CN109975749B - Short-wave single-station direct positioning method under condition of existence of correction source - Google Patents

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

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CN109975749B
CN109975749B CN201910143409.1A CN201910143409A CN109975749B CN 109975749 B CN109975749 B CN 109975749B CN 201910143409 A CN201910143409 A CN 201910143409A CN 109975749 B CN109975749 B CN 109975749B
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longitude
latitude
source
signal
target source
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CN109975749A (en
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王鼎
尹洁昕
杨宾
唐涛
张莉
吴志东
吴瑛
贾昌贵
陈鑫
李崇
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Information Engineering University of PLA Strategic Support Force
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves

Abstract

The invention relates to the technical field of short-wave single-station positioning, and discloses a short-wave single-station direct positioning method under the condition of a correction source. Due to the existence of the correction source, the invention can effectively inhibit the influence of ionosphere pseudo-high deviation on the positioning accuracy of the short-wave signal.

Description

Short-wave single-station direct positioning method under condition of existence of correction source
Technical Field
The invention relates to the technical field of short-wave single-station positioning, in particular to a short-wave single-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 single-station positioning system has the advantages of high flexibility, strong maneuverability, simple system, no need of inter-station communication and synchronization and the like.
For a long-distance target, a target radiation signal usually reaches an observation station in a way of over-the-horizon propagation, the most common way is that the signal reaches a ground observation station after being reflected by an ionosphere, and at this time, to perform positioning by using a single station, information of the ionosphere virtual height needs to be obtained, but the information is difficult to accurately obtain in practical application, and only an approximate estimation value can be obtained. Obviously, ionospheric pseudo-high errors have a large influence on the positioning accuracy of short-wave signals.
On the other hand, the existing passive positioning process 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 these parameters, the position information of the 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 the drawbacks that exist therein and have proposed the idea of single-step direct positioning, whose basic idea is to estimate the position parameters of an object directly from the signal-acquired data field without estimating other intermediate positioning parameters. Obviously, the single-step direct positioning mode is also suitable for short-wave single-station positioning scenes, but the direct positioning method is also affected by ionospheric pseudo-high errors, so that a larger positioning deviation is generated.
Disclosure of Invention
Aiming at the problem of ionosphere high-false error influence, the invention provides a short-wave single-station direct positioning method under the condition of a correction source, so as to improve the single-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 single-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 an M-element uniform circular array at an observation station, sampling the received signals, collecting K signal samples in total, and establishing an array signal model corresponding to the K signal samples;
and step 3: determining the relation between the azimuth angle and the elevation angle of a target source signal reaching the M-element uniform circular array and the longitude and latitude and the virtual height of an ionized layer of the target source respectively;
and 4, step 4: determining the relation between the azimuth angle and the elevation angle of the D-th correction source signal reaching the M-element uniform circular array and the longitude and latitude and the ionospheric virtual height of the D-th correction source signal respectively, wherein D is more than or equal to 1 and less than or equal to D;
and 5: constructing a covariance matrix by using the array signal models corresponding to the K signal samples, and performing eigenvalue decomposition on the covariance matrix to obtain a signal subspace matrix and an optimal weighting matrix;
step 6: constructing a cost function about the latitude and longitude of the target source and the virtual height of the ionized layer by using the signal subspace matrix and the optimal weighting matrix;
and 7: and performing joint estimation on the longitude and latitude of the target source and the virtual height of the ionized layer by using a Gauss-Newton iterative algorithm according to the relationship between the azimuth angle and the elevation angle of the target source signal reaching the M-element uniform circular array and the longitude and latitude and the virtual height of the target source and the relationship between the azimuth angle and the elevation angle of the d-th correction source signal reaching the M-element uniform circular array and the longitude and the latitude and the virtual height of the d-th 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 BDA0001979262320000021
wherein, x (t)k) Receiving signals for a kth array; sc,d(tk) A complex envelope for the d-th corrected source signal; st(tk) Is the complex envelope of the target source signal; n (t)k) Additive noise for the array;
Figure BDA0001979262320000037
is a complex envelope vector of the signal; a (omega)c,d,ρc,dH) is the array manifold vector, ω, for the d-th corrected source signalc,dTo correct for source longitude, pc,dCorrecting source latitude, and h is ionosphere virtual height; a (omega)t,ρtH) is the array manifold vector, ω, for the target source signaltAs the target source longitude, ρtIs the target source latitude;
Figure BDA0001979262320000038
is an array manifold matrix.
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 BDA0001979262320000031
wherein (x)t,g,yt,g,zt,g) Coordinates of the target source under a horizontal coordinate system of the observation station are obtained; omegaoAnd ρoLongitude and latitude of the observation station respectively; r is the earth radius.
Step 3.2: obtaining the azimuth angle theta according to the formula (2)tAnd longitude ωtAnd latitude rhotThe relationship of (1):
Figure BDA0001979262320000032
wherein the content of the first and second substances,
Figure BDA0001979262320000033
Figure BDA0001979262320000036
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 BDA0001979262320000034
wherein the content of the first and second substances,
Figure BDA0001979262320000035
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 BDA0001979262320000041
wherein (x)d,g,yd,g,zd,g) Coordinates of the d correction source target source under the horizontal coordinate system of the observation station;
step 4.2: obtaining the azimuth angle theta according to the formula (5)c,dAnd longitude ωc,dAnd latitude rhoc,dThe relationship of (1):
Figure BDA0001979262320000042
step 4.3: using the sine theorem of triangle to obtain the elevation angle betac,dAnd longitude ωc,dLatitude rhoc,dAnd ionospheric pseudo-height h relation:
Figure BDA0001979262320000043
wherein the content of the first and second substances,
Figure BDA0001979262320000044
further, the step 5 comprises:
step 5.1: array signal model { x (t) corresponding to K signal samplesk)}1≤k≤KConstructing a covariance matrix
Figure BDA0001979262320000045
And according to formula (8) pair
Figure BDA0001979262320000046
And (3) carrying out characteristic value decomposition:
Figure BDA0001979262320000047
wherein the content of the first and second substances,
Figure BDA0001979262320000048
is a diagonal matrix of (D +1) × (D +1) order, the pair thereofCorner element being a matrix
Figure BDA0001979262320000049
The first D +1 eigenvalues of (D);
Figure BDA00019792623200000410
is a diagonal matrix of (M-D-1) × (M-D-1) order, the diagonal elements of which are matrices
Figure BDA00019792623200000411
The last M-D-1 eigenvalues of;
Figure BDA00019792623200000412
a signal subspace matrix of order Mx (D +1), the column vector of which is a unit eigenvector corresponding to a large eigenvalue;
Figure BDA00019792623200000413
is a noise subspace matrix of order M (M-D-1), the column vector of which is a unit eigenvector corresponding to a small eigenvalue;
step 5.2: by using
Figure BDA00019792623200000414
The parameters after eigenvalue decomposition construct the optimal weighting matrix according to the formula (9)
Figure BDA00019792623200000415
Figure BDA0001979262320000051
Wherein the content of the first and second substances,
Figure BDA0001979262320000052
is a matrix
Figure BDA0001979262320000053
The jth diagonal element of (1)D+1Is an identity matrix of (D +1) × (D +1) order.
Further, the step 6 comprises:
using signal subspace matrices
Figure BDA0001979262320000054
And an optimal weighting matrix
Figure BDA0001979262320000055
Constructing a cost function about the latitude and longitude of a target source and the virtual height of an ionized layer; the cost function is:
Figure BDA0001979262320000056
wherein the content of the first and second substances,
Figure BDA00019792623200000512
Π⊥[A(ωt,ρt,h)]is an orthogonal projection matrix;
Π⊥[A(ωt,ρt,h)]＝IM-A(ωt,ρt,h)((A(ωt,ρt,h))HA(ωt,ρt,h))-1(A(ωt,ρt,h))H
wherein, IMIs an M × M order identity matrix.
Further, the step 7 includes:
according to the relation between the azimuth angle and the elevation angle of the target source signal reaching the M-element uniform circular array 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-th correction source signal reaching the M-element uniform circular array and the longitude and latitude and the virtual height of the d-th correction source signal and the virtual height of the ionized layer and the cost function, the Gaussian-Newton iterative algorithm is utilized to carry out the calculation on the longitude omega of the target source according to the formula (11)tLatitude rhotAnd jointly estimating the ionospheric virtual height h:
Figure BDA0001979262320000057
wherein mu is step size factor, mu is more than 0 and less than 1, muiFor the ith iterationA long factor;
Figure BDA0001979262320000058
and h(i)Are all the ith iteration result;
Figure BDA0001979262320000059
and h(i+1)All are the (i +1) th iteration results;
Figure BDA00019792623200000510
is a gradient vector;
Figure BDA00019792623200000511
is a Hessian matrix;
Figure BDA0001979262320000061
Figure BDA0001979262320000062
wherein the expressions of the elements are respectively
Figure BDA0001979262320000063
Figure BDA00019792623200000610
Figure BDA0001979262320000064
Figure BDA0001979262320000065
Figure BDA0001979262320000066
Figure BDA0001979262320000067
Figure BDA0001979262320000068
Figure BDA0001979262320000069
Figure BDA0001979262320000071
Wherein the content of the first and second substances,
Figure BDA0001979262320000072
Figure BDA0001979262320000073
Figure BDA0001979262320000074
Figure BDA0001979262320000075
Figure BDA0001979262320000076
Figure BDA0001979262320000077
Figure BDA0001979262320000078
Figure BDA0001979262320000079
Figure BDA00019792623200000710
Figure BDA0001979262320000081
Figure BDA0001979262320000082
Figure BDA0001979262320000083
Figure BDA0001979262320000084
wherein l is the radius of the uniform circular array, λ is the signal wavelength,
Figure BDA0001979262320000085
is an identity matrix ID+1The last column vector.
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 by using a uniform circular array in a single observation station, then determining the relation of the azimuth angle and the elevation angle of a received signal (simultaneously containing a target source signal and a correction source signal) with respect to the longitude and the latitude and the ionosphere virtual height parameter, then constructing a cost function with respect to the longitude and the latitude of the target source and the ionosphere virtual height parameter based on a signal subspace fitting criterion, and carrying out joint estimation on the longitude and the latitude of the target source and the ionosphere virtual height by using a Gauss-Newton iterative algorithm so as to determine target position information. The invention utilizes the short wave correction source with accurately known longitude and latitude to position the short wave target source based on the basic idea of direct positioning, and can effectively eliminate the positioning deviation caused by ionosphere height error, thereby improving the positioning precision of the short wave single station.
Drawings
Fig. 1 is a flowchart of a short-wave single-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 scattering diagram of the direct positioning result of the short-wave single station according to the embodiment of the 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 target source position with the number of antennas in the array according to the embodiment of the present invention.
Fig. 8 is a graph showing variation of the ionospheric pseudo-height estimated root mean square error with the number of array antennas according to the embodiment of the present invention.
Fig. 9 is a graph of variation of the root mean square error of target source positioning with the pseudo-high prior estimation error of the ionosphere according to the embodiment of the present invention.
Fig. 10 is a graph of the variation of the ionospheric pseudo-high estimated root mean square error with the ionospheric pseudo-high prior estimated error in accordance with 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 single-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 an M-element uniform circular array at an observation station, sampling the received signals, collecting K signal samples in total, and establishing an array signal model corresponding to the K signal samples;
step S103: determining the relation between the azimuth angle and the elevation angle of a target source signal reaching the M-element uniform circular array and the longitude and latitude and the virtual height of an ionized layer of the target source respectively;
step S104: determining the relation between the azimuth angle and the elevation angle of the D-th correction source signal reaching the M-element uniform circular array and the longitude and latitude and the ionospheric virtual height of the D-th correction source signal respectively, wherein D is more than or equal to 1 and less than or equal to D;
step S105: constructing a covariance matrix by using the array signal models corresponding to the K signal samples, and performing eigenvalue decomposition on the covariance matrix to obtain a signal subspace matrix and an optimal weighting matrix;
step S106: constructing a cost function about the latitude and longitude of the target source and the virtual height of the ionized layer by using the signal subspace matrix and the optimal weighting matrix;
step S107: and performing joint estimation on the longitude and latitude of the target source and the virtual height of the ionized layer by using a Gauss-Newton iterative algorithm according to the relationship between the azimuth angle and the elevation angle of the target source signal reaching the M-element uniform circular array and the longitude and latitude and the virtual height of the target source and the relationship between the azimuth angle and the elevation angle of the d-th correction source signal reaching the M-element uniform circular array and the longitude and the latitude and the virtual height of the d-th correction source and the virtual height of the ionized layer and the cost function, thereby determining the position information of the target.
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 by using a uniform circular array in a single observation station, then determining the relation of the azimuth angle and the elevation angle of a received signal (simultaneously containing a target source signal and a correction source signal) with respect to the longitude and the latitude and the ionosphere virtual height parameter, then constructing a cost function with respect to the longitude and the latitude of the target source and the ionosphere virtual height parameter based on a signal subspace fitting criterion, and carrying out joint estimation on the longitude and the latitude of the target source and the ionosphere virtual height by using a Gauss-Newton iterative algorithm so as to determine target position information. The invention utilizes the short wave correction source with accurately known longitude and latitude to position the short wave target source based on the basic idea of direct positioning, and can effectively eliminate the positioning deviation caused by ionosphere height error, thereby improving the positioning precision of the short wave single station.
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 the M-ary uniform circular array after being scattered by the ionosphere, the ionosphere virtual height is h, the M-ary uniform circular array is used for receiving the signals, K signal samples are collected, and an array signal model of the kth signal sample is:
Figure BDA0001979262320000101
wherein, x (t)k) Receiving signals for a kth array; sc,d(tk) A complex envelope for the d-th corrected source signal; st(tk) Is the complex envelope of the target source signal; n (t)k) Additive noise for the array;
Figure BDA0001979262320000102
is a complex envelope vector of the signal; a (omega)c,d,ρc,dH) is an array manifold vector for the d-th corrected source signal, which is simultaneously aligned with the corrected source longitude ωc,dLatitude rhoc,dAnd ionosphere virtual height h is related to 3 parameters; a (omega)t,ρtH) is an array manifold vector for the target source signal, which is simultaneously aligned with the target source longitude ωtLatitude rhotAnd ionosphere virtual height h is related to 3 parameters;
Figure BDA0001979262320000103
for an array manifold matrix, the correction source longitude and latitude are known exactly and therefore are only considered to be relative to the target source longitude ωtLatitude rhotAnd ionospheric pseudo-height h.
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 BDA0001979262320000111
wherein (x)t,g,yt,g,zt,g) Coordinates of the target source under a horizontal coordinate system of the observation station are obtained; omegaoAnd ρoLongitude and latitude of the observation station respectively; r is the earth radius.
Step S103.2: obtaining the azimuth angle theta according to the formula (2)tAnd longitude ωtAnd latitude rhotThe relationship of (1):
Figure BDA0001979262320000112
wherein the content of the first and second substances,
Figure BDA0001979262320000113
Figure BDA0001979262320000114
step S103.3: a triangle is constructed through the observation station, the sphere center point and the ionized layer, 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 BDA0001979262320000115
wherein the content of the first and second substances,
Figure BDA0001979262320000116
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 BDA0001979262320000117
wherein (x)d,g,yd,g,zd,g) Coordinates of the d correction source target source under the horizontal coordinate system of the observation station;
step S104.2: obtaining the azimuth angle theta according to the formula (5)c,dAnd longitude ωc,dAnd latitude rhoc,dThe relationship of (1):
Figure BDA0001979262320000121
step S104.3: from Δ ABC shown in FIG. 3, the elevation angle β is obtained by using the sine theorem of trianglesc,dAnd longitude ωc,dLatitude rhoc,dAnd ionospheric pseudo-height h relation:
Figure BDA0001979262320000122
wherein the content of the first and second substances,
Figure BDA0001979262320000123
specifically, the step S105 includes:
step S105.1: array signal model { x (t) corresponding to K signal samplesk)}1≤k≤KConstructing a covariance matrix
Figure BDA0001979262320000124
And according to formula (8) pair
Figure BDA0001979262320000125
And (3) carrying out characteristic value decomposition:
Figure BDA0001979262320000126
wherein the content of the first and second substances,
Figure BDA0001979262320000127
is a diagonal matrix of (D +1) × (D +1) order, the diagonal elements of which are matrices
Figure BDA0001979262320000128
First D +1 eigenvalues (matrix)
Figure BDA0001979262320000129
The elements of (a) are sorted from big to small);
Figure BDA00019792623200001210
is a diagonal matrix of (M-D-1) × (M-D-1) order, the diagonal elements of which are matrices
Figure BDA00019792623200001211
The last M-D-1 eigenvalues of;
Figure BDA00019792623200001212
a signal subspace matrix of order Mx (D +1), the column vector of which is a unit eigenvector corresponding to a large eigenvalue;
Figure BDA00019792623200001213
is a noise subspace matrix of order M (M-D-1), the column vector of which is a unit eigenvector corresponding to a small eigenvalue;
step S105.2: by using
Figure BDA00019792623200001214
The parameters after eigenvalue decomposition construct the optimal weighting matrix according to the formula (9)
Figure BDA00019792623200001215
Figure BDA00019792623200001216
Wherein the content of the first and second substances,
Figure BDA0001979262320000131
is a matrix
Figure BDA0001979262320000132
The jth diagonal element of (1)D+1Is an identity matrix of (D +1) × (D +1) order.
Specifically, the step S106 includes:
using signal subspace matrices
Figure BDA0001979262320000133
And an optimal weighting matrix
Figure BDA0001979262320000134
Constructing a cost function about the latitude and longitude of a target source and the virtual height of an ionized layer; the cost function is:
Figure BDA0001979262320000135
wherein the content of the first and second substances,
Figure BDA0001979262320000136
Π⊥[A(ωt,ρt,h)]is an orthogonal projection matrix;
Π⊥[A(ωt,ρt,h)]＝IM-A(ωt,ρt,h)((A(ωt,ρt,h))HA(ωt,ρt,h))-1(A(ωt,ρt,h))H
wherein, IMIs an M × M order identity matrix.
Specifically, the step S107 includes:
according to the relation between the azimuth angle and the elevation angle of the target source signal reaching the M-element uniform circular array 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-th correction source signal reaching the M-element uniform circular array and the longitude and latitude and the virtual height of the d-th correction source signal and the virtual height of the ionized layer and the cost function, the Gaussian-Newton iterative algorithm is utilized to carry out the calculation on the longitude omega of the target source according to the formula (11)tLatitude rhotAnd jointly estimating the ionospheric virtual height h:
Figure BDA0001979262320000137
wherein mu is step size factor, mu is more than 0 and less than 1, muiIs the ith iteration step size factor;
Figure BDA0001979262320000138
and h(i)Are all the ith iteration result;
Figure BDA0001979262320000139
and h(i+1)All are the (i +1) th iteration results;
Figure BDA00019792623200001310
is a gradient vector;
Figure BDA00019792623200001311
is a Hessian matrix;
Figure BDA00019792623200001312
and
Figure BDA00019792623200001313
the expressions are respectively:
Figure BDA0001979262320000141
Figure BDA0001979262320000142
wherein the expressions of the elements are respectively
Figure BDA0001979262320000143
Figure BDA0001979262320000144
Figure BDA0001979262320000145
Figure BDA0001979262320000146
Figure BDA0001979262320000147
Figure BDA0001979262320000148
Figure BDA0001979262320000149
Figure BDA00019792623200001410
Figure BDA0001979262320000151
It is worth to say that，
Figure BDA0001979262320000152
And
Figure BDA0001979262320000153
and
Figure BDA0001979262320000154
Figure BDA0001979262320000155
and
Figure BDA0001979262320000156
the expressions of the elements are respectively the same;
wherein the content of the first and second substances,
Figure BDA0001979262320000157
Figure BDA0001979262320000158
Figure BDA0001979262320000159
Figure BDA00019792623200001510
Figure BDA00019792623200001511
Figure BDA00019792623200001512
Figure BDA00019792623200001513
Figure BDA0001979262320000161
Figure BDA0001979262320000162
Figure BDA0001979262320000163
Figure BDA0001979262320000164
Figure BDA0001979262320000165
Figure BDA0001979262320000166
wherein l is the radius of the uniform circular array, λ is the signal wavelength,
Figure BDA0001979262320000167
is an identity matrix ID+1The last column vector.
To verify the effect of the present invention, the following experimental data are provided.
Suppose the longitude of a single observation station is 112.73 degrees, and the latitude is 33.25 degrees; the longitude of the short wave target source is 122.46 degrees, and the latitude is 27.82 degrees; two short wave correction sources are now placed, the longitude of the first correction source is 123.62 degrees for east longitude, 28.68 degrees for latitude for north latitude, the longitude of the second correction source is 124.54 degrees for east longitude, and 29.96 degrees for latitude for north latitude. The observation station is provided with a uniform circular array, the ratio of the radius of the circular array to the incident wavelength of a signal is 1.5, the number of signal sample points for direct positioning is 500, and the ionospheric virtual high true values of a short-wave target source signal and a correction source signal which reach the observation station are 340 kilometers.
(1) The signal-to-noise ratios of the short wave target source signal and the correction source signal are both 5dB, the number of the array antennas is 10, fig. 4 shows a positioning result scatter diagram of the single station direct positioning method disclosed by the invention and a traditional single station positioning method under the condition without the correction source, 500 Monte Carlo experiments are carried out on the two methods, and the prior estimation error of the traditional single station positioning method under the condition without the correction source on the ionospheric pseudo-height is assumed to be 15 kilometers. It can be seen from the figure that the estimation result of the single-station direct positioning method disclosed by the patent always changes near the true value, and the estimation result of the traditional single-station positioning method under the condition without the correction source obviously deviates from the true value, which shows that the single-station direct positioning method disclosed by the patent can obviously inhibit the influence caused by ionospheric pseudo-height errors, thereby obviously improving the single-station positioning accuracy of the short-wave target source.
(2) The rest experimental conditions are unchanged, and the variation curves of the target source positioning root mean square error and the ionosphere virtual height estimation root mean square error along with the signal-to-noise ratio of the target source are respectively given in fig. 5 and 6; fig. 7 and 8 show the variation curves of the target source positioning root mean square error and the ionosphere virtual height estimation root mean square error along with the number of the array antennas respectively; fig. 9 and fig. 10 show the variation curves of the target source positioning root mean square error and the ionospheric virtual high estimated root mean square error with the ionospheric virtual high prior estimated error, respectively. The advantages of the single-station direct positioning method disclosed by the present patent can be further seen from fig. 5 to fig. 10, and the advantages are significantly improved as the signal-to-noise ratio of the target source increases, and also significantly improved as the ionospheric pseudo-high prior estimation error 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 (4)

1. A short-wave single-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 an M-element uniform circular array at an observation station, sampling the received signals, collecting K signal samples in total, and establishing 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 the M-element uniform circular array and the latitude and longitude of a target source, and determining the relation between the elevation angle of the target source signal reaching the M-element uniform circular array, the latitude and longitude of the target source and the virtual height of an ionized layer;
and 4, step 4: determining the relation between the azimuth angle of the D-th correction source signal reaching the M-element uniform circular array and the longitude and latitude of the D-th correction source, and determining the relation between the elevation angle of the D-th correction source signal reaching the M-element uniform circular array, the longitude and latitude of the D-th correction source and the virtual height of an ionized layer, wherein D is more than or equal to 1 and less than or equal to D;
and 5: constructing a covariance matrix by using the array signal models corresponding to the K signal samples, and performing eigenvalue decomposition on the covariance matrix to obtain a signal subspace matrix and an optimal weighting matrix;
the step 5 comprises the following steps:
step 5.1: array signal model { x (t) corresponding to K signal samplesk)}1≤k≤KConstructing a covariance matrix
Figure FDA0002966944400000011
And according to formula (8) pair
Figure FDA0002966944400000012
And (3) carrying out characteristic value decomposition:
Figure FDA0002966944400000013
wherein the content of the first and second substances,
Figure FDA0002966944400000014
is a diagonal matrix of (D +1) × (D +1) order, the diagonal elements of which are matrices
Figure FDA0002966944400000015
The first D +1 eigenvalues of (D);
Figure FDA0002966944400000016
is a diagonal matrix of (M-D-1) × (M-D-1) order, the diagonal elements of which are matrices
Figure FDA0002966944400000017
The last M-D-1 eigenvalues of;
Figure FDA0002966944400000018
a signal subspace matrix of order Mx (D +1), the column vector of which is a unit eigenvector corresponding to a large eigenvalue;
Figure FDA0002966944400000019
is a noise subspace matrix of order M (M-D-1), the column vector of which is a unit eigenvector corresponding to a small eigenvalue;
step 5.2: by using
Figure FDA00029669444000000110
The parameters after eigenvalue decomposition construct the optimal weighting matrix according to the formula (9)
Figure FDA00029669444000000111
Figure FDA00029669444000000112
Wherein the content of the first and second substances,
Figure FDA00029669444000000113
is a matrix
Figure FDA00029669444000000114
The jth diagonal element of (1)D+1Is an identity matrix of (D +1) × (D +1) order;
step 6: constructing a cost function about the latitude and longitude of the target source and the virtual height of the ionized layer by using the signal subspace matrix and the optimal weighting matrix;
the step 6 comprises the following steps:
using signal subspace matrices
Figure FDA0002966944400000021
And an optimal weighting matrix
Figure FDA0002966944400000022
Constructing a cost function about the latitude and longitude of a target source and the virtual height of an ionized layer; the cost function is:
Figure FDA0002966944400000023
wherein the content of the first and second substances,
Figure FDA0002966944400000024
Π⊥[A(ωt,ρt,h)]being an orthogonal projection matrix, omegatAs the target source longitude, ρtIs the target source latitude, h is the ionosphere virtual height,
Figure FDA0002966944400000025
A(ωt,ρth) is an array manifold matrix;
Π⊥[A(ωt,ρt,h)]＝IM-A(ωt,ρt,h)((A(ωt,ρt,h))HA(ωt,ρt,h))-1(A(ωt,ρt,h))H
wherein, IMAn M multiplied by M order identity matrix;
and 7: performing joint estimation on the longitude and latitude of the target source and the virtual height of the ionized layer by using a Gauss-Newton iterative algorithm according to the relation between the azimuth angle of the target source signal reaching the M-element uniform circular array and the longitude and latitude of the target source, the relation between the elevation angle of the target source signal reaching the M-element uniform circular array 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-th correction source signal reaching the M-element uniform circular array and the longitude and latitude of the d-th correction source and the virtual height of the ionized layer and the cost function, so as to determine the position information of the target;
the step 7 comprises the following steps:
according to the relation between the azimuth angle of the target source signal reaching the M-element uniform circular array and the longitude and latitude of the target source, the relation between the elevation angle of the target source signal reaching the M-element uniform circular array and the longitude and latitude of the target source and the virtual height of an ionized layer, the relation between the azimuth angle of the d-th correction source signal reaching the M-element uniform circular array and the longitude and latitude of the d-th correction source, the relation between the elevation angle of the d-th correction source signal reaching the M-element uniform circular array and the longitude and latitude of the d-th correction source and the virtual height of the ionized layer and the cost function, a Gauss-Newton iterative algorithm is utilized to carry out the calculation on the longitude omegatLatitude rhotAnd jointly estimating the ionospheric virtual height h:
Figure FDA0002966944400000026
where μ is the step factor, 0<μ<1，μiIs the ith iteration step size factor;
Figure FDA0002966944400000031
and h(i)Are all the ith iteration result;
Figure FDA0002966944400000032
and h(i+1)All are the (i +1) th iteration results;
Figure FDA0002966944400000033
is a gradient vector;
Figure FDA0002966944400000034
is a Hessian matrix;
Figure FDA0002966944400000035
Figure FDA0002966944400000036
wherein the expressions of the elements are respectively
Figure FDA0002966944400000037
Figure FDA0002966944400000038
Figure FDA0002966944400000039
Figure FDA00029669444000000310
Figure FDA00029669444000000311
Figure FDA00029669444000000312
Figure FDA00029669444000000313
Figure FDA0002966944400000041
Figure FDA0002966944400000042
Wherein the content of the first and second substances,
Figure FDA0002966944400000043
Figure FDA0002966944400000044
Figure FDA0002966944400000045
Figure FDA0002966944400000046
Figure FDA0002966944400000047
Figure FDA0002966944400000048
Figure FDA0002966944400000049
Figure FDA00029669444000000410
Figure FDA0002966944400000051
Figure FDA0002966944400000052
Figure FDA0002966944400000053
Figure FDA0002966944400000054
Figure FDA0002966944400000055
wherein l is the radius of the uniform circular array, λ is the signal wavelength,
Figure FDA0002966944400000056
is an identity matrix I of (D +1) × (D +1) orderD+1Last column vector in, a (ω)t,ρtH) is the array manifold vector for the target source signal, θtIs the azimuth angle, beta, of the target source signal reaching the M-element uniform circular arraytThe elevation angle, a (omega), of the target source signal reaching the M-element uniform circular arrayc,1,ρc,1H) is the array manifold vector, ω, for the 1 st corrected source signalc,1Longitude, p, for the 1 st correction sourcec,1Is the latitude, beta, of the 1 st correction sourcec,1For the 1 st corrected source signal to reach the elevation angle, omega, of the M-element uniform circular arrayc,DLongitude, p, for the Dth correction sourcec,DIs the latitude, beta, of the D-th correction sourcec,DFor the Dth corrected source signal to arrive at M elementElevation angle of uniform circular array, a (omega)c,d,ρc,dH) an array manifold vector, β, for the d-th corrected source signalc,dFor the d-th corrected source signal to reach the elevation angle theta of the M-element uniform circular arrayc,dFor the azimuth angle of the d-th corrected source signal arriving at the M-ary uniform circular array,
Figure FDA0002966944400000057
Figure FDA0002966944400000058
Figure FDA0002966944400000061
r is the radius of the earth and r is the radius of the earth,
Figure FDA0002966944400000062
ωoand ρoLongitude and latitude of the observatory station, respectively.
2. The method for short-wave single-station direct positioning in the presence of a correction source according to claim 1, wherein the array signal model in the step 2 is:
Figure FDA0002966944400000063
wherein, x (t)k) Receiving signals for a kth array; sc,d(tk) A complex envelope for the d-th corrected source signal; st(tk) Is the complex envelope of the target source signal; n (t)k) Additive noise for the array;
Figure FDA0002966944400000064
is a complex envelope vector of the signal; a (omega)c,d,ρc,dH) is the array manifold vector, ω, for the d-th corrected source signalc,dLongitude, p, for the d correction sourcec,dThe latitude of the d correction source is shown, and h is the ionosphere virtual height; a (omega)t,ρtH) is the array manifold vector, ω, for the target source signaltAs the target source longitude, ρtIs the target source latitude;
Figure FDA0002966944400000065
is an array manifold matrix.
3. The short-wave single-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 FDA0002966944400000066
wherein (x)t,g,yt,g,zt,g) Coordinates of the target source under a horizontal coordinate system of the observation station are obtained; omegaoAnd ρoLongitude and latitude of the observation station respectively; r is the radius of the earth;
step 3.2: obtaining the azimuth angle theta according to the formula (2)tAnd longitude ωtAnd latitude rhotThe relationship of (1):
Figure FDA0002966944400000067
wherein the content of the first and second substances,
Figure FDA0002966944400000071
Figure FDA0002966944400000072
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 FDA0002966944400000073
wherein the content of the first and second substances,
Figure FDA0002966944400000074
the internal angle of the triangle with the center point as the vertex is shown.
4. The method for short-wave single-station direct positioning in the presence of a correction source according to claim 1, wherein 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 FDA0002966944400000075
wherein (x)d,g,yd,g,zd,g) Coordinates of the d correction source in a horizontal coordinate system of the observation station;
step 4.2: obtaining the azimuth angle theta according to the formula (5)c,dAnd longitude ωc,dAnd latitude rhoc,dThe relationship of (1):
Figure FDA0002966944400000076
step 4.3: using the sine theorem of triangle to obtain the elevation angle betac,dAnd longitude ωc,dLatitude rhoc,dAnd ionospheric pseudo-height h relation:
Figure FDA0002966944400000077
wherein the content of the first and second substances,
Figure FDA0002966944400000078
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