CN102749514A - Measurement method for phase difference among same-frequency signals based on SOBI (Second Order Blind Identification) and FastICA (fast Independent Component Analysis) - Google Patents

Abstract

The invention relates to a measurement method for phase difference among same-frequency signals based on SOBI (Second Order Blind Identification) and FastICA (fast independent component analysis). The method comprises the following steps: 1. extending a tested signal x(n) into a three-dimensional 3D observation signal matrix X(n); 2. operating the sequenced non-iterative SOBI algorithm for the observation signal matrix X(n) once so as to obtain a separation matrix W1; 3. adopting W1 as an initial value of the separation matrix and operating the FastICA algorithm for the observation signal matrix X(n) once so as to obtain a hybrid matrix A and a source component matrix S(n); 4. synthesizing tested signal content x'(n) according to the hybrid matrix A and the source component matrix S(n); and 5. comparing the tested signal x'(n) with a standard signal so as to obtain a phase difference, thus completing the measurement of the phase difference among the same-frequency signals. The measurement method for the phase difference among the same-frequency signals based on the SOBI and FastICA provided by the invention can lower the requirements of measurement samples and increase the measurement accuracy.

Description

Same-frequency signal phase difference measuring method based on SOBI and FastICA

Technical field

The present invention relates to the signal processing technology field, particularly a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA.

Background technology

The phase difference measurement of same frequency periodic signal all has a wide range of applications in many fields such as signal analysis, parametric test circuit, electrotechnics, industrial automation, Based Intelligent Control, communication and electronic technology, like confirming etc. of power-factor angle in the calculating at alternating circuit middle impedance angle, the electric energy metrical.

In engineering survey, because the complicacy of measuring equipment environment of living in, measured signal often has been applied like this or such noise, as: zero point drift, ringing, burr, temperature drift, harmonic interference, white noise interference etc.These noises can cause the measured signal shape to distort usually, even are submerged in the noise, cause serious difficulty to measurement.Therefore the key that influences Phase Difference Measuring Precision is the noise immunity of measuring method.

Existing method for measuring phase difference is more; And have certain denoising effect and antinoise interference performance mostly; But these methods often can only have better anti-interference to one or more noises, can't tackle the simultaneous situation of multiple noise under the complex environment, and applicability is relatively poor.The method of traditional dependence analog device, like vector method, diode phase demodulation method, pulse counting method etc., measuring system is complicated, needs dedicated devices, and hardware cost is high, poor anti jamming capability.In recent years; Computing machine and Digital Signal Processing make great progress, and phase difference measurement develops to the digitizing direction gradually, and the advantage of digitized measurement is that hardware cost is low, adaptability is strong; Only need the algorithm of reprogramming for different measuring objects, measuring accuracy is superior to analog measurement.

The phase differential digital measuring method can be divided into hardware method and software method two big classes by the realization approach.The hardware method is measured the cycle of two signals and the mistiming of initial phase through hardware circuit, will be transformed to phase differential the mistiming by software and show, because its noise removal function is born by hardware components fully, can't tackle measurement environment complicated and changeable.The software method mainly comprises two types of frequency domain technique and time domain disposal routes, and wherein frequency domain technique at first converts the signal into frequency domain, according to the spectral characteristic of signal signal is handled then, like the DFT method.This method is lower to the requirement of signal to noise ratio (S/N ratio), and multiple noise is had certain anti-interference capability, but this method need be implemented the sampling of strict complete cycle to sample, otherwise can cause spectral leakage and fence effect, and finally causes bigger measuring error.The time domain disposal route all is in time domain, to carry out to Signal Processing; Its essence is that the phase differential of the sinusoidal signal of two same frequencys can characterize with the mistiming of their corresponding zero passage points; Its great advantage is that signal processing method is simple, directly perceived, physical significance obviously, be easy to realize that and the part algorithm need not to require the sampling of complete cycle with hardware, shortcoming is that these class methods only are fit to handle the signal to noise ratio (S/N ratio) condition with higher; Poor anti jamming capability, and accuracy of measurement relies on the length of measuring sample.

In sum, prior art sinusoidal signal method for measuring phase difference has following defective: require to measure sample and have higher signal to noise ratio (S/N ratio), applicability is relatively poor, is difficult to satisfy the measurement requirement under the complex environment; The accuracy of measuring too relies on the length of measuring sample, and is difficult to the harmonic carcellation interference, and measuring speed is slow.

Summary of the invention

For solving above-mentioned one or more problems, the invention provides a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA, to reduce, improve the accuracy of measuring to measuring the requirement of sample.

The present invention provides a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA, comprises the steps:

Step 1: measured signal x (n) is extended to 3 dimension observation signal matrix X (n);

Step 2: the no iterative SOBI algorithm to observation signal matrix X (n) operation one minor sort obtains separation matrix W ₁

Step 3: with W ₁As the separation matrix initial value,, obtain hybrid matrix A and source component matrix S (n) to FastICA algorithm of observation signal matrix X (n) operation;

Step 4: synthesize measured signal composition x ' (n) according to hybrid matrix A and source component matrix S (n);

Step 5: relatively measured signal x ' (n) with the phase differential of standard signal, accomplish same-frequency signal phase difference and measure.

Can find out that from technique scheme the present invention has following technique effect:

1, the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention can effectively be avoided multiple interference of noise such as zero point drift, temperature drift, harmonic wave, ringing effect, white noise, and accuracy of measurement is high, and is applied widely.

2, the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention adopts the no iterative SOBI algorithm of ordering to find the solution the separation matrix initial value, and solution procedure is simple, and computing velocity is fast.

3, the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention through changing the frequency of standard signal, can extract and measure the different frequency composition of measured signal.

4, the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention does not have specific (special) requirements to the initial phase of measured signal, and need not integer-period sampled.

Description of drawings

For further specifying technology contents of the present invention, below in conjunction with accompanying drawing and case study on implementation to the detailed description of the invention as after, wherein:

Fig. 1: the same-frequency signal phase difference measuring method process flow diagram based on SOBI and FastICA provided by the invention;

Fig. 2: the observation signal matrix X (n) that constructs based on the same-frequency signal phase difference measuring method of SOBI and FastICA provided by the invention;

Fig. 3: the experiment sample of the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention, wherein (a) is noise signal, (b) is standard signal, (c) is measured signal;

Fig. 4: the experimental result of the same-frequency signal phase difference measuring method one-shot measurement based on SOBI and FastICA provided by the invention; Wherein (a) is noise component; (b) with (c) be sine and cosine component, (d) for synthesizing the measured signal composition that obtains through sine and cosine component.

Embodiment

As shown in Figure 1, a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention comprises the steps:

Step 101: measured signal x (n) is extended to 3 dimension observation signal matrix X (n); This observation signal matrix X (n) is made up of three signals; One is measured signal x (n); Two other signal is the standard signal of artificial two different initial phases that produce, or x (n) deducts the signal that the standard signal of these two different initial phases obtains respectively; The single frequency sinusoidal signal that measured signal x (n) disturbs for additive noise, this sinusoidal signal frequency is identical with standard signal;

The initial phase of measured signal x (n) does not have specific (special) requirements, can be arbitrary value, and need not integer-period sampledly, and sampling time and SI get final product within the specific limits.One group of reference parameter measuring 50HZ sinusoidal signal phase differential is: SIs 50 μ s, sampling time t >=0.4s;

Form the no specific (special) requirements that puts in order of three signals of observation signal matrix X (n), it is capable to make measured signal x (n) be positioned at the l of observation signal matrix X (n), then l can be 1,2, the arbitrary number among the 3}; Among the observation signal matrix X (n), two signal amplitudes except that measured signal x (n) are similar and different;

Step 102: the no iterative SOBI algorithm to observation signal matrix X (n) operation one minor sort obtains separation matrix W ₁, no iterative SOBI algorithm wherein, embodiment is:

Step 1a: observation signal matrix X (n) is carried out sample process or carries out staging treating by sequence number, obtain N 3 dimension observation signal matrix X ₁(n), X ₂(n) ..., X _N(n), wherein the length of neglecting observation signal matrix X (n) greatly of N and deciding is the sample of 8K for sampling number, and N desirable 4～8;

Step 2a: to observation signal matrix X _i(n), i=1,2 ..., N calculates autocorrelation matrix R separately _Xi, i=1,2 ..., N;

Step 3a: to R _XiSummation is also carried out characteristic value decomposition, and expression formula is:

$B=\underset{i}{\mathrm{\Σ}}{R}_{\mathrm{Xi}}={\mathrm{Q\ΛQ}}^T=\mathrm{Qdiag}({\mathrm{\λ}}_1,{\mathrm{\λ}}_2,{\mathrm{\λ}}_3)Q^T$

Wherein Q is an eigenvectors matrix, and Λ is an eigenvalue matrix, eigenvalue ₁, λ ₂, λ ₃Arrange by ascending order;

Step 4a: find the solution matrix L by following formula:

$L=\mathrm{Qdiag}(1/\sqrt{{\mathrm{\λ}}_1},1/\sqrt{{\mathrm{\λ}}_2},1/\sqrt{{\mathrm{\λ}}_3})$

At this moment, the pseudoinverse B of matrix L and B ⁺Satisfy following relation:

$B^{+}={\left[\underset{i}{\mathrm{\Σ}}{R}_{\mathrm{Xi}}\right]}^{+}={\mathrm{LL}}^T$

Step 5a: picked at random k ∈ 1,2 ..., N} is to L ^TR _XkL carries out characteristic value decomposition:

L ^TR _XkL＝TD _kT ^T

Wherein, D _kBe respectively L with T ^TR _XkThe eigenvalue matrix of L and eigenvectors matrix;

Step 6a: calculate separation matrix by following formula:

W ₁＝LT

Here, this algorithm can also adopt reduced form, and promptly step 5 and step 6 can be omitted, and obtains separation matrix W ₁Approximate expression:

W ₁≈L

At this moment, SOBI is as a kind of blind source separation algorithm, and separation matrix adopts the accuracy of its Signal Separation of approximate form to descend to some extent, but because the purpose of SOBI provides certain priori, separation matrix W in order to give the FastICA algorithm ₁Only need provide a convergence direction roughly and get final product, therefore this simplification is handled whole accuracy of measurement influence of the present invention little;

Step 103: with W ₁As the separation matrix initial value, to FastICA algorithm of observation signal matrix X (n) operation, obtain hybrid matrix A and source component matrix S (n), this source component matrix S (n) is made up of 3 source components, is respectively: noise component I _g(n), sinusoidal component sin (n) and cosine component cos (n), wherein sinusoidal component sin (n) has identical frequency with cosine component cos (n), and identical with the frequency of standard signal, with noise component I _g(n) frequency is different, and it is capable capable with j to judge that through the difference of each source component frequency relatively sinusoidal component sin (n) and cosine component cos (n) are positioned at the i of 3 dimension source component matrix S (n);

Step 104: synthesize measured signal composition x ' (n) according to hybrid matrix A and source component matrix S (n), this measured signal x ' computing formula (n) is:

x′(n)＝a _lis _i+a _lis _j

A in the formula _LiThe element of the capable i row of expression hybrid matrix A l, a _LjThe element of the capable j row of expression hybrid matrix A l, s _i, s _jThe i of expression source component matrix S (n) is capable capable vectorial with j;

Step 105: relatively measured signal x ' (n) with the phase differential of standard signal; Before phase differential relatively, can (n) carry out smoothing processing to x '; Can adopt the mode of match, can adopt zero-crossing method when comparing phase differential, also can adopt measuring methods such as fixed phase drift method.

Instance

For verifying the measurement effect of a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention, the sinusoidal signal and the standard sine signal of noise carried out the phase difference measurement experiment.Experiment sample is as shown in Figure 2, and wherein (a) is noise signal, (b) is standard signal; (c) be measured signal, it is (a) and linear hybrid (b), and signal to noise ratio (S/N ratio) is 6.07dB; Sample length is 8K; SI is 50 μ s, and experiment adopts the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention to come comparison signal (b) and phase differential (c), and this measurement result can be regarded as the measuring error of the inventive method.

According to measuring method provided by the invention; At first measured signal (c) is extended to observation signal matrix X (n); As shown in Figure 3; Wherein (a1) is measured signal, is artificial two standard signals that initial phase is different that produce with (c1) (b1), here select for use be that initial phase is 0 sinusoidal signal and cosine signal; Next observation signal matrix X (n) is implemented the SOBI algorithm, is specially:

(1) chooses N=4, observation signal matrix X (n) is divided into 4 sections, obtain 4 observation signal matrixes;

(2) above-mentioned 4 observation signal matrixes that obtain are found the solution autocorrelation matrix separately respectively, obtain 4 autocorrelation matrix R _X1, R _X2, R _X3, R _X4

(3) above-mentioned 4 autocorrelation matrix summations that obtain are obtained:

$B=\underset{i}{\mathrm{\Σ}}{R}_{\mathrm{Xi}}=\left\{\begin{array}{ccc}2.1992& 0.3552& -1.3135\\ 0.3552& 0.9402& 0.0033\\ -1.3135& 0.0033& 0.9497\end{array}\right\}\×{10}^4$

B is carried out characteristic value decomposition to be obtained:

B＝QΛQ ^T＝Qdiag(λ ₁，λ ₂，λ ₃)Q ^T

Wherein:

$Q=\left\{\begin{array}{ccc}-0.5395& 0.0039& -0.8420\\ 0.2247& 0.9644& -0.1395\\ -0.8115& 0.2645& 0.5211\end{array}\right\},$ $\mathrm{\Λ}=\left\{\begin{array}{ccc}0.0755& 0& 0\\ 0& 0.9425& 0\\ 0& 0& 3.0710\end{array}\right\}\×{10}^4;$

(4) find the solution matrix L:

$L=\mathrm{Qdiag}(1/\sqrt{{\mathrm{\λ}}_1},1/\sqrt{{\mathrm{\λ}}_2},1/\sqrt{{\mathrm{\λ}}_3})=\left\{\begin{array}{ccc}-0.0196& 0.0000& -0.0048\\ 0.0082& 0.0099& -0.0008\\ -0.0295& 0.0027& 0.0030\end{array}\right\}$

(5) make k=1, to L ^TR _XkL carries out characteristic value decomposition and obtains:

L ^TR _XkL＝TD _kT ^T

Wherein:

$T=\left\{\begin{array}{ccc}-0.8566& -0.1272& -0.5000\\ -0.1240& -0.9915& -0.0397\\ -0.5008& 0.0280& -0.8651\end{array}\right\},$ $D_k=\left\{\begin{array}{ccc}-0.0173& 0& 0\\ 0& 0.0607& 0\\ 0& 0& 0.1087\end{array}\right\};$

(6) find the solution the separation matrix initial value:

$W_1=\mathrm{LT}=\left\{\begin{array}{ccc}0.0144& 0.0024& 0.0140\\ -0.0086& 0.0088& -0.0038\\ 0.0264& 0.0065& 0.0121\end{array}\right\}$

Experiment is respectively with matrix L and W ₁Separation matrix initial value as the FastICA algorithm separates mixing credit matrix X (n), and has obtained identical experimental result, and the hybrid matrix that obtains is:

$A=\left\{\begin{array}{ccc}-13.0633& -14.2099& 32.3842\\ -0.3684& 19.2771& 15.4521\\ 0.3685& 15.5461& -19.3020\end{array}\right\},$

Three source components that obtain are as shown in Figure 4, and wherein (a2) is noise component, (b2) with (c2) be sine and cosine component, noise component was positioned at the source and divided the 1st capable of moment matrix this moment, promptly noise component at first is separated; According to formula x ' (n)=a _Lis _i+ a _Lis _j(b2) obtained tested sinusoidal signal shown in (d2) with (c2) synthesize, at this moment l=1; I=2, j=3; Relatively the phase differential of the signal (b) among (d2) and Fig. 2 is-0.0018 °; Adopting the one-shot measurement time of a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention is 0.45 second (CPU i3 530; Matlab 7.4, Windows XP SP3 platform).This case study on implementation proves that a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention has advantages such as accuracy of measurement height, computing velocity is fast, the antinoise interference performance is strong.

Above-described specific embodiment; The object of the invention, technical scheme and beneficial effect have been carried out further explain, and institute it should be understood that the above is merely specific embodiment of the present invention; Be not limited to the present invention; All within spirit of the present invention and principle, any modification of being made, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. the same-frequency signal phase difference measuring method based on SOBI and FastICA comprises the steps:

Step 1: measured signal x (n) is extended to 3 dimension observation signal matrix X (n);

Step 2: the no iterative SOBI algorithm to observation signal matrix X (n) operation one minor sort obtains separation matrix W ₁

Step 3: with W ₁As the separation matrix initial value,, obtain hybrid matrix A and source component matrix S (n) to FastICA algorithm of observation signal matrix X (n) operation;

Step 4: synthesize measured signal composition x ' (n) according to hybrid matrix A and source component matrix S (n);

Step 5: relatively measured signal x ' (n) with the phase differential of standard signal, accomplish same-frequency signal phase difference and measure.

2. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 1; Wherein measured signal x (n) is extended to 3 dimension observation signal matrix X (n); This observation signal matrix X (n) is made up of three signals; One is measured signal, and two other signal is the standard signal of artificial two different initial phases that produce, or measured signal deducts the signal that the standard signal of these two different initial phases obtains respectively.

3. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 2; Wherein measured signal x (n) is extended to 3 dimension observation signal matrix X (n); The l that measured signal x (n) is positioned at observation signal matrix X (n) is capable, and l is the arbitrary number in 1,2,3.

4. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 1, wherein the step to the no iterative SOBI algorithm of observation signal matrix X (n) operation one minor sort is:

Step 1a: observation signal matrix X (n) is carried out sample process or carries out staging treating by sequence number, obtain N 3 dimension observation signal matrix X ₁(n), X ₂(n) ..., X _N(n);

Step 2a: to observation signal matrix X _i(n), i=1,2 ..., N calculates autocorrelation matrix R _Xi, i=1,2 ..., N;

Step 3a: to R _XiSummation is also carried out characteristic value decomposition, and expression formula is:

$B=\underset{i}{\mathrm{\Σ}}{R}_{\mathrm{Xi}}={\mathrm{Q\ΛQ}}^T=\mathrm{Qdiag}({\mathrm{\λ}}_1,{\mathrm{\λ}}_2,{\mathrm{\λ}}_3)Q^T$

Eigenvalue wherein ₁, λ ₂, λ ₃Arrange by ascending order, Λ is an eigenvalue matrix, and Q is an eigenvectors matrix;

Step 4a: find the solution matrix L by following formula:

$L=\mathrm{Qdiag}(1/\sqrt{{\mathrm{\λ}}_1},1/\sqrt{{\mathrm{\λ}}_2},1/\sqrt{{\mathrm{\λ}}_3})$

Step 5a: picked at random k ∈ 1,2 ..., N} is to L ^TR _XkL carries out characteristic value decomposition:

L ^TR _XkL＝TD _kT ^T

Step 6a: calculate separation matrix by following formula:

W ₁＝LT。

5. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 4 wherein to the no iterative SOBI algorithm of observation signal matrix X (n) operation one minor sort, obtains separation matrix W ₁, this separation matrix W ₁Can adopt following approximate form:

W ₁≈L。

6. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 1; Wherein to FastICA algorithm of observation signal matrix X (n) operation; Obtain hybrid matrix A and source component matrix S (n); This source component matrix S (n) is made up of 3 source components, is respectively: noise component I _g(n), sinusoidal component sin (n) and cosine component cos (n), wherein sinusoidal component sin (n) has identical frequency with cosine component cos (n), and identical with the frequency of standard signal, with noise component I _g(n) frequency is different, and it is capable capable with j to judge that through the difference of each source component frequency relatively sinusoidal component sin (n) and cosine component cos (n) are positioned at the i of 3 dimension source component matrix S (n).

7. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 6 is wherein synthesized measured signal composition x ' (n) according to hybrid matrix A and source component matrix S (n), and this measured signal x ' computing formula (n) is:

x′(n)＝a _lis _i+a _ljs _j

A in the formula _LiThe element of the capable i row of expression hybrid matrix A l, a _LjThe element of the capable j row of expression hybrid matrix A l, s _i, s _jThe i of expression source component matrix S (n) is capable capable vectorial with j.

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