CN110208741B - Beyond-visual-range single target direct positioning method based on multi-circle array phase measurement - Google Patents

Beyond-visual-range single target direct positioning method based on multi-circle array phase measurement Download PDF

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CN110208741B
CN110208741B CN201910576373.6A CN201910576373A CN110208741B CN 110208741 B CN110208741 B CN 110208741B CN 201910576373 A CN201910576373 A CN 201910576373A CN 110208741 B CN110208741 B CN 110208741B
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李万春
魏逸凡
熊钊
魏平
彭晓燕
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/04—Position of source determined by a plurality of spaced direction-finders

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Abstract

The invention belongs to the technical field of electronic countermeasure, and particularly relates to a beyond-the-horizon single-target direct positioning method based on multi-circle array phase measurement. According to the invention, by solving the phase difference between the received signals of different array elements of the same circular array, all information related to the target position in the array flow pattern can be extracted, and the relationship between the phase difference and the pitch angle and the azimuth angle is established, so that the position point meeting the relationship can be searched in the whole observation area. In order to reduce the searching dimension in the searching process, the azimuth angle of the searching point relative to the observation station can be firstly brought into the relational expression, the optimal pitch angle is obtained by adopting a least square method, and then the azimuth angle and the obtained optimal pitch angle are brought into the relational expression to calculate whether the received signals are in line with the actual received signals. The method has the advantages that the method can accurately position the over-the-horizon single target, and is simple and good in effect.

Description

Beyond-visual-range single target direct positioning method based on multi-circle array phase measurement
Technical Field
The invention belongs to the technical field of electronic countermeasure, and discloses a method for positioning a single target through phase difference information of different array elements of a plurality of circular arrays in a geographic coordinate system space.
Background
In the electronic reconnaissance process, accurate estimation of the position of a target radiation source is beneficial to obtaining radiation source information, is a key and main basis for high-level situation estimation and threat estimation, and is also an important guarantee for realizing accurate target strike. The positioning is to approximate a certain observation area to a plane, then position by using a plane geometry method, and calculate the target position. This method works well when the curvature of the target and the observation area where the antenna is located is not large relative to the earth. However, with the continuous development of the technology, the range of motion of various naval, terrestrial and air equipment is continuously expanded, the influence of the curvature of the earth on the positioning result is larger and larger, and the observation area can not be approximated to a plane for solving.
The positioning algorithm based on the earth sphere model mostly carries out cross positioning of a square line on a sphere tangent plane or a section, solves the position of a target, and then converts the plane position of the target into the geographic position of the target. However, the precision of the pitch angle of the target obtained through microwave and infrared radiation is too poor, so that the azimuth angle and the pitch angle can not be measured at two stations in a rectangular coordinate system to realize cross positioning.
Disclosure of Invention
Aiming at the problems, the invention provides a scheme for directly positioning a single target based on multi-circle array phase measurement in a geographic coordinate system space.
The technical scheme adopted by the invention is as follows:
for a stationary target, the position information is translated into the pitch and azimuth of the target relative to the observation station, and the pitch and azimuth information is completely contained in the array flow pattern of the array received signals. By solving the phase difference between the received signals of different array elements of the same circular array, all information about the target position in the array flow pattern can be extracted, and the relationship between the phase difference and the pitch angle and the azimuth angle is established, so that the position points meeting the relationship can be searched in the whole observation area. In order to reduce the searching dimension in the searching process, the azimuth angle of the searching point relative to the observation station can be firstly brought into the relational expression, the optimal pitch angle is obtained by adopting a least square method, and then the azimuth angle and the obtained optimal pitch angle are brought into the relational expression to calculate whether the received signals are in line with the actual received signals. In order to eliminate the position ambiguity and improve the positioning accuracy, at least 2 antenna arrays are required. A multi-station based single object localization model in geographic coordinate system space is shown in fig. 1.
Assuming that there are P observers on the earth, the longitude and latitude of the P-th observer is: (L) p ,B p ) The longitude and latitude of the radiation source is (L, B). The azimuth angle of the target relative to the p observation station is theta p Angle of pitch phi p . The signal model as shown in fig. 2 can be expressed as:
Figure BDA0002112202020000021
Figure BDA0002112202020000022
representing a signal at the t-th moment received by the mth array element in the pth circular array, wherein M is the number of the array elements contained in each circular array; s is p (t) represents the envelope of the signal received by the pth circular array;
Figure BDA0002112202020000023
the phase difference generated by the mth array element in the pth circular array relative to the 1 st array element due to different positions is shown, R is the radius of the uniform circular array, and lambda is the wavelength of a received signal;
Figure BDA0002112202020000024
representing gaussian white noise.
Figure BDA0002112202020000025
Assuming that the noise satisfies:
Figure BDA0002112202020000026
wherein the content of the first and second substances,
Figure BDA0002112202020000027
for the noise variance, δ (T) is the impulse function, T and T1 represent the time instants, and T is the total sampling time.
Correlation function of two array element channels k and l receiving signals in circular array p is solved
Figure BDA0002112202020000028
Figure BDA0002112202020000029
For k ≠ l, the correlation function r kl (t) the phase angle in the statistical sense of time is:
Figure BDA00021122020200000210
the above formula is arranged into a matrix form:
Figure BDA0002112202020000031
wherein the content of the first and second substances,
Figure BDA0002112202020000032
Figure BDA0002112202020000033
Figure BDA0002112202020000034
the measurement area of the observation station is divided into Q multiplied by N grids, and each grid point represents a position coordinate (x) in a target longitude and latitude plane q ,y n ) Q =1,2, …, Q, N =1,2, …, N. Let the longitude and latitude corresponding to this position be (L) q ,B n ) Q is more than or equal to 1 and less than or equal to Q, N is more than or equal to 1 and less than or equal to N, and the longitude and latitude of the center of the pth circular array are (L) p ,B p ) And P is more than or equal to 1 and less than or equal to P (P is the total number of the circular arrays).
Utilize the followingFormula, calculating the location of the search point (L) q ,B n ) Relative to the p-th circular array center (L) p ,B p ) Azimuth angle of
Figure BDA0002112202020000035
b p,q,n ＝sin B p sin B n +cos B p cos B n cos(L p -L q ) (10)
Figure BDA0002112202020000036
Figure BDA0002112202020000037
Will be provided with
Figure BDA0002112202020000038
Substituting the formula (6) to calculate the position (L) of the search point by the least square method q ,B n ) Optimal solution for pitch angle of (c):
Figure BDA0002112202020000039
substituting equation (13) into equation (6) to obtain the error of the search point relative to the p-th observation station:
Figure BDA00021122020200000310
here, the
Figure BDA0002112202020000041
Is composed of
Figure BDA0002112202020000042
Is an idempotent matrix of powers, i.e.
Figure BDA0002112202020000043
And satisfy
Figure BDA0002112202020000044
And similarly, the error of the search point relative to all observation stations can be obtained, and the overall error is calculated:
Figure BDA0002112202020000045
taking the inverse of the error as a cost function of the search point:
Figure BDA0002112202020000046
the longitude and latitude of the final target are:
Figure BDA0002112202020000047
the method has the advantages that the method can be used for accurately positioning the over-the-horizon single target, and is simple and good in effect.
Drawings
FIG. 1 is a diagram of a multi-circle array direct positioning model in a sphere model;
FIG. 2 is a model of a received signal;
FIG. 3 is a flow chart of an over-the-horizon single target direct positioning algorithm based on multi-circle array phase measurement;
FIG. 4 is a single target pseudospectrum generated by a coarse search;
FIG. 5 is a single target pseudogram generated by the fine search.
Fig. 6 shows the positioning error for different signal-to-noise ratios.
Detailed Description
The present invention will be described in detail with reference to examples below:
examples
In this embodiment, matlab is used to verify the above-mentioned over-the-horizon single-target direct positioning algorithm scheme for multi-circle array phase measurement, and for the sake of simplicity, the following assumptions are made for the algorithm model:
1. all observation stations and targets are on the earth's surface;
2. the signals received by all observation stations have the same signal-to-noise ratio;
3. all engineering errors are superposed into equivalent noise;
4. assuming that the target is stationary or moving at a very low speed;
step 1, setting an area where a target is located: the longitude is from 90 degrees to 110 degrees, the latitude is from 20 degrees to 40 degrees, and the target longitude and latitude is (101.667,31.667) with the unit of degree. And 3 fixed observation stations are used for positioning the target, all the observation stations are also distributed in the area, and the longitude and the latitude are respectively as follows: (95,25), (105,25), (100,35) in degrees. The noise of the observation stations is assumed to be subjected to Gaussian distribution with the mean value of zero, and the noise between different array elements of each observation station is independent;
step 2, performing time synchronization on the M-channel array antenna receiving systems of each observation station, and acquiring radio signal data radiated by a target according to the Nyquist sampling theorem to obtain array signal data;
step 3, carrying out cross-correlation processing on the received signals among different channels of the same observation station to obtain the phase difference of the signals among different channels
Figure BDA0002112202020000051
k,l＝1,2,…,M,(k≠l)p＝1,…,P；
Step 4, dividing the observation area into QxN (20 x 20 is taken in the simulation) grids, and calculating the azimuth angles of the vertex positions of the grids relative to each observation station
Figure BDA0002112202020000052
q, n represents the position of the currently searched grid, and p represents the p-th observation station;
step 5, mixing
Figure BDA0002112202020000053
Solving the optimum solution related to the pitch angle by substituting in (13)
Figure BDA0002112202020000054
And 6, calculating the error of the search point relative to the p observation station according to the formula (14)
Figure BDA0002112202020000055
Step 7, accumulating the errors of the search points relative to all observation stations to obtain C q,n ；
Step 8, calculating C q,n Reciprocal Q of (A) q,n Using Q q,n Drawing a pseudo-spectral diagram of a single target, wherein a peak point is a positioning result of coarse search, namely longitude and latitude (L ', B') of the target;
and 9, continuously adopting the methods from the step 4 to the step 8 to search the range which takes (L ', B') as the center and has 2 degrees of difference between longitude and latitude, and obtaining the accurate positioning result of the target.
The direct positioning effect of the beyond-the-horizon target based on the uniform circular array is as follows:
as shown in fig. 4, the observation region is roughly divided, a pseudo spectral peak image of the target in the observation region can be seen from the image, and the position of the spectral peak is the preliminary positioning result of the target. From the rough search result, the approximate position of the target can be determined, so that the search range can be narrowed, and the search can be performed more finely. The accurate positioning of the target can be seen in fig. 5. Fig. 6 shows the trend of the positioning error with the signal-to-noise ratio.

Claims (1)

1. A beyond-the-horizon single target direct positioning method based on multi-circle array phase measurement is characterized by comprising the following steps:
s1, assuming that P observation circular arrays on the earth exist, wherein the longitude and latitude of the P-th circular array are as follows: (L) p ,B p ) The longitude and latitude of the radiation source are (L, B), and the azimuth angle of the target relative to the p observation station is theta p Angle of pitch phi p The signal model is established as follows:
Figure FDA0003879938540000011
Figure FDA0003879938540000012
representing a signal at the t-th moment received by the mth array element in the pth circular array, wherein M is the number of the array elements contained in each circular array; s is p (t) represents the envelope of the signal received by the pth circular array;
Figure FDA0003879938540000013
the phase difference generated by the mth array element in the pth circular array relative to the 1 st array element due to different positions is shown, R is the radius of the uniform circular array, and lambda is the wavelength of a received signal;
Figure FDA0003879938540000014
representing white gaussian noise;
s2, performing time synchronization on the M-channel array antenna receiving systems of each observation station, and acquiring radio signal data radiated by a target according to the Nyquist sampling theorem to obtain array signal data;
s3, performing cross-correlation processing on the received signals among different channels of the same circular array to obtain the phase difference of the signals among the different channels:
Figure FDA0003879938540000015
let the noise satisfy:
Figure FDA0003879938540000016
Figure FDA0003879938540000017
Figure FDA0003879938540000018
1≤k≤M,1≤l≤M,1≤t,t1≤T
wherein the content of the first and second substances,
Figure FDA0003879938540000019
the noise variance is adopted, delta (T) is an impulse function, T and T1 represent time, and T is total sampling time;
then the correlation function of the received signals of k and l of two different array element channels in the circular array p
Figure FDA00038799385400000110
Figure FDA0003879938540000021
For k ≠ l, the correlation function r kl (t) the phase angle in the statistical sense of time is:
Figure FDA0003879938540000022
the arrangement into a matrix form is:
Figure FDA0003879938540000023
wherein
Figure FDA0003879938540000024
Figure FDA0003879938540000025
Figure FDA0003879938540000026
S4, dividing the circular array measuring area into Q multiplied by N grids, wherein each grid point represents a position coordinate (x) in the longitude and latitude plane of the target q ,y n ) Q =1,2, …, Q, N =1,2, …, N, and the longitude and latitude corresponding to this position is set to (L) q ,B n ) Q is more than or equal to 1 and less than or equal to Q, N is more than or equal to 1 and less than or equal to N, and the longitude and latitude of the center of the pth circular array are (L) p ,B p ) P is more than or equal to 1 and less than or equal to P; the search point location (L) is calculated using the following formula q ,B n ) Relative to the p-th circular array center (L) p ,B p ) Azimuth angle of
Figure FDA0003879938540000027
b p,q,n ＝sinB p sinB n +cosB p cosB n cos(L p -L q )
Figure FDA0003879938540000028
Figure FDA0003879938540000029
S5, mixing
Figure FDA0003879938540000031
Bringing in
Figure FDA0003879938540000032
Position of search point (L) by least square method q ,B n ) Optimal solution for pitch angle of (c):
Figure FDA0003879938540000033
s6, calculating the error of the search point relative to the p observation station
Figure FDA0003879938540000034
Figure FDA0003879938540000035
Figure FDA0003879938540000036
Is composed of
Figure FDA0003879938540000037
Is an idempotent matrix of powers, i.e.
Figure FDA0003879938540000038
And satisfy
Figure FDA0003879938540000039
S7, accumulating the errors of the search points relative to all observation stations to obtain C (q,n) ：
Figure FDA00038799385400000310
1≤q≤Q,1≤n≤N
S8, calculating C (q,n) Reciprocal Q of (A) (q,n)
Figure FDA00038799385400000311
Using Q (q,n) Drawing a pseudo-spectrum of a single target, wherein a peak point is a positioning result of the rough search, namely the longitude and latitude (L ', B') of the target;
s9, continuing to adopt the method from the step S4 to the step S8, searching the range which takes (L ', B') as the center and has the difference of 2 degrees between the longitude and the latitude, and obtaining the final positioning result of the target
Figure FDA00038799385400000312
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