CN107144813B - Method and device for constructing four-array-element three-dimensional array - Google Patents
Method and device for constructing four-array-element three-dimensional array Download PDFInfo
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- G01S3/48—Systems for determining direction or deviation from predetermined direction using antennas spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems the waves arriving at the antennas being continuous or intermittent and the phase difference of signals derived therefrom being measured
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Abstract
The invention discloses a method and a system for constructing a four-array-element three-dimensional array. The method comprises the following steps: rotating a three-dimensional rectangular coordinate system where a traditional three-array element planar array is located by an angle at will, adding a non-coplanar fourth array element, and constructing a preliminary four-array element three-dimensional array; synchronously calculating the phase difference of other three array elements relative to the first array element; constructing a direction-finding model according to the calculated phase differences of the other three array elements relative to the first array element; calculating a direction finding error between an estimated value and an actual value of the direction of the wave to be measured by using a direction finding model; selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing the final four-array element three-dimensional array according to the optimal rotation angle. The four-array element stereo array constructed by the invention can improve the direction-finding precision in a smaller pitch angle area.
Description
Technical Field
The invention relates to the technical field of array antenna direction finding, in particular to a method and a device for constructing a four-array-element three-dimensional array.
Background
The array antenna direction-finding system is an important passive direction-finding device, has the advantages of interception resistance, interference resistance and the like, and also has the advantages of high direction-finding precision, small volume and weight, low cost and the like compared with an actively working radar system, is valued in recent years, and is applied to satellite-borne equipment for many times. Currently, most common direction-finding array antennas are planar arrays, namely, a plurality of array elements are in the same plane. In the application process, the planar array can obtain ideal direction-finding accuracy in the normal area of the wavefront (usually, the position of the satellite subsatellite point), but the direction-finding accuracy is reduced remarkably in the area (usually, the area with smaller pitch angle) far away from the normal azimuth of the wavefront. However, in some specific scenarios, in addition to the desire for higher direction finding accuracy of the normal position of the wavefront, it is still desirable to have higher direction finding accuracy in regions that are further from the normal orientation to meet the application requirements.
Under the condition that the direction of arrival of a radiation source is determined, in order to meet the requirement of direction finding precision in a smaller pitch angle area, the common practice is to offset a wavefront, increase the size of an array element, increase the length of a base line and the like. The wavefront offset is to rotate the installation plane of the wavefront by a certain angle to meet the application requirement, but this is done at the expense of the direction finding precision of the normal region of the original wavefront. The essence of enlarging the array elements is that the signal to noise ratio of received signals is improved, the phase difference direction finding precision is improved so as to improve the direction finding precision of each area, but the problem that the size of the array elements is originally large exists in the direction finding arrays of some low frequency bands, and the further enlargement of the size of the array elements brings more pressure to the installation and layout of the array elements. Increasing the length of the base line will also help to improve the direction-finding accuracy of each area, but will undoubtedly bring about the problem of direction-finding ambiguity.
In addition, although the existing time-sharing phase difference measurement method can save the computing resources of the system, the direction finding precision is not high because the direction finding cannot be carried out in real time.
Disclosure of Invention
The invention provides a method and a device for constructing a four-array-element three-dimensional array, which are used for solving the problems that the direction-finding precision of a smaller pitch angle area in the existing array antenna direction-finding system is low and the direction-finding precision is not high due to the fact that the time-sharing measurement phase difference cannot be measured in real time under the condition that the arrival direction of a radiation source is determined.
According to an aspect of the present invention, there is provided a method of constructing a four-element volumetric array, the method comprising: randomly rotating a three-dimensional rectangular coordinate system in which a traditional three-array element planar array is positioned by an angle, adding a non-coplanar fourth array element, and constructing a preliminary four-array element three-dimensional array, wherein the first array element is the origin of the three-dimensional rectangular coordinate system;
synchronously calculating phase differences of other three array elements relative to the first array element based on the preliminary four-array element stereo array;
constructing a direction-finding model according to the calculated phase differences of the other three array elements relative to the first array element;
calculating the direction-finding error between the estimated value and the actual value of the direction of the wave to be measured by using the direction-finding model;
selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing the final four-array element three-dimensional array according to the optimal rotation angle.
According to another aspect of the present invention, there is provided an apparatus for constructing a four-element stereoscopic array, the apparatus comprising:
the three-dimensional array initial construction unit is used for rotating a traditional three-array element planar array by an angle at will, adding a non-coplanar fourth array element and constructing an initial four-array element three-dimensional array, wherein the first array element is the origin of the three-dimensional rectangular coordinate system;
the phase difference calculation unit is used for synchronously calculating the phase difference of other three array elements relative to the first array element based on the preliminary four-array element stereo array;
the direction-finding model building unit is used for building a direction-finding model according to the calculated phase differences of the other three array elements relative to the first array element;
the direction-finding error calculation unit is used for calculating a direction-finding error between an estimated value and an actual value of the direction of the wave to be measured by using the direction-finding model;
and the three-dimensional array final construction unit is used for selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing the final four-array element three-dimensional array according to the optimal rotation angle.
The invention has the beneficial effects that: according to the technical scheme, a three-dimensional rectangular coordinate system where a traditional three-array element planar array is located is rotated by an angle at will, a non-coplanar fourth array element is added to construct a preliminary four-array element three-dimensional array, the phase differences of other three array elements relative to the first array element are synchronously calculated based on the preliminary four-array element three-dimensional array, a direction-finding model is constructed according to the calculated phase differences, and a direction-finding error between an estimated value and an actual value of the direction of a wave to be measured is calculated by using the direction-finding model; then, by selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding accuracy of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding accuracy obtained by calculation as the optimal rotation angle, and constructing a final four-array-element three-dimensional array according to the optimal rotation angle. In addition, the method adopts a mode of synchronously calculating the phase difference between the array elements, and improves the direction finding precision compared with a mode of calculating the phase difference between the array elements in a time-sharing mode.
Drawings
FIG. 1 is a flow chart of a method of constructing a four-element volumetric array in accordance with one embodiment of the present invention;
FIG. 2 is a schematic diagram of a four-array element three-dimensional rectangular array coordinate system according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of an apparatus for constructing a four-array element three-dimensional array according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a direction-finding accuracy contour line of a four-element cubic rectangular array when γ is 45 ° according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a direction-finding accuracy contour line of a four-element solid rectangular array when γ is 60 ° according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a direction-finding accuracy contour line of a four-element cubic rectangular array when γ is 120 ° according to an embodiment of the present invention;
fig. 7 is a schematic diagram of a direction-finding accuracy contour line of a four-element cubic rectangular array when γ is 135 ° according to an embodiment of the present invention;
FIG. 8 is a schematic diagram of the direction-finding accuracy contour line of a three-array element planar L-shaped rectangular array for synchronously measuring phase differences according to an embodiment of the invention;
fig. 9 is a schematic diagram of a contour line of a direction-finding accuracy ratio of a four-array element stereoscopic rectangular array (γ is 120 °) and a three-array element planar L-shaped rectangular array for synchronously measuring phase differences according to an embodiment of the present invention;
fig. 10 is a schematic diagram of a contour line of a direction-finding accuracy ratio of a four-array-element stereoscopic rectangular array (γ is 120 °) and a three-array-element planar L-shaped rectangular array for time-sharing phase difference measurement according to an embodiment of the present invention.
Detailed Description
The design concept of the invention is as follows: under the condition that the direction-finding precision of a large elevation angle area of the planar array is not reduced, the direction-finding precision of a small expected elevation angle area is improved, a three-dimensional rectangular coordinate system where the traditional three-array element planar array is located is rotated by an angle, a non-coplanar fourth array element is added, and a preliminary four-array element three-dimensional array is constructed; synchronously calculating phase differences of other three array elements relative to the same array element based on a primary four-array-element stereo array; constructing a direction-finding model according to the three phase differences obtained by calculation; calculating a direction finding error between an estimated value and an actual value of the direction of the wave to be measured by using a direction finding model; selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing the final four-array element three-dimensional array according to the optimal rotation angle.
Example one
Fig. 1 is a flow chart of a method of constructing a four-element volumetric array according to an embodiment of the present invention, as shown in fig. 1,
in step S110, a three-dimensional rectangular coordinate system in which a conventional three-array element planar array is located is rotated by an angle at will, a non-coplanar fourth array element is added, and a preliminary four-array element stereo array is constructed, where the first array element is an origin of the three-dimensional rectangular coordinate system.
In step S120, phase differences of the other three array elements with respect to the first array element are calculated based on the preliminary four-array element stereo array synchronization.
In step S130, a direction-finding model is constructed according to the calculated phase differences of the other three array elements relative to the first array element.
In step S140, a direction-finding error between the estimated value and the actual value of the direction of the wave to be measured is calculated by using the direction-finding model.
In step S150, a plurality of fourth array elements with different rotation angles are selected, the direction-finding accuracy of the direction of the wave to be measured in the desired pitch angle region is calculated according to the direction-finding error, the rotation angle corresponding to the highest direction-finding accuracy obtained by calculation is determined as the optimal rotation angle, and the final four-array element stereo array is constructed according to the optimal rotation angle.
Therefore, according to the technical scheme, a three-dimensional rectangular coordinate system where a traditional three-array element planar array is located is rotated by an angle at will, a non-coplanar fourth array element is added to construct a preliminary four-array element three-dimensional array, the phase differences of other three array elements relative to the first array element are synchronously calculated based on the preliminary four-array element three-dimensional array, a direction-finding model is constructed according to the calculated phase differences, and a direction-finding error between an estimated value and an actual value of the direction of a wave to be measured is calculated by using the direction-finding model; and then selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing a final four-array-element three-dimensional array according to the optimal rotation angle. In addition, the method adopts a mode of synchronously calculating the phase difference between the array elements, and improves the direction finding precision compared with a mode of calculating the phase difference between the array elements in a time-sharing mode.
In order to make the solution of the present invention clearer, the following explanation is given with a specific example. In one embodiment of the present invention,
(one) creating a coordinate system
Fig. 2 is a schematic diagram of a four-array element stereoscopic rectangular matrix coordinate system according to an embodiment of the present invention, as shown in fig. 2, xyz is a coordinate system of a conventional planar L-type three-array element rectangular matrix, in which three array elements of the rectangular matrix are respectively arranged at an origin O (a1), an X axis (a2), a Y axis (A3), and a length of a base line of the array is d (it should be noted that, in this embodiment, the length of the base line of the array refers to a distance between other three array elements and a first array element).
(II) phase difference calculation
In the three-dimensional array coordinate system constructed in fig. 2, based on the array element a1, a case where the base length is smaller than a half wavelength is generally considered (it should be noted that if the base length is larger than a half wavelength, direction-finding ambiguity will be caused), and then the phase difference Φ between the array elements a2 and a1 is then considered21Comprises the following steps:
in the formula 1, lambda is the wavelength in the direction of the wave to be measured, d is the length of the array base line, and delta phi21The difference between the phase difference measurement errors between array element a2 and a1 channel. On the other hand, the phase difference phi between array elements A3 and A131Comprises the following steps:
in (equation 2), Δ φ31The difference between the phase difference measurement errors between array element A3 and a1 channel. In addition, the phase difference phi between array elements A4 and A141Comprises the following steps:
in (equation 3), Δ φ41The difference between the phase difference measurement errors between array element a4 and a1 channel.
The (formula 1) - (formula 3) are expressed as a matrix:
in the case of (equation 4), the reaction,is a matrix of the measured values and,is a matrix of theoretical values, and is,
the error matrix is measured and obeys a high-dimensional normal distribution with mean 0 and covariance matrix Σ, where Σ is a positive definite matrix.
(III) constructing a direction-finding model
The least square method processing is carried out on the phase difference measurement value matrix (formula 4), and the direction-finding model is obtained as follows:
in the formula (5), T represents a transpose of a matrix, Σ is a positive definite matrix, θ is a measured wave direction vector, and θ is (α);
is an estimate of the direction vector of the wave to be measured, and 
is an estimate of the azimuth of the direction of the wave to be measured,
is the estimated value of the pitch angle of the direction of the wave to be measured.
(IV) Direction finding error derivation
For estimating the direction of arrival of the radiation source estimated by (equation 5)The accuracy of (equation 5) based direction-finding algorithm should be given to the resulting direction-finding error. For convenience of subsequent description, note:
is provided with
If it isThen at theta0To
Take a minimum value, thereby
In the same way, if
Namely, it is
And is
Then
When in use
When the ratio of the water to the oil is small,
at theta0Nearby, can be represented as
Ignoring high order errors, there are:
due to the fact that
According to (equation 7) there are:
for the left side of the equation (equation 8), the direct calculation can be found:
thus, there are:
in the (formula 10), the first step is,
for the left side of the equation (equation 8), the direct calculation can be found:
in addition, (equation 10) directly calculate
Therefore, it is not only easy to useLine full rank, taking into account ∑-1Is also a positive definite matrix, therefore
It is reversible. Then according to equation (8):
(equation 12), cov (Δ θ) refers to the covariance matrix of Δ θ.
In one embodiment of the present invention, synchronously calculating the phase differences of the other three array elements with respect to the first array element means that the phase differences of one of the three baselines A2-A1, A3-A1 and A4-A1 are measured simultaneously at a certain time (or a certain time period), in other words, the phase differences of three groups A2-A1, A3-A1 and A4-A1 are calculated in parallel in a computer programming language. Compared with a mode of calculating the phase difference among the array elements in a time-sharing mode, the method has the advantage that the direction finding precision is improved. In the process of synchronously measuring the phase difference, it is assumed that
The covariance matrix of (a) is:
in the case of (equation 13), the,
is a phase ofVariance of the difference measurement error. According to the equations (equation 10) and (equation 13), there are:
in the case of (equation 14), the,
wherein C isα＝cosα0，Cγ＝cosγ0，Sα＝sinα0，Sγ＝sinγ0。
Note the bookThen there are:
in the (formula 15), the first step is,
according to the result of the formula (formula 15), calculating the variance of the included angle between the estimated value and the actual value of the direction of the wave to be measured to be
Wherein
Is the variance of the phase difference measurement error, α0Is the theoretical value of the azimuth angle of the direction of the wave to be measured, β0Is a theoretical value of the pitch angle of the direction of the wave to be measured, and will
As a direction-finding error between the estimated value and the actual value of the direction of the wave to be measured,
(V) construction of four-array element stereo direction-finding array
As can be seen from equation 16, for a given rotation angle γ, direction-finding errors can be calculated at different azimuth angles α and different pitch angles β
That is, each rotation angle γ corresponds to the direction finding accuracy of a set of pitch angle regions.
According to actual application requirements, selecting a plurality of fourth array elements with different rotation angles, respectively and correspondingly calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error (formula 16), determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing a four-array-element three-dimensional array according to the optimal rotation angle. That is, the final three-dimensional array configuration can be determined by selecting a plurality of rotation gamma angles of the array element A4 meeting the application requirements and observing the direction-finding precision of the array element in the interested area.
Example two
Fig. 3 is a schematic structural diagram of an apparatus for constructing a four-array element stereo array according to an embodiment of the present invention, as shown in fig. 3, the apparatus includes:
a three-dimensional array preliminary construction unit 210, configured to rotate a conventional three-array element planar array by an arbitrary angle, add a non-coplanar fourth array element, and construct a preliminary four-array element three-dimensional array, where a first array element is an origin of the three-dimensional rectangular coordinate system;
and a phase difference calculating unit 220, configured to calculate phase differences of the other three array elements with respect to the first array element based on the preliminary four-array element stereo array synchronization.
A direction-finding model constructing unit 230, configured to construct a direction-finding model according to the calculated phase differences of the other three array elements with respect to the first array element;
a direction-finding error calculation unit 240, configured to calculate a direction-finding error between an estimated value and an actual value of a direction of a wave to be measured by using the direction-finding model;
and the three-dimensional array final construction unit 250 is configured to select fourth array elements of a plurality of different rotation angles, calculate direction-finding accuracies of the direction of the wave to be measured in the expected pitch angle region according to the direction-finding errors, determine a rotation angle corresponding to the highest direction-finding accuracy obtained through calculation as an optimal rotation angle, and construct a final four-array element three-dimensional array according to the optimal rotation angle.
Therefore, according to the technical scheme, a three-dimensional rectangular coordinate system where a traditional three-array element planar array is located is rotated by an angle at will, a non-coplanar fourth array element is added to construct a preliminary four-array element three-dimensional array, the phase differences of other three array elements relative to the first array element are synchronously calculated based on the preliminary four-array element three-dimensional array, a direction-finding model is constructed according to the calculated phase differences, and a direction-finding error between an estimated value and an actual value of the direction of a wave to be measured is calculated by using the direction-finding model; then, by selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding accuracy of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding accuracy obtained by calculation as the optimal rotation angle, and constructing a final four-array-element three-dimensional array according to the optimal rotation angle. In addition, the method adopts a mode of synchronously calculating the phase difference between the array elements, and improves the direction finding precision compared with a mode of calculating the phase difference between the array elements in a time-sharing mode.
In an embodiment of the present invention, the stereoscopic array preliminary construction unit 210 is configured to rotate a three-dimensional rectangular coordinate system oyx in which a conventional three-array element planar array is located by a certain angle around an X axis in a forward direction to obtain a three-dimensional rectangular coordinate system O ' X ' Y ' Z ', add the fourth array element on the Y ' axis, where the second array element is located on the X axis, the third array element is located on the Y axis, and the lengths of the second array element, the third array element, and the fourth array element are equal to the length of the base line of the first array element, respectively.
In an embodiment of the present invention, the phase difference calculating unit 220 is configured to calculate the phase difference according to a formulaCalculating the phase difference between the second array element and the first array element;
according to the formula
Calculating the phase difference between the third array element and the first array element;
according to the formula
Calculating the phase difference between the fourth array element and the first array element;
wherein d is the length of the second array element, the third array element and the fourth array element respectively relative to the base line of the first array element, λ is the wavelength in the direction of the wave to be measured, β is the pitch angle in the direction of the wave to be measured, α is the azimuth angle in the direction of the wave to be measured, γ is the rotation angle of the fourth array element relative to the three-dimensional rectangular coordinate system, and Δ φ21Is the difference, Δ, in the phase difference measurement error between the second array element and the first array elementφ31Is the difference between the phase difference measurement errors between the third array element and the first array element, delta phi41Is the difference between the phase difference measurement errors between the fourth array element and the first array element.
In an embodiment of the present invention, the direction-finding model constructing unit 230 is configured to construct a direction-finding model according to a formula
Converting the phase difference of the second array element, the third array element and the fourth array element relative to the first array element into a phase difference measurement value matrix;
performing least square method processing on the phase difference measurement value matrix to obtain a direction finding model
Where T denotes the transpose of the matrix, Σ is a positive definite matrix, θ is the wave direction vector to be measured, and θ is (α)T；
Is an estimate of the direction vector of the wave to be measured, and
is an estimate of the azimuth of the direction of the wave to be measured,
is an estimated value of the pitch angle of the wave direction to be measured;
is a phase difference theoretical value matrix;
In an embodiment of the present invention, the direction-finding error calculating unit 240 is configured to calculate an included angle between an estimated value and a theoretical value of a direction of a wave to be measured according to the direction-finding model and the phase difference measurement error matrix;
calculating a covariance matrix of an included angle between the estimated value and the theoretical value of the direction of the wave to be measured to obtain an azimuth angle measurement error variance of the direction of the wave to be measuredAnd the pitch angle measurement error variance in the direction of the wave to be measured
And is
According to the formula
Calculating the included angle variance between the estimated value and the actual value of the direction of the wave to be measured
Wherein
Is the variance of the phase difference measurement error,
b11＝Cβ(-5Sα-Cα-CαCγ),b12＝Cβ(Sα+5Cα-CαCγ)，b13＝Cβ(Sα-Cα+5CαCγ)，
b21＝Sβ(-5Cα+Sα+SαCγ)-CβSγ，b22＝Sβ(Cα-5Sα+SαCγ)-CβSγ，
b23＝Sβ(Cα+Sα-5SαCγ)+5CβSγ，
Cα＝cosα0，Cγ＝cosγ0，Sα＝sinα0，Sγ＝sinγ0，
α0is the theoretical value of the azimuth angle of the direction of the wave to be measured, β0Is a theoretical value of the pitch angle of the direction of the wave to be measured, and will
And the direction-finding error is used as the direction-finding error between the estimated value and the actual value of the direction of the wave to be measured.
It should be noted that the working process of the apparatus shown in fig. 3 is the same as the implementation steps of each embodiment of the method shown in fig. 1, and the description of the same parts is omitted.
EXAMPLE III
In the embodiment, an implementation case of a low earth orbit satellite four-array element stereo rectangular array is used to demonstrate the application steps and effects. In this embodiment, a phase difference synchronization measurement system, that is, a phase difference synchronization receiving and processing system is adopted, and the phase difference measurement error of each array element is 10 °. In practical application, besides the requirement on the direction-finding accuracy near the intersatellite point (namely near the pitching angle of 90 degrees), the direction-finding accuracy in the range of 35 degrees to 50 degrees of the pitching angle also has certain requirements. Fig. 4 is a schematic diagram of a direction-finding accuracy contour line of a four-element cubic rectangular array when γ is 45 ° according to an embodiment of the present invention; fig. 5 is a schematic diagram of a direction-finding accuracy contour line of a four-element solid rectangular array when γ is 60 ° according to an embodiment of the present invention; fig. 6 is a schematic diagram of a direction-finding accuracy contour line of a four-element cubic rectangular array when γ is 120 ° according to an embodiment of the present invention; fig. 7 is a schematic diagram of the direction-finding accuracy contour line of the four-element solid rectangular array when γ is 135 °.
As shown in fig. 4-7, when γ is 45 °, the direction finding accuracy in the region of 35 ° to 50 ° of the smaller elevation angle region is (4.6, 5.4); when γ is 60 °, the direction finding accuracy in the region of 35 ° to 50 ° of the smaller elevation angle region is (4.2, 5); when γ is 120 °, the direction finding accuracy in the region of 35 ° to 50 ° of the smaller elevation angle region is (3.5, 6); when the gamma is 135 degrees, the direction-finding accuracy in the area of 35 degrees to 50 degrees in the smaller elevation angle area is (3.5,6.5), and when the rotation angle gamma is 120 degrees, the direction-finding accuracy in the area of 35 degrees to 50 degrees in the smaller elevation angle area is the highest, so when the direction-finding accuracy in the area of 35 degrees to 50 degrees in the smaller elevation angle area is higher, the rotation angle gamma is 120 degrees to construct a four-array element three-dimensional array.
In this example, for comparison, a conventional three-array-element L-shaped planar array under the same phase difference measurement error is also considered. Fig. 8 is a schematic diagram of a direction-finding accuracy contour line of a three-array-element planar L-shaped rectangular array for synchronously measuring phase differences according to an embodiment of the present invention, and it should be noted that the array-element planar L-shaped rectangular array in fig. 8 refers to a direction-finding array formed by array elements a1, a2, and A3 in fig. 2. Fig. 9 is a schematic diagram of a contour line of a direction-finding accuracy ratio of a four-array element stereoscopic rectangular array (γ is 120 °) and a three-array element planar L-shaped rectangular array for synchronously measuring phase differences according to an embodiment of the present invention; fig. 10 is a schematic diagram of a contour line of a direction-finding accuracy ratio of a four-array-element stereoscopic rectangular array (γ is 120 °) and a three-array-element planar L-shaped rectangular array for time-sharing phase difference measurement according to an embodiment of the present invention.
Comparing and analyzing the results of fig. 8, fig. 9 and fig. 10, it can be seen that the four-array element three-dimensional rectangular array designed by the technical scheme of the present invention has significant advantages when the pitch angle is small, and the direction-finding precision of each area is superior to that of the traditional three-array element L-shaped planar array and that of the rectangular array with the same configuration adopting a time-sharing receiving processing system. It should be noted that the numbers in fig. 4 to 10 represent the accuracy.
In summary, according to the technical scheme of the invention, a three-dimensional rectangular coordinate system in which a traditional three-array element planar array is located is arbitrarily rotated by an angle, a non-coplanar fourth array element is added to construct a preliminary four-array element three-dimensional array, phase differences of other three array elements relative to the first array element are synchronously calculated based on the preliminary four-array element three-dimensional array, a direction-finding model is constructed according to the calculated phase differences, and a direction-finding error between an estimated value and an actual value of a wave direction to be measured is calculated by using the direction-finding model; then, by selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding accuracy of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding accuracy obtained by calculation as the optimal rotation angle, and constructing a final four-array-element three-dimensional array according to the optimal rotation angle. In addition, the method adopts a mode of synchronously calculating the phase difference between the array elements, and improves the direction finding precision compared with a mode of calculating the phase difference between the array elements in a time-sharing mode.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (10)
1. A method of constructing a four-element volumetric array, the method comprising:
randomly rotating a three-dimensional rectangular coordinate system in which a traditional three-array element planar array is positioned by an angle, adding a non-coplanar fourth array element, and constructing a preliminary four-array element three-dimensional array, wherein the first array element is the origin of the three-dimensional rectangular coordinate system;
synchronously calculating phase differences of other three array elements relative to the first array element based on the preliminary four-array element stereo array;
constructing a direction-finding model according to the calculated phase differences of the other three array elements relative to the first array element;
calculating the direction-finding error between the estimated value and the actual value of the direction of the wave to be measured by using the direction-finding model; selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing the final four-array element three-dimensional array according to the optimal rotation angle.
2. The method of claim 1, wherein the step of rotating the three-dimensional rectangular coordinate system of the conventional three-array element planar array by an angle, adding a non-coplanar fourth array element, and constructing the preliminary four-array element stereo array comprises:
the three-dimensional rectangular coordinate system OXYZ where the traditional three-array element planar array is located is rotated by an angle around an X axis in the forward direction to obtain a three-dimensional rectangular coordinate system O ' X ' Y ' Z ', the fourth array element is added on the Y ' axis, the second array element is located on the X axis, the third array element is located on the Y axis, and the lengths of the second array element, the third array element and the fourth array element are equal to the lengths of the base lines of the first array element.
3. The method of claim 2, wherein calculating phase differences of the other three array elements relative to the first array element based on the preliminary four-element stereo array time division comprises:
according to the formulaCalculating the phase difference between the second array element and the first array element;
according to the formula
Calculating the phase difference between the third array element and the first array element;
according to the formula
Calculating the phase difference between the fourth array element and the first array element;
wherein d is the length of the second array element, the third array element and the fourth array element respectively relative to the base line of the first array element, λ is the wavelength in the direction of the wave to be measured, β is the pitch angle in the direction of the wave to be measured, α is the azimuth angle in the direction of the wave to be measured, γ is the rotation angle of the fourth array element relative to the three-dimensional rectangular coordinate system, and Δ φ21Is the difference between the phase difference measurement errors between the second array element and the first array element, delta phi31Is the difference between the phase difference measurement errors between the third array element and the first array element, delta phi41Is the difference between the phase difference measurement errors between the fourth array element and the first array element.
4. The method of claim 3, wherein constructing a direction-finding model based on the calculated phase differences of the other three array elements relative to the first array element comprises:
according to the formula
Converting the phase difference of the second array element, the third array element and the fourth array element relative to the first array element into a phase difference measurement value matrix;
performing least square method processing on the phase difference measurement value matrix to obtain a direction finding model
Where T denotes the transpose of the matrix, Σ is a positive definite matrix, θ is the wave direction vector to be measured, and θ is (α)T；
Is an estimate of the direction vector of the wave to be measured, and
is an estimate of the azimuth of the direction of the wave to be measured,is an estimated value of the pitch angle of the wave direction to be measured;
is a phase difference theoretical value matrix;
5. The method of claim 4, wherein calculating a direction-finding error between the estimated value and the actual value of the direction of the wave to be measured using the direction-finding model comprises:
calculating an included angle between an estimated value and a theoretical value of the direction of the wave to be measured according to the direction-finding model and the phase difference measurement error matrix;
calculating a covariance matrix of an included angle between the estimated value and the theoretical value of the direction of the wave to be measured to obtain an azimuth angle measurement error variance of the direction of the wave to be measured
And the pitch angle measurement error variance in the direction of the wave to be measured
And is
According to the formula
Calculating the included angle variance between the estimated value and the actual value of the direction of the wave to be measured
Wherein
Is the variance of the phase difference measurement error,
b11＝Cβ(-5Sα-Cα-CαCγ),b12＝Cβ(Sα+5Cα-CαCγ)，b13＝Cβ(Sα-Cα+5CαCγ)，
b21＝Sβ(-5Cα+Sα+SαCγ)-CβSγ，b22＝Sβ(Cα-5Sα+SαCγ)-CβSγ，
b23＝Sβ(Cα+Sα-5SαCγ)+5CβSγ，
Cα＝cosα0，Cγ＝cosγ0，Sα＝sinα0，Sγ＝sinγ0，
α0is the theoretical value of the azimuth angle of the direction of the wave to be measured, β0Is a theoretical value of the pitch angle of the direction of the wave to be measured, and will
And the direction-finding error is used as the direction-finding error between the estimated value and the actual value of the direction of the wave to be measured.
6. An apparatus for constructing a four-element volumetric array, the apparatus comprising:
the three-dimensional array initial construction unit is used for rotating a three-dimensional rectangular coordinate system where a traditional three-array element planar array is located by an angle at will, adding a non-coplanar fourth array element, and constructing an initial four-array element three-dimensional array, wherein the first array element is the origin of the three-dimensional rectangular coordinate system;
the phase difference calculation unit is used for synchronously calculating the phase difference of other three array elements relative to the first array element based on the preliminary four-array element stereo array;
the direction-finding model building unit is used for building a direction-finding model according to the calculated phase differences of the other three array elements relative to the first array element;
the direction-finding error calculation unit is used for calculating a direction-finding error between an estimated value and an actual value of the direction of the wave to be measured by using the direction-finding model;
and the three-dimensional array final construction unit is used for selecting a plurality of fourth array elements with different rotation angles, respectively calculating the direction-finding precision of the direction of the wave to be measured in the expected pitch angle area according to the direction-finding error, determining the rotation angle corresponding to the highest direction-finding precision obtained by calculation as the optimal rotation angle, and constructing the final four-array element three-dimensional array according to the optimal rotation angle.
7. The apparatus as claimed in claim 6, wherein the stereoscopic array preliminary construction unit is configured to rotate a three-dimensional rectangular coordinate system oyx in which a conventional three-array element planar array is located by a certain angle around an X axis to obtain a three-dimensional rectangular coordinate system O ' X ' Y ' Z ', add the fourth array element on the Y ' axis, and the second array element is located on the X axis and the third array element is located on the Y axis, and the lengths of the second array element, the third array element and the fourth array element are equal to the length of the base line of the first array element, respectively.
8. The apparatus of claim 7, wherein the phase difference calculation unit is configured to calculate the phase difference according to a formula
Calculating the phase difference between the second array element and the first array element;
according to the formula
Calculating the phase difference between the third array element and the first array element;
according to the formula
Calculating the phase difference between the fourth array element and the first array element;
wherein d is the length of the second array element, the third array element and the fourth array element respectively relative to the base line of the first array element, λ is the wavelength in the direction of the wave to be measured, β is the pitch angle in the direction of the wave to be measured, α is the azimuth angle in the direction of the wave to be measured, γ is the rotation angle of the fourth array element relative to the three-dimensional rectangular coordinate system, and Δ φ21Is the difference between the phase difference measurement errors between the second array element and the first array element, delta phi31Is the difference between the phase difference measurement errors between the third array element and the first array element, delta phi41Is as followsAnd the difference of the phase difference measurement errors between the fourth array element and the first array element.
9. The apparatus of claim 8, wherein the direction-finding model building unit is configured to build the direction-finding model according to a formula
Converting the phase difference of the second array element, the third array element and the fourth array element relative to the first array element into a phase difference measurement value matrix;
performing least square method processing on the phase difference measurement value matrix to obtain a direction finding model
Where T denotes the transpose of the matrix, Σ is a positive definite matrix, θ is the wave direction vector to be measured, and θ is (α)T；
Is an estimate of the direction vector of the wave to be measured, and
is an estimate of the azimuth of the direction of the wave to be measured,
is an estimated value of the pitch angle of the wave direction to be measured;
10. The apparatus of claim 9,
the direction-finding error calculation unit is used for calculating an included angle between an estimated value and a theoretical value of the direction of the wave to be measured according to the direction-finding model and the phase difference measurement error matrix;
calculating a covariance matrix of an included angle between the estimated value and the theoretical value of the direction of the wave to be measured to obtain an azimuth angle measurement error variance of the direction of the wave to be measured
And the pitch angle measurement error variance in the direction of the wave to be measured
And is
According to the formulaCalculating the included angle variance between the estimated value and the actual value of the direction of the wave to be measured
WhereinIs the variance of the phase difference measurement error,
b11＝Cβ(-5Sα-Cα-CαCγ),b12＝Cβ(Sα+5Cα-CαCγ)，b13＝Cβ(Sα-Cα+5CαCγ)，
b21＝Sβ(-5Cα+Sα+SαCγ)-CβSγ，b22＝Sβ(Cα-5Sα+SαCγ)-CβSγ，
b23＝Sβ(Cα+Sα-5SαCγ)+5CβSγ，
Cα＝cosα0，Cγ＝cosγ0，Sα＝sinα0，Sγ＝sinγ0，
α0is the theoretical value of the azimuth angle of the direction of the wave to be measured, β0Is a theoretical value of the pitch angle of the direction of the wave to be measured, and willAnd the direction-finding error is used as the direction-finding error between the estimated value and the actual value of the direction of the wave to be measured.
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