CN112612018A - High-precision moving single-station direct positioning method based on arrival angle and Doppler frequency shift - Google Patents

High-precision moving single-station direct positioning method based on arrival angle and Doppler frequency shift Download PDF

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CN112612018A
CN112612018A CN202011365955.9A CN202011365955A CN112612018A CN 112612018 A CN112612018 A CN 112612018A CN 202011365955 A CN202011365955 A CN 202011365955A CN 112612018 A CN112612018 A CN 112612018A
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radiation source
target radiation
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CN112612018B (en
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谢坚
王秋平
汪跃先
王伶
张兆林
陈清浪
丁立超
陶明亮
范一飞
粟嘉
杨欣
韩闯
宫延云
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Northwestern Polytechnical University
715th Research Institute of CSIC
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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
    • G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
    • G01S11/02—Systems for determining distance or velocity not using reflection or reradiation using radio waves
    • G01S11/10—Systems for determining distance or velocity not using reflection or reradiation using radio waves using Doppler effect
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves

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Abstract

The invention discloses a high-precision movement single-station direct positioning method based on an arrival angle and Doppler frequency shift, which comprises the steps of firstly establishing a target source signal data receiving model containing the arrival angle and the Doppler frequency shift, and carrying out data acquisition on a target source; then, a time factor is constructed to expand the dimensionality of the received signal matrix; constructing a cost function for directly positioning the single moving station according to a target source data receiving model and data acquired by the single station for a target source and by combining the mean square error of the position of the target source; and finally, solving the radiation source position by utilizing an MVDR criterion according to the established target cost function. The invention can improve the positioning performance; for the scene needing to position a plurality of radiation sources, the number of the information sources is not required to be known in advance, and the positioning precision is effectively improved compared with a maximum likelihood method.

Description

High-precision moving single-station direct positioning method based on arrival angle and Doppler frequency shift
Technical Field
The invention belongs to the technical field of passive positioning, and particularly relates to a direct positioning method for a single motion station.
Background
The conventional passive positioning system generally adopts a two-step positioning mode, that is, the system first estimates parameters of a target source (such as angle of Arrival (DOA), Time of Arrival (TOA), Time Difference of Arrival (TDOA), doppler Difference of Arrival (FDOA), received signal strength, etc.), then performs positioning calculation on the acquired parameters, and finally obtains position information of the target source through estimation. However, when the two-step positioning method is adopted to position the target source, various data need to be collected, and the position of the target needs to be calculated through a positioning equation, so that parameter estimation and position calculation are separated, and a large error exists between a calculation result and the actual position of the target source, so that the accuracy of passive positioning is not high enough, and even the passive positioning is invalid.
Aiming at the defects of the traditional two-step positioning model, in recent years, scholars propose a Direct Position Determination (DPD) algorithm, which can realize the one-step positioning of the Position of a target radiation source without estimating parameters such as DOA (direction of arrival), TDOA (time difference of arrival) and the like in advance, and directly utilize original array data to carry out nonlinear estimation on the Position of a target in modes such as maximum likelihood, subspace data fitting and the like. Because the target arrival parameters do not need to be estimated before the target position is estimated, the loss of target information in the parameter estimation process is reduced, and the DPD algorithm has higher precision than the traditional two-step positioning method under the condition of low signal-to-noise ratio.
The traditional direct positioning method mostly adopts a multi-station passive positioning system, a large amount of communication data transmission needs to be carried out among stations, resources are consumed, and equipment is not easy to transplant. The direct positioning method for the single moving station includes intercepting and measuring the information transmitted by the target source by one single moving observation station and calculating the position information of the target source directly according to the received signal data. Compared with a multi-station passive positioning system, the direct positioning system for the single station does not need a large amount of communication data transmission, has the advantages of simple structure, flexible equipment and the like, and has wide development prospects in various civil and military fields such as navigation, aviation, satellite positioning early warning, guidance of anti-radiation weapons, electronic reconnaissance and the like.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a high-precision movement single-station direct positioning method based on an arrival angle and Doppler frequency shift, which comprises the steps of firstly establishing a target source signal data receiving model containing the arrival angle and the Doppler frequency shift, and carrying out data acquisition on a target source; then, a time factor is constructed to expand the dimensionality of the received signal matrix; constructing a cost function for directly positioning the single moving station according to a target source data receiving model and data acquired by the single station for a target source and by combining the mean square error of the position of the target source; and finally, solving the radiation source position by utilizing an MVDR criterion according to the established target cost function. The invention can improve the positioning performance; for the scene needing to position a plurality of radiation sources, the number of the information sources is not required to be known in advance, and the positioning precision is effectively improved compared with a maximum likelihood method.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: assuming that the number of target radiation sources to be positioned in a space is Q, a moving receiving single station is provided with M array elements, K position points are selected on a moving track of the moving receiving single station to respectively receive target radiation source signals, and a data receiving model of the target radiation source signals received at the K position is as follows:
Figure BDA0002805436560000021
wherein, bqkPath loss for the qth target radiation source signal to reach the kth position point of the motion receiving single station; a isk(pq) In response to the qth array of target radiation sources for the mobile receiving station,
Figure BDA0002805436560000022
ak(pq) Dimension of (d) is mx 1; d is the spacing of array elements of the single station for receiving motion, thetaqIs the angle of arrival of the q-th target radiation source signal, λ is the target radiation source signal wavelength, pqPosition coordinates of a qth target radiation source; sqk() a signal envelope for the q-th target radiation source signal incident at the kth location point of the single station of motion reception; t issIs the sampling time interval, and N is the sampling fast beat number; n isk(n) is the noise of the received signal when the moving receiving single station moves to the Kth position point;
fqk(pq) For the Doppler shift of the qth target radiation source relative to the kth position point of the moving receiving single station, the expression is:
Figure BDA0002805436560000023
wherein f iscIs the carrier frequency, v, of the target radiation sourcekFor moving the receiving station to the speed of movement at the point kkC is the propagation speed of the target radiation source signal for the position coordinate of the moving receiving single station reaching the k position point;
superposing a time factor on the data receiving model, and expanding the data receiving model of the formula (1) into:
rk(n)＝Bk(b,p)sk(n)+wk(n) (3)
wherein r isk(n)＝[xk T(n),xk T(n+1),…,xk T(n+L-1)]TThe result is obtained after the data receiving model is subjected to time factor L superposition; w is ak(n)＝[nk T(n),nk T(n+1),…,nk T(n+L-1)]TIs a noise matrix, sk(n)＝[s1k(n),s2k(n),…,sQk(n)]TIn the form of a matrix of the envelope of the signal,
Figure BDA0002805436560000031
a position coordinate matrix of the target radiation source; b isk(b,p)＝[bk(p1),bk(p2),…,bk(pQ)]Is an array flow pattern matrix after expansion, wherein
Figure BDA0002805436560000032
To introduce a steering vector after Doppler shift, bk(pq) Has a dimension of ML x 1, BkThe (b, p) dimension is ML x Q,
Figure BDA0002805436560000033
step 2: constructing a cost function for locating the position of a single target radiation source:
Figure BDA0002805436560000034
wherein,
Figure BDA0002805436560000035
s satisfying the above formula to a minimum valuekThe least squares solution of (n) is:
Figure BDA0002805436560000036
the cost function equivalence for locating a single target radiation source location is:
Figure BDA0002805436560000037
Figure BDA0002805436560000038
rewriting the above formula into a matrix form includes:
Figure BDA0002805436560000039
target radiation source signal data received by K position points on the motion trail of the motion receiving single station is introduced, and the formula (9) is equivalent to:
Figure BDA00028054365600000310
wherein B (B, p) ═ B1 T(b,p)…BK T(b,p)]T，
Figure BDA00028054365600000311
Is a block-diagonal matrix of the covariance,
Figure BDA00028054365600000312
a sample covariance matrix for the ML × ML dimension at the k location point for the motion receiving single station:
Figure BDA00028054365600000313
and step 3: using the MVDR criterion, equations (7) and (10) are rewritten into the following forms, respectively:
Figure BDA00028054365600000314
Figure BDA0002805436560000041
wherein, wopt(b, p) is an optimal weight vector, expressed as:
Figure BDA0002805436560000042
w (b, p) is a weight vector formed by weight coefficients added to each array element of the motion receiving single station;
s.t.wH(b,p)B(b,p)＝1
equation (14) is transformed by the MVDR principle into:
Figure BDA0002805436560000043
substituting formula (15) for formula (13) to obtain
Figure BDA0002805436560000044
Then
Figure BDA0002805436560000045
Let Bk(b,p)＝Λk(p) b, wherein,
Figure BDA0002805436560000046
b is the path loss vector from the target radiation source to the moving receiving single station K positions, and an equation (16) is substituted, then:
Figure BDA0002805436560000047
in the formula, λmin(. cndot.) represents the calculation of the minimum eigenvalue, and the hermitian property of the matrix of equation (17) is used to rewrite equation (17) as:
Figure BDA0002805436560000048
then p satisfying the above formula as the maximum value is the target radiation source position, and finally the target radiation source position expression is obtained:
Figure BDA0002805436560000049
and completing the positioning of the target radiation source.
Preferably, the target radiation source is a far-field narrow-band signal.
Preferably, M-8 and K-5 are used.
Due to the adoption of the high-precision movement single-station direct positioning method based on the arrival angle and the Doppler frequency shift, the following beneficial effects are achieved:
1. the single-station direct positioning method is adopted, the problem of large positioning error caused by separation of parameter estimation and position calculation in the traditional two-step positioning method is solved, and the advantages of simple structure, flexible equipment and the like of a single-station direct positioning system are effectively utilized;
2. the arrival angle of the signal and Doppler frequency shift information are fully utilized, and data received by a single station are further expanded, so that the positioning performance is improved;
3. the MVDR criterion is introduced to improve the maximum likelihood positioning solution, and the corresponding constraint on the received data is increased, so that the precision of the maximum likelihood positioning solution is further improved when a plurality of information sources are positioned.
Drawings
FIG. 1 is a schematic diagram of a physical scene of the method of the present invention.
Fig. 2 is a two-dimensional positioning result diagram according to the embodiment of the invention. Wherein fig. 2.a) is a map of the position settings of the radiation source and the moving observation station, fig. 2.b) is a top view of the positioning results, and fig. 2.c) and d) are cross-sectional and longitudinal views of the positioning results.
FIG. 3 is a diagram illustrating a relationship between an angle estimation RMS error and a signal-to-noise ratio according to an embodiment of the invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
A high-precision moving single-station direct positioning method based on an arrival angle and Doppler frequency shift comprises the following steps:
step 1: assuming that the number of target radiation sources to be positioned in a space is Q, a moving receiving single station is provided with M array elements, K position points are selected on a moving track of the moving receiving single station to respectively receive target radiation source signals, and a data receiving model of the target radiation source signals received at the K position is as follows:
Figure BDA0002805436560000051
wherein, bqkPath loss for the qth target radiation source signal to reach the kth position point of the motion receiving single station; a isk(pq) In response to the qth array of target radiation sources for the mobile receiving station,
Figure BDA0002805436560000052
ak(pq) Dimension of (d) is mx 1; d is the spacing of array elements of the single station for receiving motion, thetaqIs the angle of arrival of the q-th target radiation source signal, λ is the target radiation source signal wavelength, pqIs the q-th orderPosition coordinates of the target radiation source; sqk() a signal envelope for the q-th target radiation source signal incident at the kth location point of the single station of motion reception; t issIs the sampling time interval, and N is the sampling fast beat number; n isk(n) is the noise of the received signal when the moving receiving single station moves to the Kth position point;
fqk(pq) For the Doppler shift of the qth target radiation source relative to the kth position point of the moving receiving single station, the expression is:
Figure BDA0002805436560000061
wherein f iscIs the carrier frequency, v, of the target radiation sourcekFor moving the receiving station to the speed of movement at the point kkC is the propagation speed of the target radiation source signal for the position coordinate of the moving receiving single station reaching the k position point;
superposing a time factor on the data receiving model, and expanding the data receiving model of the formula (1) into:
rk(n)＝Bk(b,p)sk(n)+wk(n) (3)
wherein r isk(n)＝[xk T(n),xk T(n+1),…,xk T(n+L-1)]TThe result is obtained after the data receiving model is subjected to time factor L superposition; w is ak(n)＝[nk T(n),nk T(n+1),…,nk T(n+L-1)]TIs a noise matrix, sk(n)＝[s1k(n),s2k(n),…,sQk(n)]TIn the form of a matrix of the envelope of the signal,
Figure BDA0002805436560000062
a position coordinate matrix of the target radiation source; b isk(b,p)＝[bk(p1),bk(p2),…,bk(pQ)]Is an array flow pattern matrix after expansion, wherein
Figure BDA0002805436560000063
To introduce a steering vector after Doppler shift, bk(pq) Has a dimension of ML x 1, BkThe (b, p) dimension is ML x Q,
Figure BDA0002805436560000064
step 2: constructing a cost function for locating the position of a single target radiation source:
Figure BDA0002805436560000065
wherein,
Figure BDA0002805436560000066
s satisfying the above formula to a minimum valuekThe least squares solution of (n) is:
Figure BDA0002805436560000067
the cost function equivalence for locating a single target radiation source location is:
Figure BDA0002805436560000068
Figure BDA0002805436560000069
rewriting the above formula into a matrix form includes:
Figure BDA0002805436560000071
target radiation source signal data received by K position points on the motion trail of the motion receiving single station is introduced, and the formula (9) is equivalent to:
Figure BDA0002805436560000072
wherein B (B, p) ═ B1 T(b,p)…BK T(b,p)]T，
Figure BDA0002805436560000073
Is a block-diagonal matrix of the covariance,
Figure BDA0002805436560000074
a sample covariance matrix for the ML × ML dimension at the k location point for the motion receiving single station:
Figure BDA0002805436560000075
and step 3: using the MVDR criterion, equations (7) and (10) are rewritten into the following forms, respectively:
Figure BDA0002805436560000076
Figure BDA0002805436560000077
wherein, wopt(b, p) is an optimal weight vector, expressed as:
Figure BDA0002805436560000078
w (b, p) is a weight vector formed by weight coefficients added to each array element of the motion receiving single station;
s.t.wH(b,p)B(b,p)＝1
equation (14) is transformed by the MVDR principle into:
Figure BDA0002805436560000079
substituting formula (15) for formula (13) to obtain
Figure BDA00028054365600000710
Then
Figure BDA00028054365600000711
Let Bk(b,p)＝Λk(p) b, wherein,
Figure BDA00028054365600000712
b is the path loss vector from the target radiation source to the moving receiving single station K positions, and an equation (16) is substituted, then:
Figure BDA0002805436560000081
in the formula, λmin(. cndot.) represents the calculation of the minimum eigenvalue, and the hermitian property of the matrix of equation (17) is used to rewrite equation (17) as:
Figure BDA0002805436560000082
then p satisfying the above formula as the maximum value is the target radiation source position, and finally the target radiation source position expression is obtained:
Figure BDA0002805436560000083
and completing the positioning of the target radiation source.
Preferably, the target radiation source is a far-field narrow-band signal.
Preferably, M-8 and K-5 are used.
The specific embodiment is as follows:
1. and establishing a target source signal data receiving model containing the arrival angle and the Doppler frequency shift, and acquiring data of the target source. In order to effectively utilize Doppler frequency shift information, a time factor is constructed to expand the dimension of a received signal matrix;
2. constructing a cost function for directly positioning the single moving station according to the target source data receiving model established in the step 1 and the data acquired by the single station to the target source and by combining the mean square error of the position of the target source;
3. and solving the radiation source position by utilizing an MVDR criterion according to the established target cost function.
Assuming that two far-field narrow-band signals are used as target radiation sources, the two-dimensional position parameters are (x, y) — 1.2km, (x, y) — 0km,0km), and the moving receiving single station is a uniform linear array with the array element number of M ═ 8, as shown in fig. 2. a). Assuming that the target radiation source is stationary, the mobile receiving single station moves along the abscissa at a speed of 6km/h to receive data every 0.25h, and K is 5 times in total, and a specific physical scene is shown in fig. 1.
Setting SNR as 30dB, fast beat number as snap 100 and time factor L as 3, obtaining positioning result as shown in FIG. 2, fig. 2.a) is a position setting distribution diagram of the radiation source and the motion observation station, fig. 2.b) is a top view of the position positioning result, and fig. 2.c) and d) are transverse and longitudinal section diagrams of the positioning result, which shows that the method of the present invention can accurately position the position of the radiation source and has high resolution; FIG. 3 is an RMSE curve (Monte Carlo number: 500) of several localization methods, including the method of the present invention, MVDR direct localization based on angle of arrival (see references: Rieken D W, Fuhrmann D R. generalized MU and MVDR for multiple non-coherent arrays [ J ]. IEEE Transactions on Signal Processing,2004,52(9):2396 + 2406.), ML direct localization based on angle of arrival and Doppler, ML direct localization based on angle of arrival (see references: L.M.Kaplan, Qiang Le and N.Molnar,' Maximum lipid methods for bearing-target localization, "2001IEEE International Conference Acstistion, Speech, Processing, Catingprocessing, CatingProcessing, Cat. 2001-35221), and Ca.2001 + 3. No. 3, Ca < 3 > 2001 + 3, Ca < 3 > Ab > 3 < 1 > -Ab > directly localization, MVDR for multiple non-coherent orientation [ J.: I, see references: 3, SSP, No. 3, C, No. 3, C, A. As can be seen from the figure, compared with the direct positioning method using ML, the moving single-station direct positioning method provided by the invention has good positioning effect and higher positioning precision under the condition of positioning a plurality of target radiation sources; compared with MVDR direct positioning based on the arrival angle, the method of the invention utilizes Doppler information to improve the positioning precision to a certain extent. The above simulation illustrates the beneficial effects of the method of the present invention.

Claims (3)

1. A high-precision moving single-station direct positioning method based on an arrival angle and Doppler frequency shift is characterized by comprising the following steps:
step 1: assuming that the number of target radiation sources to be positioned in a space is Q, a moving receiving single station is provided with M array elements, K position points are selected on a moving track of the moving receiving single station to respectively receive target radiation source signals, and a data receiving model of the target radiation source signals received at the K position is as follows:
Figure FDA0002805436550000011
wherein, bqkPath loss for the qth target radiation source signal to reach the kth position point of the motion receiving single station; a isk(pq) In response to the qth array of target radiation sources for the mobile receiving station,
Figure FDA0002805436550000012
ak(pq) Dimension of (d) is mx 1; d is the spacing of array elements of the single station for receiving motion, thetaqIs the angle of arrival of the q-th target radiation source signal, λ is the target radiation source signal wavelength, pqPosition coordinates of a qth target radiation source; sqk() a signal envelope for the q-th target radiation source signal incident at the kth location point of the single station of motion reception; t issIs the sampling time interval, and N is the sampling fast beat number; n isk(n) is the noise of the received signal when the moving receiving single station moves to the Kth position point;
fqk(pq) For the Doppler shift of the qth target radiation source relative to the kth position point of the moving receiving single station, the expression is:
Figure FDA0002805436550000013
wherein f iscIs the carrier frequency, v, of the target radiation sourcekFor moving the receiving station to the speed of movement at the point kkC is the propagation speed of the target radiation source signal for the position coordinate of the moving receiving single station reaching the k position point;
superposing a time factor on the data receiving model, and expanding the data receiving model of the formula (1) into:
rk(n)＝Bk(b,p)sk(n)+wk(n) (3)
wherein r isk(n)＝[xk T(n),xk T(n+1),,xk T(n+L-1)]TThe result is obtained after the data receiving model is subjected to time factor L superposition; w is ak(n)＝[nk T(n),nk T(n+1),…,nk T(n+L-1)]TIs a noise matrix, sk(n)＝[s1k(n),s2k(n),…,sQk(n)]TIn the form of a matrix of the envelope of the signal,
Figure FDA0002805436550000014
a position coordinate matrix of the target radiation source; b isk(b,p)＝[bk(p1),bk(p2),…,bk(pQ)]Is an array flow pattern matrix after expansion, wherein
Figure FDA0002805436550000015
To introduce a steering vector after Doppler shift, bk(pq) Has a dimension of ML x 1, BkThe (b, p) dimension is ML x Q,
Figure FDA0002805436550000016
step 2: constructing a cost function for locating the position of a single target radiation source:
Figure FDA0002805436550000021
wherein,
Figure FDA0002805436550000022
s satisfying the above formula to a minimum valuekThe least squares solution of (n) is:
Figure FDA0002805436550000023
the cost function equivalence for locating a single target radiation source location is:
Figure FDA0002805436550000024
Figure FDA0002805436550000025
rewriting the above formula into a matrix form includes:
Figure FDA0002805436550000026
target radiation source signal data received by K position points on the motion trail of the motion receiving single station is introduced, and the formula (9) is equivalent to:
Figure FDA0002805436550000027
wherein B (B, p) ═ B1 T(b,p)…BK T(b,p)]T，
Figure FDA0002805436550000028
Is a block-diagonal matrix of the covariance,
Figure FDA0002805436550000029
a sample covariance matrix for the ML × ML dimension at the k location point for the motion receiving single station:
Figure FDA00028054365500000210
and step 3: using the MVDR criterion, equations (7) and (10) are rewritten into the following forms, respectively:
Figure FDA00028054365500000211
Figure FDA00028054365500000212
wherein, wopt(b, p) is an optimal weight vector, expressed as:
Figure FDA00028054365500000213
w (b, p) is a weight vector formed by weight coefficients added to each array element of the motion receiving single station;
s.t.wH(b,p)B(b,p)＝1
equation (14) is transformed by the MVDR principle into:
Figure FDA0002805436550000031
substituting formula (15) for formula (13) to obtain
Figure FDA0002805436550000032
Then
Figure FDA0002805436550000033
Let Bk(b,p)＝Λk(p) b, wherein,
Figure FDA0002805436550000034
b is the path loss vector from the target radiation source to the moving receiving single station K positions, and an equation (16) is substituted, then:
Figure FDA0002805436550000035
in the formula, λmin(. cndot.) represents the calculation of the minimum eigenvalue, and the hermitian property of the matrix of equation (17) is used to rewrite equation (17) as:
Figure FDA0002805436550000036
then p satisfying the above formula as the maximum value is the target radiation source position, and finally the target radiation source position expression is obtained:
Figure FDA0002805436550000037
and completing the positioning of the target radiation source.
2. The method of claim 1, wherein the target radiation source is a far-field narrow-band signal.
3. A high-precision mobile single-station direct positioning method based on angle of arrival and doppler shift according to claim 1, wherein M-8 and K-5.
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