CN109975755B - Short-wave multi-station direct positioning method under condition of existence of correction source - Google Patents

Short-wave multi-station direct positioning method under condition of existence of correction source Download PDF

Info

Publication number
CN109975755B
CN109975755B CN201910142925.2A CN201910142925A CN109975755B CN 109975755 B CN109975755 B CN 109975755B CN 201910142925 A CN201910142925 A CN 201910142925A CN 109975755 B CN109975755 B CN 109975755B
Authority
CN
China
Prior art keywords
longitude
latitude
source
station
correction
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.)
Active
Application number
CN201910142925.2A
Other languages
Chinese (zh)
Other versions
CN109975755A (en
Inventor
王鼎
尹洁昕
唐涛
杨宾
张莉
吴志东
吴瑛
李崇
贾昌贵
陈鑫
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Information Engineering University of PLA Strategic Support Force
Original Assignee
Information Engineering University of PLA Strategic Support Force
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Information Engineering University of PLA Strategic Support Force filed Critical Information Engineering University of PLA Strategic Support Force
Priority to CN201910142925.2A priority Critical patent/CN109975755B/en
Publication of CN109975755A publication Critical patent/CN109975755A/en
Application granted granted Critical
Publication of CN109975755B publication Critical patent/CN109975755B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

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
    • G01S5/04—Position of source determined by a plurality of spaced direction-finders

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 relates to the technical field of short-wave multi-station positioning, and discloses a short-wave multi-station direct positioning method under the condition of a correction source. Due to the existence of the correction source, the method provided by the invention can effectively inhibit the influence of array amplitude-phase errors on the shortwave multi-station positioning accuracy.

Description

Short-wave multi-station direct positioning method under condition of existence of correction source
Technical Field
The invention relates to the technical field of short-wave multi-station positioning, in particular to a short-wave multi-station direct positioning method under the condition of a correction source.
Background
As is well known, the wireless signal positioning technology is widely applied to the fields of communication, radar, target monitoring, navigation and telemetry, seismic surveying, radio astronomy, emergency rescue, safety management and the like, and plays an important role in industrial production and military application. The positioning (i.e. position parameter estimation) of the target can be accomplished by using active devices such as radar, laser, sonar and the like, which are called as active positioning technologies and have the advantages of all weather, high precision and the like. However, the active positioning system usually needs to transmit a high-power electromagnetic signal to implement, so that the position of the active positioning system is very easy to expose, and the active positioning system is easy to be found by the other party, and is affected by the electronic interference of the other party, so that the positioning performance is greatly deteriorated, and even the safety and reliability of the system are compromised.
Target location may also be achieved using radio signals radiated or scattered by the target (actively), a technique referred to as passive location, which refers to estimating target location parameters by receiving radio signals radiated or scattered by the target without the observation station actively transmitting electromagnetic signals. Compared with an active positioning system, the passive positioning system has the advantages of no active transmission of electromagnetic signals, strong viability, long reconnaissance action distance and the like, thereby obtaining wide attention and deep research of domestic and foreign scholars. The passive positioning system can be divided into a single-station passive positioning system and a multi-station passive positioning system according to the number of observation stations, wherein the multi-station positioning system can provide more observed quantities, so that the target positioning precision is improved.
As is known, short-wave multi-station positioning is an important multi-station passive positioning system which is mainly applied to positioning over-the-horizon long-distance targets. Array amplitude and phase errors are an important factor influencing positioning accuracy, and occur when the array antenna of each observation station is not subjected to channel correction.
On the other hand, most of the existing passive positioning processes can be generalized to a two-step estimation positioning mode, that is, first, positioning parameters (such as azimuth, delay difference, doppler, etc.) are extracted from signal data, and then, based on the parameters, position information of a target is calculated. Although this two-step positioning mode has been widely used in modern positioning systems, israeli a.j.weiss and a.amar have pointed out several drawbacks that exist therein and have proposed the idea of a single-step direct positioning, the basic idea of which is to determine the position parameters of an object directly from acquired signal data without estimating other intermediate positioning parameters. Obviously, the single-step direct positioning mode is also suitable for short-wave multi-station positioning scenes under the condition that array amplitude and phase errors exist, and only the direct positioning method is also influenced by the array amplitude and phase errors, so that larger positioning deviation is generated.
Disclosure of Invention
Aiming at the problem of influence of array amplitude-phase errors, the invention provides a short-wave multi-station direct positioning method under the condition of a correction source, so as to improve the multi-station positioning precision of a short-wave radiation source.
In order to achieve the purpose, the invention adopts the following technical scheme:
a short-wave multi-station direct positioning method under the condition of existence of a correction source comprises the following steps:
step 1: d short wave correction sources with known longitude and latitude are simultaneously placed on the periphery of the area where the short wave target source is located;
step 2: receiving a target source signal and D correction source signals by using N observation stations, wherein each observation station acquires K signal samples by using a uniform circular array which is not corrected by a channel, and establishes an array signal model corresponding to the K signal samples;
and step 3: determining the relationship between the azimuth angle and the elevation angle of a target source signal reaching N observation stations and the longitude and latitude and the virtual height of an ionosphere of the target source respectively;
and 4, step 4: determining the relation between the azimuth angle and the elevation angle of the D correction source signals reaching the N observation stations and the longitude and latitude and the ionospheric virtual height of the D correction source signals;
and 5: each observation station utilizes an array signal model corresponding to the collected K signal samples to construct a covariance matrix, and transmits the covariance matrix to a central station in the N observation stations;
step 6: the central station constructs a cost function for jointly estimating the latitude and longitude of a target source, the ionosphere virtual height and the multi-array amplitude-phase error based on the maximum likelihood criterion by using the covariance matrixes of the N observation stations;
and 7: and performing joint estimation on the longitude and latitude of the target source, the virtual height of the ionized layer and the multi-array amplitude-phase error by using an alternative iterative algorithm according to the relation between the azimuth angle and the elevation angle of the target source signal reaching the N observation stations and the longitude and latitude and the virtual height of the ionized layer of the target source, the relation between the azimuth angle and the elevation angle of the D correction source signal reaching the N observation stations and the longitude and latitude and the virtual height of the D correction source and the virtual height of the ionized layer and the cost function, thereby determining the position information of the target.
Further, the array signal model in step 2 is:
Figure RE-GDA0002057342520000021
in the formula, xn(tk) Receiving signals for a kth array of an nth observation station; sc,n,d(tk) A complex envelope for the d-th corrected source signal to reach the nth observation station; st,n(tk) A complex envelope for the target source signal to reach the nth observation station; epsilonn(tk) Uniform circular array additive noise of the nth observation station;
Figure RE-GDA0002057342520000033
a complex envelope vector for the signal arriving at the nth observation station; h isnIonospheric pseudo-heights experienced by signals arriving at the nth observation station; a isn(ωc,d,ρc,d,hn) For the array manifold vector, ω, of the d-th corrected source signal arriving at the nth observation stationc,dTo correct for source longitude, pc,dTo correct for source latitude, hnIs ionospheric pseudo-height; a isn(ωt,ρt,hn) Array manifold vector, omega, for the arrival of target source signals at the nth observation stationtAs the target source longitude, ρtIs the target source latitude;
Figure RE-GDA0002057342520000034
for the nth observationAn array manifold matrix of stations; gamma-shapednIs the amplitude-phase error matrix of the nth observation station.
Further, the step 3 comprises:
step 3.1: converting the longitude and latitude coordinates of the target source into a horizon coordinate with the observation station as the center according to the formula (2):
Figure RE-GDA0002057342520000031
in the formula (x)t,n,g,yt,n,g,zt,n,g) Coordinates of the target source under the horizontal coordinate system of the nth observation station are obtained; omegao,nAnd ρo,nLongitude and latitude of the nth observation station respectively; r is the radius of the earth;
step 3.2: obtaining the azimuth angle theta according to the formula (2)t,nAnd longitude ωtLatitude rhotAnd ionospheric pseudo-height hnThe relationship of (1):
Figure RE-GDA0002057342520000032
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002057342520000041
Figure RE-GDA0002057342520000042
step 3.3: a triangle is constructed through the observation station, the sphere center point and the ionized layer, and the elevation angle beta is obtained by utilizing the sine theorem of the triangletAnd longitude ωtLatitude rhotAnd ionospheric pseudo-height h relation:
Figure RE-GDA0002057342520000043
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002057342520000044
the internal angle of the triangle with the center point as the vertex is shown.
Further, the step 4 comprises:
step 4.1: converting the longitude and latitude coordinates of the d correction source into a horizon coordinate with the observation station as the center according to the formula (5):
Figure RE-GDA0002057342520000045
in the formula (x)d,n,g,yd,n,g,zd,n,g) Coordinates of a d correction source target source in a horizontal coordinate system of an nth observation station;
step 4.2: obtaining the azimuth angle theta according to the formula (5)c,d,nAnd longitude ωc,dAnd latitude rhoc,dThe relationship of (1):
Figure RE-GDA0002057342520000046
step 4.3: using the sine theorem of triangle to obtain the elevation angle betac,d,nAnd longitude ωc,dLatitude rhoc,dAnd ionospheric pseudo-height hnThe relationship of (1):
Figure RE-GDA0002057342520000047
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002057342520000051
further, the step 5 comprises:
step 5.1: the nth observation station utilizes an array signal model { x ] corresponding to the collected K signal samplesn(tk)}1≤k≤KConstructing an array output covariance matrix
Figure RE-GDA0002057342520000052
Figure RE-GDA0002057342520000053
Step 5.2: each of the observatory stations communicates the constructed covariance matrix to a central station of the N observatory stations.
Further, the step 6 comprises:
the central station utilizes the covariance matrix of the N observers
Figure RE-GDA0002057342520000054
Joint estimation target source longitude omega based on maximum likelihood criterion constructiontLatitude rhotAnd the ionized layer virtual height { hn}1≤n≤NAnd a multi-array amplitude-phase error matrix { gamman}1≤n≤NThe cost function of (2); the cost function is:
Figure RE-GDA0002057342520000055
wherein h ═ h1h2…hN]TIndicating ionospheric pseudo-height parameters;
Figure RE-GDA0002057342520000056
representing an array amplitude and phase error parameter; II type⊥[ΓnAn(ωt,ρt,hn)]Representing orthogonal projection matrices, Π⊥[ΓnAn(ωt,ρt,hn)]＝I-ΓnAn(ωt,ρt,hn)((ΓnAn(ωt,ρt,hn))HΓnAn(ωt,ρt,hn))-1(ΓnAn(ωt,ρt,hn))H, (1≤n≤N)
Wherein I is an identity matrix.
Further, the step 7 includes:
step 7.1: will omegat、ρtAnd { hn}1≤n≤NAs a first set of parameters, { Γn}1≤n≤NAs a second set of parameters, the second set of parameters is fixed to the current update value, i.e. { Γ }n}1≤n≤NIs fixed to
Figure RE-GDA0002057342520000061
Fix g as
Figure RE-GDA00020573425200000611
Estimating a first group of parameters according to a relation between an azimuth angle and an elevation angle of a target source signal reaching N observation stations and a longitude and latitude and an ionospheric virtual height of the target source respectively, a relation between an azimuth angle and an elevation angle of D correction source signals reaching N observation stations and a longitude and latitude and a virtual height of the ionospheric layer respectively, and the cost function according to an equation (10):
Figure RE-GDA0002057342520000062
wherein mu is a step factor, mu is more than 0 and less than 1, muiIs the ith iteration step size factor;
Figure RE-GDA0002057342520000063
and h(i)Are all the ith iteration result;
Figure RE-GDA0002057342520000064
and h(i+1)All are the (i +1) th iteration results;
Figure RE-GDA0002057342520000065
is a gradient vector;
Figure RE-GDA0002057342520000066
is a Hessian matrix;
Figure RE-GDA0002057342520000067
Figure RE-GDA0002057342520000068
wherein the expressions of the elements are respectively
Figure RE-GDA0002057342520000069
Figure RE-GDA00020573425200000610
Figure RE-GDA0002057342520000071
Figure RE-GDA0002057342520000072
In the formula (I), the compound is shown in the specification,
Figure RE-GDA0002057342520000073
Figure RE-GDA0002057342520000074
Figure RE-GDA0002057342520000081
Figure RE-GDA0002057342520000082
Figure RE-GDA0002057342520000083
Figure RE-GDA0002057342520000084
Figure RE-GDA0002057342520000085
Figure RE-GDA0002057342520000086
Figure RE-GDA0002057342520000087
Figure RE-GDA0002057342520000088
Figure RE-GDA0002057342520000091
Figure RE-GDA0002057342520000092
Figure RE-GDA0002057342520000093
in the formula InIs the radius of the uniform circular array of the nth observation station, lambda is the signal wavelength,
Figure RE-GDA0002057342520000094
is the last column vector in the (D +1) × (D +1) order identity matrix;
step 7.2: fixing the first set of parameters to the current update value, i.e. ωt、ρtAnd h are eachIs fixed to
Figure RE-GDA0002057342520000095
And
Figure RE-GDA0002057342520000096
according to the relation between the azimuth angle and the elevation angle of the target source signal reaching the N observation stations and the longitude and latitude and the virtual height of the ionized layer, the relation between the azimuth angle and the elevation angle of the D correction source signal reaching the N observation stations and the longitude and latitude and the virtual height of the ionized layer and the cost function, the second group of parameters are optimized and solved according to the formula (11):
Figure RE-GDA0002057342520000097
in the formula, g(i)Is the result of the ith iteration; g(i+1)Is the (i +1) th iteration result;
Figure RE-GDA0002057342520000098
is a gradient vector;
Figure RE-GDA0002057342520000099
is a Hessian matrix;
Figure RE-GDA00020573425200000910
Figure RE-GDA0002057342520000101
wherein the expressions of the elements are respectively
Figure RE-GDA0002057342520000102
Figure RE-GDA0002057342520000103
Step 7.3: and (3) alternately carrying out optimization solution on the first set of parameters and the second set of parameters according to the formula (10) and the formula (11) until iteration converges.
Compared with the prior art, the invention has the following beneficial effects:
the method comprises the steps of firstly, simultaneously placing a plurality of short wave correction sources with known positions near a short wave target source, receiving short wave signal data (simultaneously containing a target source signal and a correction source signal) by utilizing uniform circular arrays in a plurality of observation stations, then determining the relation between azimuth angles and elevation angles of signals reaching different observation stations, longitude and latitude degrees and ionospheric virtual height parameters of the signals, then constructing a cost function for jointly estimating the longitude and latitude degrees, ionospheric virtual height parameters and multi-array amplitude-phase errors of the target source by utilizing a maximum likelihood criterion, and finally, jointly estimating the longitude and latitude degrees, ionospheric virtual height and multi-array amplitude-phase errors of the target source by utilizing an alternating iterative algorithm, thereby determining the position information of the target. Based on the basic idea of direct positioning, the short-wave signal source is positioned by utilizing a correction source with accurately known position, and the positioning deviation caused by the amplitude-phase error of multiple arrays can be effectively eliminated, so that the short-wave multi-station positioning accuracy is improved.
Drawings
Fig. 1 is a flowchart of a shortwave multi-station direct positioning method in the presence of a calibration source according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of coordinate system transformation according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a triangle for determining an elevation expression according to an embodiment of the present invention.
Fig. 4 is a diagram illustrating multi-station data transmission according to an embodiment of the present invention.
FIG. 5 is a graph of RMS error versus SNR for a target source in accordance with an embodiment of the present invention.
Fig. 6 is a graph of variation of the ionospheric pseudo-high estimated root mean square error with the target source signal-to-noise ratio according to an embodiment of the present invention.
FIG. 7 is a graph showing the variation of the RMS error of the array amplitude-phase error estimate with the SNR of the target source according to an embodiment of the present invention.
FIG. 8 is a graph of root mean square error versus radius of a circular array for target source positioning according to an embodiment of the present invention.
Fig. 9 is a graph of variation of the ionospheric pseudo-height estimated root mean square error with the ratio of the radius of the circular array to the wavelength, in accordance with an embodiment of the present invention.
FIG. 10 is a graph showing the variation of the estimated root mean square error of the array amplitude-phase error with the ratio of the radius of the circular array to the wavelength according to the embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
the first embodiment is as follows:
as shown in fig. 1, a short-wave multi-station direct positioning method in the presence of a calibration source includes the following steps:
step S101: d short wave correction sources with known longitude and latitude are simultaneously placed on the periphery of the area where the short wave target source is located;
step S102: receiving a target source signal and D correction source signals by using N observation stations, wherein each observation station acquires K signal samples by using a uniform circular array which is not corrected by a channel, and establishes an array signal model corresponding to the K signal samples;
step S103: determining the relationship between the azimuth angle and the elevation angle of a target source signal reaching N observation stations and the longitude and latitude and the virtual height of an ionosphere of the target source respectively;
step S104: determining the relation between the azimuth angle and the elevation angle of the D correction source signals reaching the N observation stations and the longitude and latitude and the ionospheric virtual height of the D correction source signals;
step S105: each observation station utilizes an array signal model corresponding to the collected K signal samples to construct a covariance matrix, and transmits the covariance matrix to a central station in the N observation stations;
step S106: the central station constructs a cost function for jointly estimating the latitude and longitude of a target source, the ionosphere virtual height and the multi-array amplitude-phase error based on the maximum likelihood criterion by using the covariance matrixes of the N observation stations;
step S107: and performing joint estimation on the longitude and latitude of the target source, the virtual height of the ionized layer and the multi-array amplitude-phase error by using an alternative iterative algorithm according to the relation between the azimuth angle and the elevation angle of the target source signal reaching the N observation stations and the longitude and latitude and the virtual height of the ionized layer of the target source, the relation between the azimuth angle and the elevation angle of the D correction source signal reaching the N observation stations and the longitude and latitude and the virtual height of the D correction source and the virtual height of the ionized layer and the cost function, thereby determining the position information of the target.
Specifically, in step S101, D short-wave calibration sources with accurately known longitude and latitude are simultaneously placed around the area where the short-wave target source is located, where the longitude of the target source is ωtLatitude is rhotThe longitude of the D (1 ≦ D ≦ D) th correction source is ωc,dLatitude is rhoc,d。
Specifically, in step S102, D +1 short-wave signals (including D correction source signals and 1 target source signal) reach N observation stations after being subjected to ionospheric scattering, each observation station receives the short-wave signals by using a uniform circular array that is not subjected to channel correction, and acquires K signal samples in total, so that an array signal model of the nth observation station in the presence of an array amplitude-phase error is:
Figure RE-GDA0002057342520000131
in the formula, xn(tk) Receiving signals for a kth array of an nth observation station; sc,n,d(tk) A complex envelope for the d-th corrected source signal to reach the nth observation station; st,n(tk) A complex envelope for the target source signal to reach the nth observation station; epsilonn(tk) Uniform circular array additive noise of the nth observation station;
Figure RE-GDA0002057342520000133
a complex envelope vector for the signal arriving at the nth observation station; h isnIonospheric pseudo-heights experienced by signals arriving at the nth observation station; a isn(ωc,d,ρc,d,hn) For the array manifold vector of the d-th corrected source signal arriving at the nth observation stationSimultaneously with the correction of the source longitude omegac,dLatitude rhoc,dAnd ionospheric pseudo-height hnA total of 3 parameters are related; a isn(ωt,ρt,hn) Array manifold vector for target source signal to reach nth observation station, which is simultaneously with target source longitude omegatLatitude rhotAnd ionospheric pseudo-height hnA total of 3 parameters are related;
Figure RE-GDA0002057342520000134
for the array manifold matrix of the nth observation station, since the correction source longitude and latitude are precisely known, it is only considered as being with respect to the target source longitude ωtLatitude rhotAnd ionospheric pseudo-height hnA function of (a); gamma-shapednThe amplitude-phase error matrix for the nth observation station is a diagonal matrix, and the first diagonal element can be set to 1.
Specifically, the step S103 includes:
step S103.1: converting the longitude and latitude coordinates of the target source into a horizon coordinate with the observation station as the center according to the formula (2), as shown in fig. 2:
Figure RE-GDA0002057342520000132
in the formula (x)t,n,g,yt,n,g,zt,n,g) Coordinates of the target source under the horizontal coordinate system of the nth observation station are obtained; omegao,nAnd ρo,nLongitude and latitude of the nth observation station respectively; r is the radius of the earth;
step S103.2: obtaining the azimuth angle theta according to the formula (2)t,nAnd longitude ωtLatitude rhotAnd ionospheric pseudo-height hnThe relationship of (1):
Figure RE-GDA0002057342520000141
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002057342520000142
Figure RE-GDA0002057342520000143
step S103.3: a triangle is constructed through the observation station, the sphere center point and the ionosphere, the triangle is shown as delta ABC in figure 3, and the elevation angle beta is obtained by utilizing the sine theorem of the triangletAnd longitude ωtLatitude rhotAnd ionospheric pseudo-height h relation:
Figure RE-GDA0002057342520000144
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002057342520000145
the internal angle of the triangle with the center point as the vertex is shown.
Specifically, the step S104 includes:
step S104.1: converting the longitude and latitude coordinates of the d correction source into a horizon coordinate with the observation station as the center according to the formula (5):
Figure RE-GDA0002057342520000146
in the formula (x)d,n,g,yd,n,g,zd,n,g) Coordinates of a d correction source target source in a horizontal coordinate system of an nth observation station;
step S104.2: obtaining the azimuth angle theta according to the formula (5)c,d,nAnd longitude ωc,dAnd latitude rhoc,dThe relationship of (1):
Figure RE-GDA0002057342520000151
step S104.3: from Δ ABC shown in FIG. 3, the elevation angle β is obtained by using the sine theorem of trianglesc,d,nAnd longitude ωc,dLatitude rhoc,dAnd ionospheric pseudo-height hnThe relationship of (1):
Figure RE-GDA0002057342520000152
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002057342520000153
specifically, the step S105 includes:
step S105.1: the nth observation station utilizes an array signal model { x ] corresponding to the collected K signal samplesn(tk)}1≤k≤KConstructing an array output covariance matrix
Figure RE-GDA0002057342520000154
Figure RE-GDA0002057342520000155
Step S105.2: each of the observers transmits the constructed covariance matrix to a central station of the N observers, as shown in fig. 4, wherein the 1 st observer station (observer station 1) is the central station, and the other observers transmit the constructed covariance matrix to the 1 st observer station.
Specifically, the step S106 includes:
the central station utilizes the covariance matrix of the N observers
Figure RE-GDA0002057342520000156
Joint estimation target source longitude omega based on maximum likelihood criterion constructiontLatitude rhotAnd the ionized layer virtual height { hn}1≤n≤NAnd a multi-array amplitude-phase error matrix { gamman}1≤n≤NThe cost function of (2); the cost function is:
Figure RE-GDA0002057342520000157
wherein h ═ h1h2…hN]TIndicating ionospheric pseudo-height parameters;
Figure RE-GDA0002057342520000158
representing array amplitude-phase error parameters, wherein vecd () represents that diagonal elements of a diagonal matrix are extracted to form vectors; II type⊥[ΓnAn(ωt,ρt,hn)]A matrix of orthogonal projections is represented which,
Π⊥[ΓnAn(ωt,ρt,hn)]＝I-ΓnAn(ωt,ρt,hn)((ΓnAn(ωt,ρt,hn))HΓnAn(ωt,ρt,hn))-1(ΓnAn(ωt,ρt,hn))H, (1≤n≤N)
wherein I is an identity matrix.
Specifically, the step S107 includes:
step S107.1: will omegat、ρtAnd { hn}1≤n≤NAs a first set of parameters, { Γn}1≤n≤NAs a second set of parameters, the second set of parameters is fixed to the current update value, i.e. { Γ }n}1≤n≤NIs fixed to
Figure RE-GDA0002057342520000161
Fix g as
Figure RE-GDA0002057342520000162
Estimating a first group of parameters according to a relation between an azimuth angle and an elevation angle of a target source signal reaching N observation stations and a longitude and latitude and an ionospheric virtual height of the target source respectively, a relation between an azimuth angle and an elevation angle of D correction source signals reaching N observation stations and a longitude and latitude and a virtual height of the ionospheric layer respectively, and the cost function according to an equation (10):
Figure RE-GDA0002057342520000163
wherein mu is a step factor, mu is more than 0 and less than 1, muiIs the ith iteration step size factor;
Figure RE-GDA0002057342520000164
and h(i)Are all the ith iteration result;
Figure RE-GDA0002057342520000165
and h(i+1)All are the (i +1) th iteration results;
Figure RE-GDA0002057342520000166
is a gradient vector;
Figure RE-GDA0002057342520000167
is a Hessian matrix;
Figure RE-GDA0002057342520000168
and
Figure RE-GDA0002057342520000169
are respectively expressed as
Figure RE-GDA00020573425200001610
Figure RE-GDA0002057342520000171
Wherein the expressions of the elements are respectively
Figure RE-GDA0002057342520000172
Figure RE-GDA0002057342520000173
Figure RE-GDA0002057342520000174
Figure RE-GDA0002057342520000175
Figure RE-GDA0002057342520000176
Figure RE-GDA0002057342520000177
Figure RE-GDA0002057342520000178
Figure RE-GDA0002057342520000181
In the formula, n1Representing the n-th matrix1Line, n2Representing the n-th matrix2Columns;
it is worth mentioning that it is possible to show,
Figure RE-GDA0002057342520000182
and
Figure RE-GDA0002057342520000183
and
Figure RE-GDA0002057342520000184
the expressions of the elements are respectively the same;
Figure RE-GDA0002057342520000185
Figure RE-GDA0002057342520000186
Figure RE-GDA0002057342520000187
Figure RE-GDA0002057342520000188
Figure RE-GDA0002057342520000189
Figure RE-GDA00020573425200001810
Figure RE-GDA0002057342520000191
Figure RE-GDA0002057342520000192
Figure RE-GDA0002057342520000193
Figure RE-GDA0002057342520000194
Figure RE-GDA0002057342520000195
Figure RE-GDA0002057342520000196
Figure RE-GDA0002057342520000197
Figure RE-GDA0002057342520000198
in the formula InIs the radius of the uniform circular array of the nth observation station, lambda is the signal wavelength,
Figure RE-GDA0002057342520000199
is the last column vector in the (D +1) × (D +1) identity matrix.
Step S107.2: fixing the first set of parameters to the current update value, i.e. ωt、ρtAnd h are respectively fixed to
Figure RE-GDA00020573425200001910
And
Figure RE-GDA00020573425200001911
according to the relation between the azimuth angle and the elevation angle of the target source signal reaching the N observation stations and the longitude and latitude and the virtual height of the ionized layer, the relation between the azimuth angle and the elevation angle of the D correction source signal reaching the N observation stations and the longitude and latitude and the virtual height of the ionized layer and the cost function, the second group of parameters are optimized and solved according to the formula (11):
Figure RE-GDA00020573425200001912
in the formula, g(i)Is the result of the ith iteration; g(i+1)Is the (i +1) th iteration result;
Figure RE-GDA00020573425200001913
is a gradient vector;
Figure RE-GDA0002057342520000201
is a Hessian matrix;
Figure RE-GDA0002057342520000202
Figure RE-GDA0002057342520000203
wherein the expressions of the elements are respectively
Figure RE-GDA0002057342520000204
Figure RE-GDA0002057342520000205
Figure RE-GDA0002057342520000211
Figure RE-GDA0002057342520000212
Step S107.3: and (3) alternately carrying out optimization solution on the first set of parameters and the second set of parameters according to the formula (10) and the formula (11) until iteration converges.
To verify the effect of the present invention, the following experimental data are provided.
Assuming that 3 observation stations are used for positioning the short-wave target source, the longitude of the 1 st observation station is 124.49 degrees of east longitude, the latitude of the 1 st observation station is 40.75 degrees of north latitude, the longitude of the 2 nd observation station is 114.04 degrees of east longitude, the latitude of the 2 nd observation station is 34.68 degrees of north latitude, the longitude of the 3 rd observation station is 118.30 degrees of east longitude, and the latitude of the 3 rd observation station is 26.80 degrees of north latitude, wherein the 1 st observation station is defaulted as a central station; the longitude of the short wave target source is 122.46 degrees, and the latitude is 27.82 degrees; now two short wave correction sources are placed, the longitude of the 1 st correction source is 123.62 degrees for east longitude, 28.68 degrees for latitude for north latitude, the longitude of the 2 nd correction source is 124.54 degrees for east longitude, and 29.96 degrees for latitude for north latitude. Even circular arrays are installed on 3 observation stations, each circular array comprises 10 antennas, the number of signal sample points for direct positioning is 500, the ionospheric virtual heights of short-wave target source signals and correction source signals reaching the 3 observation stations are 270 kilometers, 310 kilometers and 360 kilometers respectively, and the target source signal-to-noise ratio and the correction source signal-to-noise ratio are assumed to be equal.
Firstly, fixing the ratio of the radius to the wavelength of the circular array to be 1.5, and respectively giving variation curves of the target source positioning root mean square error, the ionized layer virtual height estimation root mean square error and the array amplitude phase error estimation root mean square error along with the signal-to-noise ratio of the target source in the graphs from 5 to 7; then, the signal-to-noise ratio of the target source is fixed to be 10dB, and the variation curves of the target source positioning root-mean-square error, the ionosphere virtual height estimation root-mean-square error and the array amplitude phase error estimation root-mean-square error along with the ratio of the circle array radius to the wavelength are respectively given in the graphs from fig. 8 to fig. 10.
The advantages of the disclosed method can be seen in fig. 5-10, and are significantly improved as the target source signal-to-noise ratio increases.
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 (5)

1. A short-wave multi-station direct positioning method under the condition of existence of a correction source is characterized by comprising the following steps:
step 1: d short wave correction sources with known longitude and latitude are simultaneously placed on the periphery of the area where the short wave target source is located;
step 2: receiving a target source signal and D correction source signals by using N observation stations, wherein each observation station acquires K signal samples by using a uniform circular array which is not corrected by a channel, and establishes an array signal model corresponding to the K signal samples;
and step 3: determining the relation between the azimuth angle of a target source signal reaching N observation stations and the longitude and latitude of a target source respectively, and determining the relation between the elevation angle of the target source signal reaching the N observation stations and the longitude and latitude of the target source and the virtual height of an ionized layer respectively;
and 4, step 4: determining the relation between the azimuth angle of the D-th correction source signal reaching the N observation stations and the longitude and latitude of the D-th correction source respectively, and determining the relation between the elevation angle of the D-th correction source signal reaching the N observation stations and the longitude and latitude of the D-th correction source and the virtual height of an ionized layer respectively, wherein D is more than or equal to 1 and less than or equal to D;
and 5: each observation station utilizes an array signal model corresponding to the collected K signal samples to construct a covariance matrix, and transmits the covariance matrix to a central station in the N observation stations;
step 6: the central station constructs a cost function of a joint estimation target source longitude and latitude, ionosphere height and multi-array amplitude-phase error matrix based on a maximum likelihood criterion by using covariance matrixes of N observation stations;
the step 6 comprises the following steps:
the central station utilizes the covariance matrix of the N observers
Figure FDA0002960411550000011
Joint estimation target source longitude omega based on maximum likelihood criterion constructiontLatitude rhotAnd the ionized layer virtual height { hn}1≤n≤NAnd a multi-array amplitude-phase error matrix { gamman}1≤n≤NThe cost function of (2); the cost function is:
Figure FDA0002960411550000012
wherein h ═ h1 h2 … hN]TIndicating ionospheric pseudo-height parameters;
Figure FDA0002960411550000013
representing an array amplitude and phase error parameter; II type⊥[ΓnAn(ωt,ρt,hn)]Representing orthogonal projection matrices, Π⊥[ΓnAn(ωt,ρt,hn)]＝I-ΓnAn(ωt,ρt,hn)((ΓnAn(ωt,ρt,hn))HΓnAn(ωt,ρt,hn))-1(ΓnAn(ωt,ρt,hn))H,1≤n≤N
Wherein I is an identity matrix;
Figure FDA0002960411550000021
An(ωt,ρt,hn) For the array manifold matrix of the nth observation station, vecd () represents that the diagonal elements of the diagonal matrix are extracted to form a vector;
and 7: according to the relation between the azimuth angle of a target source signal reaching N observation stations and the longitude and latitude of a target source, the relation between the elevation angle of the target source signal reaching N observation stations and the longitude and latitude of the target source and the virtual height of an ionized layer, the relation between the azimuth angle of a d correction source signal reaching N observation stations and the longitude and latitude of a d correction source, the relation between the elevation angle of the d correction source signal reaching N observation stations and the longitude and latitude of the d correction source and the virtual height of the ionized layer and the cost function, joint estimation is carried out on the longitude and latitude of the target source, the virtual height of the ionized layer and multi-array amplitude-phase errors by using an alternating iteration algorithm, so that the position information of the target is determined;
the step 7 comprises the following steps:
step 7.1: will omegat、ρtAnd { hn}1≤n≤NAs a first set of parameters, { Γn}1≤n≤NAs a second set of parameters, the second set of parameters is fixed to the current update value, i.e. { Γ }n}1≤n≤NIs fixed to
Figure FDA0002960411550000022
Fix g as
Figure FDA0002960411550000023
Estimating a first group of parameters according to a relation between azimuth angles of a target source signal reaching N observation stations and longitude and latitude of a target source, a relation between elevation angles of the target source signal reaching the N observation stations and longitude and latitude of the target source and virtual height of an ionized layer, a relation between azimuth angles of a d correction source signal reaching the N observation stations and longitude and latitude of a d correction source, a relation between elevation angles of the d correction source signal reaching the N observation stations and longitude and latitude of the d correction source and virtual height of the ionized layer and the cost function, wherein the first group of parameters are estimated according to a formula (10):
Figure FDA0002960411550000024
where μ is the step factor, 0<μ<1，μiIs the ith iteration step size factor;
Figure FDA0002960411550000025
and h(i)Are all the ith iteration result;
Figure FDA0002960411550000026
and h(i+1)All are the (i +1) th iteration results;
Figure FDA0002960411550000027
is a gradient vector;
Figure FDA0002960411550000028
is a Hessian matrix;
Figure FDA0002960411550000031
Figure FDA0002960411550000032
wherein the expressions of the elements are respectively
Figure FDA0002960411550000033
Figure FDA0002960411550000034
Figure FDA0002960411550000035
Figure FDA0002960411550000036
Figure FDA0002960411550000037
Figure FDA0002960411550000038
Figure FDA0002960411550000041
Figure FDA0002960411550000042
Figure FDA0002960411550000043
In the formula (I), the compound is shown in the specification,
Figure FDA0002960411550000044
Figure FDA0002960411550000045
Figure FDA0002960411550000046
Figure FDA0002960411550000047
Figure FDA0002960411550000048
Figure FDA0002960411550000049
Figure FDA0002960411550000051
Figure FDA0002960411550000052
Figure FDA0002960411550000053
Figure FDA0002960411550000054
Figure FDA0002960411550000055
Figure FDA0002960411550000056
Figure FDA0002960411550000057
Figure FDA0002960411550000058
in the formula InIs the radius of the uniform circular array of the nth observation station, lambda is the signal wavelength,
Figure FDA0002960411550000059
last column vector, n, in order identity matrix1Representing the n-th matrix1Line, n2Representing the n-th matrix2The columns of the image data are,
Figure FDA00029604115500000510
is n th1The current update value of the amplitude-phase error matrix of the individual observation stations,
Figure FDA00029604115500000511
is n th1An array manifold matrix of individual observation stations,
Figure FDA00029604115500000512
for the signal to reach the n-th1Ionospheric pseudo-height, a, experienced by an observer stationn(ωt,ρt,hn) Array manifold vector for target source signal arriving at nth observation stationt,nFor the azimuth angle, beta, of the target source signal arriving at the nth observation stationt,nFor the elevation angle, beta, of the target source signal to the nth observation stationc,1,nCorrecting the elevation angle, omega, of the source signal arriving at the nth observation station for the 1 stc,1Longitude, p, for the 1 st correction sourcec,1Is the latitude, beta, of the 1 st correction sourcec,D,nCorrecting the elevation angle, omega, of the source signal arriving at the nth observation station for the Dc,DLongitude, p, for the Dth correction sourcec,DFor the latitude, ω, of the D-th correction sourcec,dLongitude, p, for the d correction sourcec,dIs the latitude, θ, of the d-th correction sourcec,d,nFor the d-th corrected source signal to the nth observation stationc,d,nFor the d-th corrected source signal to the nth observation station in terms of elevation angle, ωo,nLongitude, p, for the nth observation stationo,nAs is the latitude of the nth observation station,
Figure FDA0002960411550000061
Figure FDA0002960411550000062
r is the radius of the earth;
step 7.2: fixing the first set of parameters to the current update value, i.e. ωt、ρtAnd h are respectively fixed to
Figure FDA0002960411550000063
And
Figure FDA0002960411550000064
according to the relation between the azimuth angle of the target source signal reaching N observation stations and the longitude and latitude of the target source, the relation between the elevation angle of the target source signal reaching N observation stations and the longitude and latitude of the target source and the virtual height of the ionized layer, the relation between the azimuth angle of the d correction source signal reaching N observation stations and the longitude and latitude of the d correction source, the relation between the elevation angle of the d correction source signal reaching N observation stations and the longitude and latitude of the d correction source and the virtual height of the ionized layer and the cost function, the second group of parameters are optimized and solved according to the formula (11):
Figure FDA0002960411550000065
in the formula, g(i)Is the result of the ith iteration; g(i+1)Is the (i +1) th iteration result;
Figure FDA0002960411550000066
is a gradient vector;
Figure FDA0002960411550000067
is a Hessian matrix;
Figure FDA0002960411550000068
Figure FDA0002960411550000071
wherein the expressions of the elements are respectively
Figure FDA0002960411550000072
Figure FDA0002960411550000073
Figure FDA0002960411550000074
Figure FDA0002960411550000075
Figure FDA0002960411550000076
Figure FDA0002960411550000077
Figure FDA0002960411550000078
In the formula (I), the compound is shown in the specification,
Figure FDA0002960411550000079
Figure FDA00029604115500000710
Figure FDA00029604115500000711
step 7.3: and (3) alternately carrying out optimization solution on the first set of parameters and the second set of parameters according to the formula (10) and the formula (11) until iteration converges.
2. The shortwave multi-station direct positioning method under the condition of existence of the correction source as claimed in claim 1, wherein the array signal model in the step 2 is:
Figure FDA0002960411550000081
in the formula, xn(tk) Receiving signals for a kth array of an nth observation station; sc,n,d(tk) A complex envelope for the d-th corrected source signal to reach the nth observation station; st,n(tk) A complex envelope for the target source signal to reach the nth observation station; epsilonn(tk) Uniform circular array additive noise of the nth observation station;
Figure FDA0002960411550000082
a complex envelope vector for the signal arriving at the nth observation station; h isnIonospheric pseudo-heights experienced by signals arriving at the nth observation station; a isn(ωc,d,ρc,d,hn) For the array manifold vector, ω, of the d-th corrected source signal arriving at the nth observation stationc,dTo correct for source longitude, pc,dCorrecting the source latitude; a isn(ωt,ρt,hn) Array manifold vector, omega, for the arrival of target source signals at the nth observation stationtAs the target source longitude, ρtIs the target source latitude;
Figure FDA0002960411550000083
an array manifold matrix for an nth observation station; gamma-shapednIs the amplitude-phase error matrix of the nth observation station.
3. The shortwave multi-station direct positioning method in the presence of a correction source according to claim 1, characterized in that said step 3 comprises:
step 3.1: converting the longitude and latitude coordinates of the target source into a horizon coordinate with the observation station as the center according to the formula (2):
Figure FDA0002960411550000091
in the formula (x)t,n,g,yt,n,g,zt,n,g) Coordinates of the target source under the horizontal coordinate system of the nth observation station are obtained; omegao,nAnd ρo,nLongitude and latitude of the nth observation station respectively; r is the radius of the earth;
step 3.2: obtaining the azimuth angle theta according to the formula (2)t,nAnd longitude ωtLatitude rhotThe relationship of (1):
Figure FDA0002960411550000092
in the formula，
Figure FDA0002960411550000093
Figure FDA0002960411550000094
Step 3.3: a triangle is constructed through the observation station, the sphere center point and the ionized layer, and the elevation angle beta is obtained by utilizing the sine theorem of the trianglet,nAnd longitude ωtLatitude rhotAnd ionospheric pseudo-height hnThe relationship of (1):
Figure FDA0002960411550000095
in the formula (I), the compound is shown in the specification,
Figure FDA0002960411550000096
the internal angle of the triangle with the center point as the vertex is shown.
4. The shortwave multi-station direct positioning method in the presence of a correction source according to claim 1, characterized in that said step 4 comprises:
step 4.1: converting the longitude and latitude coordinates of the d correction source into a horizon coordinate with the observation station as the center according to the formula (5):
Figure FDA0002960411550000101
in the formula (x)d,n,g,yd,n,g,zd,n,g) Coordinates of the d correction source in a horizontal coordinate system of the nth observation station;
step 4.2: obtaining the azimuth angle theta according to the formula (5)c,d,nAnd longitude ωc,dAnd latitude rhoc,dThe relationship of (1):
Figure FDA0002960411550000102
in the formula (I), the compound is shown in the specification,
Figure FDA0002960411550000103
step 4.3: using the sine theorem of triangle to obtain the elevation angle betac,d,nAnd longitude ωc,dLatitude rhoc,dAnd ionospheric pseudo-height hnThe relationship of (1):
Figure FDA0002960411550000104
in the formula (I), the compound is shown in the specification,
Figure FDA0002960411550000105
5. the shortwave multi-station direct positioning method in the presence of a correction source according to claim 2, characterized in that said step 5 comprises:
step 5.1: the nth observation station utilizes an array signal model { x ] corresponding to the collected K signal samplesn(tk)}1≤k≤KConstructing an array output covariance matrix
Figure FDA0002960411550000106
Figure FDA0002960411550000107
Step 5.2: each of the observatory stations communicates the constructed covariance matrix to a central station of the N observatory stations.
CN201910142925.2A 2019-02-26 2019-02-26 Short-wave multi-station direct positioning method under condition of existence of correction source Active CN109975755B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910142925.2A CN109975755B (en) 2019-02-26 2019-02-26 Short-wave multi-station direct positioning method under condition of existence of correction source

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910142925.2A CN109975755B (en) 2019-02-26 2019-02-26 Short-wave multi-station direct positioning method under condition of existence of correction source

Publications (2)

Publication Number Publication Date
CN109975755A CN109975755A (en) 2019-07-05
CN109975755B true CN109975755B (en) 2021-04-20

Family

ID=67077421

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910142925.2A Active CN109975755B (en) 2019-02-26 2019-02-26 Short-wave multi-station direct positioning method under condition of existence of correction source

Country Status (1)

Country Link
CN (1) CN109975755B (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110568403B (en) * 2019-08-10 2023-02-17 中国人民解放军战略支援部队信息工程大学 Over-the-horizon target passive positioning method for cooperative short wave and satellite system
CN111308530B (en) * 2020-02-17 2021-12-03 中国人民解放军战略支援部队信息工程大学 Short wave multi-station and single-satellite cooperative direct positioning method based on two-dimensional direction of arrival
CN111736120B (en) * 2020-05-28 2022-07-26 哈尔滨工业大学 Array error correction method based on sky wave propagation correction source signal
CN112782647B (en) * 2020-12-15 2023-05-16 中国人民解放军战略支援部队信息工程大学 Information-combined quadratic constraint least square radiation source positioning method
CN113281701B (en) * 2021-04-28 2024-03-12 中国人民解放军战略支援部队信息工程大学 Direct positioning method for beyond-vision-distance target by cooperating short wave multi-station angle and three-star time difference
CN113203985B (en) * 2021-04-30 2023-07-25 大连工业大学 Direct positioning method for shortwave same-frequency signals
CN113281702B (en) * 2021-04-30 2024-02-09 中国人民解放军战略支援部队信息工程大学 Method for directly positioning beyond-view-range target by cooperating short-wave multi-station angle with satellite time frequency

Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002267733A (en) * 2001-03-14 2002-09-18 Hitachi Kokusai Electric Inc Method of detecting position of radio wave transmission source using circular array antenna
CN105467361A (en) * 2015-12-05 2016-04-06 中国人民解放军信息工程大学 Radio signal complex envelope and carrier phase information combination BVR (beyond visual range) target direct positioning method
CN106646477A (en) * 2016-12-31 2017-05-10 中国气象科学研究院 Ionospheric D layer detection system and method based on multi-station lightning low-frequency pulse signals
CN108089147A (en) * 2017-12-07 2018-05-29 西南电子技术研究所（中国电子科技集团公司第十研究所） Improved shortwave unit localization method
CN108363037A (en) * 2018-02-27 2018-08-03 武汉大学 A kind of one step positioning mode of shortwave remote radiation source based on wide-area distribution type single antenna reception
CN108845188A (en) * 2018-07-11 2018-11-20 云南电网有限责任公司电力科学研究院 A kind of mono-station location method and system of remote cloud-to-ground flash
CN108873023A (en) * 2017-05-15 2018-11-23 上海华测导航技术股份有限公司 A kind of processing method for the observed quantity improving positioning accuracy
CN108872932A (en) * 2018-05-03 2018-11-23 中国人民解放军战略支援部队信息工程大学 The direct positioning result method for correcting error of over-the-horizon target neural network based
CN109239654A (en) * 2018-08-21 2019-01-18 中国人民解放军战略支援部队信息工程大学 Positioning using TDOA result method for correcting error neural network based
CN109298388A (en) * 2018-08-21 2019-02-01 中国人民解放军战略支援部队信息工程大学 Over-the-horizon target geographical coordinate direct method estimating based on azimuth information

Patent Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002267733A (en) * 2001-03-14 2002-09-18 Hitachi Kokusai Electric Inc Method of detecting position of radio wave transmission source using circular array antenna
CN105467361A (en) * 2015-12-05 2016-04-06 中国人民解放军信息工程大学 Radio signal complex envelope and carrier phase information combination BVR (beyond visual range) target direct positioning method
CN106646477A (en) * 2016-12-31 2017-05-10 中国气象科学研究院 Ionospheric D layer detection system and method based on multi-station lightning low-frequency pulse signals
CN108873023A (en) * 2017-05-15 2018-11-23 上海华测导航技术股份有限公司 A kind of processing method for the observed quantity improving positioning accuracy
CN108089147A (en) * 2017-12-07 2018-05-29 西南电子技术研究所（中国电子科技集团公司第十研究所） Improved shortwave unit localization method
CN108363037A (en) * 2018-02-27 2018-08-03 武汉大学 A kind of one step positioning mode of shortwave remote radiation source based on wide-area distribution type single antenna reception
CN108872932A (en) * 2018-05-03 2018-11-23 中国人民解放军战略支援部队信息工程大学 The direct positioning result method for correcting error of over-the-horizon target neural network based
CN108845188A (en) * 2018-07-11 2018-11-20 云南电网有限责任公司电力科学研究院 A kind of mono-station location method and system of remote cloud-to-ground flash
CN109239654A (en) * 2018-08-21 2019-01-18 中国人民解放军战略支援部队信息工程大学 Positioning using TDOA result method for correcting error neural network based
CN109298388A (en) * 2018-08-21 2019-02-01 中国人民解放军战略支援部队信息工程大学 Over-the-horizon target geographical coordinate direct method estimating based on azimuth information

Also Published As

Publication number Publication date
CN109975755A (en) 2019-07-05

Similar Documents

Publication Publication Date Title
CN109975755B (en) Short-wave multi-station direct positioning method under condition of existence of correction source
CN109975749B (en) Short-wave single-station direct positioning method under condition of existence of correction source
CN105589086B (en) Ground emitter signals single-star positioning method based on signal intensity multi-beam spatial distribution
US10571544B2 (en) Direction finding using signal power
CN111308530B (en) Short wave multi-station and single-satellite cooperative direct positioning method based on two-dimensional direction of arrival
CN109298388B (en) Direct over-the-horizon target geographic coordinate estimation method based on azimuth information
EP2449626B1 (en) Self calibrating conformal phased array
CN108872932B (en) Beyond-visual-range target direct positioning result deviation rectifying method based on neural network
JP4592506B2 (en) Uplink interference source locating apparatus and method
CN101900819B (en) Blind adaptive space-time array anti-interference method for navigation receiver
CN110058204B (en) Satellite-borne antenna beam center calibration method based on directional diagram matching
CN110568403B (en) Over-the-horizon target passive positioning method for cooperative short wave and satellite system
CN111199280B (en) Multi-station target source geographic coordinate estimation method combining signal complex envelope and carrier phase information in presence of short wave channel model error
CN113281701B (en) Direct positioning method for beyond-vision-distance target by cooperating short wave multi-station angle and three-star time difference
CN105676166A (en) Antenna ground radiation source positioning method based on satellite borne movable spot beams
CN111199281B (en) Short wave single station direct positioning deviation compensation method based on geographical coordinate airspace position spectrum
CN112511976A (en) Processing method, device, equipment and medium for positioning control end of unmanned aerial vehicle
CN113281702B (en) Method for directly positioning beyond-view-range target by cooperating short-wave multi-station angle with satellite time frequency
CN109991564B (en) Short wave single station positioning result deviation rectifying method based on neural network
CN112240957B (en) Method for correcting amplitude-phase characteristics of antenna in satellite navigation interference direction finding
CN102023301A (en) Satellite selection method for medium earth orbit satellite search and rescue system
CN115560757B (en) Unmanned aerial vehicle direct positioning correction method based on neural network under random attitude error condition
CN110208741A (en) A kind of direct localization method of over the horizon single goal for surveying phase based on more circle battle arrays
CN111025358B (en) Orientation method based on single short baseline of navigation satellite signal
Ryzhikov et al. Distortions of characteristics of a multichannel antenna array with directional asymmetry by the compensation method in an aviation weather navigation radar

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
GR01 Patent grant
GR01 Patent grant