CN110109052A - Bearing and element position estimation method under the conditions of a kind of sensor position uncertainties - Google Patents
Bearing and element position estimation method under the conditions of a kind of sensor position uncertainties Download PDFInfo
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- CN110109052A CN110109052A CN201910436344.XA CN201910436344A CN110109052A CN 110109052 A CN110109052 A CN 110109052A CN 201910436344 A CN201910436344 A CN 201910436344A CN 110109052 A CN110109052 A CN 110109052A
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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
Abstract
Bearing and element position estimation method the present invention relates to target detection techniques field, under the conditions of especially a kind of sensor position uncertainties.Signal is received by non-linear array, and the signal received is transformed into time-frequency domain；According to distribution of the signal in time-frequency domain is received, the steering vector of each signal source is calculated, according to delay vector of each signal source of phase calculation of each signal source steering vector on each array；According to delay vector of each signal source on each array, the incident angle of each signal source is estimated using the element position that default or the last iteration updates, realizes the direction finding to target；According to delay vector sum incident angle of each signal source on each array and element position relationship, each element position is estimated, the accuracy that this method not will lead to Bearing is reduced as sensor position uncertainties increase, the complexity of calculating is lower, element position is estimated again, more can accurately obtain element position.
Description
Technical field
Bearing and battle array the present invention relates to target detection techniques field, under the conditions of especially a kind of sensor position uncertainties
First location estimation method.
Background technique
Increasingly sophisticated with electromagnetic environment, traditional amplitude-comparison direction finding has been difficult to meet the survey of multiple broadband signals simultaneously
To demand, can not for it is subsequent position, test the speed, detecing receipts and feature extraction etc. strong support is provided.Using array to target
Carrying out direction finding has high-precision, super-resolution and advantages such as multiple target simultaneously.Under conditions of accurately known array manifold, existing survey
The accurate direction finding to target can be achieved to technology.
Such as Chinese patent application publication No. is the patent application document of CN107907855A, discloses a kind of mutual pixel array
It is converted into the DOA estimation method of even linear array, this method constitutes delay set according to any two element position difference and calculates needs
The auto-correlation function value of delay is constructed Toepltz matrix according to auto-correlation function value, is searched based on MUSIC algorithm construction spatial spectrum
Rope function, the estimated value of the DOA looked for when spatial spectrum search vector is consistent with signal guide vector realize the survey of echo signal
To.Aforesaid way is carried out in the case where element position does not have error condition, but in practice, the non-ideal factors such as sensor position uncertainties
Influence, direction finding difficulty realize, existing mode is the two step alternative and iterative algorithms based on linear approximation, but the process employs
The mode of linear approximation is only capable of the processing lesser situation of array error, and with the increase of location error, Measure direction performance can be rapid
Decline.
Summary of the invention
The object of the present invention is to provide a kind of Bearing methods under the conditions of sensor position uncertainties, exist at present to solve
The problem that Bearing when sensor position uncertainties increase is inaccurate, computation complexity is high；The present invention also provides a kind of element positions
Element position estimation method under error condition, be not allowed to solve the Bearing when sensor position uncertainties increase at present,
The high problem of computation complexity.
To achieve the goals above, the present invention provides a kind of Bearing method under the conditions of sensor position uncertainties, the mesh
Mark direction-finding method the following steps are included:
1) signal is received by non-linear array, and the signal received is transformed into time-frequency domain；
2) according to distribution of the signal in time-frequency domain is received, the steering vector of each signal source is calculated, is led according to each signal source
To delay vector of each signal source of phase calculation on each array of vector；
3) the delay vector according to each signal source on each array, the array element updated using default or the last iteration
The incident angle of each signal source of position estimation realizes the direction finding to target.
Beneficial effect is will to receive signal to transform to time-frequency domain, then acquires it using the time-frequency distributions of each signal and prolongs
Slow vector finally estimates the incident angle of each signal source, realization pair using the element position that default or the last iteration updates
The direction finding of target, the accuracy that this method not will lead to Bearing is reduced as sensor position uncertainties increase, and is only led to
Cross time-frequency convert, steering vector calculate, Time-delay Vector calculating Bearing can be realized, the complexity of calculating is lower.
Further, for the accuracy of the delay vector of calculating, the delay vector of each signal source are as follows:
Wherein, K indicates that the sum of signal source, k indicate signal source k, (ta,fa) it is steering vector ak(fa) time-frequency distributions,
angle(ak(fa)) indicate to seek ak(fa) each element phase, unwrap () is used for orrection phase place, X (ta,fa) it is to receive letter
The time-frequency conversion of number vector, X (ta,fa, 1) and it is X (ta,fa) first element.
Further, it in order to be accurately obtained delay vector, when calculating the delay vector of each signal source, first calculates same
A signal source postpones vector at least two single source points, then averages to each single source point delay vector, using mean value as the letter
The delay vector in number source.
Further, for the ease of solving, the incident angle of each signal source are as follows:
Wherein, K indicates that the sum of signal source, k indicate that signal source k, M indicate array number,WithIt respectively indicatesFirst element and second element,Indicate the preset value of the position array element m or the update in the last iteration
Value, For delay of the signal source k on array element m, c indicates the spread speed of signal.
The present invention provides the element position estimation method under the conditions of a kind of sensor position uncertainties, which includes following
Step:
1) signal is received by non-linear array, and the signal received is transformed into time-frequency domain；
2) according to distribution of the signal in time-frequency domain is received, the steering vector of each signal source is calculated, is led according to each signal source
To delay vector of each signal source of phase calculation on each array of vector；
3) the delay vector according to each signal source on each array, the array element updated using default or the last iteration
The incident angle of each signal source of position estimation realizes the direction finding to target；
4) the delay vector sum incident angle according to each signal source on each array and element position relationship, to each array element
It is estimated position.
Beneficial effect is will to receive signal to transform to time-frequency domain, then acquires it using the time-frequency distributions of each signal and prolongs
Slow vector finally estimates the incident angle of each signal source, realization pair using the element position that default or the last iteration updates
The direction finding of target, the accuracy that this method not will lead to Bearing is reduced as sensor position uncertainties increase, and is only led to
Cross time-frequency convert, steering vector calculate, Time-delay Vector calculating Bearing can be realized, the complexity of calculating is lower；And lead to
It crosses and accurately obtains Bearing, then element position is estimated, more can accurately obtain element position.
Further, for the accuracy of the delay vector of calculating, the delay vector of each signal source are as follows:
Wherein, K indicates that the sum of signal source, k indicate signal source k, (ta,fa) it is steering vector ak(fa) time-frequency distributions,
angle(ak(fa)) indicate to seek ak(fa) each element phase, unwrap () is used for orrection phase place, X (ta,fa) it is to receive letter
The time-frequency conversion of number vector, X (ta,fa, 1) and it is X (ta,fa) first element.
Further, it in order to be accurately obtained delay vector, when calculating the delay vector of each signal source, first calculates same
A signal source postpones vector at least two single source points, then averages to each single source point delay vector, using mean value as the letter
The delay vector in number source.
Further, for the ease of solving, the incident angle of each signal source are as follows:
Wherein, K indicates that the sum of signal source, k indicate that signal source k, M indicate array number,WithIt respectively indicatesFirst element and second element,Indicate the position array element m preset value or the last iteration more
New value, For delay of the signal source k on array element m, c indicates the spread speed of signal.
Further, for ease of calculation, the element position of estimation are as follows:
Wherein, H=[H0 T,H1 T,...,HK-1 T]TIndicate weighting matrix,Indicate all signals
Delay vector, χ=[x1,x2,...,xM-1]TWith γ=[y1,y2,...,yM-1]TRespectively indicate the x-axis position of M-1 array element
Vector sum y-axis position vector.
Further, element position is accurately calculated in order to simple, least square method meter is used when calculating element position
It calculates.
Detailed description of the invention
Fig. 1 is the flow chart of the Bearing method under the conditions of a kind of sensor position uncertainties of the invention；
Fig. 2 is the flow chart of the element position estimation method under the conditions of a kind of sensor position uncertainties of the invention；
Fig. 3 is delay vector estimated result figure in Bearing of the invention；
Fig. 4 is the result of variations figure of estimated bias of the invention with the number of iterations.
Specific embodiment
The present invention will be further described in detail with reference to the accompanying drawing.
Direction-finding method embodiment:
The present invention provides a kind of Bearing method under the conditions of sensor position uncertainties, as shown in Figure 1, the Bearing side
Method the following steps are included:
1) signal is received by non-linear array, and the signal received is transformed into time-frequency domain.
Assuming that K broadband signal sk(t) (k=0,1..., K-1) is incident in a non-linear array, and the array is by M
Array element composition, is denoted as x for the reception signal of each array elementm(t) (m=0 ..., M-1).So, under far field condition, signal mode
Type can be expressed as
Wherein, τk,mFor signal sk(t) propagation delay to m array element relative to reference array element (array element 0), nmIt (t) is to be
It unites noise, it is assumed here that it is for white Gaussian noise.
There are when sensor position uncertainties, postpone τk,mFor
Wherein, θkIt is signal sk(t) incident angle, xmAnd ymFor predeterminated position of the m array element in x-axis and y-axis, Δ xm
With Δ ymFor its corresponding location error, i.e. the actual position of array element is (xm+Δxm,ym+Δym), c indicates the propagation speed of signal
Degree, usually takes c=3 × 108m/s。
It is identical as existing algorithm, in order to simplify expression, it is assumed here that signal and array indicate formula (1) in same plane
For vector form
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 receive signal phasor and signal sk(t) reception vector, n (t)=[n0(t),n1(t),...,nM-1
(t)]TNoise vector.
Due to therefore, also needing to array element position there are when sensor position uncertainties, being difficult to acquire accurate DOA estimated value
It sets and is estimated.For a non-linear array, when there are three or three or more differences come to signal be incident on the array, and
When the position of a known array element and the array element are to the direction of another array element, it may be implemented to element position and signal DOA
Estimate simultaneously.
Without loss of generality, it is assumed here that the position of known array element 0 is x0=0, y0=0 and array element 1 y-axis coordinate y1=0.
By formula (2) it is found that delay τk,mWith element position (xm,ym) it is linear relationship.If all τ knownk,m(k=0,1 ... K-1, m
=0,1 ..., M-1), element position directly can be obtained by solving linear equation, be not necessarily to any approximation in the process.
For either signal z (t), its time-frequency distributions can pass through Short Time Fourier Transform (short-time Fourier
Transform, STFT) it acquires
Wherein, g (t) is window function, and choosing g (t) is Hamming window；
Wherein, TmaxIndicate that window is long.
Under the conditions of without making an uproar, STFT transformation is carried out to formula (1), can be obtained
Wherein, Xm(t, f) and Sk(t, f) respectively indicates xm(t) and sk(t) time-frequency distributions.
STFT transformation is carried out to formula (3), can be obtained
X (t, f)=A (f) S (t, f) (7)
Wherein,
By formula (7), signal can will be received by time domain and transforms to time-frequency domain.
2) according to distribution of the signal in time-frequency domain is received, the steering vector of each signal source is calculated, is led according to each signal source
To delay vector of each signal source of phase calculation on each array of vector.
In signal sk(t) time-frequency distributions (ta,fa) on, formula (7) can be reduced to
X(ta,fa)=ak(fa)Sk(ta,fa)(ta,fa)∈Ωk (9)
Wherein, ΩkFor sk(t) single source point set.So, sk(t) in frequency faOn steering vector ak(fa) can pass through
Following formula acquires
Due to x0=0 and y0=0, then there is τk,0=0.Enable ak(fa, 1) and X (ta,fa, 1) and respectively indicate ak(fa) and X (ta,
fa) first element, then ak(fa, 1) and=1 and X (ta,fa, 1) and=Sk(ta,fa) set up.Therefore, formula (10) can transform to
So, postpone vector τk(ta,fa) be
Wherein, angle (ak(fa)) indicate to seek ak(fa) each element phase, unwrap () is used for orrection phase place, when
When phase difference between adjacent element is greater than π, prevents phase from jumping by being superimposed the integral multiple of ± 2 π or ± 2 π, make phase
Range is no longer limited to [- π, π].
For the same signal sk(t) the different single source point (t of twoa1,fa1) and (ta2,fa2), delay vector meets
By formula (11) and formula (12) it is found that under the conditions of without making an uproar, prolonging for corresponding signal can be acquired using a single source point
Slow vector.But under actual noise environment, required delay vector can have certain deviation.Formula (13) shows that solution can be passed through
Delay vector on the multiple single source points of the same signal, then it is averaging, to obtain more accurate estimated result.Therefore,
Final delay can be acquired by following formula
Wherein, DkFor ΩkIn time frequency point number.So far, we have acquired the delay vector of each source signal Also delay of the signal in different array elements has just been obtained
3) the delay vector according to each signal source on each array, the array element updated using default or the last iteration
The incident angle of each signal source of position estimation realizes the direction finding to target.
Utilize delayElement position and signal DOA can pass through one
It is a to be acquired without approximate two steps alternating iteration.
According to the element position that preset or the last iteration updates, DOA is solved.For array element 1 to array element M-1 (battle array
The position of member 0 is accurately known, therefore does not consider array element 0), write formula (2) as vector form
Wherein, ρk=[cos (θk),sin(θk)]TWithIt is the vector of (M-1) × 1.B
For the matrix of (M-1) × 2
Wherein,Indicate the preset value of the position array element m or in the last iteration
Updated value.
Formula (15) are solved using least square method, can be obtained
Due to ρk=[cos (θk),sin(θk)]T, and θk∈ [- π, π], then θkIt can be acquired by following formula
Wherein,WithIt respectively indicatesFirst element and second element.
Estimation method embodiment:
The present invention provides the element position estimation method under the conditions of a kind of sensor position uncertainties, as shown in Fig. 2, the estimation side
Method the following steps are included:
(1) signal is received by non-linear array, and the signal received is transformed into time-frequency domain；
(2) according to distribution of the signal in time-frequency domain is received, the steering vector of each signal source is calculated, is led according to each signal source
To delay vector of each signal source of phase calculation on each array of vector；
(3) the delay vector according to each signal source on each array, the battle array updated using default or the last iteration
The incident angle of first each signal source of position estimation realizes the direction finding to target；
(4) the delay vector sum incident angle according to each signal source on each array and element position relationship, to each battle array
It is estimated first position.
Since step (1) to step (3) has been described in detail in above-mentioned direction-finding method embodiment,
This estimation method embodiment repeats no more.
Using the DOA acquired in step (3), element position is estimated.For array element 1 to array element M-1 and all source signals
s0(t)…sK-1(t), formula (2) is write as vector form
Wherein,Indicate the delay vector of all signals, χ=[x1,x2,...,xM-1]TAnd γ
=[y1,y2,...,yM-1]TRespectively indicate the x-axis position vector and y-axis position vector of M-1 array element.H=[H0 T,H1 T,...,
HK-1 T]TIndicate weighting matrix, HkFor
Also with least square method, can acquire element position χ and γ is
What needs to be explained here is that no matter acquiringValue be it is how many, after each iteration0 will be assigned.Extremely
This, has obtained the updated value of element position.
The step in direction-finding method embodiment and estimation method embodiment is repeated until algorithmic statement, can obtain array element finally
Position and DOA.
Finally, the validity of proposed algorithm can be verified by following emulation experiments.Assuming that the uniform surface that array is 3 × 3
Battle array, three linear FM signal s0、s1、s2The array is incident on from -45 °, 20 °, 55 ° of directions respectively；Wherein, s0It is expectation letter
Number, signal-to-noise ratio 0dB, s1And s2It is interference signal, it is dry to make an uproar than being 20dB.
The frequency range of three is respectively [2.9,3.95] GHz, [3,4] GHz and [3.1,4] GHz, reference frequency selection
fmax=4GHz, presetting adjacent array element spacing is Δ d=0.5 λmin, wherein λminFor highest frequency fmaxCorresponding wavelength, but due to
Sensor position uncertainties, true array element separation delta dj-1,j(j=1,2 ..., 9) it is random in [0.7 Δ d, 1.3 Δ d] range
Value, sample rate 2fmax, number of snapshots 200.
As shown in figure 3, for the comparison diagram of estimation delay vector and true delays vector, it can be seen that the mentioned algorithm of the present invention
The delay vector of source signal can be estimated well.Further, as shown in figure 4, to coming out to estimated bias with the number of iterations
Situation of change, with the increase of the number of iterations, deviation is gradually reduced, and 50 times convergence can be realized in iteration.Finally, source signal comes
To final estimated result be -45.15 °, 19.97 °, 54.37 °.
Specific embodiment of the present invention is presented above, but the present invention is not limited to described embodiment.
The technological means in above-described embodiment is converted by the way of being readily apparent that those skilled in the art, is replaced,
Modification, and play the role of with the present invention in relevant art means it is essentially identical, realization goal of the invention it is also essentially identical,
The technical solution formed in this way is to be finely adjusted to be formed to above-described embodiment, and this technical solution still falls within protection of the invention
In range.
Claims (10)
1. a kind of Bearing method under the conditions of sensor position uncertainties, which is characterized in that the Bearing method includes following
Step:
1) signal is received by non-linear array, and the signal received is transformed into time-frequency domain；
2) according to distribution of the signal in time-frequency domain is received, the steering vector of each signal source is calculated, is oriented to and is sweared according to each signal source
Delay vector of each signal source of the phase calculation of amount on each array；
3) the delay vector according to each signal source on each array, the element position updated using default or the last iteration
It estimates the incident angle of each signal source, realizes the direction finding to target.
2. the Bearing method under the conditions of sensor position uncertainties according to claim 1, which is characterized in that each signal source
Delay vector are as follows:
Wherein, K indicates that the sum of signal source, k indicate signal source k, (ta,fa) it is steering vector ak(fa) time-frequency distributions, angle
(ak(fa)) indicate to seek ak(fa) each element phase, unwrap () is used for orrection phase place, X (ta,fa) it is to receive signal arrow
The time-frequency conversion of amount, X (ta,fa, 1) and it is X (ta,fa) first element.
3. the Bearing method under the conditions of sensor position uncertainties according to claim 1 or 2, which is characterized in that counting
When calculating the delay vector of each signal source, first calculates the same signal source and postpone vector at least two single source points, then to each
Single source point delay vector is averaged, the delay vector using mean value as the signal source.
4. the Bearing method under the conditions of sensor position uncertainties according to claim 1 or 2, which is characterized in that each letter
The incident angle in number source are as follows:
Wherein, K indicates that the sum of signal source, k indicate that signal source k, M indicate array number,WithIt respectively indicates?
One element and second element,Indicate the preset value of the position array element m or the updated value in the last iteration, For delay of the signal source k on array element m, c indicates the spread speed of signal.
5. the element position estimation method under the conditions of a kind of sensor position uncertainties, which is characterized in that the estimation method includes following
Step:
1) signal is received by non-linear array, and the signal received is transformed into time-frequency domain；
2) according to distribution of the signal in time-frequency domain is received, the steering vector of each signal source is calculated, is oriented to and is sweared according to each signal source
Delay vector of each signal source of the phase calculation of amount on each array；
3) the delay vector according to each signal source on each array, the element position updated using default or the last iteration
It estimates the incident angle of each signal source, realizes the direction finding to target；
4) the delay vector sum incident angle according to each signal source on each array and element position relationship, to each element position
It is estimated.
6. the element position estimation method under the conditions of sensor position uncertainties according to claim 5, which is characterized in that each letter
The delay vector in number source are as follows:
Wherein, K indicates that the sum of signal source, k indicate signal source k, (ta,fa) it is steering vector ak(fa) time-frequency distributions, angle
(ak(fa)) indicate to seek ak(fa) each element phase, unwrap () is used for orrection phase place, X (ta,fa) it is to receive signal arrow
The time-frequency conversion of amount, X (ta,fa, 1) and it is X (ta,fa) first element.
7. the element position estimation method under the conditions of sensor position uncertainties according to claim 5 or 6, which is characterized in that
When calculating the delay vector of each signal source, first calculates the same signal source and postpone vector at least two single source points, then
It averages to each single source point delay vector, the delay vector using mean value as the signal source.
8. the element position estimation method under the conditions of sensor position uncertainties according to claim 5 or 6, which is characterized in that
The incident angle of each signal source are as follows:
Wherein, K indicates that the sum of signal source, k indicate that signal source k, M indicate array number,WithIt respectively indicates?
One element and second element,Indicate the preset value of the position array element m or the updated value in the last iteration, For delay of the signal source k on array element m, c indicates the spread speed of signal.
9. the element position estimation method under the conditions of sensor position uncertainties according to claim 8, which is characterized in that estimation
Element position are as follows:
Wherein, H=[H0 T,H1 T,...,HK-1 T]TIndicate weighting matrix,Indicate prolonging for all signals
Slow vector, χ=[x1,x2,...,xM-1]TWith γ=[y1,y2,...,yM-1]TRespectively indicate the x-axis position vector of M-1 array element
With y-axis position vector.
10. the element position estimation method under the conditions of sensor position uncertainties according to claim 9, which is characterized in that
It is calculated when calculating element position using least square method.
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| CN114239251A (en) * | 2021-12-06 | 2022-03-25 | 中国电子科技集团公司第二十九研究所 | Method for evaluating array direction finding precision under near-end multipath condition |
| CN116593965A (en) * | 2023-07-19 | 2023-08-15 | 中国海洋大学 | Horizontal array type estimation method based on far-field opportunity sound source |
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| CN116593965A (en) * | 2023-07-19 | 2023-08-15 | 中国海洋大学 | Horizontal array type estimation method based on far-field opportunity sound source |
| 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 |
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