously on shortwave target source region periphery
Shortwave calibration source, the longitude of target source are ωt, latitude ρt, the longitude of d (1≤d≤D) a calibration source is ωc,d, latitude be
ρc,d；
Specifically, in step S102, D+1 short-wave signal (including D correction source signal and 1 target source signal) is passed through
M member uniform circular array is reached after ionospheric scattering, Ionospheric virtual height h now receives it using M member uniform circular array, adopts altogether
Collect K sample of signal, wherein the array signal model of k-th of sample of signal are as follows:
Wherein, x (tk) it is k-th of array received signal；sc,d(tk) it is d-th of complex envelope for correcting source signal；st(tk)
For the complex envelope of target source signal；n(tk) it is array additive noise；For signal
Complex envelope vector；a(ωc,d,ρc,d, h) and it is the array manifold vector that source signal is corrected about d-th, it is passed through with calibration source simultaneously
Spend ωc,d, latitude ρc,dAnd Ionospheric virtual height h totally 3 relating to parameters；a(ωt,ρt, h) and it is array stream about target source signal
Shape vector, it simultaneously with target source longitude ωt, latitude ρtAnd Ionospheric virtual height h totally 3 relating to parameters；For array manifold matrix, due to correction
Source longitude and latitude are accurately known, therefore are only regarded as about target source longitude ωt, latitude ρtAnd Ionospheric virtual height h
Function.
Specifically, the step S103 includes:
Step S103.1: the latitude and longitude coordinates of target source are converted to the Horizon centered on observation station according to formula (2) and are sat
Mark, as shown in Figure 2:
Wherein, (xt,g,yt,g,zt,g) it is coordinate of the target source under the observation station horizontal system of coordinates；ωoAnd ρoRespectively observe
The longitude and latitude stood；R is earth radius.
Step S103.2: azimuth angle theta is obtained according to formula (2)tWith longitude ωtAnd latitude ρtRelationship:
Wherein,
Step S103.3: by observation station, center point and ionization layer building triangle, the triangle is as shown in Figure 3
Δ ABC obtains elevation angle β using triangle sinetWith longitude ωt, latitude ρtAnd the relationship of Ionospheric virtual height h:
Wherein,It is the triangle using center point as the interior angle on vertex.
Specifically, the step S104 includes:
Step S104.1: the latitude and longitude coordinates of d-th of calibration source are converted to the ground centered on observation station according to formula (5)
Flat coordinate:
Wherein, (xd,g,yd,g,zd,g) it is coordinate of d-th of calibration source target source under the observation station horizontal system of coordinates；
Step S104.2: azimuth angle theta is obtained according to formula (5)c,dWith longitude ωc,dAnd latitude ρc,dRelationship:
Step S104.3: Δ ABC as shown in Figure 3 obtains elevation angle β using triangle sinec,dWith longitude ωc,d、
Latitude ρc,dAnd the relationship of Ionospheric virtual height h:
Wherein,
Specifically, the step S105 includes:
Step S105.1: the corresponding array signal model { x (t of K sample of signal is utilizedk)}1≤k≤KConstruct covariance matrixAnd it is right according to formula (8)Carry out Eigenvalues Decomposition:
Wherein,For (D+1) × (D+1) rank diagonal matrix, diagonal element is matrixPreceding D+1 characteristic value
(matrixThe descending sequence of each element)；For (M-D-1) × (M-D-1) rank diagonal matrix, diagonal element is square
Battle arrayRear M-D-1 characteristic value；For M × (D+1) rank signal subspace matrix, column vector corresponds to big characteristic value
Unit character vector；For M × (M-D-1) rank noise subspace matrix, column vector corresponds to the unit of small characteristic value
Feature vector；
Step S105.2: it utilizesParameter after Eigenvalues Decomposition constructs optimal weighting matrix according to formula (9)
Wherein,For matrixIn j-th of diagonal element, ID+1For (D+1) × (D+1) rank unit matrix.
Specifically, the step S106 includes:
Utilize signal subspace matrixWith optimal weighting matrixConstruction is empty about target source longitude and latitude and ionosphere
High cost function；The cost function are as follows:
Wherein,Π⊥[A(ωt,ρt, h)] it is orthogonal intersection cast shadow matrix；
Π⊥[A(ωt,ρt, h)]=IM-A(ωt,ρt,h)((A(ωt,ρt,h))HA(ωt,ρt,h))-1(A(ωt,ρt,h))H
Wherein, IMFor M × M rank unit matrix.
Specifically, the step S107 includes:
According to target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude and ionosphere
The relationship of virtual height, d-th correction source signal reach M member uniform circular array azimuth and the elevation angle respectively with d-th of calibration source longitude and latitude
Relationship and the cost function of degree and Ionospheric virtual height, using Gauss-Newton iterative algorithm according to formula (11) to target source
Longitude ωt, latitude ρtAnd Ionospheric virtual height h carries out Combined estimator:
Wherein, μ is step factor, 0 < μ < 1, μiFor i-th iteration step factor；And h(i)It is i-th
Secondary iteration result；And h(i+1)It is i+1 time iteration result；For gradient vector；For Hessian matrix；WithExpression formula is respectively as follows:
Wherein the expression formula of each element is respectively
It is worth noting thatWithWith WithThe expression formula difference of element is identical；
Wherein,
Wherein l is uniform circular array radius, and λ is signal wavelength,For unit matrix ID+1In the last one column vector.
To verify effect of the invention, following experimental data is provided.
Assuming that the longitude of single observation station is 112.73 ° of east longitude, latitude is 33.25 ° of north latitude；The longitude of shortwave target source is
122.46 ° of east longitude, latitude is 27.82 ° of north latitude；Two shortwave calibration sources are now placed, the longitude of first calibration source is east longitude
123.62 °, latitude is 28.68 ° of north latitude, and the longitude of second calibration source is 124.54 ° of east longitude, and latitude is 29.96 ° of north latitude.It should
Uniform circular array is installed in observation station, and circle battle array radius and signal incident wavelength ratio are 1.5, and the sample of signal points for directly positioning are
500, and it is 340 public affairs that shortwave target source signal and correction source signal, which reach observation station Ionospheric virtual height true value experienced,
In.
(1) signal-to-noise ratio of shortwave target source signal and correction source signal is 5dB, and array antenna number is that 10, Fig. 4 is provided
Disclosed by the invention singly stand erectly connects localization method and the positioning result without traditional mono-station location method under the conditions of calibration source dissipates
Butut has carried out 500 Monte Carlo experiments to both methods, and assumes singly to stand firm without the tradition under the conditions of calibration source
Position method is 15 kilometers to the prior estimate error of Ionospheric virtual height.It is connect it can be seen from the figure that singly standing erectly disclosed in this patent
The estimated result of localization method changes near true value always, and without traditional mono-station location method under the conditions of calibration source
Estimated result can deviate considerably from true value, this, which illustrates singly to stand erectly disclosed in this patent, connects localization method and can obviously inhibit to ionize
It is influenced brought by layer virtual height error, to significantly improve the mono-station location precision to shortwave target source.
(2) remaining experiment condition is constant, and target source position root-mean-square error and ionosphere void is set forth in Fig. 5 and Fig. 6
Height estimates root-mean-square error with the change curve of target source signal-to-noise ratio；Target source position root-mean-square is set forth in Fig. 7 and Fig. 8
Error and Ionospheric virtual height estimate root-mean-square error with the change curve of array antenna number；Fig. 9 and Figure 10 are set forth
Target source position root-mean-square error and Ionospheric virtual height estimate root-mean-square error with the change of Ionospheric virtual height prior estimate error
Change curve.Can be with it is further seen that singly standing erectly disclosed in this patent connect the advantage of localization method from Fig. 5~Figure 10, and this is excellent
Gesture is obviously improved with the increase of target source signal-to-noise ratio, while being shown also as the increase of Ionospheric virtual height prior estimate error
It writes and is promoted.
Illustrated above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (7)
1. the shortwave list under a kind of calibration source existence condition, which is stood erectly, connects localization method characterized by comprising
Step 1: placing shortwave calibration source known to D longitude and latitude simultaneously on shortwave target source region periphery；
Step 2: target source signal and D correction source signal being received using M member uniform circular array in observation station, docking is collected mail
It number is sampled, acquires K sample of signal altogether, and establish the corresponding array signal model of K sample of signal；
Step 3: determine target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude and ionization
The relationship of layer virtual height；
Step 4: determining that d-th of correction source signal reaches the azimuth of M member uniform circular array and the elevation angle is passed through with d-th of calibration source respectively
The relationship of latitude and Ionospheric virtual height, 1≤d≤D；
Step 5: using the corresponding array signal Construction of A Model covariance matrix of the K sample of signal, and to covariance matrix
Eigenvalues Decomposition is carried out, to obtain signal subspace matrix and optimal weighting matrix；
Step 6: empty about target source longitude and latitude and ionosphere using the signal subspace matrix and optimal weighting matrix construction
High cost function；
Step 7: according to target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude and ionization
The relationship of layer virtual height, d-th of correction source signal reach the azimuth of M member uniform circular array and the elevation angle is passed through with d-th of calibration source respectively
The relationship and the cost function of latitude and Ionospheric virtual height, using Gauss-Newton iterative algorithm to target source longitude and latitude and
Ionospheric virtual height carries out Combined estimator, so that it is determined that target position information.
2. the shortwave list under a kind of calibration source existence condition according to claim 1, which is stood erectly, connects localization method, feature exists
In array signal model in the step 2 are as follows:
Wherein, x (tk) it is k-th of array received signal；sc,d(tk) it is d-th of complex envelope for correcting source signal；st(tk) it is target
The complex envelope of source signal；n(tk) it is array additive noise；For the complex envelope of signal
Vector；a(ωc,d,ρc,d, h) and it is the array manifold vector that source signal is corrected about d-th, ωc,dFor calibration source longitude, ρc,dFor
Calibration source latitude, h are Ionospheric virtual height；a(ωt,ρt, h) and it is array manifold vector about target source signal, ωtFor target source
Longitude, ρtFor target source latitude；For battle array
Column manifold matrix.
3. the shortwave list under a kind of calibration source existence condition according to claim 1, which is stood erectly, connects localization method, feature exists
In the step 3 includes:
Step 3.1: the latitude and longitude coordinates of target source are converted to the horizontal coordinate centered on observation station according to formula (2):
Wherein, (xt,g,yt,g,zt,g) it is coordinate of the target source under the observation station horizontal system of coordinates；ωoAnd ρoRespectively observation station
Longitude and latitude；R is earth radius.
Step 3.2: azimuth angle theta is obtained according to formula (2)tWith longitude ωtAnd latitude ρtRelationship:
Wherein,
Step 3.3: elevation angle β is obtained using triangle sine by observation station, center point and ionization layer building trianglet
With longitude ωt, latitude ρtAnd the relationship of Ionospheric virtual height h:
Wherein,It is the triangle using center point as the interior angle on vertex.
4. the shortwave list under a kind of calibration source existence condition according to claim 1, which is stood erectly, connects localization method, feature exists
In the step 4 includes:
Step 4.1: the latitude and longitude coordinates of d-th of calibration source are converted to the horizontal coordinate centered on observation station according to formula (5):
Wherein, (xd,g,yd,g,zd,g) it is coordinate of d-th of calibration source target source under the observation station horizontal system of coordinates；
Step 4.2: azimuth angle theta is obtained according to formula (5)c,dWith longitude ωc,dAnd latitude ρc,dRelationship:
Step 4.3: utilizing triangle sine, obtain elevation angle βc,dWith longitude ωc,d, latitude ρc,dAnd Ionospheric virtual height h
Relationship:
Wherein,
5. the shortwave list under a kind of calibration source existence condition according to claim 2, which is stood erectly, connects localization method, feature exists
In the step 5 includes:
Step 5.1: utilizing the corresponding array signal model { x (t of K sample of signalk)}1≤k≤KConstruct covariance matrixAnd it is right according to formula (8)Carry out Eigenvalues Decomposition:
Wherein,Rank diagonal matrix, diagonal element are matrixPreceding D+1 characteristic value；For
(M-D-1) × (M-D-1) rank diagonal matrix, diagonal element are matrixRear M-D-1 characteristic value；For M × (D+1)
Rank signal subspace matrix, column vector correspond to the unit character vector of big characteristic value；For M × (M-D-1) rank noise
Subspace matrices, column vector correspond to the unit character vector of small characteristic value；
Step 5.2: utilizingParameter after Eigenvalues Decomposition constructs optimal weighting matrix according to formula (9)
Wherein,For matrixIn j-th of diagonal element, ID+1For (D+1) × (D+1) rank unit matrix.
6. the shortwave list under a kind of calibration source existence condition according to claim 1, which is stood erectly, connects localization method, feature exists
In the step 6 includes:
Utilize signal subspace matrixWith optimal weighting matrixIt constructs about target source longitude and latitude and Ionospheric virtual height
Cost function；The cost function are as follows:
Wherein, For orthogonal intersection cast shadow matrix；
Π⊥[A(ωt,ρt, h)]=IM-A(ωt,ρt,h)((A(ωt,ρt,h))HA(ωt,ρt,h))-1(A(ωt,ρt,h))HIts
In, IMFor M × M rank unit matrix.
7. the shortwave list under a kind of calibration source existence condition according to claim 1, which is stood erectly, connects localization method, feature exists
In the step 7 includes:
According to target source signal reach M member uniform circular array azimuth and the elevation angle respectively with target source longitude and latitude and Ionospheric virtual height
Relationship, d-th correction source signal reach M member uniform circular array azimuth and the elevation angle respectively with d-th of calibration source longitude and latitude with
And relationship and the cost function of Ionospheric virtual height, using Gauss-Newton iterative algorithm according to formula (11) to target source longitude
ωt, latitude ρtAnd Ionospheric virtual height h carries out Combined estimator:
Wherein, μ is step factor, 0 < μ < 1, μiFor i-th iteration step factor；And h(i)It is i-th iteration knot
Fruit；And h(i+1)It is i+1 time iteration result；For gradient vector；
For Hessian matrix；
Wherein the expression formula of each element is respectively
Wherein,
Wherein l is uniform circular array radius, and λ is signal wavelength,For unit matrix ID+1In the last one column vector.
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