CN111965595A - Multi-non-circular information source high-precision direct positioning method based on unmanned aerial vehicle - Google Patents

Multi-non-circular information source high-precision direct positioning method based on unmanned aerial vehicle Download PDF

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CN111965595A
CN111965595A CN202010619663.7A CN202010619663A CN111965595A CN 111965595 A CN111965595 A CN 111965595A CN 202010619663 A CN202010619663 A CN 202010619663A CN 111965595 A CN111965595 A CN 111965595A
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何益
张小飞
曾浩威
李建峰
沈金清
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

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Abstract

The invention discloses a multi-non-circular information source high-precision direct positioning method based on an unmanned aerial vehicle, and belongs to the technical field of passive wireless positioning. Aiming at the common non-circular signals in the modern communication system, the non-circular phase information of the signals is considered when an algorithm model is established by utilizing the non-circular characteristics of the signals, and a received signal matrix is expanded to achieve the purpose of increasing the degree of freedom; combining a data fusion idea in a direct positioning technology, taking data fusion of the positions of a plurality of observation stations into consideration, and realizing high-precision positioning of a multi-target source only by one motion observation station; and the problem of high complexity caused by the introduction of the non-circular phase is effectively solved by introducing a dimension reduction idea. The method has the advantages that the problem of matching of intermediate parameters and parameters of the traditional two-step method is solved, the position information of the target source is directly obtained from the original receiving data layer, and the positioning precision is effectively improved; the expansion of the received signal vector increases the degree of freedom of the algorithm, improves the resolution and can simultaneously estimate more information sources.

Description

Multi-non-circular information source high-precision direct positioning method based on unmanned aerial vehicle
Technical Field
The invention relates to the technical field of passive wireless positioning, in particular to a multi-noncircular information source high-precision direct positioning method based on an unmanned aerial vehicle.
Background
In the existing radiation source positioning method, radiation source signals are mostly regarded as complex circle Gaussian signals, a signal model is too simple, characteristic information of the radiation source signals cannot be fully utilized, and therefore precision is low. When the signal model is established, the algorithm model is designed in a targeted manner by combining the signal characteristics, so that the positioning accuracy of the algorithm can be improved. The non-circular signal is a signal type commonly used in modern communication systems, so that the research on the radiation source positioning method aiming at the non-circular signal type has more universal usability and has very important practical significance.
The traditional two-step positioning technology needs to estimate intermediate parameters firstly, the existence of an intermediate processing link causes that the intermediate processing link inevitably loses partial position information, and under multiple radiation sources, extra parameter matching is needed before position resolving, so that the asymptotically optimal estimation performance is difficult to obtain, and the practicability is low. The direct positioning technology directly estimates the position of the radiation source from the original received data without additional parameter estimation, thereby effectively avoiding the problem of a two-step positioning system and having higher positioning precision. The direct positioning technology can conveniently utilize original data information, so that the direct positioning technology combined with signal characteristics can obtain better estimation performance. However, the existing direct positioning technology combining signal characteristics is not generally applicable to signal types such as constant modulus signals and cyclostationary signals, does not consider the problem of dimension reduction, and has high algorithm complexity.
Disclosure of Invention
The invention aims to provide a direct positioning method for non-circular signals, which utilizes the non-circular characteristics of the non-circular signals, considers the non-circular phase information of the signals when establishing an algorithm model, and simultaneously expands received signal vectors by utilizing the characteristic that an elliptic covariance matrix of the signals is not zero, thereby achieving the purposes of increasing the algorithm freedom and improving the algorithm resolution. The thought of combining direct positioning considers the data fusion of a plurality of observation station positions, directly extracts the radiation source position information from the original received data, only needs a motion observation station, namely unmanned aerial vehicle, alright realize the accurate location of multi-target source high accuracy.
In order to solve the problems existing in the background technology, the invention adopts the technical scheme that:
a multi-noncircular information source high-precision direct positioning method based on an unmanned aerial vehicle specifically comprises the following steps:
step 1: the unmanned aerial vehicle receives a plurality of non-circular radiation source signals at L different observation positions, and samples the received signals:
suppose that Q independent far-field narrow-band non-circular signals are incident to a motion observation platform carrying M-element uniform linear arrays, namely an unmanned aerial vehicle, and target sources are respectively positioned at pq＝[xq,yq]T(Q is 1,2, …, Q), the observation platform moves along the known track, the received signal of the observation platform at the K (K is 1,2, …, K) th sampling time of the L (L is 1,2, …, L) th observation position is:
Figure BDA0002562593800000021
in the formula,
Figure BDA0002562593800000022
manifold vector, s, to antenna array in l time slot segment for q target sourcel,q(k) The signal waveform of the qth target source at the kth sampling snapshot time in the ith observation time slot is shown,
Figure BDA0002562593800000023
the noise vector of the antenna array in the l observation time slot is assumed, and the noise is complex round white Gaussian noise which is independent from the signal;
step 2: expanding the received signal to obtain an expanded received signal matrix:
by utilizing the characteristic that the elliptic covariance matrix of the non-circular signal is not zero, the vector of the expanded received signal is as follows:
Figure BDA0002562593800000024
and the maximum non-circular rate signal is characterized in that:
Figure BDA0002562593800000025
wherein,
Figure BDA0002562593800000026
is the real envelope of the signal;
thus, the spread received signal vector is:
Figure BDA0002562593800000027
wherein
Figure BDA0002562593800000028
Figure BDA0002562593800000029
The extended received signal matrix for the ith observation position is then:
Figure BDA00025625938000000210
and step 3: respectively calculating the covariance matrixes of the extended received signals at different observation positions, and decomposing the eigenvalues:
the covariance matrix of the extended received signal for the ith observation position is expressed as:
Figure BDA00025625938000000211
the above formula is decomposed into characteristic values to obtain
Figure BDA0002562593800000031
Wherein,
Figure BDA0002562593800000032
the signal subspace is formed by the eigenvectors corresponding to Q larger eigenvalues;
Figure BDA0002562593800000033
the noise subspace matrix is formed by eigenvectors corresponding to M-Q smaller eigenvalues;
and 4, step 4: establishing a cost function by utilizing the mutual orthogonality of the signal manifold vector and the noise subspace:
according to the characteristic that the signal manifold vector and the noise subspace are orthogonal to each other, by means of the thought of subspace data fusion, a cost function is constructed as follows:
Figure BDA0002562593800000034
by aligning position p and non-circular phase
Figure BDA0002562593800000035
Searching to obtain a radiation source position estimation value;
and 5: and (3) reducing the dimension of the cost function, converting the cost function into a quadratic optimization problem, and removing non-circular phase search dimension:
in step 4, the solving and searching dimensionality of the radiation source position is too large, the dimensionality reduction solving is carried out on the radiation source position, the signal vector received in step 2 is rewritten, and the position information and the non-circular phase information are separated through matrix conversion:
Figure BDA0002562593800000036
wherein
Figure BDA0002562593800000037
Figure BDA0002562593800000038
For the l observation position, order
Figure BDA0002562593800000039
Obviously, the following equation holds
Figure BDA00025625938000000310
Then
Figure BDA00025625938000000311
If defined, are
Figure BDA00025625938000000312
The above formula can be expressed as
Figure BDA0002562593800000041
For unknown parameters
Figure BDA0002562593800000042
For example, the above equation is a quadratic optimization problem; let e be [1,0 ]]TThen, then
Figure BDA0002562593800000043
The reconstruction optimization problem is then as follows:
Figure BDA0002562593800000044
adopting Lagrange multiplier method to solve and construct the following function
Figure BDA0002562593800000045
Wherein λ is a multiplier. Order the above type is to
Figure BDA0002562593800000046
Is zero, i.e.
Figure BDA0002562593800000047
Then
Figure BDA0002562593800000048
And because of
Figure BDA0002562593800000049
Thus, μ 1/(e)HJl(p)-1e) Is thus
Figure BDA00025625938000000410
The sub-cost function for the ith slot is then:
Figure BDA00025625938000000411
step 6: fusing the projection results of the noise subspace from the signal manifold vector to L different observation positions, and obtaining the non-circular radiation source position estimation result by searching:
and (3) synthesizing the descendant cost functions of all the observation time slots to obtain a reduced-dimension cost function:
Figure BDA00025625938000000412
and searching the position of the cost function, wherein the coordinates corresponding to the Q maximum peak values are the estimated values of the positions of the non-circular radiation sources.
Compared with the prior art, the invention adopts the technical scheme, and has the beneficial effects that:
firstly, the non-circular characteristic of a radiation source signal is utilized, and the positioning precision is effectively improved;
the degree of freedom of the algorithm is increased, and more information sources can be estimated simultaneously;
and thirdly, optimal fusion of multi-position information achieves an asymptotically optimal estimation result.
And fourthly, the higher information source resolution is achieved.
Drawings
Fig. 1 is a flowchart of a multi-non-circular-source high-precision direct positioning method based on an unmanned aerial vehicle provided by the invention.
Fig. 2 is a diagram of a non-circular signal based multi-source positioning scene according to the present invention.
FIG. 3 is a localization scattergram of the method of the present invention.
Fig. 4 is a comparison chart of the method of the present invention with the direct positioning method of the general signal without the array element number.
Fig. 5 is a comparison graph of the method of the present invention and a general signal direct positioning method under different signal-to-noise ratios.
Fig. 6 is a comparison graph of the method of the present invention and a direct positioning method of general signals at different snapshot numbers.
FIG. 7 is a comparison graph of the computation time before and after dimensionality reduction for different snapshots.
Detailed Description
The invention provides a multi-noncircular information source high-precision direct positioning method based on an unmanned aerial vehicle, which is explained in detail by combining the attached drawings of the specification:
as shown in fig. 1, a flow chart of a multiple non-circular source high-precision direct positioning method based on an unmanned aerial vehicle. The unmanned aerial vehicle receives signals from a plurality of non-circular radiation sources at L different positions, and samples the received signals to obtain a received signal matrix; expanding a received signal matrix by using the characteristic that the elliptic covariance is not zero; performing eigenvalue decomposition on the expanded received signal matrix, and establishing a cost function by using the characteristics of a signal manifold vector and a noise subspace and the concept of subspace data fusion; reducing the dimension of the cost function, converting the cost function into a secondary optimization problem, and removing the non-circular phase search dimension; and finally, fusing the noise subspace projection results from the signal manifold vector to L different observation positions, and obtaining the non-circular radiation source position estimation result by searching, wherein the specific steps are as follows:
step 1: the unmanned aerial vehicle receives a plurality of non-circular radiation source signals at L different observation positions, and samples the received signals:
suppose that Q independent far-field narrow-band non-circular signals are incident to a motion observation platform carrying M-element uniform linear arrays, namely an unmanned aerial vehicle, and target sources are respectively positioned at pq＝[xq,yq]T(Q ═ 1,2, …, Q), the observation platform moves along a known trajectory, its multiple source localization scene graph based on non-circular signals is shown in fig. 2, the received signal of the observation platform at the kth (K ═ 1,2, …, L) observation position (K ═ 1,2, …, K) sampling moment is:
Figure BDA0002562593800000051
in the formula,
Figure BDA0002562593800000052
manifold vector, s, to antenna array in l time slot segment for q target sourcel,q(k) The signal waveform of the qth target source at the kth sampling snapshot time in the ith observation time slot is shown,
Figure BDA0002562593800000061
the noise vector of the antenna array in the l observation time slot is assumed, and the noise is complex round white Gaussian noise which is independent from the signal;
step 2: expanding the received signal to obtain an expanded received signal matrix:
by utilizing the characteristic that the elliptic covariance matrix of the non-circular signal is not zero, the vector of the expanded received signal is as follows:
Figure BDA0002562593800000062
and the maximum non-circular rate signal is characterized in that:
Figure BDA0002562593800000063
wherein,
Figure BDA0002562593800000064
is the real envelope of the signal;
thus, the spread received signal vector is:
Figure BDA0002562593800000065
wherein
Figure BDA0002562593800000066
Figure BDA0002562593800000067
The extended received signal matrix for the ith observation position is then:
Figure BDA0002562593800000068
and step 3: respectively calculating the covariance matrixes of the extended received signals at different observation positions, and decomposing the eigenvalues:
the covariance matrix of the extended received signal for the ith observation position is expressed as:
Figure BDA0002562593800000069
the above formula is decomposed into characteristic values to obtain
Figure BDA00025625938000000610
Wherein,
Figure BDA00025625938000000611
the signal subspace is formed by the eigenvectors corresponding to Q larger eigenvalues;
Figure BDA00025625938000000612
the noise subspace matrix is formed by eigenvectors corresponding to M-Q smaller eigenvalues;
and 4, step 4: establishing a cost function by utilizing the mutual orthogonality of the signal manifold vector and the noise subspace:
according to the characteristic that the signal manifold vector and the noise subspace are orthogonal to each other, by means of the thought of subspace data fusion, a cost function is constructed as follows:
Figure BDA0002562593800000071
by aligning position p and non-circular phase
Figure BDA0002562593800000072
Searching to obtain a radiation source position estimation value;
and 5: and (3) reducing the dimension of the cost function, converting the cost function into a quadratic optimization problem, and removing non-circular phase search dimension:
in step 4, the solving and searching dimensionality of the radiation source position is too large, the dimensionality reduction solving is carried out on the radiation source position, the signal vector received in step 2 is rewritten, and the position information and the non-circular phase information are separated through matrix conversion:
Figure BDA0002562593800000073
wherein
Figure BDA0002562593800000074
Figure BDA0002562593800000075
For the l observation position, order
Figure BDA0002562593800000076
Obviously, the following equation holds
Figure BDA0002562593800000077
Then
Figure BDA0002562593800000078
If defined, are
Figure BDA0002562593800000079
The above formula can be expressed as
Figure BDA00025625938000000710
For unknown parameters
Figure BDA00025625938000000711
For example, the above equation is a quadratic optimization problem; let e be [1,0 ]]TThen, then
Figure BDA00025625938000000712
The reconstruction optimization problem is then as follows:
Figure BDA0002562593800000081
adopting Lagrange multiplier method to solve and construct the following function
Figure BDA0002562593800000082
Wherein λ is a multiplier. Order the above type is to
Figure BDA0002562593800000083
Is zero, i.e.
Figure BDA0002562593800000084
Then
Figure BDA0002562593800000085
And because of
Figure BDA0002562593800000086
Thus, μ 1/(e)HJl(p)-1e) Is thus
Figure BDA0002562593800000087
The sub-cost function for the ith slot is then:
Figure BDA0002562593800000088
step 6: fusing the projection results of the noise subspace from the signal manifold vector to L different observation positions, and obtaining the non-circular radiation source position estimation result by searching:
and (3) synthesizing the descendant cost functions of all the observation time slots to obtain a reduced-dimension cost function:
Figure BDA0002562593800000089
and searching the position of the cost function, wherein the coordinates corresponding to the Q maximum peak values are the estimated values of the positions of the non-circular radiation sources.
FIG. 3 is a positioning scattergram of the method of the present invention, wherein the number of radiation sources Q-3 is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,200](unit is m, the same below), non-circular phase
Figure BDA00025625938000000810
The unmanned aerial vehicle moves along a known track, a uniform linear array with the array element number M being 6 is mounted, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number K of each observation position is 100, and the signal-to-noise ratio is 0 dB. It can be seen from the figure that the present invention is effective in achieving simultaneous positioning of multiple non-circular radiation sources.
Fig. 4 is a comparison chart of the method of the present invention with the direct positioning method of the general signal without the array element number. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,200](unit is m, the same below), non-circular phase
Figure BDA0002562593800000091
The unmanned aerial vehicle moves along a known track, the number of array elements of the mounted uniform linear array is respectively 3, 5, 7 and 9, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number K of each observation position is 100, and the signal-to-noise ratio is 5 dB. It can be seen from the figure that the invention can still realize positioning under the condition that the number of array elements is equal to the number of radiation sources, so that the invention increases the degree of freedom of the algorithm and can simultaneously position more radiation sources.
Fig. 5 is a comparison graph of the method of the present invention and a general signal direct positioning method under different signal-to-noise ratios. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,200](unit is m, the same below), non-circular phase
Figure BDA0002562593800000092
The unmanned aerial vehicle moves along a known track, a uniform linear array with the array element number of 6 is mounted, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number K of each observation position is 100, and the signal-to-noise ratio is stepped from-5 dB to 30dB at intervals of 5 dB. It can be seen from the figure that the positioning error of the present invention is always superior to the direct positioning method of the general signal as the signal-to-noise ratio increases.
Fig. 6 is a comparison graph of the method of the present invention and a direct positioning method of general signals at different snapshot numbers. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,200](unit is m, the same below), non-circular phase
Figure BDA0002562593800000093
The unmanned aerial vehicle moves along a known track, a uniform linear array with the array element number of 6 is mounted, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number of each observation position is stepped from 50 to 300 at intervals of 50, and the signal-to-noise ratio is 10 dB. It can be seen from the figure that as the number of snapshots increases, the positioning performance of the invention is continuously improved, and the positioning error is always better than that of the direct positioning method of the general signal.
FIG. 7 is a comparison chart of the method of the present invention before and after dimension reduction under different snapshot numbers. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,200](unit is m, the same below), non-circular phase
Figure BDA0002562593800000094
The unmanned aerial vehicle moves along a known track, a uniform linear array with 6 array elements is mounted, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), and the number of sampling fast beats at each observation position isTo step from 50 to 300 at 50 intervals, the signal-to-noise ratio is 20 dB. As can be seen from the figure, the dimension reduction method can effectively reduce the complexity of the algorithm and improve the practicability of the algorithm.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (1)

1. A multi-noncircular information source high-precision direct positioning method based on an unmanned aerial vehicle is characterized by comprising the following steps:
step 1: the unmanned aerial vehicle receives a plurality of non-circular radiation source signals at L different observation positions, and samples the received signals:
suppose that Q independent far-field narrow-band non-circular signals are incident to a motion observation platform carrying M-element uniform linear arrays, namely an unmanned aerial vehicle, and target sources are respectively positioned at pq＝[xq,yq]T(Q is 1,2, …, Q), the observation platform moves along the known track, the received signal of the observation platform at the K (K is 1,2, …, K) th sampling time of the L (L is 1,2, …, L) th observation position is:
Figure FDA0002562593790000011
in the formula,
Figure FDA0002562593790000012
manifold vector, s, to antenna array in l time slot segment for q target sourcel,q(k) The signal waveform of the qth target source at the kth sampling snapshot time in the ith observation time slot is shown,
Figure FDA0002562593790000013
for the antenna array in the first observation time slotThe noise vector of the column, wherein the noise is assumed to be complex round white Gaussian noise independent from the signal;
step 2: expanding the received signal to obtain an expanded received signal matrix:
by utilizing the characteristic that the elliptic covariance matrix of the non-circular signal is not zero, the vector of the expanded received signal is as follows:
Figure FDA0002562593790000014
and the maximum non-circular rate signal is characterized in that:
Figure FDA0002562593790000015
wherein,
Figure FDA0002562593790000016
Figure FDA0002562593790000017
is the real envelope of the signal;
thus, the spread received signal vector is:
Figure FDA0002562593790000018
wherein
Figure FDA0002562593790000019
Figure FDA00025625937900000110
The extended received signal matrix for the ith observation position is then:
Figure FDA0002562593790000021
and step 3: respectively calculating the covariance matrixes of the extended received signals at different observation positions, and decomposing the eigenvalues:
the covariance matrix of the extended received signal for the ith observation position is expressed as:
Figure FDA0002562593790000022
the above formula is decomposed into characteristic values to obtain
Figure FDA0002562593790000023
Wherein,
Figure FDA0002562593790000024
the signal subspace is formed by the eigenvectors corresponding to Q larger eigenvalues;
Figure FDA0002562593790000025
the noise subspace matrix is formed by eigenvectors corresponding to M-Q smaller eigenvalues;
and 4, step 4: establishing a cost function by utilizing the mutual orthogonality of the signal manifold vector and the noise subspace:
according to the characteristic that the signal manifold vector and the noise subspace are orthogonal to each other, by means of the thought of subspace data fusion, a cost function is constructed as follows:
Figure FDA0002562593790000026
by aligning position p and non-circular phase
Figure FDA0002562593790000027
Searching to obtain a radiation source position estimation value;
and 5: and (3) reducing the dimension of the cost function, converting the cost function into a quadratic optimization problem, and removing non-circular phase search dimension:
in step 4, the solving and searching dimensionality of the radiation source position is too large, the dimensionality reduction solving is carried out on the radiation source position, the signal vector received in step 2 is rewritten, and the position information and the non-circular phase information are separated through matrix conversion:
Figure FDA0002562593790000028
wherein
Figure FDA0002562593790000029
Figure FDA00025625937900000210
For the l observation position, order
Figure FDA00025625937900000211
Obviously, the following equation holds
Figure FDA00025625937900000212
Then
Figure FDA0002562593790000031
If defined, are
Figure FDA0002562593790000032
The above formula can be expressed as
Figure FDA0002562593790000033
For unknown parameters
Figure FDA0002562593790000034
For example, the above equation is a quadratic optimization problem; let e be [1,0 ]]TThen, then
Figure FDA0002562593790000035
The reconstruction optimization problem is then as follows:
Figure FDA0002562593790000036
adopting Lagrange multiplier method to solve and construct the following function
Figure FDA0002562593790000037
Wherein λ is a multiplier. Order the above type is to
Figure FDA0002562593790000038
Is zero, i.e.
Figure FDA0002562593790000039
Then
Figure FDA00025625937900000310
And because of
Figure FDA00025625937900000311
Thus, μ 1/(e)HJl(p)-1e) Is thus
Figure FDA00025625937900000312
The sub-cost function for the ith slot is then:
Figure FDA00025625937900000313
step 6: fusing the projection results of the noise subspace from the signal manifold vector to L different observation positions, and obtaining the non-circular radiation source position estimation result by searching:
and (3) synthesizing the descendant cost functions of all the observation time slots to obtain a reduced-dimension cost function:
Figure FDA00025625937900000314
and searching the position of the cost function, wherein the coordinates corresponding to the Q maximum peak values are the estimated values of the positions of the non-circular radiation sources.
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CN113359086A (en) * 2021-06-25 2021-09-07 南京航空航天大学 Weighted subspace data fusion direct positioning method based on augmented co-prime array
CN113391266A (en) * 2021-05-28 2021-09-14 南京航空航天大学 Direct positioning method based on non-circular multi-nested array dimensionality reduction subspace data fusion
CN113835063A (en) * 2021-11-24 2021-12-24 南京航空航天大学 Unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method
CN114636970A (en) * 2022-02-21 2022-06-17 中国人民解放军战略支援部队信息工程大学 Multi-unmanned aerial vehicle cooperative direct positioning method based on passive synthetic aperture

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