CN109613583B - Passive target positioning method based on single star and ground station direction finding and combined time difference - Google Patents
Passive target positioning method based on single star and ground station direction finding and combined time difference Download PDFInfo
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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
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
- G01S19/46—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being of a radio-wave signal type
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention belongs to the technical field of electronic countermeasure, and particularly relates to a passive target positioning method based on single star and ground station direction finding and combined time difference measuring. According to the method, aiming at a positioning scene of an aerial target radiation source, the single star and the ground station are used for respectively measuring the directions of the target radiation source signals reaching the respective residual angles, and the time difference of the target radiation source signals reaching the satellite and the ground observation station is used for giving a weighted least square analysis solution of the target position through pseudo-linearization processing of the directions of the residual angles and fusion of a time difference measurement equation. The method can realize single instantaneous high-precision positioning, does not have the problem of positioning and de-blurring, and the mean square error of positioning errors can approach the lower limit of the Keramen-Row.
Description
Technical Field
The invention belongs to the technical field of electronic countermeasure, and particularly relates to a passive target positioning method based on single star and ground station direction finding and combined time difference measuring.
Background
On the one hand, in a modern electronic information battle system, by utilizing an electronic reconnaissance means, electromagnetic wave signals from enemy battle units are measured, analyzed, sorted and identified to obtain strategic deployment of the enemy units, platform type and other information, the electronic reconnaissance system has important reference values for strategic decision making of the higher layers of the enemy, protection of the enemy battle units and strategic striking of the enemy. The passive reconnaissance positioning technology has the advantages of good concealment, long acting distance, high anti-interference capability, high system safety protection and the like, occupies an increasingly important position in an electronic reconnaissance system, and has been valued by the military of various countries.
On the other hand, along with development of the aerospace technology and breakthrough of the satellite-borne detection technology, the passive reconnaissance positioning is more and more dependent on the electronic reconnaissance satellite, and the single-satellite passive positioning system only utilizes one observation satellite to realize positioning of the ground radiation source, so that the single-satellite passive positioning system has the advantages of low cost, flexible positioning system and the like, but simultaneously, the single-satellite passive positioning system only utilizes one observation satellite to realize positioning of the radiation source, the target information amount obtained by a single platform is less, the positioning precision is not high enough, and under the normal condition, the space position and the motion parameter of the target radiation source can be estimated only by continuously observing the ground target radiation source for a plurality of times. At present, a single-star passive positioning method based on a kinematics principle obtains relatively high positioning precision through information such as the change rate of the arrival angle of a target radiation source signal, the change rate of Doppler frequency and the like, but the method needs multiple observations and cannot realize instantaneous single-time high-precision positioning.
Disclosure of Invention
The invention aims to solve the problems and provides a passive target positioning method based on single-satellite and ground station direction finding and combined time difference. Aiming at a positioning scene of an aerial target radiation source, measuring the directions and the residual angles of the target radiation source signals reaching the respective directions respectively through a single satellite and a ground station, and obtaining the time difference of the target radiation source signals reaching the satellite and the ground observation station respectively, and obtaining a weighted least square analysis solution of the target position through pseudo-linearization processing of the directions and the residual angles and fusing a time difference measurement equation. The method can realize single instantaneous high-precision positioning, does not have the problem of positioning and de-blurring, and the mean square error of positioning errors can approach the Cramer-Row lower limit (CRLB).
And (3) giving a weighted least square analytical solution of the target radiation source under the condition constraint by pseudo-linearization of a direction finding equation and fusion of WGS-84 ellipsoid constraint. The method can uniformly realize the positioning solution of the target when the two satellites are in the same orbit and different orbits, the satellite configuration is flexible under the positioning method, the iterative solution is not needed, the calculated amount is small, and the problem of positioning solution ambiguity does not exist.
The technical scheme adopted by the invention is as follows:
according to the method, the single star and the ground station are used for respectively measuring the complementary angles of directions of target radiation source signals reaching the single star and the ground station, and the time difference of the target radiation source signals respectively reaching the satellite and the ground observation station is deduced through an algorithm, so that a weighted least square analytic calculation formula of the target position is given. The positioning model is shown in fig. 1. In the figure, the satellite position is x under the ECEF of the ground fixed coordinate system S,e ＝[x s,e ,y s,e ,z s,e ] T The position of the ground observation station is x r,e ＝[x r,e ,y r,e ,z r,e ] T The position of the target radiation source is x T,e ＝[x t,e ,y t,e ,z t,e ] T . In the star coordinate system b, the position of the target radiation source is x T,b ＝[x t,b ,y t,b ,z t,b ] T From document [1]As can be seen, in the satellite-borne direction-finding positioning system, there is the following coordinate conversion relationship: x is x T,b ＝M(x S,e -x T,e ) The specific expression is
The method comprises the following steps: satellite x S,e Corresponding latitude B of point under satellite in geodetic coordinate system S And longitude L S By satellite x S,e Several angle information output by the satellite-borne attitude sensor: yaw angle ψ, pitch angle θ, roll angle φ. And simultaneously, in the formula:
the invention mainly comprises the following steps:
a. measuring the residual angles of directions of the target radiation source signals reaching the satellite and the ground observation station respectively through a single satellite and a ground station, and the time difference of the target radiation source signals reaching the satellite and the ground observation station respectively;
b. establishing a target positioning model by pseudo-linearization processing of the directional residual angle and fusing a time difference measurement equation;
c. and c, solving the model established in the step b by adopting a weighted least square method to obtain the target position.
Specifically, in the step a, the present invention is based on the following principle:
the observations of the positioning system can be expressed as follows:
A. single star measuring target radiation source signal arrival direction residual angle alpha 1 and β1 The expression of the measured value is:
in the formula ：Dx ＝[1,0,0]，D y ＝[0,1,0]，D z ＝[0,0,1]，
Respectively represent the direction residual angle alpha 1 and β1 Is true of>
and />
Representing their measurement errors, respectively. Meanwhile, there are:
in the formula ：
true value, gamma, representing the angle of the directional residual 1 Representing the angle alpha of the tailline from direction 1 and β1 The calculated direction residual angle is calculated from the measured value of (2).
B. Ground observation station measures the direction residual angle alpha of arrival of target radiation source signal 2 and β2 The expression of the measured value is:
similarly, in the formula:
respectively represent the direction residual angle alpha 2 and β2 Is true of>
and />
Representing the measurement errors respectively, and simultaneously:
in the formula ：
true value, gamma, representing the angle of the directional residual 2 Represented by azimuth angle alpha 2 And pitch angle beta 2 The calculated direction residual angle is calculated from the measured value of (2).
C. The time difference measurement value is converted into a distance difference, and the expression of the measurement value is as follows:
ρ＝ρ 0 +n ρ
＝d t,s -d t,r +n ρ
＝||(x T,e -x S,e )||-||(x T,e -x r,e )||+n ρ
in the formula ：nρ Is the distance difference measurement error converted from the time difference measurement error.
The positioning of the target radiation source is converted into the problem of solving the position of the target radiation source by utilizing the plurality of groups of nonlinear equations, and from the basic principle of geometric positioning, the weighted least square solution of the target can be determined by measuring a spatial positioning line formed by direction finding, a spatial positioning hyperboloid formed by time difference measurement, intersecting the line and intersecting the line and the plane.
In the step b, the method specifically comprises the following steps:
a) From the above formula A:
namely:
and according to the first-order Taylor series expansion principle, the method can be as follows:
the carrying-in arrangement can be obtained:
b) From the above formula A:
the method can obtain:
and according to the first-order Taylor series expansion principle, the method can be as follows:
the carrying-in arrangement can be obtained:
c) From the above formula B:
the same principle can be obtained:
d) From the above formula B:
the same principle can be obtained:
e) From the above formula A, B:
in the formula ,
the arrangement can be:
in the formula ui ，C i ，n i (i=1, 2) is represented by the following expression:
then, in summary, it is available:
b-Ax T,e ＝Nn
wherein ,
thus, a weighted least squares solution for the target radiation source can be obtained as:
wherein q=cov (Nn) =nwn T And (3) recording:
is the covariance matrix of the noise. Since the matrix N contains the position of the object to be solved, it is done here by first solving for +.>
Giving the required target position in the matrix N to obtain the matrix N, and further obtaining the weighted least square solution of the target radiation source>
In combination with the scheme, the method provided by the invention is used for carrying out the following error analysis:
positioning the air target radiation source, wherein the influence factors of the system positioning accuracy mainly comprise the direction finding error of the satellite
Direction finding error of ground station>
Time difference measurement error n ρ Analytical calculations are performed below on the lower keramen-lo limit (CRLB) of the positioning error in the presence of these three measurement errors, and a Geometric Distribution (GDOP) diagram of the positioning error is thus given. The specific expression of the measurement equation of the system is as follows: />
Let the parameter vector be x T,e Then the system observation equation is related to the target position vector x T,e Jacobian matrix of (a)
The method comprises the following steps:
the covariance matrix of the measured noise is recorded as:
the theoretical accuracy bound for the target positioning error is:
CRLB(x T,e )＝G T W -1 G
the invention has the beneficial effects that the auxiliary observation information of the ground station is introduced to carry out auxiliary optimization on the existing positioning system based on the satellite passive positioning, so that the combined passive positioning of the earth and the sky is realized, the advantages of passive positioning and space electronic satellite reconnaissance are realized, and the accuracy and the instantaneity of target positioning and tracking are improved.
Drawings
FIG. 1 is a positioning model diagram of a two-star direction finding positioning based on a WGS-84 model;
FIG. 2 is a GDOP map of positioning errors;
FIG. 3 is a simulation plot of the position solution error as a function of the direction finding error of the satellite;
FIG. 4 is a simulation plot of the position solution error as a function of ground station direction error;
fig. 5 is a simulation diagram of the variation of the positioning solution error with time difference measurement error.
Detailed Description
The above positioning method is verified and described below with reference to the accompanying drawings, and the following reasonable assumption is made on the system model:
1. assuming that the satellite is a low orbit satellite, the orbit altitude is relatively low, typically 500km to 1000km;
2. unifying satellite attitude measurement errors existing in engineering practice into satellite direction finding errors;
3. the measurement errors are assumed to follow a gaussian distribution with zero mean and are independent of each other.
(1) GDOP map of positioning error:
as shown in FIG. 2, assume that the orbital height of a single star is H S =800 km, the corresponding satellite points below the satellite have a longitude and latitude of (L S ,B S ) = (103 °,37 °), see star point labels in the figure. The longitude and latitude of the ground observation station are respectively (L) r ,B r ) = (100 °,34 °), see triangle point labels in the figure. Error of direction finding of satellite
The root mean square error of (2) is set to 0.1 DEG, the direction finding error of the ground station is +.>
The root mean square error of (2) is set to 0.5 DEG, and the time difference measurement error n ρ The root mean square error of (2) is set to be 10us, and the GDOP map for the positioning calculation of the direction finding and the combined time difference of the single star and the ground station is obtained through simulation.
From the above figures, it can be seen that the GDOP map of positioning errors is approximately symmetrically distributed about the undersea point of a single star, has certain deformation and deflection locally, and is stably distributed in the wide-area longitude and latitude range.
Setting the orbit height of a single star as H S =800 km, the corresponding satellite points below the satellite have a longitude and latitude of (L S ,B S ) = (103 °,37 °), the longitude and latitude of the ground observation station are (L r ,B r ) = (100 °,34 °), the longitude and latitude of the earth surface target radiation source are (L t ,B t ) = (102 °,36 °) when the target radiation source is about 300km from the ground observation station. In the following simulations the satellite, ground station and target positions were set as described above.
(2) Influence of satellite direction finding errors:
as shown in fig. 3, the direction finding error of the ground station
The root mean square error of (2) is set to 1 DEG, and the time difference measurement error n ρ The root mean square error of (2) is set to 10us, and the direction finding error of the satellite is set to +.>
The root mean square error of the satellite is changed from 0.1 degree to 2.5 degrees, and positioning simulation solution is carried out to obtain the change of the positioning solution error along with the direction finding error of the satellite.
(3) Effect of ground station direction finding error:
error of direction finding of satellite
The root mean square error of (2) is set to 0.3 DEG, and the time difference measurement error n ρ The root mean square error of (2) is set to 10us, and the direction finding error of the ground station is +.>
The root mean square error of the ground station is changed from 0.1 degrees to 3.1 degrees, and positioning simulation solution is carried out to obtain the change of the positioning solution error along with the direction finding error of the ground station.
(4) Effect of time difference measurement errors:
error of direction finding of satellite
The root mean square error of (2) is set to 0.3 DEG, and the direction finding error of the ground station
The root mean square error of (2) is set to 1 DEG, and the time difference measurement error n ρ The root mean square error of (1) is changed from 1us to 31us, and positioning simulation solution is carried out to obtain the change of the positioning solution error with time difference measurement error.
As can be seen from fig. 3, 4 and 5, the solution proposed herein approximates the CRLB well, and deviates slightly from the CRLB by about 0.1km only after the measurement error is large.
Claims (1)
1. The passive target positioning method based on single star and ground station direction finding and joint time difference is characterized by comprising the following steps:
a. measuring the residual angles of directions of the target radiation source signals reaching the satellite and the ground observation station respectively through a single satellite and a ground station, and the time difference of the target radiation source signals reaching the satellite and the ground observation station respectively; the specific method comprises the following steps:
the satellite position is x under the ECEF fixed coordinate system S,e ＝[x s,e ,y s,e ,z s,e ] T The position of the ground observation station is x r,e ＝[x r,e ,y r,e ,z r,e ] T The position of the target radiation source is x T,e ＝[x t,e ,y t,e ,z t,e ] T In the star coordinate system b, the position of the target radiation source is x T,b ＝[x t,b ,y t,b ,z t,b ] T In the satellite-borne direction-finding positioning system, the following coordinate conversion relation exists: x is x T,b ＝M(x S,e -x T,e), wherein 
Including satellite x S,e Corresponding latitude B of point under satellite in geodetic coordinate system S And longitude L S By satellite x S,e Is based on satellite-borne attitude sensingSeveral angle information output by the device: yaw angle ψ, pitch angle θ, roll angle φ:
a1, measuring the direction residual angle alpha of arrival of the target radiation source signal by a single star 1 and β1 ：
in the formula ：Dx ＝[1,0,0]，D y ＝[0,1,0]，D z ＝[0,0,1]，
Respectively represent the direction residual angle alpha 1 and β1 Is true of>
and />
Representing the measurement errors thereof respectively;
order the
in the formula ：
true value, gamma, representing the angle of the directional residual 1 Representing the angle alpha of the tailline from direction 1 and β1 Measuring meter of (2)Calculating the obtained direction residual chord angle;
a2, measuring the direction residual angle alpha of arrival of the target radiation source signal by the observation station 2 and β2 ：
in the formula ：
respectively represent the direction residual angle alpha 2 and β2 Is true of>
and />
Representing the measurement errors thereof respectively; />
Order the
in the formula ：
true value, gamma, representing the angle of the directional residual 2 Represented by azimuth angle alpha 2 And pitch angle beta 2 A direction residual angle obtained by calculation of the measured value of (2);
a3, obtaining time differences of the target radiation source signals respectively reaching the satellite and the ground observation station, and converting the time difference measured value into a distance difference:
ρ＝||(x T,e -x S,e )||-||(x T,e -x r,e )||+n ρ
in the formula ：nρ A distance difference measurement error converted from the time difference measurement error;
b. establishing a target positioning model by pseudo-linearization processing of the directional residual angle and fusing a time difference measurement equation; the specific method comprises the following steps:
b1, pseudo-linearizing the direction residual angle obtained in the step a1 to obtain:
b2, pseudo-linearizing the direction residual angle obtained in the step a2 to obtain:
x r,e cosβ 2 -y r,e cosα 2 -(cosβ 2 D x -cosα 2 D y )x T,e ＝sinα 2 (y r,e -y t,e )n α2 +sinβ 2 (x t,e -x r,e )n β2
b3, fusing a time difference measurement equation, and establishing a positioning model, wherein the method specifically comprises the following steps of:
from the pseudo-linearization equation described above
in the formula ui ，C i ，n i See the following expression:
fusion results in:
b-Ax T,e ＝Nn
wherein ,
c. b, solving the model established in the step b by adopting a weighted least square method to obtain a target position; the specific method comprises the following steps:
solving by adopting a weighted least square method to obtain a weighted least square solution of the target radiation source, wherein the weighted least square solution is as follows:
in which q=cov (N) =nwn T And (3) recording:
is the covariance matrix of the noise; the matrix N contains the position of the target to be solved, and the least square solution of the target is firstly adopted
Giving the required target position in the matrix N to obtain the matrix N, and further obtaining the weighted least square solution of the target radiation source>
/>
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| CN109991571B (en) * | 2019-04-17 | 2022-11-18 | 电子科技大学 | Long-distance distributed passive direction finding positioning array arrangement method |
| CN110061801B (en) * | 2019-04-25 | 2020-11-17 | 电子科技大学 | Abnormal target discrimination system and method in aviation monitoring system |
| CN110988851B (en) * | 2019-12-19 | 2023-11-21 | 南京邮电大学 | Different-orbit single-star time-sharing frequency measurement positioning method based on star optimization |
| CN111273223A (en) * | 2020-01-20 | 2020-06-12 | 西安交通大学 | Passive positioning countermeasure method based on double-antenna time delay |
| CN111308530B (en) * | 2020-02-17 | 2021-12-03 | 中国人民解放军战略支援部队信息工程大学 | Short wave multi-station and single-satellite cooperative direct positioning method based on two-dimensional direction of arrival |
| CN112051543B (en) * | 2020-08-30 | 2023-08-08 | 西南电子技术研究所（中国电子科技集团公司第十研究所） | Passive positioning system for ground terminal of low-orbit satellite mobile communication |
| CN112462328B (en) * | 2020-11-17 | 2024-01-26 | 安徽理工大学 | Weighted orientation method based on sensor array arrival time difference measurement subset |
| CN113189625A (en) * | 2021-04-29 | 2021-07-30 | 中国电子科技集团公司第三十六研究所 | Error correction method and device based on single-star interferometer direction finding system and satellite |
| CN113642252B (en) * | 2021-08-31 | 2022-05-17 | 中国人民解放军国防科技大学 | Target positioning method and device based on single satellite, electronic equipment and medium |
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