CN102749514B - 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 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, as determining of power-factor angle in the calculating at alternating circuit middle impedance angle, electric energy metrical etc.

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

Existing method for measuring phase difference is more, and mostly there is certain denoising effect and anti-noise jamming ability, but these methods often can only have good anti-interference to one or more noises, cannot tackle the simultaneous situation of multiple noise under complex environment, applicability is poor.The method of traditional dependence analog device, as 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 is gradually to digitizing future development, and the advantage of digitized measurement is that hardware cost is low, strong adaptability, for different measuring objects, only need the algorithm of reprogramming, measuring accuracy is better than analog measurement.

Phase differential digital measuring method can be divided into hardware method and the large class of Software Method two by the approach of realization.Hardware method is measured the cycle of two signals and the mistiming of initial phase by hardware circuit, will be transformed to phase differential the mistiming show by software, because its noise removal function is born by hardware components completely, cannot tackle measurement environment complicated and changeable.Software Method mainly comprises frequency domain technique and time domain disposal route two classes, and wherein first frequency domain technique converts the signal into frequency domain, then according to the spectral characteristic of signal, signal is processed, as DFT method.The method is lower to the requirement of signal to noise ratio (S/N ratio), and multiple noise is had to certain antijamming capability, but the method need to be implemented to sample the sampling of strict complete cycle, otherwise can cause spectral leakage and fence effect, and finally causes larger measuring error.Time domain disposal route is all to carry out in time domain to the processing of signal, its essence is that the phase differential of the sinusoidal signal of two same frequencys can characterize with the mistiming of their corresponding zero crossings, its great advantage is that signal processing method is simple, directly perceived, physical significance is obvious, is easy to realize with hardware, and some algorithm is without the sampling that requires complete cycle, shortcoming is that these class methods are only suitable for processing the situation that signal to noise ratio (S/N ratio) is 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 defect: require to measure sample and have higher signal to noise ratio (S/N ratio), applicability is poor, is difficult to meet the measurement requirement under complex environment; The accuracy of measuring too relies on the length of measuring sample, and is difficult to 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 measuring the requirement of sample, improve the accuracy of measuring.

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

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

Step 2: to observation signal matrix X (n) operation one minor sort without iterative SOBI algorithm, obtain separation matrix W ₁;

Step 3: by W ₁as separation matrix initial value, to a FastICA algorithm of observation signal matrix X (n) operation, obtain hybrid matrix A and source Component Matrices S (n);

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

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

From technique scheme, can find out, 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 avoid the interference of the multiple noises such as zero point drift, temperature drift, harmonic wave, ringing effect, white noise, and accuracy of measurement is high, applied widely.

2, the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention, adopt sequence without iterative SOBI Algorithm for Solving separation matrix initial value, solution procedure is simple, computing velocity is fast.

3, the same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention, by 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, to the initial phase of measured signal without specific (special) requirements, and without integer-period sampled.

Accompanying drawing explanation

For further illustrating 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 rear, 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) of the same-frequency signal phase difference measuring method structure based on 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, is (b) standard signal, is (c) 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 by sine and cosine component the measured signal composition obtaining.

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 comprised 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 respectively the signal that the standard signal of these two different initial phases obtains; 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), without specific (special) requirements, can be arbitrary value, and without integer-period sampled, sampling time and sampling interval are within the specific limits.One group of reference parameter measuring 50HZ sinusoidal signal phase differential is: sampling interval 50 μ s, sampling time t >=0.4s;

The putting in order without specific (special) requirements of three signals that forms observation signal matrix X (n), makes measured signal x (n) be positioned at the l of observation signal matrix X (n) capable, and l can be { the Arbitrary Digit in 1,2,3}; In observation signal matrix X (n), two signal amplitudes except measured signal x (n) are similar and different;

Step 102: to observation signal matrix X (n) operation one minor sort without iterative SOBI algorithm, obtain separation matrix W ₁, wherein without iterative SOBI algorithm, 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), the length of neglecting greatly observation signal matrix X (n) of N and determining wherein, the sample that is 8K for sampling number, 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 _xisue for peace and carry out Eigenvalues Decomposition, 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 eigenvectors matrix, and Λ is eigenvalue matrix, eigenvalue λ ₁, λ ₂, λ ₃by ascending order, arrange;

Step 4a: press following formula solution matrix L:

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

Now, the pseudoinverse B of matrix L and B ⁺meet following relation:

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

Step 5a: choose at random k ∈ 1,2 ..., N}, to L ^tr _xkl carries out Eigenvalues 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: be calculated as follows separation matrix:

W ₁＝LT

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

W ₁≈L

Now, SOBI is as a kind of blind source separation algorithm, and separation matrix adopts the accuracy of its signal separation of approximate form to decline to some extent, but because the object of SOBI is in order to provide certain priori, separation matrix W to FastICA algorithm ₁only need provide a convergence direction roughly, therefore this simplification is processed whole accuracy of measurement impact of the present invention little;

Step 103: by W ₁as separation matrix initial value, to a FastICA algorithm of observation signal matrix X (n) operation, obtain hybrid matrix A and source Component Matrices S (n), this source Component Matrices S (n) is comprised of 3 source components, 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, judges that sinusoidal component sin (n) and cosine component cos (n) are positioned at the i of 3 dimension source Component Matrices S (n) capable capable with j by the difference of each source component frequency relatively;

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

x′(n)＝a _lis _i+a _lis _j

A in formula _lithe element that represents the capable i row of hybrid matrix A l, a _ljthe element that represents the capable j row of hybrid matrix A l, s _i, s _jthe i of expression source Component Matrices S (n) capable with j row vector;

Step 105: compare measured signal x ' (n) and the phase differential of standard signal, before phase differential relatively, can to x ', (n) carry out smoothing processing, can adopt the mode of matching, while comparing phase differential, can adopt zero-crossing method, also can adopt the measuring methods such as fixed phase drift method.

Example

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 of noise and standard sine signal have been carried out to phase difference measurement experiment.Experiment sample as shown in Figure 2, wherein (a) is noise signal, (b) be 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, sampling interval 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 seen as the measuring error of the inventive method.

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

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

(2) 4 observation signal matrixes obtained above are solved respectively to autocorrelation matrix separately, obtain 4 autocorrelation matrix R _x1, R _x2, R _x3, R _x4;

(3) 4 autocorrelation matrixes summation obtained above is 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 to Eigenvalues 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) 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 Eigenvalues 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) solve 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 by matrix L and W ₁separation matrix initial value as FastICA algorithm has carried out separation to mixing credit matrix X (n), and has obtained identical experimental result, and the hybrid matrix obtaining is:

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

As shown in Figure 4, wherein (a2) is noise component to three source components that obtain, (b2) with (c2) be sine and cosine component, now noise component is positioned at the 1st row of source Component Matrices, first noise component is separated; According to formula x ' (n)=a _lis _i+ a _lis _jto (b2) with (c2) synthesize and obtain tested sinusoidal signal as shown in (d2), l=1 now; I=2, j=3; Relatively the phase differential of the signal (b) in (d2) and Fig. 2 is-0.0018 °, the one-shot measurement time that adopts 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 proof a kind of same-frequency signal phase difference measuring method based on SOBI and FastICA provided by the invention has the advantages such as accuracy of measurement is high, computing velocity fast, anti-noise jamming ability is strong.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (5)

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: to observation signal matrix X (n) operation one minor sort without iterative SOBI algorithm, obtain separation matrix W ₁;

Step 3: by W ₁as separation matrix initial value, to a FastICA algorithm of observation signal matrix X (n) operation, obtain hybrid matrix A and source Component Matrices S (n), wherein to observation signal matrix X (n) operation one minor sort without iterative SOBI algorithm, obtain separation matrix W ₁, this separation matrix W ₁can adopt following approximate form:

W ₁≈L；

To the step without iterative SOBI algorithm of observation signal matrix X (n) operation one minor sort, be wherein:

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 _xisue for peace and carry out Eigenvalues Decomposition, expression formula is:

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

Eigenvalue λ wherein ₁, λ ₂, λ ₃by ascending order, arrange, Λ is eigenvalue matrix, and Q is eigenvectors matrix:

Step 4a: press following formula solution matrix L:

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

Step 5a: choose at random k ∈ 1,2 ..., N}, to L ^tr _xkl carries out Eigenvalues Decomposition:

L ^TR _XkL＝TD _kT ^T

Step 6a: be calculated as follows separation matrix:

W ₁＝LT；

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

Step 5: compare measured signal x ' (n) and the phase differential of standard signal, complete 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 comprised of three signals, one is measured signal, two other signal is the standard signal of artificial two different initial phases that produce, or measured signal deducts respectively the signal that the standard signal of these two different initial phases obtains.

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 Digit in 1,2,3.

4. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 1, wherein to a FastICA algorithm of observation signal matrix X (n) operation, obtain hybrid matrix A and source Component Matrices S (n), this source Component Matrices S (n) is comprised of 3 source components, 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, judges that sinusoidal component sin (n) and cosine component cos (n) are positioned at the i of 3 dimension source Component Matrices S (n) capable capable with j by the difference of each source component frequency relatively.

5. the same-frequency signal phase difference measuring method based on SOBI and FastICA as claimed in claim 4, wherein according to hybrid matrix A and source Component Matrices S (n), synthesize measured signal composition x ' (n), this measured signal x ' computing formula (n) is:

x′(n)＝a _lis _i+a _ljs _j

A in formula _lithe element that represents the capable i row of hybrid matrix A l, a _ljthe element that represents the capable j row of hybrid matrix A l, s _i, s _jthe i of expression source Component Matrices S (n) capable with j row vector.