CN109633724B - Passive target positioning method based on single-satellite and multi-ground-station combined measurement - Google Patents
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- 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
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- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
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Abstract
The invention belongs to the technical field of electronic countermeasure, and particularly relates to a passive target positioning method based on single-satellite and multi-ground-station combined measurement. Aiming at a positioning scene of an aerial target radiation source, the invention respectively measures the cosine angles of the directions from which target radiation source signals reach the target radiation source signals to the respective ground stations through a single satellite and a plurality of ground stations, and the time difference and the frequency difference from which the target radiation source signals reach the satellite and a plurality of ground observation stations, and gives a weighted least square analytic solution of the target position through pseudo-linear processing of the cosine angles of the directions and fusing a time difference measurement equation and a frequency difference measurement equation. The method can realize single instantaneous high-precision positioning, has no positioning ambiguity problem, and the mean square error of the positioning error can approach the Clarmet-Roche lower limit.
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-satellite and multi-ground-station combined measurement.
Background
On one hand, the key points of the modern electronic information war are the competition of electromagnetic space between enemy and my and the detection and monitoring of key targets of the opponent, so as to obtain information of strategic deployment, platform type and the like of enemy units. Therefore, the reconnaissance and positioning technology for the target plays a very important role in the field of electronic countermeasure. Compared with an active positioning method, passive positioning has the advantages of long acting distance, hidden reception, difficulty in being discovered by the opposite side and the like, and has important significance for improving the survival capability and the operational capability of the weapon system in the electronic warfare environment.
On the other hand, with the development of the aerospace technology and the breakthrough of the satellite-borne detection technology, passive detection and positioning of a ground radiation source by using satellite-borne electronic detection equipment has become one of the leading-edge issues of the space military technology which is disputed and developed in various countries at present. Although the single-satellite passive positioning system has the advantages of low cost, flexible positioning system and the like, the single-satellite passive positioning system realizes the positioning of the radiation source based on one observation satellite, so the obtained target information amount is less, and the positioning accuracy is not high enough. Therefore, the single star is considered to be combined with a plurality of ground observation stations to realize the space-ground combined target positioning.
Disclosure of Invention
The invention aims to solve the problems and provides a passive target positioning method based on single-satellite and multi-ground-station direction finding and combined time difference and frequency difference. Aiming at a positioning scene of an aerial target radiation source, a single satellite and a plurality of ground stations are used for respectively measuring the cosine angles of the directions from which target radiation source signals reach to the single satellite and the plurality of ground stations, and the time difference and the frequency difference from which the target radiation source signals reach to the satellite and the plurality of ground observation stations, and a weighted least square analytic solution of a target position is given by carrying out pseudo-linear processing on the cosine angles of the directions and fusing a time difference measurement equation and a frequency difference measurement equation. The method can realize single instantaneous high-precision positioning, has no positioning ambiguity problem, and the mean square error of the positioning error can approach the Cramer-Rao lower limit (CRLB).
The technical scheme adopted by the invention is as follows:
according to the method, cosine angles of the directions of the target radiation source signals reaching the single satellite and the multiple ground stations and time difference and frequency difference of the target radiation source signals reaching the satellite and the multiple ground observation stations are measured respectively, and a weighted least square analytic calculation formula of a target position is given through algorithm derivation. The localization model is shown in fig. 1. In the figure, the coordinate system of ground fixation is recorded in the { e system (x) e ,y e ,z e ) At x, the position of the satellite is S,e ＝[x s,e ,y s,e ,z s,e ] T The position of the target radiation source is x T,e ＝[x t,e ,y t,e ,z t,e ] T And the positions of the three ground observation stations are respectively marked as x r1,e ＝[x r1,e ,y r1,e ,z r1,e ] T ，x r2,e ＝[x r1,e ,y r1,e ,z r1,e ] T And x r3,e ＝[x r3,e ,y r3,e ,z r3,e ] T . In the system b of the star coordinate system, the position of the target radiation source is x T,b ＝[x t,b ,y t,b ,z t,b ] T . In a satellite-borne direction finding positioning system, the following coordinate transformation relationship is provided: x is a radical of a fluorine atom T,b ＝M(x S,e -x T,e ) Detailed description of the invention
Which comprises the following steps: satellite x S,e Corresponding subsatellite point latitude B in geodetic coordinate system S And longitude L S And by satellite x S,e The satellite-borne attitude sensor outputs several angle information: yaw angle psi, pitch angle theta, roll angle phi. Simultaneously, in the formula:
the invention mainly comprises the following steps:
a. respectively measuring the cosine angles of the directions from which the target radiation source signals reach to the single satellite and the multiple ground stations, and the time difference and the frequency difference between the target radiation source signals respectively reaching the satellite and the multiple ground observation stations;
b. establishing a target positioning model by performing pseudo-linear processing on the direction cosine angles and fusing a time difference measurement equation and a frequency 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 invention is based on the following principle:
the various observations of the positioning system can be expressed as follows:
A. single-star measurement target radiation source signal arrival direction cosine angle alpha s And beta s The expression of the measured value is:
in the formula: d x ＝[1,0,0]，D y ＝[0,1,0]，D z ＝[0,0,1]，
Respectively represent the direction cosine angle alpha s And beta s The true value of (c) is,
and
respectively, representing the measurement error thereof. Meanwhile, the following steps are included:
in the formula:
true value, γ, representing the cosine angle of the direction s Representing the cosine angle alpha of direction s And beta s The resulting direction cosine angle is calculated.
B. Ith ground observation station x ri,e Measuring the cosine angle alpha of the arrival direction of the target radiation source signal ri And beta ri The expression of the measured value is:
similarly, in the formula:
respectively represent the direction cosine angle alpha ri And beta ri The true value of (a) is,
and
respectively represent the measurement error, and simultaneously, the following are:
in the formula:
representing true values of direction cosine angles, gamma ri Representing the cosine angle alpha of direction ri And beta ri The resulting direction cosine angle is calculated.
C. Converting the time difference measurement value into a distance difference, and then expressing the measurement value as follows:
in the formula:
representative frequency difference ρ s,ri The true value of (a) is,
representing its measurement error.
D. The frequency difference measurement can be converted to a rate of change of the range difference over time, and the expression:
in the formula:
representative frequency difference xi s,ri The true value of (a) is,
representing its measurement error.
Based on various measured values of the positioning system, the positioning and the speed fixing of the hollow target radiation source are realized at the same time, and the derivation of a weighted least square positioning algorithm is carried out.
In the step b, the method specifically adopted by the invention is as follows:
a) From the above formula A:
namely:
and according to the first-order Taylor series expansion principle, the following can be obtained:
the finishing is carried out to obtain:
b) From the above formula A:
the following can be obtained:
according to the first-order Taylor series expansion principle, the following can be obtained:
the carrying-in finishing can be carried out as follows:
c) From the above formula B:
the same can be obtained:
d) From the above formula B:
the following can be obtained by the same way:
e) From the above formula D:
further, according to the above definition of the cosine angle of direction a, it can be obtained:
namely:
similarly, according to the first-order Taylor series expansion principle:
the finishing can be carried out as follows:
wherein let H = M (v) S,e -v T,e ) Then, there are:
then on the basis of the above algorithm derivation:
wherein, the specific expressions of b, A, N and N are detailed as follows:
wherein u is s And u ri The following are explicit:
wherein:
wherein C is s And C ri The following are explicitly stated:
thus, a weighted least squares solution of the position and velocity vector Ω of the target radiation source can be obtained as:
wherein Q = cov (Nn) = NWN T Wherein W is a covariance matrix of the noise,
since the matrix N contains the target position to be obtained, the method is firstly to solve the target by the least square solution
Giving out the target position and speed needed in the matrix N to obtain the matrix N, and further obtaining the weighted least square solution of the target radiation source
By combining the scheme, the method provided by the invention is subjected to the following error analysis:
the influence factors of the positioning accuracy of the system for positioning the hollow target radiation source mainly include the direction-finding error of the satellite
Direction finding error of ground station
Time difference measurement error
And frequency difference measurement error
The Clarmet-Rao lower limit (CRLB) of the positioning error in the presence of these four systematic measurement errors is analyzed and calculated below, and the geometric distribution GDOP of the positioning error is given. The specific expression of the measurement equation of the system is as follows:
if the parameter vector is set to be omega, the Jacobian matrix of the system observation equation relative to the target position vector omega
The method comprises the following specific steps:
the theoretical precision bound of the target positioning error without the constraint of the WGS-84 earth ellipsoid model is obtained as follows:
CRLB(Ω)＝G T W -1 G
the passive positioning system has the advantages that high-precision positioning and constant speed in a wide area range are realized by jointly measuring the time difference, the frequency difference and the direction cosine angles by the single satellite and the plurality of ground stations, the conventional satellite-based passive positioning system is subjected to auxiliary optimization by combining auxiliary observation information of the ground stations, the space-ground combined passive positioning is realized, the passive positioning system has the advantages of passive positioning and space electronic satellite reconnaissance, and the precision and the real-time performance of target positioning and tracking are improved.
Drawings
FIG. 1 is a diagram of a WGS-84 model-based positioning model for two-star direction-finding positioning;
FIG. 2 is a GDOP plot of positioning error;
FIG. 3 is a simulation diagram of the variation of the position positioning resolving error with the direction finding error of the satellite;
FIG. 4 is a simulation diagram of the variation of the position positioning resolving error with the direction finding error of the ground station;
FIG. 5 is a diagram showing a simulation of the variation of the position-locating resolving error with time-difference measurement error;
FIG. 6 is a simulation diagram of the variation of velocity positioning calculation error with frequency difference measurement error.
Detailed Description
The following verification and explanation of the above positioning method with reference to the drawings first make the following reasonable assumptions 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 a mean value of zero, and the errors are independent of each other.
(1) GDOP map of positioning error:
as shown in FIG. 2, assume that the orbit height of a single star is H S =800km, and the longitude and latitude of the corresponding satellite sub-satellite point are respectively (L) S ,B S ) = (103 °,37 °), in the figure the star points are marked, the velocity vector is v S,e ＝[6,4,2] T km/s. The longitude and latitude of the three ground observation stations are respectively (L) r1 ,B r1 )＝(100°,34°)，(L r2 ,B r2 ) = (101 °,36 °) and (L) r1 ,B r1 ) = (102 °,34 °), see triangle dot notation in the figure, simulations all assuming the ground observation station to be stationary. Set the velocity vector of the target to v T,e ＝[0.2,0.15,0.02] T km/s. Direction finding error of satellite
The root mean square error of (2) is set to be 0.1 degrees, and the direction-finding errors of three ground stations
The root mean square error is set to be 0.5 DEG, and the time difference measurement error is set to be
The size of the root mean square error of (2) is set to be 10us, and the frequency difference measurement error is
The size of the root mean square error is set to be 10Hz, and a GDOP diagram for positioning and resolving the target position of single-satellite and multi-ground-station direction finding and combined time difference and frequency difference is obtained through simulation.
As can be seen from the upper graph, the GDOP graphs of the positioning errors are approximately symmetrically distributed about the single star and the intersatellite points of the three ground stations, the root mean square error of the positioning errors of the target positions near the ground stations is small, a certain deflection exists near the local intersatellite point of the single star, and the root mean square error of the positioning errors in the wide-area longitude and latitude range is stably distributed.
Assuming a single star orbit height ofH S =800km, the longitude and latitude of the satellite are (L) S ,B S ) = (103 °,37 °), in the figure the star points are marked, the velocity vector is v S,e ＝[6,4,2] T km/s. The longitude and latitude of three ground observation stations are respectively (L) r1 ,B r1 )＝(100°,34°)，(L r2 ,B r2 ) = (101 °,36 °) and (L) r1 ,B r1 ) = (102 °,34 °), see the triangular dot marks in the figure, and the ground observation station is assumed to be stationary in the simulation. Setting the longitude, latitude and elevation of the aerial target radiation source as (L) t ,B t ,H t ) = 102 °,36 °,15km, the velocity vector of the target radiation source is v T,e ＝[0.2,0.15,0.02] T km/s. The satellite, ground station and target positions in the following simulations are all 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 is set to 0.5 DEG, and the time difference measurement error
The root mean square error of (1) is set to be 10us, and the frequency difference measurement error is
All set as 10Hz, and the direction-finding error of the satellite
The size of the root mean square error is changed from 0.1 degree to 1 degree, positioning simulation calculation is carried out, and the change of the position positioning calculation error along with the direction-finding error of the satellite is obtained.
(3) Influence of ground station direction finding error:
as shown in FIG. 4, the direction finding error of the satellite
The root mean square error is set to be 0.3 DEG, and the time difference measurement error is set to be
The size of the root mean square error of (2) is set to be 10us, and the frequency difference measurement error is
All set as 10Hz, and the direction-finding error of the ground station
The size of the root mean square error is changed from 0.2 degrees to 2 degrees, positioning simulation calculation is carried out, and the change of the positioning calculation error along with the direction-finding error of the ground station is obtained.
(4) Influence of time difference measurement error:
direction finding error of satellite
The root mean square error is set to be 0.3 degrees, and the direction-finding error of the ground station
The root mean square error of (2) is set to 0.5 DEG, and the frequency difference measurement error
Are all set to 10Hz, and the time difference measurement error n is ρ The size of the root mean square error is changed from 5us to 50us, positioning simulation calculation is carried out, and the change of the positioning calculation error along with the difference measurement error is obtained, as shown in figure 5.
(5) Influence of frequency difference measurement error:
direction finding error of satellite
The root mean square error is set to be 0.3 degrees, and the direction-finding error of the ground station
The root mean square error is set to 0.5 DEG, and the time difference measurement error n ρ The root mean square error of (2) is set to 10us, and the frequency difference measurement error is set
The size of the root mean square error is changed from 2Hz to 20Hz, positioning simulation calculation is carried out, and the change of the speed calculation error along with the time difference measurement error is obtained, as shown in figure 6.
As can be seen from fig. 3, 4, 5, 6, the solution proposed herein can well approximate CRLB, only slightly deviating from CRLB by about 0.1km after measurement errors are large.
Claims (1)
1. The passive target positioning method based on the single-satellite and multi-ground-station combined measurement is characterized by comprising the following steps of:
a. respectively measuring the cosine angles of the directions from which target radiation source signals arrive to the single satellite and the multiple ground stations, and the time difference and the frequency difference between the target radiation source signals respectively arrive at the satellite and the multiple ground observation stations; the specific method comprises the following steps:
setting the coordinate system of ground fixation { e system (x) e ,y e ,z e ) At x, the position of the satellite is S,e ＝[x s,e ,y s,e ,z s,e ] T The number of the ground observation stations is 3, and the positions are x respectively r1,e ＝[x r1,e ,y r1,e ,z r1,e ] T ，x r2,e ＝[x r1,e ,y r1,e ,z r1,e ] T And x r3,e ＝[x r3,e ,y r3,e ,z r3,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 system b of the star coordinate system, 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 transformation relationship is provided: x is the number of T,b ＝M(x S,e -x T,e ) Wherein
Including satellite x S,e Corresponding subsatellite point latitude B in geodetic coordinate system S And longitude L S And by satellite x S,e The satellite-borne attitude sensor outputs several angle information: yaw angle ψ, pitch angle θ, roll angle Φ:
a1, measuring the cosine angle alpha of the arrival direction of the target radiation source signal by a single star s And beta s ：
In the formula: d x ＝[1,0,0]，D y ＝[0,1,0]，D z ＝[0,0,1]，
Respectively representing the cosine angle alpha of the direction s And beta s The true value of (c) is,
and
respectively representing the measurement errors;
order to
In the formula:
true value, γ, representing the cosine angle of the direction s Is represented by a direction cosine angle α s And beta s Calculating the direction cosine angle obtained by the measured value;
a2, i-th ground observation station x ri,e Measuring the cosine angle alpha of the arrival direction of the target radiation source signal ri And beta ri ：
In the formula:
respectively represent the direction cosine angle alpha ri And beta ri The true value of (c) is,
and
respectively representing the measurement errors;
order to
In the formula:
representing true values of direction cosine angles, gamma ri Is represented by a direction cosine angle α ri And beta ri Calculating the direction cosine angle obtained by the measured value;
a3, obtaining time differences of target radiation source signals respectively reaching a satellite and a ground observation station, and converting time difference measurement values into distance differences:
in the formula:
representative time difference p s,ri The true value of (a) is,
representing the measurement error thereof;
a4, obtaining frequency differences of target radiation source signals respectively reaching the satellite and the ground observation station, and converting frequency difference measurement values into the change rate of distance differences along with time:
in the formula:
representative frequency difference xi s,ri The true value of (a) is,
representing the measurement error thereof;
b. establishing a target positioning model by performing pseudo-linear processing on the direction cosine angles and fusing a time difference measurement equation and a frequency difference measurement equation; the specific method comprises the following steps:
b1, performing pseudo linearization on the direction cosine angle obtained in the step a1 to obtain:
b2, performing pseudo linearization on the direction cosine angle obtained in the step a2 to obtain:
b3, fusing the time difference measurement equation and the frequency difference measurement equation, and establishing a positioning model, which specifically comprises the following steps:
from the above pseudo-linearization equation
Wherein, let H = M (v) S,e -v T,e ) Then, there are:
then the fusion yields:
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:
and solving by adopting a weighted least square method to obtain a weighted least square solution of the target radiation source as follows:
wherein Q = cov (Nn) = NWN T And W 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 used
Giving out the target position and speed needed 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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