CN105044660A - Rapid correction method of array channel inconsistency error - Google Patents

Abstract

The invention discloses a rapid correction method of an array channel inconsistency error. A single correction source is used to correct an array channel inconsistency error. Simultaneously, an orientation of the correction source and waveform information are used to estimate an array channel inconsistency error parameter. A covariance matrix does not need to be estimated and eigenvalue decomposition does not need to be performed. A small operand is possessed. The method of the invention has the advantages that an orientation of an array source and the waveform information are used to carry out correction; the covariance matrix does not need to be estimated and the eigenvalue decomposition does not need to be performed; the operand is small; amplitude phase parameter estimation performance which is basically the same with that of a characteristic decomposition method is possessed. Calculating complexities of an EACDM algorithm and the characteristic decomposition method are O (3MN) and O (M2N+4M3/3) respectively. The operand of the method is only O (MN).

Description

A kind of array channel inconsistency error method for quickly correcting

Technical field

The present invention relates to Array Signal Processing field, more precisely, is a kind of array error difference between channels error method for quickly correcting.The method can be used for the correction field of the array channel such as radar, sonar inconsistency.

Background technology

In the direction-finding system of reality, production technology, alignment error and platform disturbance etc. make sensor array produce amplitude phase error, sensor position uncertainties and mutual coupling phenomenon, and this is by different for the array steering vector and desirable array steering vector causing reality.In this case, conventional high-resolution DOA algorithm for estimating, such as degradation even lost efficacy by the Measure direction performance of MVDR, MUSIC, ESPRIT and ML scheduling algorithm.Therefore, before use sensor array carries out DOA estimation, the correction work of array error is indispensable.The amplitude caused for array channel inconsistency and phase error, the people such as JungtaiKim mention in " the Blindcalibrationforalineararraywithgainandphaseerrorusin gindependentcomponentanalysis " to deliver for 2010, utilize independent component analysis method (IndependentComponentAnalysis, ICA) amplitude of recoverable array and phase error, this algorithm needs larger calculated amount and requires that correcting information source is non-Gaussian signal.The people such as Liu Aifei mention in " the AneigenstructuremethodforestimatingDOAandsensorgain-phas eerrors " to deliver for 2011, utilize the Hadamard of array output matrix and conjugate matrices thereof to amass and form new covariance matrix, and feature decomposition is carried out to it thus achieves the Combined estimator of amplitude phase error and DOA, this algorithm is without the need to iteration, avoid the local convergence of parameter estimation, but the method requires that number of source need be greater than 2 and not be suitable for linear array.As the preprocessing process of Array Signal Processing, array calibration work should be simple, and have less calculated amount, otherwise will be unfavorable for the subsequent treatment of Array Signal Processing, and therefore, the Fast Correction algorithm of research array error has great importance.

Summary of the invention

The object of the invention is to the Correction Problems solving array channel inconsistency error, a kind of method for quickly correcting of array channel inconsistency error is provided, can pair array difference between channels error corrects fast and effectively.

Specific embodiment of the invention step is as follows:

(1) arrange the far field place that the accurately known calibration source in an orientation is positioned at array to be corrected, then the signal that array receives is:

X(t)＝Γa _s(θ)S _s(t)+N(t)(1)

Wherein, the half-wavelength even linear array of array to be corrected to be array element number be M, X (t)=[x ₁(t), x ₂(t) ..., x _m(t)] ^tfor the data vector of observation is tieed up in M × 1, S _st () for power is calibration source, N (t)=[n ₁(t), n ₂(t) ..., n _m(t)] ^tfor zero mean Gaussian white noise vector is tieed up in M × 1.A (θ _s)=[1, e ^{-j ω}, e ^{-j2 ω}..., e ^{-j (M-1) ω}] ^tfor desirable array manifold steering vector, ω=2 π dsin (θ _s)/λ, for the M × M comprising width phase information ties up diagonal matrix, g _iwith represent gain and the phase place of i-th array element respectively;

(2) obtain orientation and the shape information of calibration source, use following formula to obtain the steering vector that there is amplitude phase error:

$h=E\left[X\left(t\right)S_s^H\left(t\right)\right]/{\left|\right|E\left[X\left(t\right)S_s^H\left(t\right)\right]\left|\right|}_2---\left(2\right)$

In formula, H represents conjugate transpose, || || ₂represent 2-norm;

By formula (1) for people's formula (2), can obtain through deriving:

$h=\frac{\mathrm{\Γ}{a}_s\left(\mathrm{\θ}\right)}{\sqrt{M(g_1^2+g_2^2+...+g_M^2)}}---\left(3\right)$

Formula (3) shows, h and A (θ _s) be directly proportional, and scale-up factor is an amount relevant with array element number and array element gain;

If for the value after h normalization, then can be obtained fom the above equation i-th (i=1,2 ..., M) individual array element Γ _iestimated value:

${\widehat{\mathrm{\Γ}}}_i=\frac{\stackrel{\‾}{h_i}}{a_i\left({\mathrm{\θ}}_s\right)}---\left(4\right)$

In formula, and a _i(θ _s) be respectively vector with a (θ _s) in i-th element;

The estimated value that can be obtained gain and phase place by formula (4) is:

${\hat{g}}_i=\left|{\widehat{\mathrm{\Γ}}}_i\right|;---\left(5\right)$

The gain obtained by formula (5) and (6) and phase estimation value with pair array corrects.

Advantage of the present invention utilizes the orientation in array source and shape information pair array to correct, and without the need to estimate covariance matrix and carry out Eigenvalues Decomposition, operand is less, and has the width phase parameter estimated performance substantially identical with feature decomposition method.The computation complexity of EACDM algorithm and feature decomposition method is respectively O (3MN) and O (M ²n+4M ³/ 3), operand of the present invention is only O (MN).

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention; Fig. 2 is array calibration schematic diagram of the present invention;

Fig. 3 is comparison diagram before and after array calibration of the present invention; Fig. 4 is the change curve one of of the root-mean-square error estimated of array gain of the present invention with signal to noise ratio (S/N ratio); Fig. 5 is the change curve two of root-mean-square error with signal to noise ratio (S/N ratio) of array phase of the present invention estimation;

Fig. 6 is the change curve three of root-mean-square error with signal to noise ratio (S/N ratio) of array phase of the present invention estimation;

Fig. 7 is the change curve four of root-mean-square error with signal to noise ratio (S/N ratio) of array phase of the present invention estimation.

Embodiment

With reference to accompanying drawing 1, it is realization flow figure of the present invention, gives specific embodiment of the invention step in figure:

(1) first arrange the far field place that the accurately known calibration source in an orientation is positioned at array to be corrected, then the signal that array receives is:

X(t)＝Γa _s(θ)S _s(t)+N(t)(1)

Wherein, the half-wavelength even linear array of array to be corrected to be array element number be M, X (t)=[x ₁(t), x ₂(t) ..., x _m(t)] ^tfor the data vector of observation is tieed up in M × 1, S _st () for power is calibration source, N (t)=[n ₁(t), n ₂(t) ..., n _m(t)] ^tfor zero mean Gaussian white noise vector is tieed up in M × 1.A (θ _s)=[1, e ^{-j ω}, e ^{-j2 ω}..., e ^{-j (M-1) ω}] ^tfor desirable array manifold steering vector, ω=2 π dsin (θ _s)/λ, for the M × M comprising width phase information ties up diagonal matrix, g _iwith represent gain and the phase place of i-th array element respectively;

(2) obtain orientation and the shape information of calibration source, use following formula to obtain the steering vector that there is amplitude phase error:

$h=E\left[X\left(t\right)S_s^H\left(t\right)\right]/{\left|\right|E\left[X\left(t\right)S_s^H\left(t\right)\right]\left|\right|}_2---\left(2\right)$

In formula, H represents conjugate transpose, || || ₂represent 2-norm;

By formula (1) for people's formula (2), can obtain through deriving:

$h=\frac{\mathrm{\Γ}{a}_s\left(\mathrm{\θ}\right)}{\sqrt{M(g_1^2+g_2^2+...+g_M^2)}}---\left(3\right)$

Formula (3) shows, h and A (θ _s) be directly proportional, and scale-up factor is an amount relevant with array element number and array element gain;

If for the value after h normalization, then can be obtained fom the above equation i-th (i=1,2 ..., M) individual array element Γ _iestimated value:

${\widehat{\mathrm{\Γ}}}_i=\frac{\stackrel{\‾}{h_i}}{a_i\left({\mathrm{\θ}}_s\right)}---\left(4\right)$

In formula, and a _i(θ _s) be respectively vector with a (θ _s) in i-th element;

The estimated value that can be obtained gain and phase place by formula (4) is:

${\hat{g}}_i=\left|{\widehat{\mathrm{\Γ}}}_i\right|;---\left(5\right)$

The gain obtained by formula (5) and (6) and phase estimation value with pair array corrects.

Effect of the present invention can be further illustrated by following simulation result.

Simulated conditions describes: suppose that a scalar array equidistantly lays along x-axis with d=λ/2, element number of array is 8, and centered by calibration source, frequency is 2000Hz, bandwidth is the narrowband Gaussian signal of 40Hz, orientation is 30 °, if first array element is reference array element, its gain and phase place are respectively g ₁=1 He array gain error is 20% (relative to unity gain), i.e. g _i(i=2,3 ..., 8) and obey stochastic distribution in (0.8,1.2), phase place obey the stochastic distribution in (-1,1) rad.

Fig. 3 represents the Estimation of Spatial Spectrum and enlarged drawing thereof that correct front and back array MUSIC algorithm.Wherein, the incident angle of 3 separate constant power far field narrow band signals is respectively 15 °, 20 ° and 60 °, and signal to noise ratio (S/N ratio) is 20dB, and fast umber of beats is 200.As can be seen from the figure, in uncorrected situation, MUSIC algorithm performance is very poor, can not differentiate the signal that two angles are close, and angle estimation exists larger deviation.Use the MUSIC algorithm after directional correction of the present invention can estimate the accurate orientation of 3 targets exactly.

Fig. 4 and Fig. 5 represents gain and phase parameter are estimated under different signal to noise ratio (S/N ratio) condition the root-mean-square error change curve with fast umber of beats respectively.Wherein, signal to noise ratio (S/N ratio) is 20dB, and transverse axis is fast umber of beats, and from 20, interval 30, changes to 320.As can be seen from the figure, the root-mean-square error of the array gain that estimates of the inventive method and phase place reduces with the increase of fast umber of beats.

Fig. 5 and Fig. 6 represents gain and phase parameter are estimated under different signal to noise ratio (S/N ratio) condition the root-mean-square error change curve with signal to noise ratio (S/N ratio) respectively.Wherein, fast umber of beats is 100, and transverse axis is signal to noise ratio (S/N ratio), and from 0dB, interval 2dB, changes to 20dB.As can be seen from the figure, the root-mean-square error of the array gain that estimates of the inventive method and phase place reduces with the increase of fast umber of beats.

As can be seen from emulation and basin test result, this method effectively can correct the amplitude phase error that array channel inconsistency causes.

Claims (1)

1. an array channel inconsistency error method for quickly correcting, is characterized in that:

(1) single calibration source pair array difference between channels error is used to correct;

(2) utilize the orientation of calibration source and shape information pair array difference between channels error parameter to estimate simultaneously;

(3) without the need to estimate covariance matrix and carry out Eigenvalues Decomposition, there is less operand;

An arrowband calibration source S is placed at the far field place of array _st (), it is θ relative to the orientation of array _s, then array exports and can be expressed as:

X(t)＝Γa _s(θ)S _s(t)+N(t)

Wherein, the half-wavelength even linear array of array to be corrected to be array element number be M, X (t)=[x ₁(t), x ₂(t) ..., x _m(t)] ^tfor the data vector of observation is tieed up in M × 1, N (t)=[n ₁(t), n ₂(t) ..., n _m(t)] ^tfor zero mean Gaussian white noise vector is tieed up in M × 1.A (θ _s)=[1, e ^{-j ω}, e ^{-j2 ω}..., e ^{-j (M-1) ω}] ^tfor desirable array manifold steering vector, ω=2 π dsin (θ _s)/λ, for the M × M comprising width phase information ties up diagonal matrix, g _iwith (i=1,2 ..., M) represent the gain of i-th array element and phase place respectively;

Following formula is used to obtain the steering vector that there is amplitude phase error:

$h=E\left[X\left(t\right)S_s^H\left(t\right)\right]/{\left|\right|E\left[X\left(t\right)S_s^H\left(t\right)\right]\left|\right|}_2$

In formula, H represents conjugate transpose, || || ₂represent 2-norm;

(4) by the derivation to above formula, h and Γ a can be obtained _s(θ) relation is as follows

$h=\frac{\mathrm{\Γ}{a}_s\left(\mathrm{\θ}\right)}{\sqrt{M(g_1^2+g_2^2+...+g_M^2)}}$

(5) establish for the value after h normalization, then can be obtained fom the above equation i-th (i=1,2 ..., M) individual array element Γ _iestimated value:

${\widehat{\mathrm{\Γ}}}_i=\frac{{\stackrel{\‾}{h}}_i}{a_i\left({\mathrm{\θ}}_s\right)}$

Wherein and a _i(θ _s) be respectively vector with a (θ _s) in i-th element;

(6) estimated value of gain and phase place is can be obtained fom the above equation:

${\hat{g}}_i=\left|{\widehat{\mathrm{\Γ}}}_i\right|,$

(7) gain obtained by above formula and phase estimation value with pair array corrects.