CN110109052B - Target direction finding and array element position estimation method under array element position error condition - Google Patents

Target direction finding and array element position estimation method under array element position error condition Download PDF

Info

Publication number
CN110109052B
CN110109052B CN201910436344.XA CN201910436344A CN110109052B CN 110109052 B CN110109052 B CN 110109052B CN 201910436344 A CN201910436344 A CN 201910436344A CN 110109052 B CN110109052 B CN 110109052B
Authority
CN
China
Prior art keywords
signal source
array
vector
array element
delay
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910436344.XA
Other languages
Chinese (zh)
Other versions
CN110109052A (en
Inventor
刘成城
刘亚奇
胡德秀
赵拥军
黄洁
赵勇胜
刘智鑫
黄东华
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Information Engineering University of PLA Strategic Support Force
Original Assignee
Information Engineering University of PLA Strategic Support Force
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Information Engineering University of PLA Strategic Support Force filed Critical Information Engineering University of PLA Strategic Support Force
Priority to CN201910436344.XA priority Critical patent/CN110109052B/en
Publication of CN110109052A publication Critical patent/CN110109052A/en
Application granted granted Critical
Publication of CN110109052B publication Critical patent/CN110109052B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/28—Systems for determining direction or deviation from predetermined direction using amplitude comparison of signals derived simultaneously from receiving antennas or antenna systems having differently-oriented directivity characteristics
    • G01S3/32—Systems for determining direction or deviation from predetermined direction using amplitude comparison of signals derived simultaneously from receiving antennas or antenna systems having differently-oriented directivity characteristics derived from different combinations of signals from separate antennas, e.g. comparing sum with difference
    • G01S3/36—Systems for determining direction or deviation from predetermined direction using amplitude comparison of signals derived simultaneously from receiving antennas or antenna systems having differently-oriented directivity characteristics derived from different combinations of signals from separate antennas, e.g. comparing sum with difference the separate antennas having differently-oriented directivity characteristics
    • 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
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention relates to the technical field of target detection, in particular to a target direction finding and array element position estimation method under the condition of array element position error. Receiving the signals through a nonlinear array, and converting the received signals into a time-frequency domain; calculating the guide vector of each signal source according to the distribution of the received signals in a time-frequency domain, and calculating the delay vector of each signal source on each array according to the phase of the guide vector of each signal source; estimating the incident angle of each signal source by utilizing the array element position which is preset or updated by the last iteration according to the delay vector of each signal source on each array, thereby realizing the direction finding of the target; according to the delay vector and the incidence angle of each signal source on each array and the position relation of the array elements, the position of each array element is estimated, the method cannot cause the accuracy of target direction finding to be reduced along with the increase of the position error of the array elements, the calculation complexity is low, the position of the array elements is estimated, and the position of the array elements can be accurately obtained.

Description

Target direction finding and array element position estimation method under array element position error condition
Technical Field
The invention relates to the technical field of target detection, in particular to a target direction finding and array element position estimation method under the condition of array element position error.
Background
With the increasing complexity of electromagnetic environment, the traditional amplitude comparison method has difficulty in meeting the direction-finding requirements of a plurality of broadband signals at the same time, and cannot provide powerful support for subsequent positioning, speed measurement, detection and reception, feature extraction and the like. The array is used for direction finding of the target, and the advantages of high precision, super resolution, simultaneous multiple targets and the like are achieved. Under the condition of accurately knowing the array flow pattern, the existing direction-finding technology can realize accurate direction finding of the target.
For example, a patent application document with chinese patent application publication No. CN107907855A discloses a DOA estimation method for converting a reciprocal element array into a uniform linear array, which includes forming a delay set according to the position difference of any two array elements, calculating an autocorrelation function value to be delayed, constructing a Toepltz matrix according to the autocorrelation function value, constructing a spatial spectrum search function based on a MUSIC algorithm, and finding an estimated value of DOA when a spatial spectrum search vector is consistent with a signal steering vector, thereby achieving direction finding of a target signal. The method is carried out under the condition that the position of the array element has no error, but in practice, direction finding is difficult to realize due to the influence of non-ideal factors such as the position error of the array element, and the like.
Disclosure of Invention
The invention aims to provide a target direction finding method under the condition of array element position error, which is used for solving the problems of inaccurate target direction finding and high calculation complexity when the array element position error is increased at present; the invention also provides an array element position estimation method under the condition of array element position error, which is used for solving the problems of inaccurate target direction finding and high calculation complexity when the array element position error is increased at present.
In order to achieve the above object, the present invention provides a target direction finding method under the condition of array element position error, which comprises the following steps:
1) receiving the signals through a nonlinear array, and converting the received signals into a time-frequency domain;
2) calculating the guide vector of each signal source according to the distribution of the received signals in a time-frequency domain, and calculating the delay vector of each signal source on each array according to the phase of the guide vector of each signal source;
3) and according to the delay vector of each signal source on each array, estimating the incident angle of each signal source by using the array element position which is preset or updated in the last iteration, and realizing the direction finding of the target.
The method has the advantages that received signals are converted to a time-frequency domain, then the delay vector of each signal is obtained by utilizing the time-frequency distribution of each signal, finally the incidence angle of each signal source is estimated by utilizing the array element position which is preset or updated in the last iteration, the direction of the target is measured, the accuracy of the target direction measurement is not reduced along with the increase of the position error of the array element, the target direction measurement can be realized only through time-frequency conversion, guide vector calculation and delay vector calculation, and the calculation complexity is low.
Further, for the accuracy of the calculated delay vector, the delay vector of each signal source is:
Figure BDA0002070641530000021
Figure BDA0002070641530000022
wherein K represents the total number of signal sources, K represents the signal source K, (t)a,fa) Is a guide vector ak(fa) Of the time-frequency distribution, angle (a)k(fa) A) represents solving for ak(fa) The phase of each element, unwrap (-) is used to correct the phase, X (t)a,fa) For time-frequency transformation of received signal vectors, X (t)a,fa1) is X (t)a,fa) The first element of (1).
Further, in order to accurately obtain the delay vector, when the delay vector of each signal source is calculated, the delay vectors of the same signal source on at least two single-source points are calculated, then the average value of the delay vectors of the single-source points is calculated, and the average value is used as the delay vector of the signal source.
Further, for the convenience of solution, the incident angle of each signal source is:
Figure BDA0002070641530000031
Figure BDA0002070641530000032
Figure BDA0002070641530000033
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,
Figure BDA0002070641530000034
and
Figure BDA0002070641530000035
respectively represent
Figure BDA0002070641530000036
The first element and the second element of (a),
Figure BDA0002070641530000037
a preset value representing the position of an array element m or an updated value at the last iteration,
Figure BDA0002070641530000038
Figure BDA0002070641530000039
for the delay of signal source k on array element m, c represents the propagation speed of the signal.
The invention provides an array element position estimation method under the condition of array element position error, which comprises the following steps:
1) receiving the signals through a nonlinear array, and converting the received signals into a time-frequency domain;
2) calculating the guide vector of each signal source according to the distribution of the received signals in a time-frequency domain, and calculating the delay vector of each signal source on each array according to the phase of the guide vector of each signal source;
3) estimating the incident angle of each signal source by utilizing the array element position which is preset or updated by the last iteration according to the delay vector of each signal source on each array, thereby realizing the direction finding of the target;
4) and estimating the position of each array element according to the delay vector of each signal source on each array and the relation between the incident angle and the position of the array element.
The method has the advantages that received signals are converted to a time-frequency domain, then the delay vector of each signal is obtained by utilizing the time-frequency distribution of each signal, finally the incident angle of each signal source is estimated by utilizing the array element position which is preset or updated in the last iteration, and the direction of the target is measured, so that the accuracy of the target direction measurement is not reduced along with the increase of the position error of the array element, the target direction measurement can be realized only by time-frequency conversion, guide vector calculation and delay vector calculation, and the calculation complexity is low; and the array element position can be accurately obtained by accurately obtaining the target direction finding and then estimating the array element position.
Further, for the accuracy of the calculated delay vector, the delay vector of each signal source is:
Figure BDA0002070641530000041
Figure BDA0002070641530000042
wherein K represents the total number of signal sources, K represents the signal source K, (t)a,fa) Is a guide vector ak(fa) Of the time-frequency distribution, angle (a)k(fa) A) represents solving for ak(fa) The phase of each element, unwrap (-) is used to correct the phase, X (t)a,fa) For time-frequency transformation of received signal vectors, X (t)a,fa1) is X (t)a,fa) The first element of (1).
Further, in order to accurately obtain the delay vector, when the delay vector of each signal source is calculated, the delay vectors of the same signal source on at least two single-source points are calculated, then the average value of the delay vectors of the single-source points is calculated, and the average value is used as the delay vector of the signal source.
Further, for the convenience of solution, the incident angle of each signal source is:
Figure BDA0002070641530000043
Figure BDA0002070641530000044
Figure BDA0002070641530000045
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,
Figure BDA0002070641530000051
and
Figure BDA0002070641530000052
respectively represent
Figure BDA0002070641530000053
The first element and the second element of (a),
Figure BDA0002070641530000054
a preset value representing the position of an array element m or an updated value at the last iteration,
Figure BDA0002070641530000055
Figure BDA0002070641530000056
for the delay of signal source k on array element m, c represents the propagation speed of the signal.
Further, for the convenience of calculation, the estimated array element positions are:
Figure BDA0002070641530000057
wherein H ═ H0 T,H1 T,...,HK-1 T]TA weighting matrix is represented by a matrix of weights,
Figure BDA0002070641530000058
delay vectors representing all signals, χ ═ x1,x2,...,xM-1]TAnd y ═ y1,y2,...,yM-1]TRespectively representing the x-axis position vector and the y-axis position vector of the M-1 array elements.
Further, for calculating the position of the array element simply and accurately, a least square method is adopted for calculating the position of the array element.
Drawings
FIG. 1 is a flow chart of a target direction finding method under an array element position error condition according to the present invention;
FIG. 2 is a flow chart of a method for estimating the position of an array element under the condition of an error in the position of the array element according to the present invention;
FIG. 3 is a diagram of the target direction-finding delay vector estimation result of the present invention;
FIG. 4 is a graph of the variation of the estimated bias with iteration number of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The embodiment of the direction finding method comprises the following steps:
the invention provides a target direction finding method under the condition of array element position error, as shown in figure 1, the target direction finding method comprises the following steps:
1) the signal is received by a nonlinear array and the received signal is converted to the time-frequency domain.
Suppose K broadband signals sk(t)(k＝0,1.. K-1) is incident on a non-linear array consisting of M array elements, the received signal of each array element being denoted xm(t) (M ═ 0.., M-1). Then, under far-field conditions, the signal model may be expressed as
Figure BDA0002070641530000061
Wherein, tauk,mIs a signal sk(t) propagation delay of the mth array element relative to the reference array element (array element 0), nm(t) is the system noise, which is assumed here to be white gaussian noise.
Delay tau in the presence of array element position errorsk,mIs composed of
Figure BDA0002070641530000062
Wherein, thetakIs the signal sk(t) angle of incidence, xmAnd ymFor the m-th array element at the preset positions on the x-axis and the y-axis, Δ xmAnd Δ ymFor its corresponding position error, i.e. the true position of the array element is (x)m+Δxm,ym+Δym) And c represents the propagation speed of the signal, and is usually 3 × 108m/s。
Like the existing algorithm, for the sake of simplifying the expression, it is assumed here that the signal and the array are in the same plane, and expression (1) is expressed in the form of a vector
Figure BDA0002070641530000063
Wherein x (t) ═ x0(t),x1(t),...,xM-1(t)]TAnd xk(t)＝[sk(t-τk,0),sk(t-τk,1),...,sk(t-τk,M-1)]TRespectively a received signal vector and a signal sk(t) a received vector of (n), (t) n0(t),n1(t),...,nM-1(t)]TA noise vector.
Since it is difficult to obtain an accurate DOA estimation value when there is an array element position error, it is also necessary to estimate the array element position. For a non-linear array, simultaneous estimation of the position of an array element and the DOA of a signal can be achieved when three or more signals of different incoming directions are incident on the array and the position of one array element and the direction of the array element to another array element are known.
Without loss of generality, it is assumed here that the position of array element 0 is known as x0＝0，y 00, and the y-axis coordinate y of array element 110. As can be seen from the formula (2), the delay τk,mAnd array element position (x)m,ym) Is a linear relationship. If all τ are knownk,m(K-0, 1.. K-1, M-0, 1.. K., M-1), the array element positions can be directly obtained by solving linear equations without any approximation in the process.
For any signal z (t), its time-frequency distribution can be obtained by short-time Fourier transform (STFT)
Figure BDA0002070641530000071
Wherein g (t) is a window function, and g (t) is selected as a Hamming window;
Figure BDA0002070641530000072
wherein, TmaxIndicating the window length.
Under the noise-free condition, the formula (1) is subjected to STFT conversion to obtain
Figure BDA0002070641530000073
Wherein, Xm(t, f) and Sk(t, f) each represents xm(t) and sk(t) time-frequency distribution.
STFT conversion is performed on the formula (3) to obtain
X(t,f)＝A(f)S(t,f) (7)
Wherein the content of the first and second substances,
Figure BDA0002070641530000074
by equation (7), the received signal can be transformed from the time domain to the time-frequency domain.
2) And calculating the steering vector of each signal source according to the distribution of the received signals in the time-frequency domain, and calculating the delay vector of each signal source on each array according to the phase of the steering vector of each signal source.
At the signal sk(t) time-frequency distribution (t)a,fa) In the above, the formula (7) can be simplified to
X(ta,fa)＝ak(fa)Sk(ta,fa)(ta,fa)∈Ωk (9)
Wherein omegakIs s isk(t) single source point set. Then, sk(t) at frequency faUpper guide vector ak(fa) Can be obtained by the following formula
Figure BDA0002070641530000081
Due to x00 and y0When 0, then τ isk,00. Let ak(fa1) and X (t)a,faAnd 1) each represents ak(fa) And X (t)a,fa) The first element of (1), then ak(fa1) 1 and X (t)a,fa,1)＝Sk(ta,fa) This is true. Thus, formula (10) can be transformed into
Figure BDA0002070641530000082
Then, the delay vector τk(ta,fa) Is composed of
Figure BDA0002070641530000083
Wherein, angle (a)k(fa) A) represents solving for ak(fa) The phase of each element, unwrap (-) is used to correct the phase, when the phase difference between adjacent elements is larger than pi, the phase jump is prevented by superposing integral multiple of + -2 pi or + -2 pi, so that the phase range is no longer limited to-pi, pi]。
For the same signal sk(t) two different single source points (t)a1,fa1) And (t)a2,fa2) Whose delay vector satisfies
Figure BDA0002070641530000084
As can be seen from equations (11) and (12), the delay vector of the corresponding signal can be obtained using a single source point under noise-free conditions. However, in an actual noise environment, the delay vector to be calculated has a certain deviation. Equation (13) shows that more accurate estimation results can be obtained by solving the delay vectors at multiple single source points of the same signal and then averaging the delay vectors. Therefore, the final delay can be determined by the following equation
Figure BDA0002070641530000091
Wherein D iskIs omegakThe number of the middle time-frequency points. To this end, we have found a delay vector for each source signal
Figure BDA0002070641530000092
Figure BDA0002070641530000093
Then the delay of the signal on different array elements is obtained
Figure BDA0002070641530000094
Figure BDA0002070641530000095
3) And according to the delay vector of each signal source on each array, estimating the incident angle of each signal source by using the array element position which is preset or updated in the last iteration, and realizing the direction finding of the target.
Using delays
Figure BDA0002070641530000096
The position of the array elements and the signal DOA can be determined by a two-step alternating iteration without approximation.
And solving the DOA according to the array element position which is preset or updated by the latest iteration. For array element 1 through array element M-1 (the location of array element 0 is known exactly, so array element 0 is not considered), equation (2) is written in vector form
Figure BDA0002070641530000097
Where ρ isk＝[cos(θk),sin(θk)]TAnd
Figure BDA0002070641530000098
are vectors of (M-1) × 1. B is a matrix of (M-1) × 2
Figure BDA0002070641530000099
Wherein the content of the first and second substances,
Figure BDA00020706415300000910
a preset value representing the position of the array element m or an updated value at the last iteration.
The equation (15) is solved by the least square method, and the result is obtained
Figure BDA0002070641530000101
Due to rhok＝[cos(θk),sin(θk)]TAnd thetak∈[-π,π]Then thetakCan be obtained by the following formula
Figure BDA0002070641530000102
Wherein the content of the first and second substances,
Figure BDA0002070641530000103
and
Figure BDA0002070641530000104
respectively represent
Figure BDA0002070641530000105
The first element and the second element of (1).
The embodiment of the estimation method comprises the following steps:
the invention provides an array element position estimation method under the condition of array element position error, as shown in figure 2, the estimation method comprises the following steps:
(1) receiving the signals through a nonlinear array, and converting the received signals into a time-frequency domain;
(2) calculating the guide vector of each signal source according to the distribution of the received signals in a time-frequency domain, and calculating the delay vector of each signal source on each array according to the phase of the guide vector of each signal source;
(3) estimating the incident angle of each signal source by utilizing the array element position which is preset or updated by the last iteration according to the delay vector of each signal source on each array, thereby realizing the direction finding of the target;
(4) and estimating the position of each array element according to the delay vector of each signal source on each array and the relation between the incident angle and the position of the array element.
Since the steps (1) to (3) have been described in detail in the above embodiment of the direction finding method, the embodiment of the estimation method is not described again.
And (4) estimating the position of the array element by using the DOA obtained in the step (3). For array element 1 to array element M-1 and all source signals s0(t)…sK-1(t) writing the formula (2) in vector form
Figure BDA0002070641530000106
Wherein the content of the first and second substances,
Figure BDA0002070641530000107
delay vectors representing all signals, χ ═ x1,x2,...,xM-1]TAnd y ═ y1,y2,...,yM-1]TRespectively representing the x-axis position vector and the y-axis position vector of the M-1 array elements. H ═ H0 T,H1 T,...,HK-1 T]TRepresents a weighting matrix, HkIs composed of
Figure BDA0002070641530000111
Similarly, the least square method is used to obtain the array element positions χ and γ
Figure BDA0002070641530000112
It should be noted that the above method is not limited to obtaining
Figure BDA0002070641530000113
Is the value of (d), after each iteration
Figure BDA0002070641530000114
Will be assigned a value of 0. Thus, an updated value of the array element position is obtained.
And repeating the steps in the direction finding method embodiment and the estimation method embodiment until the algorithm converges, and obtaining the final array element position and DOA.
Finally, the method can be achieved byAnd (4) simulating experiments to verify the effectiveness of the algorithm. Assuming a 3 × 3 uniform area array, three chirp signals s0、s1、s2The light is incident to the array from-45 degrees, 20 degrees and 55 degrees respectively; wherein s is0Is the desired signal with a signal-to-noise ratio of 0dB, s1And s2Are interference signals, and the dry-to-noise ratio is 20 dB.
The frequency ranges of the three are respectively [2.9,3.95 ]]GHz、[3,4]GHz and [3.1,4]GHz, reference frequency selection fmax4GHz, presetting the distance between adjacent array elements as 0.5 lambdaminWherein λ isminIs the highest frequency fmaxCorresponding wavelength, but true array element spacing Δ d due to array element position errorj-1,j(j-1, 2, …,9) is [0.7 Δ d,1.3 Δ d]Random value in the range, sampling rate 2fmaxThe fast beat number is 200.
As shown in fig. 3, a comparison graph of the estimated delay vector and the real delay vector shows that the algorithm of the present invention can well estimate the delay vector of the source signal. Further, as shown in fig. 4, the variation of the estimated deviation with the iteration number is given, and the deviation gradually decreases with the increase of the iteration number, so that convergence can be realized after 50 iterations. Finally, the final estimation of the source signal arrival direction is-45.15 °, 19.97 °, 54.37 °.
The present invention has been described in relation to particular embodiments thereof, but the invention is not limited to the described embodiments. The technical means in the above embodiments are changed, replaced, modified in a manner that will be easily imaginable to those skilled in the art, and the functions of the technical means are substantially the same as those of the corresponding technical means in the present invention, and the objectives of the invention are also substantially the same, so that the technical solution formed by fine tuning the above embodiments still falls into the protection scope of the present invention.

Claims (8)

1. A target direction finding method under the condition of array element position error is characterized by comprising the following steps:
1) receiving the signals through a nonlinear array, and converting the received signals into a time-frequency domain;
2) calculating the guide vector of each signal source according to the distribution of the received signals in a time-frequency domain, and calculating the delay vector of each signal source on each array according to the phase of the guide vector of each signal source;
3) estimating the incident angle of each signal source by utilizing the array element position which is preset or updated by the last iteration according to the delay vector of each signal source on each array, thereby realizing the direction finding of the target;
the incident angle of each signal source is:
Figure FDA0003253058390000011
Figure FDA0003253058390000012
Figure FDA0003253058390000013
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,
Figure FDA0003253058390000014
and
Figure FDA0003253058390000015
respectively represent
Figure FDA0003253058390000016
The first element and the second element of (a),
Figure FDA0003253058390000017
a preset value representing the position of an array element m or an updated value at the last iteration,
Figure FDA0003253058390000018
Figure FDA0003253058390000019
for the delay of signal source k on array element m, c represents the propagation speed of the signal.
2. The method of claim 1, wherein the delay vector of each signal source is:
Figure FDA0003253058390000021
Figure FDA0003253058390000022
wherein K represents the total number of signal sources, K represents the signal source K, (t)a,fa) Is a guide vector ak(fa) Of the time-frequency distribution, angle (a)k(fa) A) represents solving for ak(fa) The phase of each element, unwrap (-) is used to correct the phase, X (t)a,fa) For time-frequency transformation of received signal vectors, X (t)a,fa1) is X (t)a,fa) The first element of (1).
3. The method according to claim 1 or 2, wherein when calculating the delay vector of each signal source, the delay vectors of the same signal source at least two single-source points are calculated, and then the average value of the delay vectors of the single-source points is calculated, and the average value is used as the delay vector of the signal source.
4. A method for estimating the position of an array element under the condition of array element position error is characterized by comprising the following steps:
1) receiving the signals through a nonlinear array, and converting the received signals into a time-frequency domain;
2) calculating the guide vector of each signal source according to the distribution of the received signals in a time-frequency domain, and calculating the delay vector of each signal source on each array according to the phase of the guide vector of each signal source;
3) estimating the incident angle of each signal source by utilizing the array element position which is preset or updated by the last iteration according to the delay vector of each signal source on each array, thereby realizing the direction finding of the target;
4) estimating the position of each array element according to the delay vector of each signal source on each array and the relation between the incident angle and the position of the array element;
the incident angle of each signal source is:
Figure FDA0003253058390000031
Figure FDA0003253058390000032
Figure FDA0003253058390000033
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,
Figure FDA0003253058390000034
and
Figure FDA0003253058390000035
respectively represent
Figure FDA0003253058390000036
The first element and the second element of (a),
Figure FDA0003253058390000037
indicating m position of array elementA preset value of or an updated value at the last iteration,
Figure FDA0003253058390000038
Figure FDA0003253058390000039
for the delay of signal source k on array element m, c represents the propagation speed of the signal.
5. The method according to claim 4, wherein the delay vector of each signal source is:
Figure FDA00032530583900000310
Figure FDA00032530583900000311
wherein K represents the total number of signal sources, K represents the signal source K, (t)a,fa) Is a guide vector ak(fa) Of the time-frequency distribution, angle (a)k(fa) A) represents solving for ak(fa) The phase of each element, unwrap (-) is used to correct the phase, X (t)a,fa) For time-frequency transformation of received signal vectors, X (t)a,fa1) is X (t)a,fa) The first element of (1).
6. The method according to claim 4 or 5, characterized in that when calculating the delay vector of each signal source, the delay vectors of the same signal source at least two single source points are calculated first, then the average value of the delay vectors of the single source points is calculated, and the average value is used as the delay vector of the signal source.
7. A method for estimating a position of an array element under an error condition according to claim 4 or 5, characterized in that the estimated position of the array element is:
Figure FDA0003253058390000041
wherein H ═ H0 T,H1 T,...,HK-1 T]TA weighting matrix is represented by a matrix of weights,
Figure FDA0003253058390000042
delay vectors representing all signals, χ ═ x1,x2,...,xM-1]TAnd y ═ y1,y2,...,yM-1]TRespectively representing the x-axis position vector and the y-axis position vector of the M-1 array elements.
8. The method as claimed in claim 7, wherein the method comprises calculating the position of the array element by least squares.
CN201910436344.XA 2019-05-23 2019-05-23 Target direction finding and array element position estimation method under array element position error condition Active CN110109052B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910436344.XA CN110109052B (en) 2019-05-23 2019-05-23 Target direction finding and array element position estimation method under array element position error condition

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910436344.XA CN110109052B (en) 2019-05-23 2019-05-23 Target direction finding and array element position estimation method under array element position error condition

Publications (2)

Publication Number Publication Date
CN110109052A CN110109052A (en) 2019-08-09
CN110109052B true CN110109052B (en) 2021-12-31

Family

ID=67491890

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910436344.XA Active CN110109052B (en) 2019-05-23 2019-05-23 Target direction finding and array element position estimation method under array element position error condition

Country Status (1)

Country Link
CN (1) CN110109052B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114239251B (en) * 2021-12-06 2023-05-05 中国电子科技集团公司第二十九研究所 Evaluation method for array direction-finding precision under near-end multipath condition
CN116593965B (en) * 2023-07-19 2023-09-29 中国海洋大学 Horizontal array type estimation method based on far-field opportunity sound source

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE19909553A1 (en) * 1999-03-04 2000-11-02 Posinom Orientierungssysteme G Direction and position determination method for tracking people, animals or machines, involves short circuiting one or more antennas and measuring attenuation of received field strength at active antennas
CN105242236A (en) * 2015-09-28 2016-01-13 黑龙江大学 Array element position error correction method in broadband signal super-resolution direction measurement
CN107907855A (en) * 2017-10-25 2018-04-13 天津大学 A kind of coprime array switching DOA estimation method and device for even linear array
CN109001672A (en) * 2018-06-14 2018-12-14 中国人民解放军战略支援部队信息工程大学 A kind of time difference frequency difference method for parameter estimation and device
CN109743078A (en) * 2019-01-11 2019-05-10 河南宏泰控飞信息技术有限公司 Unmanned plane frequency hopping remote signal intercept receiving method and equipment based on array antenna
CN109782238A (en) * 2018-11-19 2019-05-21 西北工业大学 A kind of sensor array array element width mutually responds the joint calibration method with element position

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4910526A (en) * 1987-05-18 1990-03-20 Avion Systems, Inc. Airborne surveillance method and system
JP2001249173A (en) * 2000-03-07 2001-09-14 Matsushita Electric Ind Co Ltd Radio wave azimuth/position detection device
CN104931919B (en) * 2015-06-08 2017-06-13 西安电子科技大学 A kind of direction-finding method of two dimensional surface circle ring array
CN107544051A (en) * 2017-09-08 2018-01-05 哈尔滨工业大学 Wave arrival direction estimating method of the nested array based on K R subspaces
CN108020811B (en) * 2017-12-06 2021-02-19 吉林大学 1-dimensional uniform linear array direction finding method based on target source phase shift difference technology

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE19909553A1 (en) * 1999-03-04 2000-11-02 Posinom Orientierungssysteme G Direction and position determination method for tracking people, animals or machines, involves short circuiting one or more antennas and measuring attenuation of received field strength at active antennas
CN105242236A (en) * 2015-09-28 2016-01-13 黑龙江大学 Array element position error correction method in broadband signal super-resolution direction measurement
CN107907855A (en) * 2017-10-25 2018-04-13 天津大学 A kind of coprime array switching DOA estimation method and device for even linear array
CN109001672A (en) * 2018-06-14 2018-12-14 中国人民解放军战略支援部队信息工程大学 A kind of time difference frequency difference method for parameter estimation and device
CN109782238A (en) * 2018-11-19 2019-05-21 西北工业大学 A kind of sensor array array element width mutually responds the joint calibration method with element position
CN109743078A (en) * 2019-01-11 2019-05-10 河南宏泰控飞信息技术有限公司 Unmanned plane frequency hopping remote signal intercept receiving method and equipment based on array antenna

Also Published As

Publication number Publication date
CN110109052A (en) 2019-08-09

Similar Documents

Publication Publication Date Title
CN107064861B (en) Apparatus for estimating angle of arrival and apparatus for beamforming
US10539645B2 (en) Angle of arrival estimation
US10571544B2 (en) Direction finding using signal power
JP6778336B2 (en) RF signal arrival angle determination method and system
CN108776330B (en) High-precision calibration method and device for multiple receiving channels of FMCW radar
CN108398669B (en) Space-time broadband self-adaptive monopulse angle measurement method based on non-pre-delay processing
CN108710103B (en) Strong and weak multi-target super-resolution direction finding and information source number estimation method based on sparse array
KR101564730B1 (en) Method for arranging array plane of phase array antenna
JP2009243947A (en) Arrival direction estimation apparatus, arrival direction estimation method, and arrival direction estimation program
CN110109052B (en) Target direction finding and array element position estimation method under array element position error condition
Liu et al. A novel channel phase bias estimation method for spaceborne along-track multi-channel HRWS SAR in time-domain
CN110082750B (en) Amplitude comparison angle measurement method capable of eliminating phase errors among channels
CN108089146B (en) High-resolution broadband direction-of-arrival estimation method for pre-estimated angle error robustness
KR101239165B1 (en) Method and apparatus for estimating target direction
RU2305294C2 (en) Method for direction finding with regard to correlation interaction between beams
KR101032299B1 (en) Self-calibration for direction finding in multi-baseline interferometer system
CN112363108A (en) Signal subspace weighted super-resolution direction-of-arrival detection method and system
CN111693979A (en) Digital array monopulse angle measurement method based on Taylor expansion
CN109613474B (en) Angle measurement compensation method suitable for short-distance vehicle-mounted radar
CN107490780B (en) Direction finding method capable of restraining uniformly distributed phase errors
KR102557459B1 (en) Method and apparatus for measuring target elevation angle of Radar in multipath environment
Vermesan et al. Ghost image cancellation algorithm through numeric beamforming for multi‐antenna radar imaging
KR102189867B1 (en) Calibration system, apparatus and method for phased array antenna
Wang et al. Joint calibration of mutual coupling and channel gain/phase inconsistency using a near-field auxiliary source
US11402488B2 (en) Sidelobe detector and angle/angle-rate estimator for a slewing monopulse antenna

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant