CN107229032A - A kind of method and apparatus for building four array element solid arrays - Google Patents

A kind of method and apparatus for building four array element solid arrays Download PDF

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Publication number
CN107229032A
CN107229032A CN201710486540.9A CN201710486540A CN107229032A CN 107229032 A CN107229032 A CN 107229032A CN 201710486540 A CN201710486540 A CN 201710486540A CN 107229032 A CN107229032 A CN 107229032A
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array element
angle
rotation
estimate
measurement error
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CN107229032B (en
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尤明懿
陆安南
邱焱
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CETC 36 Research Institute
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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
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction

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  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
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Abstract

The invention discloses a kind of method for building four array element solid arrays, it is characterised in that method includes：The array element three-dimensional array of Primary Construction four；According to the initial rotation angle and direction finding model of the 4th array element, the first estimate of radiation source direction of arrival is obtained；According to the first estimate and angle measurement error of radiation source direction of arrival, first anglec of rotation of corresponding 4th array element when obtaining angle measurement error minimum value；The N rotation angle values of the 4th array element, N >=2 are obtained further according to first anglec of rotation of the 4th array element, direction finding model and angle measurement error iteration；Judge whether whether the difference of N rotation angle values and the anglecs of rotation of N 1 be less than angle difference preset value and/or iterations N more than iterations preset value；If so, then stopping iteration, four final array element solid arrays are built according to the N anglecs of rotation；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.By the anglec of rotation of iteration optimization part array element, the estimated accuracy of radiation source direction of arrival is lifted.

Description

A kind of method and apparatus for building four array element solid arrays
Technical field
The present invention relates to array antenna direction finding technology field, and in particular to a kind of method of the array element solid array of structure four and Device.
Background technology
Array antenna direction-finding system is a kind of important passive type direction finding equipment, relative to the radar system of active, Except having the advantages that anti-intercepting and capturing, it is anti-interference in addition to, also with direction finding precision is high, volume weight is small, low cost and other advantages, in recent years It is taken seriously, and has been applied multiple times in spaceborne equipment.Currently conventional direction finding array antenna is generally planar array, i.e., at multiple array elements In same plane.In application process, such planar array often may be used front normal direction region (being usually sub-satellite point position) To obtain more satisfactory direction finding precision, but deviateing the region (being usually compared with flat attitude region) of front normal direction orientation farther out Direction finding precision is remarkably decreased.However, in some special scenes, in addition to wishing front normal direction position and there is higher direction finding precision, Still desire to that there is higher direction finding precision to meet application demand deviateing the region of normal direction orientation farther out.
In the case of radiation source direction of arrival is uncertain, in order to meet in the need compared with flat attitude region direction finding precision Ask, common practice has front biasing, increases array element size, increases baseline length etc..Wherein, front biasing is exactly by by battle array The mounting plane in face rotates to an angle to meet application demand, but this way is smart to sacrifice former front normal direction region direction finding Spend for cost.The essence for increasing array element is the signal to noise ratio that signal is received by being lifted, and improves phase difference direction finding precision to be lifted The direction finding precision in each region, but for some low-frequency ranges direction finding battle array exist array element size originally with regard to it is larger the problem of, further Bigger pressure will be brought to the installation of array element, layout by increasing array element size.Increase baseline length and also will be helpful to each region The lifting of direction finding precision, but can undoubtedly bring the problem of direction finding is obscured.
The content of the invention
The invention provides a kind of method and apparatus for building four array element solid arrays, to solve in radiation source direction of arrival In the case of uncertain, existing planar array is in the low problem of direction finding precision compared with flat attitude region.
According to an aspect of the invention, there is provided a kind of method for building four array element solid arrays, methods described includes：
By arbitrarily one initial angle of rotation of the three-dimensional cartesian coordinate system where traditional three array element planar array, a non-co- is added 4th array element in face, the array element solid array of Primary Construction four, and four array element solid arrays based on structure obtain direction finding model and Angle measurement error；
According to the initial rotation angle of the 4th array element and the direction finding model, the first estimation of radiation source direction of arrival is obtained Value；
According to the first estimate and the angle measurement error of the radiation source direction of arrival, when obtaining angle measurement error minimum value First anglec of rotation of corresponding 4th array element；
First anglec of rotation, the direction finding model and the angle measurement error iteration further according to the 4th array element obtain the 4th gust The N rotation angle values of member, N >=2；
Judge whether the difference of N rotation angle values and the N-1 anglecs of rotation is less than angle difference preset value and/or iteration Whether times N is more than iterations preset value；If so, then stopping iteration, final four gusts are built according to the N anglecs of rotation First solid array；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.
There is provided a kind of device for building four array element solid arrays, described device bag according to another aspect of the present invention Memory and processor are included, is communicated and connected by internal bus between the memory and the processor, the memory is deposited Containing be able to can be realized by the computer program of the computing device, the computer program during computing device Following steps：
By arbitrarily one initial angle of rotation of the three-dimensional cartesian coordinate system where traditional three array element planar array, a non-co- is added 4th array element in face, the array element solid array of Primary Construction four, and four array element solid arrays based on structure obtain direction finding model and Angle measurement error；
According to the initial rotation angle of the 4th array element and the direction finding model, the first estimation of radiation source direction of arrival is obtained Value；
According to the first estimate and the angle measurement error of the radiation source direction of arrival, when obtaining angle measurement error minimum value First anglec of rotation of corresponding 4th array element；
First anglec of rotation, the direction finding model and the angle measurement error iteration further according to the 4th array element obtain the 4th gust The N rotation angle values of member, N >=2；
Judge whether the difference of N rotation angle values and the N-1 anglecs of rotation is less than angle difference preset value and/or iteration Whether times N is more than iterations preset value；If so, then stopping iteration, final four gusts are built according to the N anglecs of rotation First solid array；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.
The beneficial effects of the invention are as follows：Technical scheme, by by the three-dimensional where traditional three array element planar array Rectangular coordinate system arbitrarily one initial angle of rotation, one non-coplanar 4th array element of addition, the array element solid array of Primary Construction four, And the four array element solid arrays based on structure obtain direction finding model and angle measurement error；According to the initial rotation angle of the 4th array element and The direction finding model, obtains the first estimate of radiation source direction of arrival；According to the first of the radiation source direction of arrival the estimation Value and the angle measurement error, first anglec of rotation of corresponding 4th array element when obtaining angle measurement error minimum value；Further according to the 4th First anglec of rotation of array element, the direction finding model and the angle measurement error iteration obtain the N rotation angle values of the 4th array element, N≥2；Judge whether the difference of N rotation angle values and the N-1 anglecs of rotation is less than angle difference preset value and/or iteration time Whether number N is more than iterations preset value；If so, then stopping iteration, four final array elements are built according to the N anglecs of rotation Solid array；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.The four array element solid arrays finally built using the present invention, Both it can ensure, in larger elevation angle region direction finding precision, can also be lifted at the direction finding precision compared with flat attitude region, satisfaction is treated Survey ripple direction and expect the direction finding precision of pitching angular zone.In addition, in the case of radiation source direction of arrival is uncertain, Neng Gouji In the anglec of rotation of the estimated result iterative part array element of radiation source direction of arrival, radiation source ripple can be lifted to greatest extent up to side To estimated accuracy.
Brief description of the drawings
Fig. 1 is a kind of flow chart of the array element solid array method of structure four of one embodiment of the invention；
Fig. 2 is the flow chart of the array element solid array method of another structure four of one embodiment of the invention；
Fig. 3 is a kind of schematic diagram of the three-dimensional right angle battle array coordinate system of four array element of one embodiment of the invention；
Fig. 4 is a kind of structural representation of the array element solid array device of structure four of one embodiment of the invention；
Fig. 5 be one embodiment of the invention when γ=120 °, four array elements solid right angle battle array direction finding precision contour Schematic diagram；
Fig. 6 be one embodiment of the invention when γ=135 °, four array elements solid right angle battle array direction finding precision contour Schematic diagram；
Fig. 7 is that the utilization grid data service of one embodiment of the invention calculates the signal of radiation source Mutual coupling value Figure；
Fig. 8 is that the iteration of one embodiment of the invention obtains the corresponding relation of the 4th array element anglec of rotation and angle measurement error Figure.
Embodiment
The present invention design concept be：, can be to greatest extent in order in the case of radiation source direction of arrival is uncertain Ground lifts the estimated accuracy of radiation source direction of arrival, the rotation of the estimated result iterative part array element based on radiation source direction of arrival Angle.
Embodiment one
Fig. 1 is a kind of flow chart of the array element solid array method of optimization four of one embodiment of the invention, as shown in figure 1,
In step s 110, by arbitrarily one initial angle of rotation of the three-dimensional cartesian coordinate system where traditional three array element planar array Degree, adds non-coplanar 4th array element, the array element solid array of Primary Construction four, and the four array element solid arrays based on structure Obtain direction finding model and angle measurement error；
In one embodiment of the invention, the four array element solid arrays based on structure obtain direction finding model and direction finding Error includes：
The direction finding model that the four array element solid arrays based on structure are obtained is：
According to formulaCalculate the estimate of radiation source direction of arrival；
Wherein, the transposition of T representing matrixs, Σ is positive definite matrix, and θ is ripple direction vector to be measured, andIt is The estimate of ripple direction vector to be measured, andIt is azimuthal estimate in ripple direction to be measured,It is ripple to be measured The estimate of the angle of pitch in direction；
It is phase difference measurement value matrix；
It is that phase difference is theoretical Value matrix；
It is phase difference measurement error matrix, and it is that 0, covariance matrix is Σ to obey average Multi-dimension Normal distribution；
The angle measurement error that the four array element solid arrays based on structure are obtained is：
According to formulaCalculate the angle between the estimate and actual value in the ripple direction to be measured VarianceWhereinIt is the variance of phase difference measurement error, α0It is the azimuthal theoretical value in ripple direction to be measured, β0It is ripple to be measured The theoretical value of the direction angle of pitch, willIt is used as the angle measurement error between the estimate and actual value in the ripple direction to be measured.
In the step s 120, according to the initial rotation angle of the 4th array element and the direction finding model, obtain radiation source ripple and reach First estimate in direction；
In one embodiment of the invention, the corresponding spoke of minimum value of the direction finding model is calculated using grid data service Penetrate source Mutual coupling value.
In one embodiment of the invention, the utilization grid data service calculates the minimum value correspondence of the direction finding model Radiation source Mutual coupling value include：
Direction finding model progress equivalence transformation is obtained：
Calculated using grid data serviceThe corresponding radiation source ripple of maximum up to side To estimate conduct
In step s 130, according to the first estimate and the angle measurement error of the radiation source direction of arrival, obtain and survey First anglec of rotation of corresponding 4th array element during to error minimum value；
In one embodiment of the invention, first estimate according to the radiation source direction of arrival and the survey To error, first anglec of rotation of corresponding 4th array element includes when obtaining angle measurement error minimum value：
WillSubstitute into the angle measurement error
According to formulaThe first optimization rotation angle value is calculated, wherein, γk For the described first optimization rotation angle value, β0It is the theoretical value of the ripple direction to be measured angle of pitch, the azimuth determination in ripple direction to be measured Error varianceWith the elevation measurement error variance in ripple direction to be measured
In step S140, first anglec of rotation, the direction finding model and the angle measurement error further according to the 4th array element Iteration obtains the N rotation angle values of the 4th array element, N >=2；
In step S150, judge whether the difference of N rotation angle values and the N-1 anglecs of rotation is pre- less than angle difference If whether value and/or iterations N are more than iterations preset value；If so, then stopping iteration, according to the N anglecs of rotation Build four final array element solid arrays；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.
It follows that technical scheme, by by the three-dimensional cartesian coordinate system where traditional three array element planar array One initial angle of any rotation, adds non-coplanar 4th array element, the array element solid array of Primary Construction four, and is based on building Four array element solid arrays obtain direction finding model and angle measurement error；According to the initial rotation angle of the 4th array element and the direction finding mould Type, obtains the first estimate of radiation source direction of arrival；According to the first estimate of the radiation source direction of arrival and the survey To error, first anglec of rotation of corresponding 4th array element when obtaining angle measurement error minimum value；Further according to the first of the 4th array element The anglec of rotation, the direction finding model and the angle measurement error iteration obtain the N rotation angle values of the 4th array element, N >=2；Judge The difference of N rotation angle values and the N-1 anglecs of rotation whether is less than angle difference preset value and/or whether iterations N is big In iterations preset value；If so, then stopping iteration, four final array element solid arrays are built according to the N anglecs of rotation； If it is not, then continuing iteration obtains the N+1 anglecs of rotation.The four array element solid arrays finally built using the present invention, can both be protected Card can also be lifted at the direction finding precision compared with flat attitude region, meet ripple direction to be measured in larger elevation angle region direction finding precision Expecting the direction finding precision of pitching angular zone.In addition, in the case of radiation source direction of arrival is uncertain, radiation source can be based on The anglec of rotation of the estimated result iteration optimization part array element of direction of arrival, radiation source direction of arrival can be lifted to greatest extent Estimated accuracy.
In order that the solution of the present invention becomes apparent from, it is explained for a specific example below.Fig. 2 is this hair Another flow chart of the array element solid array method of optimization four of bright one embodiment, as shown in Fig. 2
S21, set up coordinate system
Fig. 3 is a kind of schematic diagram of the three-dimensional right angle battle array coordinate system of four array element of one embodiment of the invention, as shown in figure 3, OXYZ is the coordinate system of the array element right angle of conventional planar L-type three battle array, and three array elements of wherein right angle battle array are respectively arranged in origin of coordinates O (A1), X-axis (A2), Y-axis (A3), array baseline length is d (it should be noted that array baseline length refers in the present embodiment It is distance of other three array elements relative to the first array element).On this basis, coordinate system OXYZ is rotated forward into angle around its X-axis γ then obtains another coordinate system O ' X ' Y ' Z ', and the 4th array element A4 is added on Y ' axles, and array baseline length is similarly d. In coordinate system OXYZ, it is assumed that radiation source direction of arrival is β with OXY plane included angles, is designated as the angle of pitch.Moreover, it is assumed that radiation source ripple In projection and the OX angles of OXY planes it is α up to direction vector, is designated as azimuth.Counted for simplicity, radiation source direction of arrival is unified It is designated as (α, β).
S22, set up direction finding model
(1) phase difference calculating
In the three-dimensional array coordinate system that Fig. 3 is built, on the basis of array element A1, generally consider that baseline length is less than half-wavelength Situation is (if it should be noted that baseline length is more than half-wavelength, then direction finding will be caused to obscure.), then now array element A2 and A1 Phase difference21For：
λ is the wavelength in ripple direction to be measured in (formula 1), and d is array baseline length, Δ φ21For array element A2 and A1 passages it Between phase difference measurement error difference.On the other hand, array element A3 and A1 phase difference31For：
In (formula 2), Δ φ31For the difference of the phase difference measurement error between array element A3 and A1 passage.In addition, array element A4 with A1 phase difference41For：
In (formula 3), Δ φ41For the difference of the phase difference measurement error between array element A4 and A1 passage.
(formula 1)-(formula 3) is expressed in matrix as：
In (formula 4),It is measurement value matrix,It is theoretical value matrix,For measurement error matrix, and it is the multi-dimension Normal distribution that 0, covariance matrix is Σ to obey average, Wherein Σ is positive definite matrix.
Least Square in Processing is carried out to phase difference measurement value matrix (formula 4), obtaining direction finding model is：
It should be noted that in (formula 5), the transposition of T representing matrixs, Σ is positive definite matrix, θ is ripple direction arrow to be measured Amount, and θ=(α, β)；It is the estimate of ripple direction vector to be measured, andIt is the azimuthal of ripple direction to be measured Estimate,It is the estimate of the angle of pitch in ripple direction to be measured.
S23, angle measurement error are derived
To estimate the radiation source direction of arrival obtained via (formula 5) estimationLevels of precision, base must be provided The angle measurement error caused by Direction Finding Algorithm in (formula 5).For ease of follow-up statement, note：
If IfThen in θ0PlaceMinimum value is obtained, so thatSimilarly, ifI.e.AndThenWhenWhen smaller,In θ0Near, it is represented byIgnore height Rank error, has：
Due toHad according to (formula 7)：
For on the left of (formula 8) equation, directly can be calculated：
Therefore, have：
In (formula 10),
For on the left of (formula 8) equation, directly can be calculated：
In addition, directly being calculated in (formula 10) hasSoRow full rank, it is contemplated that Σ-1 It is also positive definite matrix, thereforeIt is reversible.Then obtained according to formula (formula 8)：
(formula 12), cov (Δ θ) refers to Δ θ covariance matrix.
In one embodiment of the invention, timesharing calculates what other three array elements referred to relative to the phase difference of the first array element It is the phase difference that at a time (or certain time period) only measures one group in A2-A1, A3-A1, tri- groups of baselines of A4-A1, according to One group of phase difference in tri- groups of baselines of secondary measurement A2-A1, A3-A1, A4-A1, in other words, as in computer programming language Tri- groups of phase differences of serial computing A2-A1, A3-A1, A4-A1.It should be noted that assuming the phase difference between measurement A2-A1 When, it is necessary to which two test machine, then in whole timesharing measurement process, it is only necessary to two test machine, saved system Computing resource.
During timesharing measurement phase difference, it is assumed thatCovariance matrix be For phase difference measurement The variance of error, I3It is 3 rank unit matrixs, then：
In (formula 13),
Then
According to (formula 12), have：
σ in (formula 14)α 2As azimuth measurement error variance, σβ 2As elevation measurement error variance, wherein,
According to the result of (formula 14), the angle variance calculated between the estimate and actual value in the ripple direction to be measured is
WhereinIt is the variance of phase difference measurement error, α0It is the azimuthal theoretical value in ripple direction to be measured, β0It is ripple to be measured The theoretical value of the direction angle of pitch, willIt is used as the angle measurement error between the estimate and actual value in the ripple direction to be measured
In one embodiment of the invention, synchronously calculate what other three array elements referred to relative to the phase difference of the first array element Be at a time (or certain time period) while measure A2-A1, A3-A1, one group of phase difference in tri- groups of baselines of A4-A1, In other words, as tri- groups of phase differences of parallel computation A2-A1, A3-A1, A4-A1 in computer programming language.It is synchronous to calculate battle array Phase difference between member, compared to the mode that timesharing calculates the phase difference between array element, improves direction finding precision.In synchro measure phase In the process of difference, it is assumed thatCovariance matrix be：
In (formula 16),For the variance of phase difference measurement error.According to formula (formula 10) and (formula 16), have：
In (formula 17),
Wherein cα=cos α, cγ=cos γ, sα=sin α, sγ=sin γ.
NoteThen have：
In (formula 18),
According to the result of formula (formula 18), the angle variance between the estimate and actual value in the ripple direction to be measured is calculated For
WhereinIt is the variance of phase difference measurement error, α0It is the azimuthal theoretical value in ripple direction to be measured, β0It is ripple to be measured The theoretical value of the direction angle of pitch, willAs the angle measurement error between the estimate and actual value in the ripple direction to be measured,
It is that phase difference is surveyed Measure the variance of error.
S24, array configuration iteration optimization
S241, direction finding result are obtained
Due in radiation source direction of arrival measurement process, it is understood that there may be the undesirable situation of array configuration, therefore can base In the estimated result of radiation source direction of arrivalGuiding improves anglec of rotation γk, and then obtain the radiation source ripple that measures next time and reach The estimated result in directionWhereinγkRespectively kth time radiation source Mutual coupling result is adjusted with array element A4 kth time The anglec of rotation after whole, k=1,2,3 ....In addition, defining γ0, generally can be according to interested for array element A4 initial rotation angle Roughly chosen by the direction finding precision height of relatively more several conventional anglecs of rotation in azimuth pitch region.According to formula (5), there is K times radiation source Mutual coupling result is：
In formula (5),The phase difference matrix obtained for kth time measurement, and have： For kth time measurement Measurement error matrix.Based on formula (16), it can be asked for using its equivalence transformation form
Based on (formula 21), can be asked for using grid data service so thatAll Value on possible θ, and selection makes its maximum θ conductWherein θ=(α, β)T, α=αL,αL+Δα,...,αU, β=βL, βL+Δβ,...,βU, αL、αURespectively the lower limit and higher limit in orientation, β are searched in azimuthL、βURespectively the angle of pitch searches scope Lower limit and higher limit, Δ α, Δ β be respectively azimuth and the angle of pitch search sizing grid, should be generally less than direction finding precision will Ask.
Try to achieveAfterwards, willAs input condition, further optimization ask for so thatNeighbouring direction finding precision highest rotation Gyration γk, i.e.,：
(formula 22)
Based on (formula 22), all possible anglec of rotation γ is chosen, chooses and causes formulaMinimum γ is γkAnd array configuration is adjusted with this, then asked for according to (formula 20)Continuous iteration according to this.
S242, judge whether direction finding result meets stopping iterated conditional
In application process, then stop above-mentioned iterative process when meeting certain condition and determine the final anglec of rotation with Mutual coupling result.Here following optimization stop conditions are used：
k≥NsOr γk+1-γk≤ Δ γ (formula 23)
I.e. iterations is more than the difference of N (N >=2) and/or the front and rear angle for requiring array element A4 rotations twice less than achievable Rotation stepping Δ γ.If being judged as YES, step S243 is performed；If being judged as NO, step S244 is performed.
It should be noted that in actual applications, iteration optimization condition can will be stopped according to actual test accuracy requirement Iterations only be could be arranged to more than N, or iteration optimization condition only be could be arranged into N rotation angle values and N-1 Whether the difference of the anglec of rotation is less than anglec of rotation preset value, or it is that iterations should that will stop iteration optimization condition setting Whether the difference more than N N rotation angle values and the N-1 anglecs of rotation again is less than anglec of rotation preset value.
If S243, judging that direction finding result is met and stopping iterated conditional, it is determined that final array configuration and radiated wave ripple are up to side To estimated result.
If S244, judging that direction finding result does not meet stopping iterated conditional, repeat step S241, the rotation to the 4th array element Angle continues iteration, that is, continues iteration and obtain the N+1 anglecs of rotation.
Embodiment two
Fig. 4 is a kind of structural representation of the array element solid array device of optimization four of one embodiment of the invention, such as Fig. 4 institutes Show,
Described device includes memory 320 and processor 310, passes through between the memory 320 and the processor 310 The communication connection of internal bus 330, the memory 320 is stored with can be described by the computer program of the computing device Computer program can realize following steps when being performed by the processor 310：
By arbitrarily one initial angle of rotation of the three-dimensional cartesian coordinate system where traditional three array element planar array, a non-co- is added 4th array element in face, the array element solid array of Primary Construction four, and four array element solid arrays based on structure obtain direction finding model and Angle measurement error；
According to the initial rotation angle of the 4th array element and the direction finding model, the first estimation of radiation source direction of arrival is obtained Value；
According to the first estimate and the angle measurement error of the radiation source direction of arrival, when obtaining angle measurement error minimum value First anglec of rotation of corresponding 4th array element；
First anglec of rotation, the direction finding model and the angle measurement error iteration further according to the 4th array element obtain the 4th gust The N rotation angle values of member, N >=2；
Judge whether the difference of N rotation angle values and the N-1 anglecs of rotation is less than angle difference preset value and/or iteration Whether times N is more than iterations preset value；If so, then stopping iteration, final four gusts are built according to the N anglecs of rotation First solid array；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.
In one embodiment of the invention, the direction finding model of the four array element solid arrays acquisition based on structure is：
According to formulaCalculate the estimate of radiation source direction of arrival；
Wherein, the transposition of T representing matrixs, Σ is positive definite matrix, and θ is ripple direction vector to be measured, and It is to treat The estimate of ripple direction vector is surveyed, andIt is azimuthal estimate in ripple direction to be measured,It is ripple side to be measured To the angle of pitch estimate；
It is phase difference measurement value matrix；
It is that phase difference is theoretical Value matrix；
It is phase difference measurement error matrix, and it is that 0, covariance matrix is Σ to obey average Multi-dimension Normal distribution；
The angle measurement error that four array element solid arrays based on structure are obtained is：
According to formulaCalculate the angle between the estimate and actual value in the ripple direction to be measured VarianceWhereinIt is the variance of phase difference measurement error, α0It is the azimuthal theoretical value in ripple direction to be measured, β0It is ripple to be measured The theoretical value of the direction angle of pitch, willIt is used as the angle measurement error between the estimate and actual value in the ripple direction to be measured.
In one embodiment of the invention, the initial rotation angle and the direction finding model according to the 4th array element, Obtaining the first estimate of radiation source direction of arrival includes：
Direction finding model progress equivalence transformation is obtained into formula：
The initial rotation angle of 4th array element is substituted into above-mentioned formula, calculated using grid data serviceThe corresponding radiation source direction of arrival of maximum estimateBy the estimateIt is used as the first estimate of radiation source direction of arrival.
In one embodiment of the invention, first estimate according to the radiation source direction of arrival and the survey To error, first anglec of rotation of corresponding 4th array element includes when obtaining angle measurement error minimum value：
WillSubstitute into the angle measurement error
According to formulaFirst rotation angle value is calculated, wherein, γkFor institute State the first rotation angle value, β0It is the theoretical value of the ripple direction to be measured angle of pitch,It is the azimuth measurement error in ripple direction to be measured Variance,It is the elevation measurement error variance in ripple direction to be measured.
In one embodiment of the invention, what memory 320 was stored is computer program.The computer program is by institute The method and step shown in Fig. 1 can be realized by stating when processor 310 is performed.
In various embodiments, memory 320 can be internal memory or nonvolatile memory.It is wherein non-volatile to deposit Reservoir can be：Memory driver (such as hard disk drive), solid state hard disc, any kind of storage dish (such as CD, DVD), Either similar storage medium or combinations thereof.Internal memory can be：RAM (Radom Access Memory, arbitrary access Memory), volatile memory, nonvolatile memory, flash memory.Further, nonvolatile memory and internal memory can as machine Storage medium is read, the computer program 321 of the array element solid array of optimization four performed by processor 310 can be stored thereon.
It should be noted that in the present embodiment it is claimed optimization four array element solid arrays device 300 it is worked Journey realizes that step is corresponding identical with each embodiment of the method shown in Fig. 1, and identical part is repeated no more.
Embodiment three
In order to which the realization for the method and step for preferably demonstrating the three-dimensional right angle battle array of rotatable four array element of above-mentioned 4th array element is imitated Really, a specific example is named to be shown.
As described above, measurement mechanism can also be same using phase difference when technical scheme can use phase difference Measurement mechanism is walked, in the present embodiment using Instrumentation system during phase difference, it is assumed that the 4th array element A4 initial rotation angle γ= 135 ° and phase difference between channels measurement error is 5 °.4th array element A4 initial rotation angle is not rotated as the 4th array element A4 Situation (γ=135 ° array configuration is determined using the 4th array element A4 initial rotation angle).Fig. 5 is one implementation of the present invention Example when γ=120 °, four array elements solid right angle battle array direction finding precision contour schematic diagram；From figure 5 it can be seen that working as During γ=120 °, the smaller 35 ° of direction finding precisions to 50 ° of regions in elevation angle region are (4.2,4.9)；When γ=135 °, four array elements The schematic diagram of the direction finding precision contour of three-dimensional right angle battle array is as shown in Figure 6.From fig. 6 it can be seen that when γ=135 °, it is smaller The 35 ° of direction finding precisions to 50 ° of regions in elevation angle region are (4.2,5.4)；By comparative analysis Fig. 4 and Fig. 5, when γ=120 ° When four array element three-dimensional arrays, four array elements when the smaller 35 ° of direction finding precisions to 50 ° of regions in elevation angle region are higher than when γ=135 ° it is three-dimensional Battle array is in the smaller 35 ° of direction finding precisions to 50 ° of regions in elevation angle region, that is to say, that the different anglecs of rotation is to different azimuth pitching area Be present considerable influence in the direction finding precision in domain, it is therefore necessary to changed in application process according to the estimated result of radiation source direction of arrival In generation, optimizes the anglec of rotation to obtain higher direction finding precision.
Fig. 7 is that the utilization grid data service of one embodiment of the invention calculates the signal of radiation source Mutual coupling value Figure, as shown in fig. 7, in the range of the angle of pitch (0 °~90 °), azimuth (0 °~180 °), meeting by orientation, the angle of pitch Even distribution has randomly selected 1000 samples.In present case, selection grid stepping Δ α=Δ β=1 ° carries out grid search, from figure 7 is visible, the short baseline case considered for this patent, and radiation source ripple can be preferably estimated using formula (formula 21) described algorithm Up to direction.
Fig. 8 is that the iteration of one embodiment of the invention obtains the corresponding relation of the 4th array element anglec of rotation and angle measurement error Figure.In the present embodiment, selection anglec of rotation preset value Δ γ=1 °, iteration optimization times Ns=5.Fig. 8 shows the 4th gust When member rotates different angles, corresponding direction finding precision, as seen from Figure 8, anglec of rotation γ=128 ° correspondence highest direction finding precision, Therefore result of calculation adjusts the 4th array element A4 anglec of rotation according to this, that is to say, that, can when γ=128 ° four array element three-dimensional arrays of structure So that direction finding precision reaches most preferably.Finally, all final estimation orientation vectors of sample and the angle of its actual orientation vector are counted, The angle measurement error average for the direction-finding system that this patent proposes is used for 4.23 °, and use array element A4 initial rotation angle determine it is solid The direction-finding system angle measurement error average for determining array configuration is 5.02 °, demonstrates the direction-finding system of this patent proposition in lifting direction finding The validity of precision aspect.
In summary, technical scheme, by by the three-dimensional cartesian coordinate system where traditional three array element planar array One initial angle of any rotation, adds non-coplanar 4th array element, the array element solid array of Primary Construction four, and is based on building Four array element solid arrays obtain direction finding model and angle measurement error；According to the initial rotation angle of the 4th array element and the direction finding mould Type, obtains the first estimate of radiation source direction of arrival；According to the first estimate of the radiation source direction of arrival and the survey To error, first anglec of rotation of corresponding 4th array element when obtaining angle measurement error minimum value；Further according to the first of the 4th array element The anglec of rotation, the direction finding model and the angle measurement error iteration obtain the N rotation angle values of the 4th array element, N >=2；Judge The difference of N rotation angle values and the N-1 anglecs of rotation whether is less than angle difference preset value and/or whether iterations N is big In iterations preset value；If so, then stopping iteration, four final array element solid arrays are built according to the N anglecs of rotation； If it is not, then continuing iteration obtains the N+1 anglecs of rotation.The four array element solid arrays finally built using the present invention, can both be protected Card can also be lifted at the direction finding precision compared with flat attitude region, meet ripple direction to be measured in larger elevation angle region direction finding precision Expecting the direction finding precision of pitching angular zone.In addition, in the case of radiation source direction of arrival is uncertain, radiation source can be based on The anglec of rotation of the estimated result iteration optimization part array element of direction of arrival, radiation source direction of arrival can be lifted to greatest extent Estimated accuracy.
It the above is only presently preferred embodiments of the present invention, be not intended to limit the scope of the present invention.It is all in this hair Any modification, equivalent substitution and improvements made within bright spirit and principle etc., are all contained in protection scope of the present invention.

Claims (8)

1. a kind of method for building four array element solid arrays, it is characterised in that methods described includes：
By arbitrarily one initial angle of rotation of the three-dimensional cartesian coordinate system where traditional three array element planar array, addition one is non-coplanar 4th array element, the array element solid array of Primary Construction four, and the four array element solid arrays based on structure obtain direction finding model and direction finding Error；
According to the initial rotation angle of the 4th array element and the direction finding model, the first estimate of radiation source direction of arrival is obtained；
According to the first estimate and the angle measurement error of the radiation source direction of arrival, correspondence when obtaining angle measurement error minimum value The 4th array element first anglec of rotation；
First anglec of rotation, the direction finding model and the angle measurement error iteration further according to the 4th array element obtain the 4th array element N rotation angle values, N >=2；
Judge whether the difference of N rotation angle values and the N-1 anglecs of rotation is less than angle difference preset value and/or iterations Whether N is more than iterations preset value；If so, then stopping iteration, building four final array elements according to the N anglecs of rotation stands Volume array；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.
2. the method as described in claim 1, it is characterised in that
The direction finding model that four array element solid arrays based on structure are obtained is：
According to formulaCalculate the estimate of radiation source direction of arrival；
Wherein, the transposition of T representing matrixs, Σ is positive definite matrix, and θ is ripple direction vector to be measured, and θ=(α, β)；It is ripple to be measured The estimate of direction vector, and It is azimuthal estimate in ripple direction to be measured,It is bowing for ripple direction to be measured The estimate at the elevation angle；
It is phase difference measurement value matrix；
It is phase difference theoretical value square Battle array；
Phase difference measurement error matrix, and obey average be 0, covariance matrix be Σ height Tie up normal distribution；
The angle measurement error that four array element solid arrays based on structure are obtained is：
According to formulaCalculate the angle variance between the estimate and actual value in the ripple direction to be measuredWhereinIt is the variance of phase difference measurement error, α0It is the azimuthal theoretical value in ripple direction to be measured, β0It is ripple direction to be measured The theoretical value of the angle of pitch, willIt is used as the angle measurement error between the estimate and actual value in the ripple direction to be measured.
3. method as claimed in claim 2, it is characterised in that the initial rotation angle according to the 4th array element and the survey To model, obtaining the first estimate of radiation source direction of arrival includes：
Direction finding model progress equivalence transformation is obtained into formula：
The initial rotation angle of 4th array element is substituted into above-mentioned formula, calculated using grid data service The corresponding radiation source direction of arrival of maximum estimateBy the estimateIt is used as the of radiation source direction of arrival One estimate.
4. method as claimed in claim 3, it is characterised in that first estimate according to the radiation source direction of arrival With the angle measurement error, first anglec of rotation of corresponding 4th array element includes when obtaining angle measurement error minimum value：
WillSubstitute into the angle measurement error
According to formulaFirst rotation angle value is calculated, wherein, γkFor described One rotation angle value, β0It is the theoretical value of the ripple direction to be measured angle of pitch,It is the azimuth measurement error variance in ripple direction to be measured,It is the elevation measurement error variance in ripple direction to be measured.
5. a kind of device for building four array element solid arrays, it is characterised in that described device includes memory and processor, described Communicated and connected by internal bus between memory and the processor, the memory storage, which has, to be held by the processor Capable computer program, the computer program can be realized following steps during the computing device：
By arbitrarily one initial angle of rotation of the three-dimensional cartesian coordinate system where traditional three array element planar array, addition one is non-coplanar 4th array element, the array element solid array of Primary Construction four, and the four array element solid arrays based on structure obtain direction finding model and direction finding Error；
According to the initial rotation angle of the 4th array element and the direction finding model, the first estimate of radiation source direction of arrival is obtained；
According to the first estimate and the angle measurement error of the radiation source direction of arrival, correspondence when obtaining angle measurement error minimum value The 4th array element first anglec of rotation；
First anglec of rotation, the direction finding model and the angle measurement error iteration further according to the 4th array element obtain the 4th array element N rotation angle values, N >=2；
Judge whether the difference of N rotation angle values and the N-1 anglecs of rotation is less than angle difference preset value and/or iterations Whether N is more than iterations preset value；If so, then stopping iteration, building four final array elements according to the N anglecs of rotation stands Volume array；If it is not, then continuing iteration obtains the N+1 anglecs of rotation.
6. device as claimed in claim 5, it is characterised in that the direction finding model that the four array element solid arrays based on structure are obtained For：
According to formulaCalculate the estimate of radiation source direction of arrival；
Wherein, the transposition of T representing matrixs, Σ is positive definite matrix, and θ is ripple direction vector to be measured, and θ=(α, β)；It is ripple to be measured The estimate of direction vector, and It is azimuthal estimate in ripple direction to be measured,It is bowing for ripple direction to be measured The estimate at the elevation angle；
It is phase difference measurement value matrix；
It is the theoretical value matrix of phase difference；
Phase difference measurement error matrix, and obey average be 0, covariance matrix be Σ height Tie up normal distribution；
The angle measurement error that four array element solid arrays based on structure are obtained is：
According to formulaCalculate the angle variance between the estimate and actual value in the ripple direction to be measuredWhereinIt is the variance of phase difference measurement error, α0It is the azimuthal theoretical value in ripple direction to be measured, β0It is ripple direction to be measured The theoretical value of the angle of pitch, willIt is used as the angle measurement error between the estimate and actual value in the ripple direction to be measured.
7. device as claimed in claim 6, it is characterised in that the initial rotation angle according to the 4th array element and the survey To model, obtaining the first estimate of radiation source direction of arrival includes：
Direction finding model progress equivalence transformation is obtained into formula：
The initial rotation angle of 4th array element is substituted into above-mentioned formula, calculated using grid data service The corresponding radiation source direction of arrival of maximum estimateBy the estimateIt is used as the of radiation source direction of arrival One estimate.
8. device as claimed in claim 7, it is characterised in that first estimate according to the radiation source direction of arrival With the angle measurement error, first anglec of rotation of corresponding 4th array element includes when obtaining angle measurement error minimum value：
WillSubstitute into the angle measurement error
According to formulaFirst rotation angle value is calculated, wherein, γkFor described One rotation angle value, β0It is the theoretical value of the ripple direction to be measured angle of pitch,It is the azimuth measurement error variance in ripple direction to be measured,It is the elevation measurement error variance in ripple direction to be measured.
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CN109959892A (en) * 2019-04-11 2019-07-02 中国电子科技集团公司第三十六研究所 A kind of uniform circular array two-channel interferometer direction-finding method, device and system
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CN110487282B (en) * 2019-09-11 2021-04-06 中国电子科技集团公司第三研究所 Time delay estimation correction method and system for improving baseline positioning robustness
CN111487581A (en) * 2020-04-20 2020-08-04 中国人民解放军军事科学院国防科技创新研究院 Broadband lightning VHF radiation source direction finding method based on rudder vector pattern matching
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