CN110988923B - Satellite navigation interference source passive positioning method based on multi-platform cooperation - Google Patents

Satellite navigation interference source passive positioning method based on multi-platform cooperation Download PDF

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CN110988923B
CN110988923B CN201911152016.3A CN201911152016A CN110988923B CN 110988923 B CN110988923 B CN 110988923B CN 201911152016 A CN201911152016 A CN 201911152016A CN 110988923 B CN110988923 B CN 110988923B
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interference source
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CN110988923A (en
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李江
吴林旭
姚锦涛
王宇琦
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CETC 20 Research Institute
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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
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/21—Interference related issues ; Issues related to cross-correlation, spoofing or other methods of denial of service
    • 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
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/015—Arrangements for jamming, spoofing or other methods of denial of service of such systems

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Abstract

The invention provides a satellite navigation interference source passive positioning method based on multi-platform cooperation, which utilizes the satellite navigation interference source position data sharing acquired by a plurality of operation platforms under the networking cooperation condition of the plurality of operation platforms, adopts a multi-platform passive direction-finding cross positioning technology to calculate the position of a defense interference source, provides effective battlefield information for subsequent attack and destruction and improves the operation performance of each operation unit. The invention has good concealment and does not expose the position information of the invention; the problems of dead angle calculation and false point solution in double-platform positioning can be effectively avoided, and the interference source can be positioned in a three-dimensional manner in real time; the data volume is greatly reduced, the calculation amount is smaller, the calculation capacity is saved, and the influence on the normal operation of other functions is small; false points which may appear in positioning calculation are effectively reduced, the calculation pressure of the battle member platform equipment is reduced, the utilization efficiency of battlefield networking information data is enhanced, and the accuracy of battle instructions is improved.

Description

Satellite navigation interference source passive positioning method based on multi-platform cooperation
Technical Field
The invention relates to the field of radio navigation and positioning, in particular to a satellite navigation interference source positioning method.
Background
Because the satellite navigation interference equipment has small volume and small transmitting power, even if special satellite navigation interference source reconnaissance equipment (such as a signal sentry 1000 GPS interference source detection system in the United states) is adopted, the direction (or the position) of the satellite navigation interference source is difficult to be accurately detected, and the active detection satellite navigation interference source equipment is easy to expose the target position of the equipment and increases the equipment cost of an application platform.
Passive localization techniques use a receiving device to receive a signal from a radiation source and determine the location of the radiation source. Therefore, for the detection of the satellite navigation interference source, some research works can obtain the position of the satellite navigation interference source by processing the received satellite navigation interference source signal at the satellite navigation anti-interference antenna device, but cannot locate the specific position of the satellite navigation interference source. Although the mobile measuring platform is used for obtaining the direction-finding result of the interference signal for many times and the position of the interference source can be located by adopting the direction-finding cross positioning principle, the base line between the movements of the measuring platform is short, so that the positioning error is large. Moreover, when the defense interference source is a moving target, a single-station passive positioning method is adopted, and the measuring platform is required to track the signal of the radiation source for a long enough time, however, the requirement is difficult to meet in practical application, which is also the biggest defect of the method. The multi-station positioning has good application foundation under the actual conditions of modern clustering and networked cooperation. And the multi-station positioning coverage range is wider, the implementation is easy, the positioning is quick, and the large-scale real-time tracking can be carried out on the maneuvering target. However, when multi-target positioning is performed, a false positioning result occurs, the existing false point elimination method needs more additional auxiliary information such as frequency spectrum and energy of an interference source, and has a higher requirement on a measurement system, and with the increase of measurement information, the data volume is increased, and a higher requirement on data transmission capability and data processing and computing capability between platforms is also achieved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a satellite navigation interference source passive positioning method based on multi-platform cooperation. In order to solve the problem that the member satellite navigation positioning equipment cannot normally work due to interference in the current environment, the invention aims to solve the technical problems that: under the condition that a plurality of platforms are networked and cooperated, satellite navigation interference source azimuth data acquired by the plurality of platforms are shared, a multi-platform passive direction-finding cross positioning technology is adopted, the position of a satellite navigation interference source is resolved, effective information is provided for subsequent impact destroy, and the performance of each unit is improved.
The technical scheme adopted by the invention for solving the technical problem specifically comprises the following steps:
step 1: measuring the direction of the interference source and interacting data;
step 1.1: when influenced by a navigation interference source, the azimuth angle eta and the pitch angle of the interference source relative to the self are obtained by adopting a measuring antenna
Figure GDA0003717249740000021
And recording the measurement time; wherein, the azimuth angle is the included angle between the connecting line of the target interference source and the measuring platform and the north direction, the clockwise rotation is positive, and the pitch angle is the connecting line of the measuring platform and the interference source and the north directionThe included angle between the horizontal planes ranges from minus 90 degrees to plus 90 degrees;
step 1.2: each measuring platform measures the direction between the measuring platform and the interference source to form a measuring combination
Figure GDA0003717249740000022
Wherein eta,
Figure GDA0003717249740000023
Respectively measured azimuth angle and pitch angle, and t is measurement time;
step 1.3: packaging and sending the measured measurement combination to a data operation center, carrying out data preprocessing by the data operation center, and entering step 2 to judge which group of measurement values are used for positioning the satellite-borne interference source;
step 2: the data operation center analyzes and judges the received measurement information;
step 2.1: arranging and combining the measurement combinations to obtain related combinations with correlation;
according to the condition that the interference source exists, namely all the measuring lines intersect at one point, all the combinations are analyzed, unreasonable combinations are eliminated, and the method specifically comprises the following steps:
if N satellite-borne interference sources and M interfered members exist in a certain area and only one interference source exists on each measurement line, a set of azimuth angles and pitch angles measured by M measurement platforms is represented as Z 1 ，Z 2 ，…Z i ，…Z M Wherein, Z i ＝[z i1 ，z i2 ，…，z ij ，…，z iN ]，i＝1，2，…，M；
And is
Figure GDA0003717249740000024
Where j is 1, 2, …, N, N is the number of guard guided interferers, eta ij And
Figure GDA0003717249740000025
respectively the azimuth angle and the pitch angle, Delta eta, of the measuring platform relative to the interference source ij And
Figure GDA0003717249740000026
the measurement errors of the azimuth angle and the pitch angle are respectively;
taking an element from M measurement angle sets acquired from M measurement platforms to form an association combination, and defining a jth association combination as:
Figure GDA0003717249740000027
wherein j is 1, 2, …, N;
step 2.2: preliminary screening of associations
Step 2.1 associative combination has N M When the measurement lines corresponding to all the angles in one measurement angle combination intersect at the same point, the correct combination is obtained, and each measurement line is represented as:
Figure GDA0003717249740000031
wherein (x) i ，y i ，z i ) Representing a measuring platform M i If the measurement lines corresponding to all the measurement angles in a certain association combination are to intersect at a single point, the following conditions are satisfied:
Figure GDA0003717249740000032
wherein
Figure GDA0003717249740000033
The intermediate parameters are specifically as follows:
Figure GDA0003717249740000034
at this time, all the measuring lines in the associated combination intersect at the same point, if the measuring lines corresponding to the selected measuring angles in a certain associated combination cannot converge to a point, the combination is an invalid combination, and the combination is removed;
step 2.3: secondary screening of the association combination;
because N interference sources exist, N association combinations are selected to form an interference source combination, and the selected association combinations of N measurement angles are respectively expressed as
Figure GDA0003717249740000035
And (3) forming an interference source combination by the correlation combination of the measurement angles, and recording as:
Figure GDA0003717249740000036
since there is only one interference source on each measurement line, when the associated combination of N measurement angles satisfies the following condition:
Figure GDA0003717249740000037
i.e. the elements of each measured angle combination are not present in the other combinations, only if
Figure GDA0003717249740000038
When this condition is satisfied, the control unit is allowed to,
Figure GDA0003717249740000039
the method comprises the following steps that a feasible combination is obtained, and cross positioning calculation is carried out on the feasible combination to obtain the positions of a group of interference sources;
and 3, step 3: iteratively solving the position of the interference source by adopting a least square method;
resolving the feasible association combination screened in the step 2 by adopting a least square method, and solving the position of the interference source by utilizing all effective measurement information;
step 3.1: establishing an interference source position solution equation set;
assuming that the coordinates of the interference source J are (x, y, z) unknown, the measurement platform M i Has a position coordinate of (x) i ，y i ，z i ) I is 1, 2, …, n and is known as a measuring platform M i Measured azimuth and pitch angles for interference source J
Figure GDA00037172497400000310
The relationship between the measurement angle of the interference source and the actual position of the interference source measured by each measurement platform is as follows:
Figure GDA0003717249740000041
in the formula, Δ η i 、
Figure GDA0003717249740000042
The direction finding errors of the azimuth angle and the pitch angle respectively,
Figure GDA0003717249740000043
and
Figure GDA0003717249740000044
for intermediate calculation parameters, the expression is as follows:
Figure GDA0003717249740000045
wherein
Figure GDA0003717249740000046
The distance of the projection of a connecting line between the interference source and the measuring platform on the horizontal plane is determined;
when the number N of the interfered platforms is more than or equal to 2, the position of the interference source can be obtained by the formula (8);
step 3.2: linearization and least square solution;
let equation (8) at an initial point J 0 ＝(x 0 ，y 0 ，z 0 ) The position of the source of the interference source is linearized by a Taylor series expansion, the position error of the position of the interference source from a given initial value is [ Delta x, Delta y, Delta z ]] T Keeping the first two available:
Figure GDA0003717249740000047
wherein
Figure GDA0003717249740000048
Error of position of the platform, which is self-positioning device-generated error, Δ η i 、
Figure GDA0003717249740000049
The measurement errors of the azimuth angle and the pitch angle are respectively, and the expression of each parameter in the formula is as follows:
Figure GDA00037172497400000410
Figure GDA00037172497400000411
Figure GDA00037172497400000412
the observation equation for the M measurement platforms is thus expressed as:
B＝FΔP+Δθ (14)
Figure GDA0003717249740000051
ΔP＝[x-x 0 y-y 0 z-z 0 ] T ＝[Δx Δy Δz] T (16)
Figure GDA0003717249740000052
b is the deviation of the measured value and the given initial value, F is an intermediate calculation parameter, delta P is the deviation of the position of the interference source and the given initial value, and delta theta is the measurement error of the measurement angle;
from the least squares estimate, one can obtain:
ΔP＝(F T F) -1 F T B
thus, the position of the interference source can be calculated as:
P g ＝(F T F) -1 F T (Z-H(P 0 ))+P 0
wherein P is g For an estimate of the location of the source of the interference, Z is a measure of the azimuth and pitch angles, P 0 Is the initial value of the iteration;
selecting an initial value P 0 After many times of iterative calculation, when the calculation result tends to be stable, the calculation result can be used as a final positioning result.
The invention has the beneficial effects that:
(1) compared with active detection means such as active radar and the like, the passive multi-station positioning method adopts passive multi-station positioning, cannot be detected by the other party, has good concealment, and does not expose self position information. Meanwhile, the detection action distance of the passive equipment is longer than that of the active equipment, the equipment cost of an application platform is not increased, excessive energy is not additionally consumed, and the passive equipment has great advantages in practical cooperation.
(2) Compared with a passive single-station and double-station direction-finding positioning mode, the multi-station passive positioning method adopts a multi-station passive positioning scheme, and can be simultaneously suitable for positioning a static target and a maneuvering target. Meanwhile, the problems of dead angle calculation and false point solution in the double-platform positioning can be effectively avoided (as shown in fig. 3), and the real-time three-dimensional positioning of the interference source can be realized.
(3) The existing multi-station interference source positioning method needs more auxiliary measurement information in the process of eliminating false points, such as measurement information of carrier frequency, carrier frequency type, pulse width type, repetition frequency type and the like of target signals, has higher requirements on measurement equipment, and has higher requirements on data transmission and data processing capacity along with the increase of information quantity.
(4) Under the background of modern multi-member cluster cooperation, the interference source positioning scheme provided by the invention can fully utilize the measurement information of each member to add more constraint conditions, and effectively reduce false points possibly occurring in positioning calculation (the specific description schematic diagrams are shown in fig. 3 and 4). Meanwhile, a node of a data operation center is added into a network system, so that the data processing capacity is greatly enhanced, support is provided for huge computing capacities of data processing, data association, false positioning result elimination and the like which are required to be processed by multi-station cooperative positioning, the computing pressure of member platform equipment is reduced, the utilization efficiency of networked information data is enhanced, and the instruction accuracy is improved.
Drawings
FIG. 1 is a cross-direction orientation geometry of the present invention.
Fig. 2 is a method for positioning a satellite navigation interference source under multi-platform cooperation according to the present invention.
FIG. 3 is a schematic diagram of the dual-platform direction-finding cross-location of false points according to the present invention.
FIG. 4 is a schematic diagram of multi-platform direction-finding cross-location false point elimination according to the present invention.
FIG. 5 is a schematic diagram of the distribution of interference sources and measurement platforms according to the present invention.
Fig. 6 is a diagram of the multi-station positioning result of the interference source 1 of the present invention.
Fig. 7 is a diagram of the multi-station positioning result of the interference source 2 of the present invention.
Fig. 8 is a diagram of the multi-station positioning result of the interference source 3 according to the present invention.
FIG. 9 is a diagram illustrating the dual stage positioning results of the present invention.
Fig. 10 is a flow chart of the interference solution of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
The invention provides a satellite navigation interference source passive positioning method based on multi-platform cooperation on the basis of a passive direction finding cross positioning principle. The method uses the idea of passive radar networking positioning for reference, stores the direction-finding data of the satellite navigation interference source acquired by a plurality of platforms in a data operation center in real time by using data communication links on the platforms, realizes position estimation of the satellite navigation interference source by using target azimuth information measured by the plurality of platforms and adopting a passive direction-finding cross-positioning algorithm, and simultaneously eliminates false positioning results without excessive additional auxiliary measurement information and has less requirements on measurement equipment. The method provides a good technical approach for solving the problem of positioning the satellite-guided interference source.
Step 1: measuring the direction of the interference source and exchanging data;
1.1 when the member is influenced by the satellite navigation interference source, the azimuth angle eta and the pitch angle of the interference source relative to the member are obtained by adopting the measuring antenna
Figure GDA0003717249740000071
And recording the measuring time; wherein, the azimuth angle is an included angle between a connecting line of the target interference source and the measuring platform and the north direction, the clockwise rotation is positive, the pitch angle is an included angle between the connecting line of the measuring platform and the interference source and the horizontal plane, and the value range is (-90 degrees to +90 degrees);
1.2 Each measuring platform measures the direction between itself and the interference source to form a measuring combination
Figure GDA0003717249740000072
Wherein eta,
Figure GDA0003717249740000073
Respectively the measured azimuth angle and the pitch angle, and t is the measurement time, as shown in fig. 1;
1.3, packaging and sending the measured measurement combination to a data operation center, carrying out data preprocessing by the data operation center, and entering the step 2 to judge and decide which group of measurement values are used for positioning the satellite-borne interference source, as shown in fig. 2;
and 2, step: the data operation center analyzes and judges the received measurement information;
2.1, carrying out permutation and combination on the measurement combinations to obtain a series of correlation combinations with correlation;
analyzing all combinations according to the condition of the interference source, namely all the measuring lines are intersected at one point, and eliminating unreasonable combinations, and the method comprises the following specific steps:
if N satellite-borne interference sources and M interfered members exist in a certain area and only one interference source exists on each measurement line, a set of azimuth angles and pitch angles measured by M measurement platforms is represented as Z 1 ，Z 2 ，…Z i ，…Z M Wherein Z is i ＝[z i1 ，z i2 ，…，z ij ，…，z iN ]，i＝1，2，…，M；
And is provided with
Figure GDA0003717249740000074
Where j is 1, 2, …, N, N is the number of guard guided interferers, eta ij And
Figure GDA0003717249740000075
respectively the azimuth angle and the pitch angle, Delta eta, of the measuring platform relative to the interference source ij And
Figure GDA0003717249740000076
the measurement errors of the azimuth angle and the pitch angle are respectively;
as shown in the schematic diagram of the direction-finding cross positioning principle shown in fig. 1, an element is taken from each of M measurement angle sets obtained from M measurement platforms to form an association combination, and a jth association combination is defined as:
Figure GDA0003717249740000077
wherein j is 1, 2, …, N;
2.2 preliminary screening of associations
Step 2.1 Association combinations have N M Therefore, all combinations need to be screened, and unreasonable combinations are removed. According to the principle of cross-positioning, when the measurement lines corresponding to all the angles in a measurement angle combination intersect at the same point, the combination is likely to be the correct combination, and each measurement line is represented as:
Figure GDA0003717249740000078
wherein (x) i ，y i ，z i ) Representing a measuring platform M i If the measurement lines corresponding to all the measurement angles in a certain association combination are to intersect at a single point, the following conditions are satisfied:
Figure GDA0003717249740000081
wherein
Figure GDA0003717249740000082
The intermediate parameters are specifically as follows:
Figure GDA0003717249740000083
at this time, all the measuring lines in the associated combination intersect at the same point, if the measuring lines corresponding to the selected measuring angles in a certain associated combination cannot converge to a point, the combination is an invalid combination, and the combination is removed;
2.3 secondary screening of the association combination;
in addition, because N interference sources exist, N correlation combinations are selected to form an interference source combination, and the selected correlation combinations of N measurement angles are respectively expressed as
Figure GDA0003717249740000084
And forming an interference source combination by the associated combination of the measurement angles, and recording as:
Figure GDA0003717249740000085
since there is only one interference source on each measurement line, when the associated combination of N measurement angles satisfies the following condition:
Figure GDA0003717249740000086
i.e. the elements in each measured angle combination are not present in other combinations, only if
Figure GDA0003717249740000087
When this condition is satisfied, the process is carried out,
Figure GDA0003717249740000088
the method comprises the following steps that a feasible combination is subjected to cross positioning calculation to obtain the positions of a group of interference sources;
after the series of judgment and elimination, false points in interference detection can be greatly reduced, and the accuracy of the interference detection is improved.
And step 3: iteratively solving the position of the interference source by adopting a least square method;
resolving the feasible association combination screened in the step 2 by adopting a least square method, and solving the position of the interference source by utilizing all effective measurement information;
3.1 establishing an interference source position solving equation set;
assuming that the coordinates of the interference source J are (x, y, z) unknown, the measurement platform M i Has a position coordinate of (x) i ，y i ，z i ) I 1, 2, …, n and known, measuring platform M i Measured azimuth and pitch angles for interference source J
Figure GDA0003717249740000089
The relationship between the measurement angle of the interference source and the actual position of the interference source measured by each measurement platform is as follows:
Figure GDA0003717249740000091
in the formula, Δ η i 、
Figure GDA0003717249740000092
The direction finding errors of the azimuth angle and the pitch angle respectively,
Figure GDA0003717249740000093
and
Figure GDA0003717249740000094
for intermediate calculation parameters, the expression is as follows:
Figure GDA0003717249740000095
wherein
Figure GDA0003717249740000096
The distance of the projection of a connecting line between the interference source and the measuring platform on the horizontal plane is determined;
when the number N of the interfered platforms is more than or equal to 2, the position of the interference source can be obtained by the formula (8);
3.2 linearization and least squares solution
Let equation (8) at an initial point J 0 ＝(x 0 ，y 0 ，z 0 ) Linearized by Taylor series expansion, the position error of the interference source position and the given initial value is [ Delta x Delta y Delta z] T Keeping the first two available:
Figure GDA0003717249740000097
wherein
Figure GDA0003717249740000098
Error in the position of the platform, which is the error produced by the self-positioning device, Δ η i 、
Figure GDA0003717249740000099
The measurement errors of the azimuth angle and the pitch angle are respectively, and the expression of each parameter in the formula is as follows:
Figure GDA00037172497400000910
Figure GDA00037172497400000911
Figure GDA00037172497400000912
the observation equation for the M measurement platforms is thus expressed as:
B＝FΔP+Δθ (14)
Figure GDA0003717249740000101
ΔP＝(x-x 0 y-y 0 z-z 0 ] T ＝[Δx Δy Δz] T (16)
Figure GDA0003717249740000102
b is the deviation of the measured value and the given initial value, F is an intermediate calculation parameter, delta P is the deviation of the position of the interference source and the given initial value, and delta theta is the measurement error of the measurement angle;
from the least squares estimation, one can obtain:
ΔP＝(F T F) -1 F T B
thus, the interference source position can be found as follows:
P g ＝(F T F) -1 F T (Z-H(P 0 ))+P 0
wherein P is g For an estimate of the location of the source of the interference, Z is a measure of the azimuth and pitch angles, P 0 Is the initial value of the iteration.
Selecting an initial value P 0 After repeated iterative calculation, when the calculation result tends to be stable, the calculation result can be used as a final positioning result.
A data operation center is added in a network node, data interaction is carried out with other measuring platforms through a data communication link on the measuring platform, and related data of all the platforms are stored on the platform provided with data processing center equipment for analysis and processing, so that the positioning of a satellite navigation interference source is realized; and finally, the data processing center sends the position information of the defense-induced interference source to a decision-making main control display unit for display, and sends the position information to other platforms through data communication links between the platforms to guide the weapon system to carry out cooperative attack.
Simulation embodiment
The positions of the 3 measurement platforms given are platform 1(118.9, 23.8, 0), platform 2(119.0, 23.7, 0), and platform 3(119.1, 23.8, 0), respectively. The positions of the 3 guard-guided interferers are interferer 1(118.9, 24, 1000), interferer 2(119, 24, 1000), and interferer 3(119.1, 24, 1000), respectively. The distance between the interference source and the platform and the distribution thereof are shown in fig. 1. The satellite navigation interference source positioning method provided by the invention is adopted, 3 measuring stations are adopted for positioning, the direction-finding precision of the platform to the interference source is 0.5 degrees, 1000 times of measurement positioning calculation is carried out, and the positioning result after positioning calculation is shown in table 1 and the following charts in fig. 6-8.
TABLE 1 statistical table of interference source positioning and resolving results
Figure GDA0003717249740000111
From the analysis results given in table 1, it can be seen that the present invention obtains a more accurate interference source position, the positioning error of which is between 200m and 300 m.
If the traditional double-platform geometric direction-finding cross positioning method is adopted for positioning calculation, the positions of three satellite-borne interference sources are kept unchanged, and the measuring platform only keeps two measuring terminals (118.9, 23.8, 0) and (119.1, 23.8, 0). The positioning result is shown in fig. 9 if the direction-finding accuracy of the platform to the interference source is still set to 0.5 °. It can be seen from the figure that when the heights of the 3 interference sources are the same and the interference sources are coplanar with the 2 measurement terminals, the positioning result obtains the positions of the interference sources, and 3 false interference source position information also appears, so that the application platform cannot accurately and effectively obtain the true positions of the interference sources.
The simulation result fully shows the effectiveness and the correctness of the method, and the accuracy and the positioning precision of the detection of the satellite navigation interference source are greatly improved.

Claims (1)

1. A passive positioning method of a satellite navigation interference source based on multi-platform cooperation is characterized by comprising the following steps:
step 1: measuring the direction of the interference source and interacting data;
step 1.1: when influenced by a navigation interference source, the azimuth angle eta and the pitch angle of the interference source relative to the self are obtained by adopting a measuring antenna
Figure FDA0003717249730000011
And recording the measurement time; wherein, the azimuth angle is an included angle between a connecting line of the target interference source and the measuring platform and the north direction, the clockwise rotation is positive, the pitch angle is an included angle between the connecting line of the measuring platform and the interference source and the horizontal plane, and the value range is (-90 degrees to +90 degrees);
step 1.2: each measuring platform measures the direction between the measuring platform and the interference source to form a measuring combination
Figure FDA0003717249730000012
Wherein eta,
Figure FDA0003717249730000013
Are respectively measuredAzimuth angle and pitch angle, t is measurement time;
step 1.3: packaging and sending the measured measurement combination to a data operation center, carrying out data preprocessing by the data operation center, and entering step 2 to judge which group of measurement values are used for positioning the satellite-borne interference source;
step 2: analyzing and judging the received measurement information by the battlefield data operation center;
step 2.1: arranging and combining the measurement combinations to obtain related combinations with correlation;
according to the condition that the interference source exists, namely all the measuring lines intersect at one point, all the combinations are analyzed, unreasonable combinations are eliminated, and the method specifically comprises the following steps:
if N satellite-guided interference sources and M interfered members exist in a certain area and only one interference source exists on each measuring line, a set of azimuth angles and pitch angles measured by M measuring platforms is represented as Z 1 ，Z 2 ，…Z i ，…Z M Wherein, Z i ＝[z i1 ，z i2 ，…，z ij ，…，z iN ]，i＝1，2，…，M；
And is
Figure FDA0003717249730000014
Wherein j is 1, 2, …, N, N is the number of guard pilot interference sources, eta ij And
Figure FDA0003717249730000015
respectively the azimuth angle and the pitch angle of the measuring platform relative to the interference source, delta eta ij And
Figure FDA0003717249730000016
the measurement errors of the azimuth angle and the pitch angle are respectively;
taking an element from M measurement angle sets acquired from M measurement platforms to form an association combination, and defining a jth association combination as:
Figure FDA0003717249730000017
wherein j is 1, 2, …, N;
step 2.2: preliminary screening of associations
Step 2.1 Association combinations have N M When the measurement lines corresponding to all the angles in one measurement angle combination intersect at the same point, the correct combination is obtained, and each measurement line is represented as:
Figure FDA0003717249730000021
wherein (x) i ，y i ，z i ) Representing a measuring platform M i If the measurement lines corresponding to all the measurement angles in a certain association combination are to intersect at a single point, the following conditions are satisfied:
Figure FDA0003717249730000022
wherein
Figure FDA0003717249730000023
The intermediate parameters are specifically as follows:
Figure FDA0003717249730000024
at this time, all the measuring lines in the associated combination intersect at the same point, if the measuring lines corresponding to the selected measuring angles in a certain associated combination cannot converge to a point, the combination is an invalid combination, and the combination is removed;
step 2.3: secondary screening of the association combination;
due to the existence of N interference sourcesSelecting N associated combinations to form an interference source combination, and respectively representing the selected associated combinations of the N measurement angles as
Figure FDA0003717249730000025
And forming an interference source combination by the associated combination of the measurement angles, and recording as:
Figure FDA0003717249730000026
since there is only one interference source on each measurement line, when the associated combination of N measurement angles satisfies the following condition:
Figure FDA0003717249730000027
i.e. the elements in each measured angle combination are not present in other combinations, only if
Figure FDA0003717249730000028
When this condition is satisfied, the process is carried out,
Figure FDA0003717249730000029
the method comprises the following steps that a feasible combination is obtained, and cross positioning calculation is carried out on the feasible combination to obtain the positions of a group of interference sources;
and step 3: iteratively solving the position of the interference source by adopting a least square method;
resolving the feasible association combination screened in the step 2 by adopting a least square method, and solving the position of the interference source by utilizing all effective measurement information;
step 3.1: establishing an interference source position solving equation set;
assuming that the coordinates of the interference source J are (x, y, z) unknown, the measurement platform M i Has a position coordinate of (x) i ，y i ，z i ) I 1, 2, …, n and known, measuring platform M i Azimuth angle and pitch angle measured for interference source JIs composed of
Figure FDA00037172497300000210
The relationship between the measurement angle of the interference source and the actual position of the interference source measured by each measurement platform is as follows:
Figure FDA0003717249730000031
in the formula, Δ η i 、
Figure FDA0003717249730000032
The direction finding errors of the azimuth angle and the pitch angle respectively,
Figure FDA0003717249730000033
and
Figure FDA0003717249730000034
for intermediate calculation parameters, the expression is as follows:
Figure FDA0003717249730000035
wherein
Figure FDA0003717249730000036
The distance of a connecting line between the interference source and the measuring platform projected on a horizontal plane is 1, 2.. n;
when the number N of the interfered platforms is more than or equal to 2, the position of the interference source can be obtained by the formula (8);
step 3.2: linearization and least square solution;
let equation (8) at an initial point J 0 ＝(x 0 ，y 0 ，z 0 ) Linearized by Taylor series expansion, the position error of the interference source position and the given initial value is [ Delta x Delta y Delta z] T Keeping the first two available:
Figure FDA0003717249730000037
wherein
Figure FDA0003717249730000038
Error in the position of the battle platform, caused by self-positioning equipment, Δ η i 、
Figure FDA0003717249730000039
The measurement errors of the azimuth angle and the pitch angle are respectively, and the expression of each parameter in the formula is as follows:
Figure FDA00037172497300000310
Figure FDA00037172497300000311
Figure FDA00037172497300000312
the observation equations for the M measurement platforms are thus expressed as:
B＝FΔP+Δθ (14)
Figure FDA0003717249730000041
ΔP＝[x-x 0 y-y 0 z-z 0 ] T ＝[Δx Δy Δz] T (16)
Figure FDA0003717249730000042
wherein B is the deviation of the measured value from the given initial value, F is an intermediate calculation parameter, Δ P is the deviation of the position of the interference source from the given initial value, and Δ θ is the measurement error of the measurement angle;
from the least squares estimate, one can obtain:
ΔP＝(F T F) -1 F T B
thus, the interference source position can be found as follows:
P g ＝(F T F) -1 F T (Z-H(P 0 ))+P 0
wherein P is g For an estimate of the location of the source of the interference, Z is a measure of the azimuth and pitch angles, P 0 Is the initial value of the iteration;
selecting an initial value P 0 After many times of iterative calculation, when the calculation result tends to be stable, the calculation result can be used as a final positioning result.
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