CN114636970A - Multi-unmanned aerial vehicle cooperative direct positioning method based on passive synthetic aperture - Google Patents
Multi-unmanned aerial vehicle cooperative direct positioning method based on passive synthetic aperture Download PDFInfo
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- 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
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Abstract
The invention discloses a multi-unmanned aerial vehicle cooperative direct positioning method based on a passive synthetic aperture, which comprises the following steps: establishing an array signal time domain model related to an arrival signal complex envelope, a carrier phase and Doppler frequency offset based on a plurality of unmanned aerial vehicle array receiving models; each unmanned aerial vehicle arranges the array signal time domain data according to time sequence to form an expanded array signal time domain model based on the passive synthetic aperture idea, and then converts the array signal time domain data into frequency domain data by utilizing a radix-2-FFT algorithm; the central station makes the frequency domain data into a multi-machine frequency domain observation vector, establishes a mathematical optimization model for jointly estimating a target position vector and a propagation coefficient according to a subspace orthogonality criterion, extracts an information matrix only containing a target position, and performs grid search of a plurality of regions by taking the minimum characteristic value of the minimized information matrix as a target to realize accurate positioning of multiple targets. The invention can obviously improve the multi-target positioning precision and the multi-target resolution capability and can avoid the problem of data association in the multi-target positioning process.
Description
Technical Field
The invention belongs to the technical field of radio positioning, and particularly provides a multi-unmanned-aerial-vehicle cooperative direct positioning method based on a passive synthetic aperture, aiming at a multi-target positioning scene based on a plurality of moving unmanned aerial vehicles.
Background
As is known, radio signal detection and positioning have very important significance for target discovery and situation perception thereof, and space-based detection and positioning systems play irreplaceable benefits. With the development of the avionics equipment being unmanned, the unmanned reconnaissance plane becomes an important supplementary and enhancement means for reconnaissance of satellites and manned reconnaissance planes. Compared with a reconnaissance satellite, the reconnaissance satellite system has the characteristics of low cost, flexible control of reconnaissance regions and the like; compared with a manned scout, the unmanned scout has the capability of continuous scout day and night without considering the problems of fatigue, casualties and the like of pilots, and particularly shows the superiority when the scout is carried out in important regions which are strictly protected by enemies or under the condition that the manned scout is difficult to access. Under the current situation of emphasizing hidden attacks and hard kills, passive positioning technology based on unmanned aerial vehicle platforms will play an increasingly important role.
However, although the unmanned aerial vehicle reconnaissance equipment has the characteristics of flexibility and freedom, the unmanned aerial vehicle reconnaissance equipment can only rely on an antenna array with the smallest aperture as possible to realize reconnaissance positioning due to the small volume and the light loading capacity, so that the problems of limited accuracy, insufficient resolution and the like exist in target positioning. In contrast, the invention introduces a passive synthetic aperture technology to virtually expand a small aperture array into a large aperture array. The passive synthetic aperture technology equivalently moves coherent signals received by a moving array in different periods to the same reference period, so that spliced signals in each period are equivalent to the synthetic aperture of a newly added array aperture in the reference period. In addition, this patent utilizes the time delay inequality information between the multimachine received signal, further expands array aperture, can effectively promote precision and the resolving power to multi-target location under the limited condition in small-size motion unmanned aerial vehicle platform array aperture.
On the other hand, in the existing unmanned aerial vehicle positioning system, acquired digital signals are transmitted back to a rear computing center through an unmanned aerial vehicle gateway, positioning and resolving of targets are completed by the computing center, and the computing center adopts a two-step estimation and positioning mode, namely, positioning parameters such as angles are extracted from signals transmitted back by all unmanned aerial vehicles, and then according to information such as positions and speeds of the unmanned aerial vehicles, a positioning equation is established to resolve position information of the targets from the parameters. According to the information theory, a certain uncertainty is introduced into a processing loop from the original data to the final estimation result, so that information loss is caused, the positioning performance is affected, especially when multiple targets exist, data association or human intervention is also needed, and the positioning error and the processing time are further increased. In this respect, the patent introduces a (single step) direct localization approach, whose basic idea is to directly obtain the target location from the original signal samples without estimating other intermediate observations. Compared with the traditional two-step positioning method, the single-step positioning technology has the advantages of high estimation precision, strong resolving power, no need of data association and the like.
Disclosure of Invention
Aiming at the problem that the positioning performance of a miniaturized unmanned aerial vehicle is limited, the invention provides a multi-unmanned aerial vehicle cooperative direct positioning method based on a passive synthetic aperture, which can obviously improve the positioning accuracy and resolution capability of multiple targets.
In order to solve the problems, firstly, an array signal time domain model related to an arrival signal complex envelope, a carrier phase and Doppler frequency offset is established by utilizing a mathematical relation of an arrival signal angle, propagation delay and Doppler frequency offset on a target position parameter based on a plurality of unmanned aerial vehicle array receiving models; secondly, arranging the array signal time domain data in a time sequence by each unmanned aerial vehicle based on a passive synthetic aperture idea to form an expanded array signal time domain model, and converting the expanded array signal time domain data into frequency domain data by utilizing a radix-2-FFT algorithm; then, each unmanned aerial vehicle transmits the expanded array signal frequency domain data to a computing central station, and the central station enables the frequency domain data of the plurality of unmanned aerial vehicles to form a high-dimensional multi-machine frequency domain observation vector; and finally, the central station establishes a mathematical optimization model for jointly estimating a target position vector and a propagation coefficient according to a subspace orthogonality criterion, extracts an information matrix only containing the target position, and performs grid search of a plurality of regions by taking the minimum characteristic value of the minimized information matrix as a target function so as to realize accurate positioning of multiple targets. The invention discloses a multi-unmanned aerial vehicle cooperative direct positioning method based on a passive synthetic aperture, which comprises the following specific implementation steps:
step 1: time synchronization is carried out on M-channel array antenna receiving systems of L unmanned aerial vehicles, and T is used according to the Nyquist sampling theoremsCollecting radio signal data radiated by the Q targets for a time interval so as to obtain array signal time domain data of each unmanned aerial vehicle;
step 2: each unmanned aerial vehicle arranges the obtained array signal time domain data according to a time sequence, and the array signal time domain data of every continuous N sampling points form an expanded array signal time domain observation vector;
and step 3: each unmanned aerial vehicle divides the expanded array signal time domain data into K segments, each segment is J sample points, and base 2-FFT operation is carried out on each segment of data, so that K segments of expanded array signal frequency domain data are obtained;
and 4, step 4: each unmanned aerial vehicle transmits the K sections of the extended array signal frequency domain data obtained by calculation to a calculation central station, and the central station enables the extended array signal frequency domain data of L unmanned aerial vehicles to form K sections of high-dimensional multi-machine frequency domain observation vectors;
and 5: the central station sequentially estimates K sections of high-dimensional multi-machine frequency domain data to obtain covariance matrixes of J frequency domain components, and obtains noise subspace projection matrixes on each frequency component through eigenvalue decomposition;
step 6: the central station establishes a mathematical optimization model for jointly estimating a target position vector and a propagation coefficient based on a subspace orthogonality criterion;
and 7: the central station extracts an information matrix only containing a target position vector;
and 8: the central station sets a grid searching range of each target and calculates the minimum eigenvalue of an information matrix on a grid point;
and step 9: and the central station carries out grid search of Q areas in sequence, and grid coordinates corresponding to the minimum value of the minimum characteristic value of the information matrix in each search range are the positioning result of each target.
Further, in step 1, a time domain model of a signal received by the array antenna of the ith drone at the nth sampling time is:
wherein p isqA position vector representing the qth object; t is tq0Representing the transmit signal time of the qth target; sq(nTs-τl(pq)-tq0) Indicating that the q-th target signal is transmitted at the time tq0Time delay of τl(pq) The discrete complex envelope of (a); a isl(pq) An array manifold vector representing the q-th target signal relative to the l-th drone receiving array, and the angle of arrival θ of the signall(pq) (ii) related; beta is aqlRepresenting a channel propagation coefficient between the qth target signal to the l drone; epsilonl(n) represents an antenna array noise vector for the l-th drone; tau isl(pq) Representing the propagation delay of the qth target signal to the ith unmanned aerial vehicle; f. ofl(pq) Watch (A)Indicating the Doppler frequency offset of the qth target signal reaching the ith unmanned aerial vehicle;
wherein the time delay taul(pq) And Doppler frequency offset fl(pq) The algebraic relation with the target position vector is
In two-dimensional planar positioning, angle of arrival θl(pq) The algebraic relation with the target position vector is
In the formula fcIs the carrier frequency of the signal; c is the propagation velocity of the electric wave; u. oflAnd with
Respectively representing the position vector and velocity vector of the ith drone.
Further, in step 2, the first drone arranges the obtained array signal time domain data in a time sequence, and the array signal time domain data of each consecutive N sampling points form an extended array signal time domain observation vector, which may be represented as:
wherein the content of the first and second substances,
for extended array noise vectors, bl(pq) The vector is an extended space-time manifold vector, and the expression is as follows:
wherein the content of the first and second substances,
a Kronecker product representing the matrix;
further, in step 3, the frequency domain model corresponding to the kth segment of extended array signal time domain observation vector of the ith unmanned aerial vehicle is:
wherein the content of the first and second substances,
and
respectively represent
And wl(n) frequency components at the j-th digital frequency point during the k-th observation time.
Further, in step 4, each unmanned aerial vehicle transmits the calculated K-segment extended array signal frequency domain data to the calculation central station, and the central station combines the extended array signal frequency domain data of L unmanned aerial vehicles into a high-dimensional multi-machine frequency domain observation vector, where the expression is:
wherein, the first and the second end of the pipe are connected with each other,
βq＝[βq1,βq2,...,βqL]T，Γ(j,pq) The expressions for T are respectively:
wherein blkdiag {. cndot } represents a block-shaped diagonal matrix composed of a matrix or vector as diagonal elements; I.C. ALRepresenting an L-dimensional identity matrix; 1MRepresenting an M-dimensional all-1 vector.
Further, in step 5, the covariance matrix of the high-dimensional multi-machine frequency domain observation vector on the jth frequency domain component is estimated by the following formula
To pair
And (3) carrying out eigenvalue decomposition, and dividing the eigenvector matrix into two parts: u shapes(j) Is the signal subspace corresponding to the Q large eigenvalues; u shapen(j) Is a noise subspace corresponding to the MLN-Q small eigenvalues;
and then obtaining a noise subspace projection matrix on the jth frequency domain component as follows:
further, in step 6, the central station estimates the target position vector p jointly based on the subspace orthogonality criterionqAnd propagation coefficient betaqThe mathematical optimization model of (2) is as follows:
further, in step 7, the information matrix extracted by the central station and only including the target position vector is:
further, in step 8, the minimum eigenvalue of the information matrix at the geographic grid point is:
C(p)＝λmin(Q(p))。
further, in step 9, the central station sequentially performs grid search of Q areas, and a grid coordinate corresponding to a minimum value of a minimum eigenvalue of the information matrix in each search range is a positioning result of each target:
wherein the content of the first and second substances,
indicating the set grid search range of the qth object.
Compared with the prior art, the invention has the following beneficial effects:
compared with the traditional positioning mode of firstly finding directions and then concentrating intersection, the method provided by the invention can obviously improve the multi-target positioning precision and can avoid the data association problem in the multi-target positioning process. In addition, the positioning method disclosed by the invention utilizes a passive synthetic aperture technology, and can further improve the resolution capability of multiple targets.
Drawings
Fig. 1 is a schematic diagram of a principle of cooperative direct positioning of multiple unmanned aerial vehicles according to an embodiment of the present invention;
fig. 2 is a basic flowchart of a method for cooperative and direct positioning of multiple drones based on a passive synthetic aperture according to an embodiment of the present invention;
fig. 3 is a schematic diagram of data transmission between an unmanned aerial vehicle and a central station according to an embodiment of the present invention;
FIG. 4 is a schematic view of a multi-target positioning example scenario of multiple UAVs according to an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating a comparison of positioning error results of the positioning method according to the embodiment of the present invention;
fig. 6 is a schematic diagram illustrating comparison of resolution results of the positioning method according to the embodiment of the invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in fig. 1, the method for cooperative and direct positioning of multiple unmanned aerial vehicles based on passive synthetic aperture disclosed by the present invention requires that an array antenna is installed on each unmanned aerial vehicle, each unmanned aerial vehicle transmits observation frequency domain data to a central station, and the central station directly (jointly) estimates position parameters of multiple targets in a signal data domain according to the subspace orthogonality of signals on each frequency point.
As shown in fig. 2, a method for cooperative and direct positioning of multiple drones based on passive synthetic aperture includes the following steps:
step 1: time synchronization is carried out on M-channel array antenna receiving systems of L unmanned aerial vehicles, and T is used according to the Nyquist sampling theoremsRadio signal data radiated by the Q targets are collected for a time interval, so that array signal time domain data of each unmanned aerial vehicle are obtained.
Step 2: each unmanned aerial vehicle arranges the acquired array signal time domain data in time sequence, and each continuous N sampling points (the signal bandwidth is far less than 1/(NT)s) ) form an extended array signal time domain observation vector.
And step 3: each unmanned aerial vehicle divides the expanded array signal time domain data into K sections, each section of J (integral power of 2) sample points performs base 2-FFT operation on each section of data, and therefore K sections of expanded array signal frequency domain data (each section of J frequency domain components) are obtained.
And 4, step 4: and each unmanned aerial vehicle transmits the K sections of the extended array signal frequency domain data obtained by calculation to a calculation central station, and the central station forms the extended array signal frequency domain data of the L unmanned aerial vehicles into K sections of high-dimensional multi-machine frequency domain observation vectors.
And 5: the central station sequentially estimates K sections of high-dimensional multi-machine frequency domain data to obtain covariance matrixes of J frequency domain components, and obtains noise subspace projection matrixes on all the frequency components through eigenvalue decomposition.
Step 6: and the central station establishes a mathematical optimization model for jointly estimating the target position vector and the propagation coefficient based on the subspace orthogonality criterion.
And 7: the central station extracts an information matrix containing only the target position vector.
And step 8: the central station sets the grid search range of each target and calculates the minimum eigenvalue of the information matrix on the grid points.
And step 9: and the central station carries out grid search of Q areas in sequence, and grid coordinates corresponding to the minimum value of the minimum characteristic value of the information matrix in each search range are the positioning result of each target.
Further, in step 1, a time domain model of a signal received by the array antenna of the ith drone at the nth sampling time is:
wherein p isqA position vector representing the qth object; t is tq0Representing the transmitted signal time of the qth target; sq(nTs-τl(pq)-tq0) Indicating that the q-th target signal is transmitted at the time tq0Time delay of τl(pq) The discrete complex envelope of (a); a isl(pq) Array manifold vector representing the qth target signal relative to the lth drone receive array, and the angle of arrival θ of the signall(pq) (ii) related; beta is aqlRepresenting a channel propagation coefficient between the qth target signal to the l drone; epsilonl(n) represents an antenna array noise vector for the l-th drone; tau isl(pq) Representing the qth objectPropagation delay of a signal to the first unmanned aerial vehicle; f. ofl(pq) Indicating the doppler shift of the qth target signal to the ith drone.
Wherein the time delay taul(pq) And Doppler frequency offset fl(pq) The algebraic relation with the target position vector is
Angle of arrival theta, for example, using two-dimensional planar positioningl(pq) The algebraic relation with the target position vector is
In the formula fcIs the carrier frequency of the signal; c is the propagation velocity of the electric wave; u. ulAnd
respectively representing the position vector and velocity vector of the ith drone.
Further, in step 2, the first drone arranges the obtained array signal time domain data in time sequence, and each continuous N sampling points (meeting the requirement that the signal bandwidth is far less than 1/(NT)s) ) form an extended array signal time-domain observation vector, which can be expressed as
Wherein the content of the first and second substances,
for extended array noise vectors，bl(pq) Is an extended space-time manifold vector expressed as
Wherein the content of the first and second substances,
a Kronecker product representing the matrix;
further, in step 3, the frequency domain model corresponding to the kth segment of extended array signal time domain observation vector of the ith unmanned aerial vehicle is
Wherein the content of the first and second substances,
and
respectively represent
And wl(n) frequency components at the j-th digital frequency point during the k-th observation time.
Further, in step 4, each of the unmanned aerial vehicles transmits the calculated K-segment extended array signal frequency domain data to the calculation central station, as shown in fig. 3, the central station combines the extended array signal frequency domain data of L unmanned aerial vehicles into a high-dimensional multi-machine frequency domain observation vector, where the expression is
Wherein, the first and the second end of the pipe are connected with each other,
βq＝[βq1,βq2,...,βqL]T，Γ(j,pq) And T are respectively
Wherein blkdiag {. cndot } represents a block-shaped diagonal matrix composed of a matrix or vector as diagonal elements; I.C. ALRepresenting an L-dimensional identity matrix; 1MRepresenting an M-dimensional all-1 vector.
Further, in step 5, the covariance matrix of the high-dimensional multi-machine frequency domain observation vector on the jth frequency domain component is estimated by the following formula
To pair
And (3) carrying out eigenvalue decomposition, and dividing the eigenvector matrix into two parts: u shapes(j) Is the signal subspace corresponding to the Q large eigenvalues; u shapen(j) Is the noise subspace corresponding to the MLN-Q small eigenvalues. And then obtaining a noise subspace projection matrix on the jth frequency domain component as follows:
further, in step 6, the central station estimates the target position vector p jointly based on the subspace orthogonality criterionqAnd propagation coefficient betaqIs mathematically optimized as
Further, in step 7, the central station extracts an information matrix including only the target position vector as
Further, in step 8, the minimum eigenvalue of the information matrix on the geographical grid point is
C(p)＝λmin(Q(p))
Further, in step 9, the central station sequentially performs grid search of Q areas, and a grid coordinate corresponding to a minimum value of the minimum eigenvalue of the information matrix in each search range is a positioning result of each target:
wherein, the first and the second end of the pipe are connected with each other,
indicating the set grid search range of the qth object.
To verify the effect of the present invention, the following specific examples are performed:
as shown in fig. 4, fig. 4 is a schematic diagram of 2 examples of object location. Assuming that the position coordinates of the target are (10km, -10km) and (0km, 20km), the existing 3 unmanned aerial vehicles position the target, the initial position coordinates are (30km, -30km), (30km ) and (-30km, 30km), the speed is 70m/s, along the direction of an X axis, each unmanned aerial vehicle is provided with a 3-element uniform linear array, the time domain expansion factor of the array data is 2, the signal bandwidth is 0.3kHz, each unmanned aerial vehicle collects 50 segments of signals, and the duration of each segment of signals is about 40 ms. The performance of the cooperative direct positioning method disclosed by the patent is compared with the performance of the traditional direction finding and intersection positioning method, wherein the direction finding adopts a multiple signal classification estimation (MUSIC) algorithm, and the intersection positioning adopts a Taylor series iterative positioning algorithm.
In fig. 5, 5a shows the variation curve of the root mean square error of the estimation of the 1 st target position with the signal-to-noise ratio for the two positioning methods, and in fig. 5, 5b shows the variation curve of the root mean square error of the estimation of the 2 nd target position with the signal-to-noise ratio for the two positioning methods. Then, the snr is fixed to 20dB, assuming that 3 targets exist, and the location coordinates are (10km, -10km), (-5km, 0km), and (10km, 0km), respectively, 6a in fig. 6 gives the location spectrogram of cooperative direct positioning disclosed in this patent, and 6b in fig. 6 gives the location spectrogram of direct positioning using only angle information.
As can be seen from fig. 5a and 5b in fig. 5, compared with the conventional direction-finding and intersection-prior positioning method, the cooperative direct positioning method disclosed by the present invention can significantly improve the positioning accuracy, and the lower the signal-to-noise ratio, the more significant the advantages thereof. As can be seen from fig. 6a and 6b in fig. 6, compared with the direct positioning method using only angle information, the cooperative direct positioning method disclosed in this patent can further improve the resolution capability for multiple target positions.
Compared with the traditional positioning mode of firstly finding directions and then concentrating intersection, the method provided by the invention can obviously improve the multi-target positioning precision and can avoid the data association problem in the multi-target positioning process. In addition, the positioning method disclosed by the invention utilizes a passive synthetic aperture technology, and can further improve the resolution capability of multiple targets.
The above shows only the preferred embodiments of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should also be considered as the protection scope of the present invention.
Claims (10)
1. A multi-unmanned aerial vehicle cooperative direct positioning method based on a passive synthetic aperture is characterized by comprising the following steps:
step 1: to the M-channel array antenna receiving system of L unmanned aerial vehiclesGood time synchronization and according to the Nyquist sampling theorem by TsCollecting radio signal data radiated by the Q targets for a time interval so as to obtain array signal time domain data of each unmanned aerial vehicle;
step 2: each unmanned aerial vehicle arranges the obtained array signal time domain data according to a time sequence, and the array signal time domain data of every continuous N sampling points form an expanded array signal time domain observation vector;
and step 3: each unmanned aerial vehicle divides the expanded array signal time domain data into K segments, each segment is J sample points, and base 2-FFT operation is carried out on each segment of data, so that K segments of expanded array signal frequency domain data are obtained;
and 4, step 4: each unmanned aerial vehicle transmits K sections of the calculated extended array signal frequency domain data to a calculation central station, and the central station enables the extended array signal frequency domain data of L unmanned aerial vehicles to form K sections of high-dimensional multi-machine frequency domain observation vectors;
and 5: the central station sequentially estimates K sections of high-dimensional multi-machine frequency domain data to obtain covariance matrixes of J frequency domain components, and obtains noise subspace projection matrixes on each frequency component through eigenvalue decomposition;
step 6: the central station establishes a mathematical optimization model for jointly estimating a target position vector and a propagation coefficient based on a subspace orthogonality criterion;
and 7: the central station extracts an information matrix only containing a target position vector;
and 8: the central station sets a grid searching range of each target and calculates the minimum eigenvalue of an information matrix on a grid point;
and step 9: and the central station carries out grid search of Q areas in sequence, and grid coordinates corresponding to the minimum value of the minimum characteristic value of the information matrix in each search range are the positioning result of each target.
2. The method according to claim 1, wherein in step 1, the time domain model of the signal received by the array antenna of the ith drone at the nth sampling time is:
wherein p isqA position vector representing the qth object; t is tq0Representing the transmitted signal time of the qth target; sq(nTs-τl(pq)-tq0) Indicating that the q-th target signal is transmitted at the time tq0Time delay of τl(pq) The discrete complex envelope of (a); a isl(pq) An array manifold vector representing the q-th target signal relative to the l-th drone receiving array, and the angle of arrival θ of the signall(pq) (ii) related; beta is a betaqlRepresenting a channel propagation coefficient between the qth target signal to the l drone; epsilonl(n) represents an antenna array noise vector for the l-th drone; tau.l(pq) Representing the propagation delay of the qth target signal to the ith unmanned aerial vehicle; f. ofl(pq) Indicating the Doppler frequency offset of the qth target signal to the l drone;
wherein the time delay taul(pq) And Doppler frequency offset fl(pq) The algebraic relation with the target position vector is
In two-dimensional planar positioning, angle of arrival θl(pq) Algebraic relation to the target position vector is
In the formula fcIs the carrier frequency of the signal; c is the propagation velocity of the electric wave; u. oflAnd
respectively representing the position vector and velocity vector of the ith drone.
3. The cooperative and direct positioning method for multiple drones based on the passive synthetic aperture according to claim 2, wherein in step 2, the ith drone arranges the obtained array signal time domain data in time sequence, and the array signal time domain data of each consecutive N sampling points form an extended array signal time domain observation vector, which can be expressed as:
wherein the content of the first and second substances,
for extended array noise vectors, bl(pq) The vector is an extended space-time manifold vector, and the expression is as follows:
wherein the content of the first and second substances,
a Kronecker product representing the matrix;
4. the method according to claim 3, wherein in step 3, the frequency domain model corresponding to the kth segment of extended array signal time domain observation vector of the ith UAV is:
wherein the content of the first and second substances,
and
respectively represent
And wl(n) frequency components at the j-th digital frequency point in the k-th observation time.
5. The method as claimed in claim 4, wherein in step 4, each drone transmits the calculated K segments of spread array signal frequency domain data to the central station, and the central station combines the spread array signal frequency domain data of L drones into a high-dimensional multi-drone frequency domain observation vector, whose expression is:
wherein the content of the first and second substances,
βq＝[βq1,βq2,...,βqL]T，Γ(j,pq) The expressions for T are respectively:
wherein blkdiag {. cndot } represents a block-shaped diagonal matrix composed of a matrix or vector as diagonal elements; i isLRepresenting an L-dimensional identity matrix; 1MRepresenting an M-dimensional all-1 vector.
6. The method as claimed in claim 5, wherein in step 5, the covariance matrix of the j-th frequency domain component of the high-dimensional multi-machine frequency domain observation vector is estimated by the following formula
To pair
And (3) carrying out eigenvalue decomposition, and dividing the eigenvector matrix into two parts: u shapes(j) Is the signal subspace corresponding to the Q large eigenvalues; u shapen(j) Is a noise subspace corresponding to the MLN-Q small eigenvalues;
and then obtaining a noise subspace projection matrix on the jth frequency domain component as follows:
7. the method according to claim 6, wherein in step 6, the central station estimates the target position vector p based on the joint established by subspace orthogonality criterionqAnd propagation coefficient betaqThe mathematical optimization model of (1) is as follows:
8. the method according to claim 5, wherein in step 7, the central station extracts an information matrix containing only the target position vector as follows:
9. the method according to claim 8, wherein in step 8, the minimum eigenvalue of the information matrix at the geographical grid point is:
C(p)＝λmin(Q(p))。
10. the method according to claim 9, wherein in step 9, the central station sequentially performs grid search of Q areas, and a grid coordinate corresponding to a minimum value of a minimum eigenvalue of the information matrix in each search range is a positioning result of each target:
wherein the content of the first and second substances,
indicating the set grid search range of the qth object.
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| CN115267662A (en) * | 2022-06-25 | 2022-11-01 | 中国人民解放军战略支援部队信息工程大学 | Correlation interferometer direct positioning method based on single motion array passive synthetic aperture |
| CN115616482B (en) * | 2022-11-15 | 2023-03-14 | 理工全盛(北京)科技有限公司 | Single-station passive unmanned aerial vehicle monitoring method, device and system |
| CN116184320A (en) * | 2023-04-27 | 2023-05-30 | 之江实验室 | Unmanned aerial vehicle acoustic positioning method and unmanned aerial vehicle acoustic positioning system |
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| CN115616482B (en) * | 2022-11-15 | 2023-03-14 | 理工全盛(北京)科技有限公司 | Single-station passive unmanned aerial vehicle monitoring method, device and system |
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| CN116184320B (en) * | 2023-04-27 | 2023-07-18 | 之江实验室 | Unmanned aerial vehicle acoustic positioning method and unmanned aerial vehicle acoustic positioning system |
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