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 PDFInfo
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- 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
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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
- 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
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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
- 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
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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
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:
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:
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,andrespectively representThe first element and the second element of (a),a preset value representing the position of an array element m or an updated value at the last iteration, 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:
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:
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,andrespectively representThe first element and the second element of (a),a preset value representing the position of an array element m or an updated value at the last iteration, 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:
wherein H ═ H0 T,H1 T,...,HK-1 T]TA weighting matrix is represented by a matrix of weights,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
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
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
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)
Wherein g (t) is a window function, and g (t) is selected as a Hamming window;
wherein, TmaxIndicating the window length.
Under the noise-free condition, the formula (1) is subjected to STFT conversion to obtain
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,
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
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
Then, the delay vector τk(ta,fa) Is composed of
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
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
Wherein D iskIs omegakThe number of the middle time-frequency points. To this end, we have found a delay vector for each source signal Then the delay of the signal on different array elements is obtained
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 delaysThe 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
Wherein the content of the first and second substances,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
Due to rhok=[cos(θk),sin(θk)]TAnd thetak∈[-π,π]Then thetakCan be obtained by the following formula
Wherein the content of the first and second substances,andrespectively representThe 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
Wherein the content of the first and second substances,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
Similarly, the least square method is used to obtain the array element positions χ and γ
It should be noted that the above method is not limited to obtainingIs the value of (d), after each iterationWill 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:
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,andrespectively representThe first element and the second element of (a),a preset value representing the position of an array element m or an updated value at the last iteration, 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:
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:
wherein K represents the total number of signal sources, K represents the signal source K, M represents the number of array elements,andrespectively representThe first element and the second element of (a),indicating m position of array elementA preset value of or an updated value at the last iteration, 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:
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:
8. The method as claimed in claim 7, wherein the method comprises calculating the position of the array element by least squares.
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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 |
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