CN112269160A - Multi-information-source direct positioning method based on unmanned aerial vehicle loading nested array - Google Patents
Multi-information-source direct positioning method based on unmanned aerial vehicle loading nested array Download PDFInfo
- Publication number
- CN112269160A CN112269160A CN202010622449.7A CN202010622449A CN112269160A CN 112269160 A CN112269160 A CN 112269160A CN 202010622449 A CN202010622449 A CN 202010622449A CN 112269160 A CN112269160 A CN 112269160A
- Authority
- CN
- China
- Prior art keywords
- aerial vehicle
- unmanned aerial
- received signal
- signals
- positioning
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 48
- 230000005855 radiation Effects 0.000 claims abstract description 25
- 239000011159 matrix material Substances 0.000 claims abstract description 21
- 238000005070 sampling Methods 0.000 claims abstract description 17
- 238000012545 processing Methods 0.000 claims abstract description 6
- 230000006870 function Effects 0.000 claims description 11
- 238000003491 array Methods 0.000 claims description 3
- 230000005540 biological transmission Effects 0.000 claims description 3
- 238000005562 fading Methods 0.000 claims description 3
- 238000005516 engineering process Methods 0.000 description 5
- 238000011835 investigation Methods 0.000 description 4
- 238000004088 simulation Methods 0.000 description 4
- 230000007547 defect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000000284 extract Substances 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Images
Classifications
-
- 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
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The invention discloses a multi-information-source direct positioning method based on an unmanned aerial vehicle loading nested array, which comprises the steps that the unmanned aerial vehicle receives a plurality of radiation source signals at different positions and samples the received signals; respectively calculating a received signal sampling covariance matrix of each position, and carrying out vectorization processing on the received signal sampling covariance matrix; fusing the vectorized observation signals to obtain processed virtual receiving signals; and constructing a loss function of the position estimation by adopting a direct correlation method, and obtaining a final radiation source position estimation result through grid search. The method can effectively avoid the secondary loss of the position information, improve the positioning accuracy, realize the simultaneous positioning of multiple information sources without additional information matching, break through the limitation of the freedom degree of the array antenna and realize the simultaneous positioning of the multiple information sources when the number of the information sources is greater than the number of the array elements.
Description
Technical Field
The invention relates to the technical field of passive positioning, in particular to a multi-source direct positioning method based on an unmanned aerial vehicle loading nested array.
Background
Aiming at the problem of radiation source positioning, most of the traditional ground investigation modes are based on ground moving vehicles, and the traditional ground investigation modes are combined with handheld equipment, so that a large amount of manpower and material resources are needed, the traditional ground investigation modes are limited by the influence of complex environments and obstacles, the positioning accuracy is low, the positioning time is long, and the traditional ground investigation modes are very limited in practical application. Compare in ground platform, aerial platform based on unmanned aerial vehicle possess not influenced by ground complex environment, observation scope is wide, the advantage that the flexibility is strong. Therefore, the research of the positioning of the radiation source based on the unmanned aerial vehicle has very important engineering application value.
However, because of the dependence on the estimation of intermediate parameters such as the signal arrival angle, the signal arrival time difference and the like, the traditional two-step positioning technology is difficult to obtain the asymptotically optimal estimation precision, and the success or failure of the intermediate parameter estimation directly affects the result of subsequent positioning. In addition, when the problem of simultaneous positioning of multiple information sources is solved by the traditional two-step positioning, an additional information matching step is needed, and the practical application is not facilitated. The direct positioning technology directly extracts the position information from the original data layer without estimating intermediate parameters, effectively avoids the loss of useful information, and realizes the simultaneous positioning of multiple information sources while improving the positioning precision. However, because of the limitation of the degree of freedom of the array antenna, the existing direct positioning technology can only realize the simultaneous positioning of multiple information sources with the information source number smaller than the array element number. Therefore, how to break through the limitation of the degree of freedom of the array antenna while ensuring the positioning accuracy is a key problem.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a multi-information-source direct positioning method based on an unmanned aerial vehicle loading nested array, and by organically combining the advantages of an array antenna with a high-precision direct positioning technology, the problems that the positioning precision of the traditional two-step positioning method is limited and an additional information matching step is relied on are solved, and the problem that the existing direct positioning technology cannot realize the simultaneous positioning of multiple information sources when the number of the information sources exceeds the number of array elements is solved, and the multi-information-source precise positioning can be completed only by one unmanned aerial vehicle, so that the method has important engineering application value.
The invention provides the following technical scheme for achieving the aim:
the utility model provides a multi-source direct positioning method based on unmanned aerial vehicle loading nested array, its basic thinking is: the unmanned aerial vehicle receives a plurality of radiation source signals at L different positions and samples the received signals; respectively calculating a received signal sampling covariance matrix of each position, and carrying out vectorization processing on the received signal sampling covariance matrix; fusing the L vectorized observation signals to obtain vectorized virtual receiving signals; and constructing a loss function of the position estimation by adopting a direct correlation method, and obtaining a final radiation source position estimation result through grid search.
The invention is characterized by comprising the following steps:
step 1: the unmanned aerial vehicle receives a plurality of radiation source signals in L different positions, and samples the received signal:
suppose that the K source positions are respectively pk=[xk,yk]TThe unmanned aerial vehicle mounts a nested array with M elements, wherein M is N1+N2,N1And N2The number of the array elements of the two uniform linear arrays is respectively. The number of observation positions of the unmanned aerial vehicle is L, and the coordinates of the observation positions are respectivelyThen the receiving signal of the unmanned plane at the l position is
Wherein,is the power fading coefficient, λ is the wavelength, β is the path loss factor,dmindicating the position of the mth array element relative to the reference array element under the nested array pattern,sl,kand (t) is a transmission signal of a kth source.
Step 2: respectively calculating a received signal sampling covariance matrix of each position, and carrying out vectorization treatment on the received signal sampling covariance matrix:
because the actual signal sampling length is limited, the signal covariance matrix is replaced by the sampling covariance matrix and is calculated as
Wherein J is the number of fast beats. Vectorization processing is carried out on the covariance matrix of the received signal samples at the ith position to obtain
And step 3: fusing the L vectorized observation signals to obtain vectorized virtual receiving signals:
The virtual received signals of all L positions are fused to obtain the virtual received signals of L positions as
and 4, step 4: constructing a loss function of position estimation by adopting a direct correlation method, and obtaining a final radiation source position estimation result by grid search:
constructing a loss function according to the virtual received signal in step 3
Wherein, wl(p)=||p-ulThe | | is a balance factor,and searching the loss function to obtain coordinates corresponding to the first K peak values, namely the radiation source position estimation result.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the secondary loss of the position information is avoided, and the positioning precision is effectively improved;
the simultaneous positioning of multiple information sources can be realized without additional information matching;
and thirdly, the limitation of the degree of freedom of the array antenna is broken through, and the simultaneous positioning of multiple information sources when the number of the information sources is greater than the number of the array elements is realized.
Drawings
Fig. 1 is a flowchart of a multi-source direct positioning method based on an unmanned aerial vehicle-mounted nested array provided by the invention.
Fig. 2 is a multi-source positioning scene graph based on the unmanned aerial vehicle according to the present invention.
Fig. 3 is a comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method under different noise powers when the number of signal sources is less than the number of array elements.
Fig. 4 shows the comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method at different snapshots when the number of the information sources is less than the number of the array elements.
Fig. 5 is a comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method under different noise powers when the number of the source is greater than the number of the array elements.
Fig. 6 shows the comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method at different snapshots when the number of the source is greater than the number of the array elements.
Fig. 7 is a comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method at different snapshots when the number of the source is greater than the number of the array elements.
Detailed Description
The technical scheme of the invention is further described in detail by combining the drawings and the specific embodiments:
the detailed flow of the multi-information-source direct positioning method based on the unmanned aerial vehicle loading nested array is shown in fig. 1, wherein the unmanned aerial vehicle receives a plurality of radiation source signals at L different positions and samples the received signals; respectively calculating a received signal sampling covariance matrix of each position, and carrying out vectorization processing on the received signal sampling covariance matrix; fusing the L vectorized observation signals to obtain vectorized virtual receiving signals; and constructing a loss function of the position estimation by adopting a direct correlation method, and obtaining a final radiation source position estimation result through grid search. The concrete implementation is as follows:
step 1: the unmanned aerial vehicle receives a plurality of radiation source signals in L different positions, and samples the received signal:
suppose that the K source positions are respectively pk=[xk,yk]TThe unmanned aerial vehicle mounts a nested array with M elements, wherein M is N1+N2,N1And N2The number of the array elements of the two uniform linear arrays is respectively. The number of observation positions of the unmanned aerial vehicle is L, and the coordinates of the observation positions are respectivelyThen the receiving signal of the unmanned plane at the l position is
Wherein,is the power fading coefficient, λ is the wavelength, β is the path loss factor,dmindicating the position of the mth array element relative to the reference array element under the nested array pattern,sl,kand (t) is a transmission signal of a kth source.
Step 2: respectively calculating a received signal sampling covariance matrix of each position, and carrying out vectorization treatment on the received signal sampling covariance matrix:
because the actual signal sampling length is limited, the signal covariance matrix is replaced by the sampling covariance matrix and is calculated as
Wherein J is the number of fast beats. Vectorization processing is carried out on the covariance matrix of the received signal samples at the ith position to obtain
And step 3: fusing the L vectorized observation signals to obtain vectorized virtual receiving signals:
The virtual received signals of all L positions are fused to obtain the virtual received signals of L positions as
and 4, step 4: constructing a loss function of position estimation by adopting a direct correlation method, and obtaining a final radiation source position estimation result by grid search:
constructing a loss function according to the virtual received signal in step 3
Wherein, wl(p)=||p-ulThe | | is a balance factor,and searching the loss function to obtain coordinates corresponding to the first K peak values, namely the radiation source position estimation result.
FIG. 3 is a scattergram of the radiation source position estimation of the method of the present invention at a noise power of 0.8-watt, the number of elements of the nested array is 6, and the number of fast beats is 100. The signal power of the radiation source is 100-watt, the number of the radiation sources is 7, and the positions are respectively (400,200), (200,700), (600,400), (400,900), (300,500), (500,700) and (200,300), and the unit is m. The initial position of the unmanned aerial vehicle is used as the original point, the unmanned aerial vehicle continuously flies 10 observation points along the x axis, the flying speed is 20m/s, and the observation is carried out once every 5s of flying. As can be seen from the figure, the invention can effectively realize the simultaneous positioning of a plurality of radiation sources when the number of the information sources is greater than that of the array elements.
Fig. 4 is a comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method under different noise powers when the number of signal sources is less than the number of array elements. The simulation parameters are set as follows: the number of radiation sources is 3, and the positions are (400,200), (200,700) and (900,400) respectively, and the unit is m; the unmanned aerial vehicle carries a nested array with the array element number of 6, the unmanned aerial vehicle continuously flies 10 observation points along the x axis by taking the initial position of the unmanned aerial vehicle as an original point, the flying speed is 20m/s, and the observation is carried out once every 5 s; the number of fast beats is 100 and the noise power setting is shown in figure 4. It can be seen from the figure that when the number of the information sources is less than the number of the array elements, the positioning error of the method is reduced along with the reduction of the noise power, and the positioning error of the method is always lower than that of the traditional positioning method, so that the performance is obviously improved.
Fig. 5 shows the comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method at different snapshots when the number of the source is less than the number of the array elements. The simulation parameters are set as follows: the number of radiation sources is 3, the positions are (400,200), (200,700) and (900,400), the unit is m, and the source signal power is 50-watt; the unmanned aerial vehicle carries a nested array with the array element number of 6, the unmanned aerial vehicle continuously flies 10 observation points along the x axis by taking the initial position of the unmanned aerial vehicle as an original point, the flying speed is 20m/s, and the observation is carried out once every 5 s; the fast beat number setting is shown in fig. 5. It can be seen from the figure that when the number of the information sources is less than the number of the array elements, the positioning accuracy of the two methods is reduced along with the increase of the fast beat number, and the method disclosed by the invention always has lower positioning error.
Fig. 6 is a comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method under different noise powers when the number of the source is greater than the number of the array elements. The simulation parameters are set as follows: the number of radiation sources is 7, the positions are respectively (400,200), (200,700), (600,400), (400,900), (300,500), (500,700), (200,300), the unit is m, the power of the source signal is 80-watt; the unmanned aerial vehicle carries a nested array with the array element number of 6, the unmanned aerial vehicle continuously flies 10 observation points along the x axis by taking the initial position of the unmanned aerial vehicle as an original point, the flying speed is 20m/s, and the observation is carried out once every 5 s; the number of fast beats is 100 and the noise power setting is shown in figure 6. It can be seen from the figure that when the number of the information sources is greater than the number of the array elements, the method still has higher positioning accuracy under the condition of higher noise power, and compared with the traditional two-step positioning method, the method provided by the invention has the advantage that the positioning accuracy is obviously improved.
Fig. 7 is a comparison of the positioning performance of the method of the present invention and the conventional two-step positioning method at different snapshots when the number of the source is greater than the number of the array elements. The simulation parameters are set as follows: the number of radiation sources is 7, the positions are respectively (400,200), (200,700), (600,400), (400,900), (300,500), (500,700), (200,300), the unit is m, the power of the source signal is 50-watt; the unmanned aerial vehicle carries a nested array with the array element number of 6, the unmanned aerial vehicle continuously flies 10 observation points along the x axis by taking the initial position of the unmanned aerial vehicle as an original point, the flying speed is 20m/s, and the observation is carried out once every 5 s; the fast beat number setting is shown in fig. 7. As can be seen from the figure, when the number of the information sources is greater than the number of the array elements, the method still has higher positioning accuracy under the condition of small snapshot number, and compared with the traditional two-step positioning method, the method provided by the invention has the advantage that the positioning accuracy is obviously improved.
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-information-source direct positioning method based on an unmanned aerial vehicle loaded nested array is characterized by comprising the following steps:
step 1: the unmanned aerial vehicle receives a plurality of radiation source signals in L different positions, and samples the received signal:
let K information source positions be p respectivelyk=[xk,yk]TThe unmanned aerial vehicle mounts a nested array with M elements, wherein M is N1+N2,N1And N2The number of the array elements of the two uniform linear arrays is respectively; the number of observation positions of the unmanned aerial vehicle is L, and the coordinates of the observation positions are respectivelyThen the receiving signal of the unmanned plane at the l position is
Wherein,is the power fading coefficient, λ is the wavelength, β is the path loss factor,dmindicating the position of the mth array element relative to the reference array element under the nested array pattern,sl,k(t) is a transmission signal of a kth source;
step 2: respectively calculating a received signal sampling covariance matrix of each position, and carrying out vectorization treatment on the received signal sampling covariance matrix:
due to the finite length of the actual signal samples, the signal covariance matrix is replaced by the sampling covariance matrix as follows:
wherein J is the number of fast beats; vectorization processing is carried out on the covariance matrix of the received signal samples at the ith position to obtain
and step 3: fusing the L vectorized observation signals to obtain vectorized virtual receiving signals:
The virtual received signals of all L positions are fused to obtain the virtual received signals of L positions as
and 4, step 4: constructing a loss function of position estimation by adopting a direct correlation method, and obtaining a final radiation source position estimation result by grid search:
constructing a loss function according to the virtual received signal in step 3
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010622449.7A CN112269160A (en) | 2020-12-17 | 2020-12-17 | Multi-information-source direct positioning method based on unmanned aerial vehicle loading nested array |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010622449.7A CN112269160A (en) | 2020-12-17 | 2020-12-17 | Multi-information-source direct positioning method based on unmanned aerial vehicle loading nested array |
Publications (1)
Publication Number | Publication Date |
---|---|
CN112269160A true CN112269160A (en) | 2021-01-26 |
Family
ID=74349068
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202010622449.7A Pending CN112269160A (en) | 2020-12-17 | 2020-12-17 | Multi-information-source direct positioning method based on unmanned aerial vehicle loading nested array |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN112269160A (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
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 |
CN113406564A (en) * | 2021-05-31 | 2021-09-17 | 西北工业大学 | Loop stationary signal direct positioning method based on nested array |
Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN107907855A (en) * | 2017-10-25 | 2018-04-13 | 天津大学 | A kind of coprime array switching DOA estimation method and device for even linear array |
CN109239657A (en) * | 2018-09-05 | 2019-01-18 | 南京航空航天大学 | Load the radiation source high-precision locating method under nested battle array unmanned aerial vehicle platform |
CN110333480A (en) * | 2019-06-27 | 2019-10-15 | 南京航空航天大学 | A kind of single unmanned plane multiple target AOA localization method based on cluster |
CN111123197A (en) * | 2019-12-21 | 2020-05-08 | 杭州电子科技大学 | TDOA-based target radiation source positioning method |
CN111766560A (en) * | 2020-06-29 | 2020-10-13 | 南京航空航天大学 | Multi-information-source high-precision direct positioning method based on unmanned aerial vehicle mobile monitoring |
-
2020
- 2020-12-17 CN CN202010622449.7A patent/CN112269160A/en active Pending
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN107907855A (en) * | 2017-10-25 | 2018-04-13 | 天津大学 | A kind of coprime array switching DOA estimation method and device for even linear array |
CN109239657A (en) * | 2018-09-05 | 2019-01-18 | 南京航空航天大学 | Load the radiation source high-precision locating method under nested battle array unmanned aerial vehicle platform |
CN110333480A (en) * | 2019-06-27 | 2019-10-15 | 南京航空航天大学 | A kind of single unmanned plane multiple target AOA localization method based on cluster |
CN111123197A (en) * | 2019-12-21 | 2020-05-08 | 杭州电子科技大学 | TDOA-based target radiation source positioning method |
CN111766560A (en) * | 2020-06-29 | 2020-10-13 | 南京航空航天大学 | Multi-information-source high-precision direct positioning method based on unmanned aerial vehicle mobile monitoring |
Non-Patent Citations (1)
Title |
---|
ZHAN SHI,ET AL: "DOA estimation with synthetic nested array using moving sensor", 《ADVANCES IN ENGINEERING RESEARCH》 * |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
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 |
CN113406564A (en) * | 2021-05-31 | 2021-09-17 | 西北工业大学 | Loop stationary signal direct positioning method based on nested array |
CN113406564B (en) * | 2021-05-31 | 2024-03-22 | 西北工业大学 | Direct positioning method for cyclostationary signal based on nested array |
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 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN112269160A (en) | Multi-information-source direct positioning method based on unmanned aerial vehicle loading nested array | |
CN111766560B (en) | Multi-information-source high-precision direct positioning method based on unmanned aerial vehicle mobile monitoring | |
CN112698264B (en) | DOA estimation method for coherent information source under augmented inter-mass array impulse noise environment | |
CN109975749B (en) | Short-wave single-station direct positioning method under condition of existence of correction source | |
CN110297213A (en) | Radiation source positioning device and method based on the unmanned aerial vehicle platform for loading relatively prime linear array | |
CN108663654B (en) | 360-degree all-dimensional dynamic direction finding method based on continuous quantum pigeon group | |
CN114488034A (en) | Passive detection and interference reconnaissance integrated device and method | |
CN113835063A (en) | Unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method | |
CN110231589B (en) | Multipath signal direction-of-arrival estimation method with large diffusion angle | |
CN110413939B (en) | Arrival angle estimation method based on atomic norm | |
CN109696651B (en) | M estimation-based direction-of-arrival estimation method under low snapshot number | |
CN113759303B (en) | Gridless angle of arrival estimation method based on particle swarm optimization | |
CN113391261A (en) | Extended co-prime array rapid DOA estimation method based on Taylor expansion | |
CN113625220A (en) | New method for quickly estimating direction of arrival and diffusion angle of multipath signal | |
CN115826004A (en) | Three-satellite cooperative direct positioning method based on two-dimensional angle and time difference combination | |
CN115616477A (en) | Non-plane wave monopulse angle measurement method | |
CN113777558A (en) | Rotation-invariant PM direct positioning method for unmanned aerial vehicle target | |
CN112255590B (en) | Low-altitude sound source inversion positioning method and device based on fuzzy function matching | |
CN114019445A (en) | Two-dimensional arrival angle measuring method based on position clustering dynamic sparse reconstruction | |
Wu et al. | Improving line-of-sight pointing accuracy of laser communication system based on Kalman filter | |
CN109358312B (en) | Method, device, medium and equipment for determining incoming wave direction of incident signal | |
CN111382830A (en) | Signal arrival angle estimation method and device based on hybrid particle swarm optimization | |
CN111948620A (en) | Target passive cooperative detection method and system based on multi-type external radiation sources | |
CN116087875B (en) | Indoor non-line-of-sight scene passive tag three-dimensional positioning method based on environment information | |
CN111585631A (en) | Beam forming method for improving transmission gain of distributed polarization sensitive array |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
WD01 | Invention patent application deemed withdrawn after publication | ||
WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20210126 |