CN109001670B - Distributed passive positioning method and device combining time difference and angle - Google Patents

Distributed passive positioning method and device combining time difference and angle Download PDF

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CN109001670B
CN109001670B CN201810556997.7A CN201810556997A CN109001670B CN 109001670 B CN109001670 B CN 109001670B CN 201810556997 A CN201810556997 A CN 201810556997A CN 109001670 B CN109001670 B CN 109001670B
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胡德秀
刘智鑫
赵拥军
黄洁
赵勇胜
张睿
刘亚奇
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Information Engineering University of PLA Strategic Support Force
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations

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Abstract

The invention relates to the field of distributed passive positioning, in particular to a distributed passive positioning method and device combining time difference and angle. According to the method, a positioning equation of an azimuth angle, a pitch angle and a time difference is linearized, then a least square method is carried out to solve to obtain a position initial solution of a target radiation source, a weighting matrix is constructed according to the position initial solution, and a position accurate solution is further obtained through the weighting least square method. The invention reduces the synchronization difficulty between observation points and reduces the dependence of the system on the reference station; the distributed target radiation source positioning of joint time difference and angle can be realized without the need of initial value prior of the position of the target radiation source; meanwhile, the invention is in a form of algebraic closed-form solution of unknown parameters, so that the solution is a global optimal solution.

Description

Distributed passive positioning method and device combining time difference and angle
Technical Field
The invention relates to the field of distributed passive positioning, in particular to a distributed passive positioning method and device combining time difference and angle.
Background
Passive localization techniques are important means of target information acquisition, monitoring and localization by receiving the radiation signal of the target radiation source itself. The positioning system combining angles and time differences is high in positioning accuracy, is widely concerned and applied at home and abroad in recent years, and is widely applied to radars, sonars and multi-wireless sensors.
The traditional centralized passive positioning technology combining time difference and angle is mature in development, and in an actual environment, the time synchronization difficulty of the constitution is high, so that the method is not suitable for the situations of multiple sensors and multiple receiving stations. Sometimes, the number of observation stations is increased while the positioning accuracy is improved, and at the moment, the application of a centralized time difference and angle positioning system is limited, the cost is high, and the realization is difficult. In order to announce the positioning accuracy without increasing the hardware implementation difficulty, a distributed time difference and angle positioning system is proposed in recent years to solve the problem of high implementation difficulty of a centralized platform under multiple observation nodes.
The distributed positioning system pairwise pairs observation nodes on a centralized basis, does not have a public reference station, and only needs to highly synchronize the observation stations in pairs. However, for the positioning algorithm under the system, generally, based on iteration, the angle and time difference positioning formula is subjected to first-order or second-order taylor series expansion to realize linearization, and then the target position is calculated by utilizing iteration, which is greatly affected by local convergence and acquisition of initial positioning values.
Disclosure of Invention
The invention aims to provide a distributed passive positioning method and device combining time difference and angle, which are used for solving the problem of inaccurate positioning caused by local convergence and difficulty in obtaining initial positioning values in the conventional passive positioning technology.
In order to achieve the above object, the present invention provides a distributed passive positioning method combining time difference and angle, comprising the following steps:
respectively converting positioning equations of an azimuth angle, a pitch angle and a time difference as well as the distance between a target radiation source and an observation station into linear expressions, and constructing a matrix equation according to the linear expressions;
solving the matrix equation to obtain an initial position solution of the target radiation source;
and constructing a weighting matrix by using the position initial solution, and solving the matrix equation by combining a weighted least square method to obtain a position accurate solution of the target radiation source.
Further, solving the matrix equation according to a least square method to obtain an initial position solution of the target radiation source.
Further, the target radiation source u ═ xy z]TTo the ith said observation station siA distance of r betweeni＝|| u-s i1,2, … and M/2, wherein M is the number of the observation stations; the matrix equation is:
Figure GDA0002598804150000021
wherein:
Figure GDA0002598804150000022
Figure GDA0002598804150000023
Figure GDA0002598804150000024
Figure GDA0002598804150000025
Figure GDA0002598804150000026
Figure GDA0002598804150000031
Ga＝[fa(1)Tfa(2)T… fa(M/2)T]T
Ge＝[fe(1)Tfe(2)T… fe(M/2)T]T
r＝[r(1)r(2) …r(M/2)]T
a＝[a(1)a(2) …a(M/2)]T
e＝[e(1)e(2) …e(M/2)]T
Figure GDA0002598804150000032
Figure GDA0002598804150000033
wherein θ is the azimuth angle, β is the pitch angle,a(i)、r(i) ande(i) the observation error of the ith azimuth angle, the observation error of the ith time difference equation and the observation error of the ith pitch angle are respectively; and has:
Figure GDA0002598804150000034
fa(i)＝[sin(θ2i)-cos(θ2i) 0]T
Figure GDA0002598804150000041
Figure GDA0002598804150000042
then obtaining the initial solution of the position as u by using a least square method1＝(GTG)-1GTh。
Further, the process of solving to obtain the position accurate solution of the target radiation source includes:
constructing the weighting matrix from the initial position solution, combining B [ Delta r [ ]T,ΔθT,ΔβT]TObtaining the weighting matrix as follows:
W＝(E[T])-1＝B-TQ-1B-1
Figure GDA0002598804150000043
obtaining by using the weighted least squares method:
u2＝(GTWG)-1GTWh
wherein u is2An exact solution to the position.
The invention also provides a distributed passive positioning device combining time difference and angle, which comprises a processor and a memory, wherein the memory stores instructions for realizing the following method by the processor:
respectively converting positioning equations of an azimuth angle, a pitch angle and a time difference as well as the distance between a target radiation source and an observation station into linear expressions, and constructing a matrix equation according to the linear expressions;
solving the matrix equation to obtain an initial position solution of the target radiation source;
and constructing a weighting matrix by using the position initial solution, and solving the matrix equation by combining a weighted least square method to obtain a position accurate solution of the target radiation source.
Further, solving the matrix equation according to a least square method to obtain an initial position solution of the target radiation source.
Further, the target radiation source u ═ x y z]TTo the ith said observation station siA distance of r betweeni＝|| u-s i1,2, … and M/2, wherein M is the number of the observation stations; the matrix equation is:
Figure GDA0002598804150000057
wherein:
Figure GDA0002598804150000051
Figure GDA0002598804150000052
Figure GDA0002598804150000053
Figure GDA0002598804150000054
Figure GDA0002598804150000055
Figure GDA0002598804150000056
Ga＝[fa(1)Tfa(2)T… fa(M/2)T]T
Ge＝[fe(1)Tfe(2)T… fe(M/2)T]T
r＝[r(1)r(2) …r(M/2)]T
a＝[a(1)a(2) …a(M/2)]T
e＝[e(1)e(2) …e(M/2)]T
Figure GDA0002598804150000061
Figure GDA0002598804150000062
wherein θ is the azimuth angle, β is the pitch angle,a(i)、r(i) ande(i) the observation error of the ith azimuth angle, the observation error of the ith time difference equation and the observation error of the ith pitch angle are respectively; and has:
Figure GDA0002598804150000063
fa(i)＝[sin(θ2i)-cos(θ2i) 0]T
Figure GDA0002598804150000064
Figure GDA0002598804150000065
then useObtaining the initial solution of the position as u by a least square method1＝(GTG)-1GTh。
Further, the process of solving to obtain the position accurate solution of the target radiation source includes:
constructing the weighting matrix from the initial position solution, combining B [ Delta r [ ]T,ΔθT,ΔβT]TObtaining the weighting matrix as follows:
W＝(E[T])-1＝B-TQ-1B-1
Figure GDA0002598804150000071
obtaining by using the weighted least squares method:
u2＝(GTWG)-1GTWh
wherein u is2An exact solution to the position.
The invention has the beneficial effects that: the positioning equation of the azimuth angle, the pitch angle and the time difference is linearized, then a least square method is carried out to solve to obtain a position initial solution of the target radiation source, a weighting matrix is constructed according to the position initial solution, and further the weighted least square method is used to solve to obtain a position accurate solution of the target radiation source. The invention reduces the synchronization difficulty between observation points and reduces the dependence of the system on the reference station; the distributed target radiation source positioning of joint time difference and angle can be realized without the need of initial value prior of the position of the target radiation source; meanwhile, the invention is in a form of algebraic closed-form solution of unknown parameters, so that the solution is a global optimal solution.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the geographical location of a target radiation source and a viewing station in accordance with the present invention;
FIG. 3 is a schematic view of the geometric position of the observation station and the target radiation source of the present invention;
FIG. 4 is a comparison graph of the performance simulation of the present invention with time difference measurement error variation and with time difference or angle positioning alone;
FIG. 5 is a comparison graph of the simulation of the performance of the present invention as a function of the angle measurement error versus time difference or angle location alone.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the distributed passive positioning method combining time difference and angle provided by the present invention includes: 1) using the azimuth angle parameters to calculate the azimuth angle and the target radiation source and each observation station siThe distance relationship between the two is transformed into a linear expression; 2) using the pitch angle parameter to calculate the pitch angle, the target radiation source and each observation station siThe distance relationship between the two is transformed into a linear expression; 3) by means of the angle information, the time difference parameter is transformed into a time difference parameter for the target radiation source and the observation stations siA linear expression of (a); 4) integrating respective linear expressions of an azimuth angle, a pitch angle and a time difference, and obtaining a position initial solution of a target radiation source by using least squares; 5) and (4) constructing a weighting matrix by using the position initial solution in the step 4), and obtaining a position accurate solution of the target radiation source by using weighted least squares. The specific process is as follows:
1. using the azimuth angle parameters to calculate the azimuth angle and the target radiation source and each observation station siThe specific solving method for transforming the distance relationship between the two into a linear expression is as follows:
target radiation source u ═ x y z]TThe distance between the observation node and the ith observation node is ri＝||u-siL. According to the node geometric relationship between the target radiation source and the observation station in fig. 2, the distributed equation for positioning the time difference, the azimuth angle and the pitch angle is as follows:
r2i,2i-1＝r2i-r2i-1(1)
Figure GDA0002598804150000081
Figure GDA0002598804150000082
wherein i is 1,2, …, M/2, M represents the number of observation stations,
Figure GDA0002598804150000083
then using the trigonometric relation tan (theta)2i)＝sin(θ2i)/cos(θ2i) Equation (2) is modified as:
Figure GDA0002598804150000084
wherein f isa(i)＝[sin(θ2i)-cos(θ2i) 0]T(ii) a Substituting the angle measurement error into formula (4) to obtain the azimuth linear expression in step 1):
Figure GDA0002598804150000091
wherein the content of the first and second substances,a(i) is the observation error at the ith azimuth angle,
Figure GDA0002598804150000092
2. using the pitch angle parameter to calculate the pitch angle, the target radiation source and each observation station siThe specific process of transforming the distance relationship into a linear expression is as follows:
from the geometric relationship between the observation station and the target radiation source, equation (3) can be transformed into:
l2i＝(x-x2i)cos(θ2i)+(y-y2i)sin(θ2i) (6)
the pitch angle and the target radiation source and each observation station s can be written into a formula (6) by substituting the pitch angle observation error into the sameiThe linear expression in between, namely:
e(i)＝Δfe,1(i)Δθ2i+Δfe,2(i)Δβ2i＝fe T(i)s2i-fe T(i)u (7)
wherein i is 1,2, …, M/2,e(i) the observation error for the ith pitch angle, and having:
Figure GDA0002598804150000093
Figure GDA0002598804150000094
Figure GDA0002598804150000095
3. by means of the angle information, the time difference parameter is transformed into a time difference parameter for the target radiation source and the observation stations siThe specific process of the linear expression of (2) is as follows:
transform equation (1) to r2i,2i-1+r2i-1＝r2iSquare on both sides, reuse ri＝||u-si| | l is given by:
Ci-2r2i,2i-1r2i＝2(s2i-s2i-1)Tu (11)
wherein the content of the first and second substances,
Figure GDA0002598804150000101
since the unknown number r still exists in the formula (11)2iTherefore we are based on the angle and the unknowns r2iThe relationship of (1), namely:
r2i＝||u-s2i||＝fr T(i)(u-s2i) (12)
wherein:
Figure GDA0002598804150000103
will r is2i＝fr T(i)(u-s2i) Substitution of r in formula (11)2iObtaining:
Figure GDA0002598804150000105
then, the observed values are also taken into account, and equation (14) can be written as the time difference and the target radiation source and the observation stations siThe linear expression in between, namely:
Figure GDA0002598804150000106
whereinr(i) Is the observed error of the ith equation of moveout, and:
Δfr，1(i)＝2r2i，2i-1-2fr T(θ2i，β2i)(u-s2i) (16)
Figure GDA0002598804150000108
Figure GDA0002598804150000111
wherein i is 1,2, …, M/2.
4. Integrating respective linear expressions of an azimuth angle, a pitch angle and a time difference, and obtaining a position initial solution by using least squares comprises the following specific processes:
from the errors of the three observations obtained in the first three steps, we write them in the form of a matrix:
Figure GDA0002598804150000112
wherein:
Figure GDA0002598804150000113
Figure GDA0002598804150000114
Figure GDA0002598804150000115
Figure GDA0002598804150000116
Figure GDA0002598804150000117
Figure GDA0002598804150000118
Ga＝[fa(1)Tfa(2)T… fa(M/2)T]T(26)
Ge＝[fe(1)Tfe(2)T… fe(M/2)T]T(27)
r＝[r(1)r(2) …r(M/2)]T(28)
a＝[a(1)a(2) …a(M/2)]T(29)
e＝[e(1)e(2) …e(M/2)]T(30)
Figure GDA0002598804150000121
Figure GDA0002598804150000122
then, obtaining an initial solution of the position of the target radiation source by using least squares:
u1＝(GTG)-1GTh (33)
5. and (3) constructing a weighting matrix by using the initial solution in the step (4), and obtaining a position accurate solution of the target radiation source by means of weighted least squares, wherein the specific steps are as follows:
using u obtained in step 41Constructing a weighting matrix, where B [ Delta r ]T,ΔθT,ΔβT]TThen the weighting matrix mayExpressed as:
W＝(E[T])-1＝B-TQ-1B-1(34)
finally, the accurate positioning of the target radiation source is realized by using weighted least squares:
u2＝(GTWG)-1GTWh (35)
6. the invention is simulated by using the observation points and the geometric position schematic diagram of the target radiation source in FIG. 3. FIG. 4 shows a comparison diagram of the positioning performance simulation of the present invention with time difference measurement error variation; fig. 5 shows a simulation comparison diagram of the positioning performance when the angle measurement error of the present invention changes, and it can be seen that the positioning accuracy of the existing methods gradually becomes worse with the gradual increase of the time difference or the angle measurement error.
The above embodiments of the present invention are provided, but the present invention is not limited to the described embodiments, for example, different selection of specific parameters, or equivalent simple transformation of formula, and the technical solution formed by the above embodiments is formed by fine tuning, and still falls within the protection scope of the present invention.

Claims (4)

1. A distributed passive positioning method combining time difference and angle is characterized by comprising the following steps:
respectively converting positioning equations of an azimuth angle, a pitch angle and a time difference as well as the distance between a target radiation source and an observation station into linear expressions, and constructing a matrix equation according to the linear expressions;
solving the matrix equation to obtain an initial position solution of the target radiation source;
constructing a weighted matrix by using the position initial solution, and solving the matrix equation by combining a weighted least square method to obtain a position accurate solution of the target radiation source;
solving the matrix equation according to a least square method to obtain an initial position solution of the target radiation source;
the target radiation source u ═ x y z]TTo the ith said observation station siA distance of r betweeni＝||u-si1,2, … and M/2, wherein M is the number of the observation stations; the matrix equation is:
Figure FDA0002598804140000011
wherein:
Figure FDA0002598804140000012
Figure FDA0002598804140000013
Figure FDA0002598804140000014
Figure FDA0002598804140000015
Figure FDA0002598804140000016
Figure FDA0002598804140000021
Ga＝[fa(1)Tfa(2)T…fa(M/2)T]T
Ge＝[fe(1)Tfe(2)T…fe(M/2)T]T
r＝[r(1)r(2)…r(M/2)]T
a＝[a(1)a(2)…a(M/2)]T
e＝[e(1)e(2)…e(M/2)]T
Figure FDA0002598804140000022
Figure FDA0002598804140000023
wherein θ is the azimuth angle, β is the pitch angle,a(i)、r(i) ande(i) the observation error of the ith azimuth angle, the observation error of the ith time difference equation and the observation error of the ith pitch angle are respectively; and has:
Figure FDA0002598804140000024
fa(i)＝[sin(θ2i) )-cos(θ2i) 0]T
Figure FDA0002598804140000025
Figure FDA0002598804140000031
then obtaining the initial solution of the position as u by using a least square method1＝(GTG)-1GTh。
2. The method of claim 1, wherein solving for a position-accurate solution for the target radiation source comprises:
constructing the weighting matrix from the initial position solution, combining B [ Delta r [ ]T,ΔθT,ΔβT]TObtaining the weighting matrix as follows:
W＝(E[T])-1＝B-TQ-1B-1
Figure FDA0002598804140000032
obtaining by using the weighted least squares method:
u2＝(GTWG)-1GTWh
wherein u is2An exact solution to the position.
3. A distributed passive positioning apparatus for joint moveout and angle, comprising a processor and a memory, wherein the memory stores instructions for the processor to implement a method comprising:
respectively converting positioning equations of an azimuth angle, a pitch angle and a time difference as well as the distance between a target radiation source and an observation station into linear expressions, and constructing a matrix equation according to the linear expressions;
solving the matrix equation to obtain an initial position solution of the target radiation source;
constructing a weighted matrix by using the position initial solution, and solving the matrix equation by combining a weighted least square method to obtain a position accurate solution of the target radiation source;
solving the matrix equation according to a least square method to obtain an initial position solution of the target radiation source;
the target radiation source u ═ x y z]TTo the ith said observation station siA distance of r betweeni＝||u-si1,2, … and M/2, wherein M is the number of the observation stations; the matrix equation is:
Figure FDA0002598804140000041
wherein:
Figure FDA0002598804140000042
Figure FDA0002598804140000043
Figure FDA0002598804140000044
Figure FDA0002598804140000045
Figure FDA0002598804140000046
Figure FDA0002598804140000047
Ga＝[fa(1)Tfa(2)T…fa(M/2)T]T
Ge＝[fe(1)Tfe(2)T…fe(M/2)T]T
r＝[r(1)r(2)…r(M/2)]T
a＝[a(1)a(2)…a(M/2)]T
e＝[e(1)e(2)…e(M/2)]T
Figure FDA0002598804140000048
Figure FDA0002598804140000051
wherein θ is the azimuth angle, β is the pitch angle,a(i)、r(i) ande(i)the observation error of the ith azimuth angle, the observation error of the ith time difference equation and the observation error of the ith pitch angle are respectively; and has:
Figure FDA0002598804140000052
fa(i)＝[sin(θ2i) -cos(θ2i) 0]T
Figure FDA0002598804140000053
Figure FDA0002598804140000054
then obtaining the initial solution of the position as u by using a least square method1＝(GTG)-1GTh。
4. The distributed passive positioning apparatus for joint time difference and angle according to claim 3, wherein the process of solving for the position-accurate solution of the target radiation source comprises:
constructing the weighting matrix from the initial position solution, combining B [ Delta r [ ]T,ΔθT,ΔβT]TObtaining the weighting matrix as follows:
W＝(E[T])-1＝B-TQ-1B-1
Figure FDA0002598804140000055
obtaining by using the weighted least squares method:
u2＝(GTWG)-1GTWh
wherein u is2An exact solution to the position.
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