CN107037397A - A kind of method that a variety of array errors are corrected in Mutual coupling - Google Patents
A kind of method that a variety of array errors are corrected in Mutual coupling Download PDFInfo
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- CN107037397A CN107037397A CN201710475991.2A CN201710475991A CN107037397A CN 107037397 A CN107037397 A CN 107037397A CN 201710475991 A CN201710475991 A CN 201710475991A CN 107037397 A CN107037397 A CN 107037397A
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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
-
- 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
- G01S3/78—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 electromagnetic waves other than radio waves
- G01S3/782—Systems for determining direction or deviation from predetermined direction
-
- 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
- G01S3/80—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 ultrasonic, sonic or infrasonic waves
- G01S3/802—Systems for determining direction or deviation from predetermined direction
Abstract
The present invention relates to the error estimation in Mutual coupling, specifically related to a kind of method that a variety of array errors are corrected in Mutual coupling, the present invention is often corrected to solve existing array error processing method for a kind of error, cause the shortcoming that processing speed is relatively low, complexity is higher, and a kind of method that a variety of array errors are corrected in Mutual coupling is proposed, including：Obtain amplitude phase error matrix and mutual coupling matrix；Feature decomposition covariance matrix, noise subspace matrix and estimated matrix are obtained according to MUSIC algorithms；Definition space is composed；Scan for obtaining the DOA estimations of N number of peak value in spatial spectrum；Seek the estimate of amplitude phase unbalance error matrix；Seek the estimate of mutual coupling error matrix；Calculation cost function；Given thresholding, if the cost function difference of adjacent iteration twice is more than thresholding, continues iteration；If less than or equal to thresholding, exiting circulation, obtaining parameter to be estimated.The present invention is applied to the Mutual coupling for having in the case of array error.
Description
Technical field
The present invention relates to the error estimation in Mutual coupling, and in particular to one kind is in Mutual coupling lieutenant colonel
The method of just a variety of array errors.
Background technology
Mutual coupling is an important research direction in array signal processing, numerous in radar, communication, sonar etc.
There is extremely wide application prospect in field.And in Estimation of Spatial Spectrum, array error is the class errors of form being difficult to avoid that,
It is possible thereby to cause array manifold not to be inconsistent with hypothesized model, so that the DOA algorithm performances based on ideal model are decreased obviously, this will
The actualization application of DOA algorithms is influenceed, therefore carries out the research for making Mutual coupling that there is more stable property in actual applications
With realistic meaning.Traditional array error processing mode is often corrected for a certain error, and in actual applications
Be generally basede on a variety of errors it is common in the presence of estimate arrival bearing, respectively handle error reduce processing speed and increase
Complexity.
The content of the invention
The invention aims to solve existing array error processing method to be often corrected for a kind of error,
Cause the shortcoming that processing speed is relatively low, complexity is higher, and propose one kind and a variety of array errors are corrected in Mutual coupling
Method.
A kind of method that a variety of array errors are corrected in Mutual coupling, the even linear array that methods described is used is by M
Individual array element composition, spatial distribution far-field signal source is N number of, azimuth angle thetaiFor amount to be estimated, i=1,2 ..., N, array number and letter
Number source number is metWherein L is mutual coupling matrix parameter number, and r represents array system azimuth dimension；The side
The even linear array that method is used is made up of M array element, and spatial distribution far-field signal source is N number of, azimuth angle thetaiFor amount to be estimated, i=
1,2 ..., N, array number are met with signal numberWherein L is mutual coupling matrix parameter number, and r represents array
System attitude angle dimension；Characterized in that, methods described includes：
Step 1: initialization iteration count value n, obtains amplitude phase unbalance error matrix Γ and mutual coupling Matrix C；According to
MUSIC algorithms obtain feature decomposition covariance matrixNoise subspace matrix U and estimate of noise subspace matrix
Step 2: definition space is composedWherein a (θ) is steering vector；For
The amplitude phase unbalance error matrix estimate that kth time iteration is obtained；The mutual coupling Matrix Estimation value obtained for kth time iteration.
Step 3: the DOA for scanning for obtaining N number of peak value by MUSIC algorithms in the spatial spectrum estimates
Step 4: solving the estimate of the amplitude phase unbalance error matrix of+1 iteration of kth
Step 5: solving the estimate of the mutual coupling error matrix of+1 iteration of kth
Step 6: calculating the cost function J of+1 iteration of kthc, an arbitrarily small thresholding ε ＞ 0 is given, if
N=n+1 is then made, and returns to step 2 and continues iteration；If
Iterated conditional has then been met, circulation is exited, it is at this moment resultingWithAs need
Parameter to be estimated.
Beneficial effects of the present invention are：1st, reduce the complexity of Error processing and improve processing speed；2nd, it is corrected
Root-mean-square error afterwards is about 0.05 or so, and compared with uncorrected 0.8, error is greatly lowered；3rd, method base of the invention
Estimate arrival bearing in the presence of a variety of errors are common, more meet practical situations.
Brief description of the drawings
Fig. 1 is the flow chart of the method that a variety of array errors are corrected in Mutual coupling of the present invention；
Fig. 2 is invention and there is estimated result and ideally array error correction contrast that error is
Figure；
Fig. 3 is is defined by root-mean-square error, influence of the signal to noise ratio to the estimated result degree of accuracy of the present invention.
Fig. 4 is is defined by root-mean-square error, influence of the fast umber of beats to the estimated result degree of accuracy of the present invention.
Embodiment
Embodiment one：The method that a variety of array errors are corrected in Mutual coupling of present embodiment, institute
The even linear array that the method for stating is used is made up of M array element, and spatial distribution far-field signal source is N number of, azimuth angle thetaiTo be to be estimated
Amount, i=1,2 ..., N, array number is met with signal numberWherein L is mutual coupling matrix parameter number, r tables
Show array system azimuth dimension；Characterized in that, methods described includes：
Step 1: initialization iteration count value n, obtains amplitude phase unbalance error matrix Γ and mutual coupling Matrix C；According to
MUSIC algorithms obtain feature decomposition covariance matrixNoise subspace matrix U and estimate of noise subspace matrix
Step 2: definition space is composedWherein a (θ) is steering vector；For
The amplitude phase unbalance error matrix estimate that kth time iteration is obtained；The mutual coupling Matrix Estimation value obtained for kth time iteration.
Step 3: the DOA for scanning for obtaining N number of peak value by MUSIC algorithms in the spatial spectrum estimates
Step 4: solving the estimate of the amplitude phase unbalance error matrix of+1 iteration of kth
Step 5: solving the estimate of the mutual coupling error matrix of+1 iteration of kth
Step 6: calculating the cost function J of+1 iteration of kthc, an arbitrarily small thresholding ε ＞ 0 is given, if
N=n+1 is then made, and returns to step 2 and continues iteration；If
Iterated conditional has then been met, circulation is exited, it is at this moment resultingWithAs need
Parameter to be estimated.
Embodiment two：Present embodiment from unlike embodiment one：Step 4 is specially：
Keep the angle of DOA estimationsWith mutual coupling matrixIt is constant, calculation formula
K is current iteration count value；The vector being made up of amplitude phase unbalance error matrix Γ diagonal elements is δ=[Γ11,
Γ22,…,ΓMM], Q1(n)=diag { a (θn)}。
Use expression formulaThe estimate that formula obtains the amplitude phase unbalance matrix of kth time iteration is brought into as δWherein ObtainProcess be, select first
Individual array element is reference point, in constraints δHW=1, w=minimize J under [1,0 ..., 0]c。
Other steps and parameter are identical with embodiment one.
Embodiment three：Present embodiment from unlike embodiment one or two：Step 5 is specially：
Keep DOA estimatesWith the estimate of amplitude phase unbalance errorIt is constant, calculation formula
K is current iteration count value； Use expression formula Formula is brought into as c initial value to obtainEstimated result, constraints is C11=1, write as
Equation isGenerally make W1=[1,0 ..., 0]T, u=1.Again by expression formula ci=C1i(i=1,2 ..., L) obtain mutually
Coupling matrixEstimate.Wherein
Present embodiment iteration is meant that, is incited somebody to actionInitial as c is brought into JcTable
First time iteration is carried out up in formula, c value is continually changing during this, the result conduct of iterationEstimated result.Then will
Estimated result is iterated as the initial value of second of iteration, by that analogy.What iteration was obtained after terminatingElement c thereiniWith
C1iAlso there is certain relation, i.e. ci=C1i, then by this replacement, just obtained mutual coupling matrixEstimate.
Other steps and parameter are identical with embodiment one or two.
Embodiment four：Unlike one of present embodiment and embodiment one to three：In step 6, appoint
Anticipate small thresholding ε=10-10。
Other steps and parameter are identical with one of embodiment one to three.
<Emulation experiment>
Emulated according to embodiment one to four, simulation parameter setting is as follows in simulation process：Two in space
Irrelevant sinusoidal narrow band signal incides the even linear array of 10 array element from far field, and array element spacing is half-wavelength, and two, space is not
Relevant far field point signal source is respectively from -20 ° and -10 °, and noise is white Gaussian noise, and signal to noise ratio is 10dB.The fast umber of beats of data
For 256 times.Mutual coupling effect can be ignored when thinking array element away from more than wavelength, and the mutual coupling coefficient vector is set as [1,0.48-
0.04i, 0.16-0.05i, 0.02-0.01i], randomly select amplitude-phase error.
Performance evaluation：Signal to noise ratio (SNR) rises to 50dB by 0, at intervals of 5dB, and signal to noise ratio, which often changes once to become, carries out 100
Secondary to repeat estimation angle, -20 ° and -10 ° are compared with standard value, and calculate standard deviation；Fast umber of beats (L) scope arrives for 100 times
800 times, at intervals of 70, fast umber of beats, which often changes once to become, carries out 100 repetition estimation angles, with -20 ° and -10 ° progress of standard value
Compare and make the difference, and calculate standard deviation,
Simulated environment is：Matlab R2016a, as shown in Figures 2 to 4, algorithm is simulation result after joint correction in figure
The method of the present invention.It can be obtained by the simulation result of accompanying drawing to draw a conclusion：
From figure 2 it can be seen that common MUSIC algorithm spectral peaks are substantially reduced under experimental error environment, and the present invention is proposed
The spatial spectrum estimated of Self-Tuning Algorithm composed closely with ideal space.The true of mutual coupling and amplitude phase error is listed in table 1
Value and the estimate after iteration self-correcting.Thus we can see that iterative method is to the calibration result of even linear array, by joint
After correction, error estimate is with angle estimation value with being actually sufficiently close to
Table 1
Accuracy of estimation is had little influence in the non-timing of error, signal to noise ratio and fast umber of beats it can be seen from Fig. 3 and Fig. 4,
And be always maintained at a relatively large numerical value, and utilize after the algorithm process array error of the present invention, with signal to noise ratio with
The increase of fast umber of beats, root-mean-square error is substantially reduced.
The present invention can also have other various embodiments, in the case of without departing substantially from spirit of the invention and its essence, this area
Technical staff works as can make various corresponding changes and deformation according to the present invention, but these corresponding changes and deformation should all belong to
The protection domain of appended claims of the invention.
Claims (4)
1. a kind of method that a variety of array errors are corrected in Mutual coupling, the even linear array that methods described is used is by M
Array element is constituted, and spatial distribution far-field signal source is N number of, azimuth angle thetaiFor amount to be estimated, i=1,2 ..., N, array number and signal
Source number is metWherein L is mutual coupling matrix parameter number, and r represents array system azimuth dimension；Its feature
It is, methods described includes：
Step 1: initialization iteration count value n, obtains amplitude phase unbalance error matrix Γ and mutual coupling Matrix C；Calculated according to MUSIC
Method obtains feature decomposition covariance matrixNoise subspace matrix U and estimate of noise subspace matrix
Step 2: definition space is composedWherein a (θ) is steering vector；For kth time
The amplitude phase unbalance error matrix estimate that iteration is obtained；The mutual coupling Matrix Estimation value obtained for kth time iteration；
Step 3: the DOA for scanning for obtaining N number of peak value by MUSIC algorithms in the spatial spectrum estimatesStep
4th, the estimate of the amplitude phase unbalance error matrix of+1 iteration of kth is solved
Step 5: solving the estimate of the mutual coupling error matrix of+1 iteration of kth
Step 6: calculating the cost function J of+1 iteration of kthc, an arbitrarily small thresholding ε ＞ 0 is given, if
N=n+1 is then made, and returns to step 2 and continues iteration；If
Iterated conditional has then been met, circulation is exited, it is at this moment resultingWithWaiting of as needing is estimated
Count parameter.
2. the algorithm according to claim 1 that a variety of array errors are corrected in Mutual coupling, it is characterised in that step
Rapid four are specially：
Keep the angle of DOA estimationsWith mutual coupling matrixIt is constant, calculation formula
K is current iteration count value；The vector being made up of amplitude phase unbalance error matrix Γ diagonal elements is δ=[Γ11,Γ22,,
ΓMM], Q1(n)=diag { a (θn)}；
Use expression formulaThe estimate that formula obtains the amplitude phase unbalance matrix of kth time iteration is brought into as δWhereinW=[1,0 ..., 0].
3. the algorithm according to claim 2 that a variety of array errors are corrected in Mutual coupling, it is characterised in that step
Rapid five are specially：
Keep DOA estimatesWith the estimate of amplitude phase unbalance errorIt is constant, calculation formula
K is current iteration count value；Use expression formula Formula is brought into as c initial value to obtainEstimated result, then by expression formula ci=C1i(i=
1,2 ..., L) obtain mutual coupling matrixEstimate.
4. the algorithm as claimed in any of claims 1 to 3 that a variety of array errors are corrected in Mutual coupling,
Characterized in that, in step 6, arbitrarily small thresholding ε=10-10。
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| CN107843881A (en) * | 2017-10-24 | 2018-03-27 | 中国人民解放军空军工程大学 | Radar angular estimates and error calibration method |
| CN108375752A (en) * | 2018-02-05 | 2018-08-07 | 中国人民解放军战略支援部队信息工程大学 | Amplitude phase error single radiation source direction-finding method based on full angle search |
| CN108469599A (en) * | 2018-02-28 | 2018-08-31 | 哈尔滨工程大学 | A kind of acoustic vector sensors amplitude weighting MUSIC direction-finding methods |
| CN108680891A (en) * | 2018-01-05 | 2018-10-19 | 大连大学 | The DOA estimation method of mutual coupling effect is considered under the conditions of non-uniform noise |
| CN108828506A (en) * | 2018-06-27 | 2018-11-16 | 中国电子科技集团公司第二十九研究所 | A kind of electromagnetic target Estimation of Spatial Spectrum method based on sparse decomposition |
| CN109212467A (en) * | 2018-09-17 | 2019-01-15 | 燕山大学 | Deficient standing wave arrival direction estimating method under amplitude phase error based on partial collimation nested array |
| CN109239649A (en) * | 2018-04-04 | 2019-01-18 | 唐晓杰 | A kind of relatively prime array DOA under the conditions of array error estimates new method |
| CN109270484A (en) * | 2018-07-24 | 2019-01-25 | 南京航空航天大学 | A kind of multiple source DOA estimation method based on movement integrated array |
| CN109407047A (en) * | 2018-09-19 | 2019-03-01 | 江苏大学 | A kind of amplitude phase error calibration and Wave arrival direction estimating method based on order damage rooting |
| CN109633527A (en) * | 2018-12-14 | 2019-04-16 | 南京理工大学 | Inlaid flat microphone array sound source direction-finding method based on low-rank and geometrical constraint |
| CN109725298A (en) * | 2019-01-10 | 2019-05-07 | 江苏大学 | A kind of array manifold based on order damage rooting calibrates for error and Wave arrival direction estimating method |
| CN110086520A (en) * | 2019-03-29 | 2019-08-02 | 中国人民解放军火箭军工程大学 | A kind of mutual coupling error calibration method of uniform octagon battle array |
| CN111736110A (en) * | 2020-07-14 | 2020-10-02 | 中国石油大学(华东) | DOA estimation method based on improved Gauss-Newton algorithm |
| CN112816938A (en) * | 2020-12-25 | 2021-05-18 | 中国船舶重工集团有限公司第七一0研究所 | Active sonar pulse signal direction finding method |
| CN112986935A (en) * | 2021-02-24 | 2021-06-18 | 湖北中南鹏力海洋探测系统工程有限公司 | Multi-element array channel passive calibration method based on landform conformal arrangement |
| CN114624665A (en) * | 2022-03-24 | 2022-06-14 | 电子科技大学 | Mutual coupling error DOA self-correction method based on dynamic parameter iterative optimization |
| CN115372892A (en) * | 2022-08-10 | 2022-11-22 | 中国人民解放军战略支援部队信息工程大学 | Array amplitude and phase error correction method for cooperative multi-array |
| CN115494447A (en) * | 2022-09-21 | 2022-12-20 | 哈尔滨理工大学 | Mutual coupling error and amplitude-phase error-based combined calibration DOA estimation method |
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| CN107843881B (en) * | 2017-10-24 | 2020-04-03 | 中国人民解放军空军工程大学 | Radar angle estimation and error correction method |
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| CN108680891A (en) * | 2018-01-05 | 2018-10-19 | 大连大学 | The DOA estimation method of mutual coupling effect is considered under the conditions of non-uniform noise |
| CN108680891B (en) * | 2018-01-05 | 2022-02-22 | 大连大学 | DOA estimation method considering mutual coupling effect under non-uniform noise condition |
| CN108375752A (en) * | 2018-02-05 | 2018-08-07 | 中国人民解放军战略支援部队信息工程大学 | Amplitude phase error single radiation source direction-finding method based on full angle search |
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| CN109407047A (en) * | 2018-09-19 | 2019-03-01 | 江苏大学 | A kind of amplitude phase error calibration and Wave arrival direction estimating method based on order damage rooting |
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| CN110086520B (en) * | 2019-03-29 | 2020-07-21 | 中国人民解放军火箭军工程大学 | Mutual coupling error calibration method for uniform octagonal array |
| CN110086520A (en) * | 2019-03-29 | 2019-08-02 | 中国人民解放军火箭军工程大学 | A kind of mutual coupling error calibration method of uniform octagon battle array |
| CN111736110A (en) * | 2020-07-14 | 2020-10-02 | 中国石油大学(华东) | DOA estimation method based on improved Gauss-Newton algorithm |
| CN112816938A (en) * | 2020-12-25 | 2021-05-18 | 中国船舶重工集团有限公司第七一0研究所 | Active sonar pulse signal direction finding method |
| CN112816938B (en) * | 2020-12-25 | 2022-08-09 | 中国船舶重工集团有限公司第七一0研究所 | Active sonar pulse signal direction finding method |
| CN112986935A (en) * | 2021-02-24 | 2021-06-18 | 湖北中南鹏力海洋探测系统工程有限公司 | Multi-element array channel passive calibration method based on landform conformal arrangement |
| CN112986935B (en) * | 2021-02-24 | 2022-12-20 | 湖北中南鹏力海洋探测系统工程有限公司 | Multi-element array channel passive calibration method based on landform conformal arrangement |
| CN114624665A (en) * | 2022-03-24 | 2022-06-14 | 电子科技大学 | Mutual coupling error DOA self-correction method based on dynamic parameter iterative optimization |
| CN114624665B (en) * | 2022-03-24 | 2023-11-07 | 电子科技大学 | Mutual coupling error DOA self-correction method based on dynamic parameter iterative optimization |
| CN115372892A (en) * | 2022-08-10 | 2022-11-22 | 中国人民解放军战略支援部队信息工程大学 | Array amplitude and phase error correction method for cooperative multi-array |
| CN115494447A (en) * | 2022-09-21 | 2022-12-20 | 哈尔滨理工大学 | Mutual coupling error and amplitude-phase error-based combined calibration DOA estimation method |
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