CN105675983B - The detection of weak harmonic signal and method for reconstructing under a kind of strong Chaotic Background - Google Patents

The detection of weak harmonic signal and method for reconstructing under a kind of strong Chaotic Background Download PDF

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CN105675983B
CN105675983B CN201610032307.9A CN201610032307A CN105675983B CN 105675983 B CN105675983 B CN 105675983B CN 201610032307 A CN201610032307 A CN 201610032307A CN 105675983 B CN105675983 B CN 105675983B
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harmonic signal
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CN105675983A (en
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胡进峰
段杰
谢浩
陈汉文
胡天威
薛长飘
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University of Electronic Science and Technology of China
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Abstract

The invention discloses under a kind of strong Chaotic Background weak harmonic signal detection and method for reconstructing, belong to chaotic signal detection technique field.The present invention obtains the frequencies omega of L different values by the way that the frequency range of the weak harmonic signal in signal to be detected is divided into L aliquotl；To each ωlIt is ω that the autocorrelation matrix for being based respectively on signal to be detected, which calculates and removes frequency,lHarmonic components after autocorrelation matrix, then be based on each frequencies omegalCorresponding signal frequency vector calculates corresponding output Signal to Interference plus Noise Ratio SINR (ωl), take maximum SINR (ωl) corresponding to frequencyFor the frequency of the weak harmonic signal in signal to be detected, and the amplitude and phase of weak harmonic signal can be accurately estimated simultaneously, thus accurately restoration and reconstruction weak harmonic signal.Brought technical effect: implementation of the invention without necessarily referring to sequence, thus can be used for the detection of the harmonic signal under non-homogeneous Chaotic Background；(2) it can detecte the weak harmonic signal under lower Signal to Interference plus Noise Ratio, and have strong noise robustness.

Description

The detection of weak harmonic signal and method for reconstructing under a kind of strong Chaotic Background
Technical field
The invention belongs to chaotic signal detection technique field, in particular to the inspection of weak harmonic signal under non-homogeneous Chaotic Background The algorithm surveyed and rebuild.
Background technique
The research of Testing of Feeble Signals under Chaotic Background has extensive practical meaning in engineering.Studies have shown that many engineerings It is all the Testing of Feeble Signals problem under Chaotic Background in question essence, such as the abnormal signal in electrocardiosignal detects (see document “C.Hamann,R.P.Bartsch,A.Y.Schumann,T.Penzel,S.Havlin, J.W.Kantelhardt.Automated synchrogram analysis applied to heartbeat and Reconstructed Respiration.CHAOS 19,015106 (2009 "), mechanical oscillation fault diagnosis, network public-opinion are pre- It surveys, the weak signal target signal detection in ocean clutter is (see document " J.Guan, N.B.Liu, Y.Huang, Y.He.Fractal characteristic in frequency domain for target detection within sea clutter.IET Radar,Sonar&Navigation.2012 Jun；6 (5): 293-306. ") etc..Therefore, strong Chaotic Background Under Testing of Feeble Signals receive significant attention.
There are two main classes for the method for Testing of Feeble Signals under Chaotic Background at present: first kind method is based on Takens phase space The detection method of reconstruction, such methods are all the features different from the geometry of harmonic signal using chaotic signal in phase space Chaotic Background is rebuild, realizes weak harmonic signal detection.Wherein, document " Xing H Y, Xu W.The neural networks Method for detecting weak signals under chaotic background.2007. [a row letter man of virtue and ability, xuwei Neural network method [J] Acta Physica Sinica of Detection of Weak Signals, 2007,56 (7): 3771-3776. in Chaotic Background] " use mind Chaotic Background signal is reconstructed through network method, to realize the detection and reconstruction of Weak Signal.Second class method is to be based on The detection method of optimal filter is (see document: J.F.Hu, Y.X.Zhang, H.Y.Li, and W.Xia, Harmonic Signal Detection Method from Strong Chaotic Background Based on Optimal Filter.Acta Physica Sinica, 64,220504 (2015)), such methods concentrate on some frequency using harmonic signal energy to be detected The characteristics of, by designing optimal filter, so that filtered gross energy is minimum, while keeping harmonic signal undistorted again, from And realize the detection of weak harmonic signal.
However, the above method has the disadvantage that (1) above method usually requires reference sequences, and in Practical Project, by In the heterogeneity of environment, be generally difficult to obtain stable reference sequences (bibliography " W.Q.Liu, E.Volkov, J.H.Xiao,W.Zou,M.Zhan,J.Z.Yang,Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators.CHAOS 22,033144(2012)")；(2) above method is logical Often it is difficult to accurately recover weak harmonic signal；(3) above method is usually more sensitive to white noise.
Summary of the invention
Goal of the invention of the invention is: in view of the above problems, providing a kind of without necessarily referring to the strong mixed of sequence The detection of weak harmonic signal and method for reconstructing, this method under ignorant background can be used for uniform Chaotic Background, can be used for non-homogeneous The detection of weak harmonic signal and reconstruction under Chaotic Background.This method is guaranteeing that harmonic signal to be detected is distortionless while pressing down as far as possible Strong Chaotic Background interference is made, and can accurately estimate the amplitude and phase of harmonic signal simultaneously.
Weak harmonic signal detection under Chaotic Background includes two aspects, i.e., Testing of Feeble Signals under uniform Chaotic Background and Testing of Feeble Signals under non-homogeneous Chaotic Background.It is existing to study the Testing of Feeble Signals being concentrated mainly under uniform Chaotic Background, And the present invention is under the premise of being suitable for uniform Chaotic Background, moreover it is possible to suitable for the Testing of Feeble Signals under non-homogeneous Chaotic Background.
Assuming that there is two sections of observation sequence x1(n) and x2(n):
Wherein, x1It (n) is sequence to be detected, s (n)=β ejωnIt is weak harmonic signal, β is the multiple width of the weak harmonic signal Degree (including amplitude and phase), ω is the frequency of the weak harmonic signal, and e is the nature truth of a matter, and j is imaginary unit, c1It (n) is strong Chaotic Background signal；x2It (n) is reference sequences, c2It (n) is chaos sequence, N is the length of sequence to be detected, and N ' is reference sequences Length.
Testing of Feeble Signals problem under Chaotic Background then can be described as: from sequence x to be detected1(n) the weak harmonic wave of detection in Signal s (n).
Testing of Feeble Signals under the Chaotic Background of literature research at present usually assumes that Chaotic Background is uniform.
Uniform Chaotic Background refers to the c in formula (1) in sequence to be detected1(n) and reference sequences in c2(n) there is phase Dynamic characteristics together, identical phase space geometry.It, can be according to the c in reference sequences when then detecting weak signal2(n) To estimate and rebuild the Chaotic Background signal c in sequence to be detected1(n), to realize inhibition and the weak harmonic wave letter of Chaotic Background Number detection.
In practical engineering applications, Chaotic Background situation heterogeneous is often faced.Non-homogeneous Chaotic Background refers to C in formula (1) in sequence to be detected1(n) and reference sequences in c2(n) have different dynamic characteristics, different phase spaces several What structure, therefore cannot be according to reference sequences c2(n) estimate the Chaotic Background signal c in sequence to be detected1It (n), can only be direct Weak harmonic signal is directly detected from one section of sequence to be detected.
Weak harmonic signal detection method under a kind of strong Chaotic Background of the invention, comprising the following steps:
Step 1: data processing being done to the sequence to be detected { x (n), n=1,2 ..., N } that length is N, is converted to y (n), i.e., By series arrangement to be detected at Hankel matrix form y (n):
Wherein, L indicates the division number (value of L is determined by the precision detected) to the frequency range of weak harmonic signal, And M=N-L+1, subscript T representing matrix transposition.
Step 2: using [ωlow,ωhigh] indicate the frequency range of weak harmonic signal in signal to be detected, with fixed step sizeFrequency range is divided into L aliquot, obtains the frequencies omega of L different valuesl=ωlow+(l-1)Δω, L=1,2 ..., L.Calculating frequency in the autocorrelation matrix and sequence to be detected of sequence to be detected by y (n) is ωlHarmonic components g(ωl)。
The autocorrelation matrix of sequence to be detectedAre as follows:
Signal intermediate frequency rate to be detected is ωlHarmonic components g (ωl) are as follows:
Wherein, subscript H representing matrix transposition, e are the nature truth of a matter, and j is imaginary unit.
Step 3: calculating frequency is ωlChaotic Background autocorrelation matrix
Step 4: calculating frequency is ωlSignal frequency vector a (ωl):
Step 5: output Signal to Interference plus Noise Ratio SINR (ωl):
Step 6: to the ω of L different valueslSINR (ω corresponding to (l=1,2 ..., L)l), search maximum SINR (ωl), and remember maximum SINR (ωl) corresponding to frequency beI.e. by frequencyAs the weak harmonic signal in signal to be detected Frequency and output, complete weak under background to strong chaos (being suitable under non-homogeneous background, be also applied under homogeneous background) Harmonic signal detection.
Frequency based on the weak harmonic signal in signal to be detected acquired in step (6)It is calculated according to formula (8) weak The complex magnitude of harmonic signal(amplitude and phase comprising the weak harmonic signal).According to the frequency of required harmonic signal, width Degree, phase recovery reconstruct weak harmonic signal.
Calculating frequency isWeak harmonic signal complex magnitude
In conclusion by adopting the above-described technical solution, the beneficial effects of the present invention are:
(1) present invention, can be directly to one section of weak harmonic signal of Sequence Detection to be detected without necessarily referring to sequence；
(2) present invention can detecte the weak harmonic signal under lower Signal to Interference plus Noise Ratio without reference to sequence；
(3) the anti-white noise function admirable of the present invention；
(4) present invention can be with the weak harmonic signal of accurate reconstruction while detecting signal.
Detailed description of the invention
Fig. 1 is the time-domain diagram and spectrogram of sequence to be detected in specific embodiment.
Fig. 2 is the weak harmonic signal detection knot under the uniform Chaotic Background in specific embodiment, without white Gaussian noise Fruit, wherein Fig. 2-a is the testing result of neural network method；Fig. 2-b is the testing result of the method for the present invention；
Fig. 3 is the output Signal to Interference plus Noise Ratio figure in specific embodiment, under difference input Signal to Interference plus Noise Ratio；
Fig. 4 is in specific embodiment, and the weak harmonic signal detection being mixed under the uniform Chaotic Background of white Gaussian noise is tied Fruit, wherein Fig. 4-a is the testing result of neural network method；Fig. 4-b is the testing result of the method for the present invention；
Fig. 5 is the weak harmonic signal testing result in specific embodiment, in the case of non-homogeneous Chaotic Background, wherein Fig. 5- A is the testing result of neural network method；Fig. 5-b is the testing result of the method for the present invention；
Fig. 6 is the restoration and reconstruction result figure that weak harmonic signal is detected in specific embodiment, and wherein Fig. 6-a is nerve The restoration and reconstruction result figure of network method；Fig. 6-b is the restoration and reconstruction result figure of the method for the present invention；S (n) indicates true weak harmonic wave Signal, s ' (n) indicate the harmonic signal of restoration and reconstruction.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, below with reference to embodiment and attached drawing, to this hair It is bright to be described in further detail.
The present invention is needed from sequence to be detected { x (n)=s (n)+c1(n), n=1 ... N } in detect and rebuild the weak harmonic wave Signal, wherein s (n)=β ejωnIt is weak harmonic signal, c1It (n) is strong Chaotic Background.By the way that one section of sequence to be detected is decoupled Hankel matrix is constructed at multiple subsegments, from physical principle, has actually reconfigured reference sequences, is solved non- The problem of uniform Chaotic Background is without reference to sequence.
Signal to Interference plus Noise Ratio SINR (ω is exported in order to obtainl), in specific embodiment, pass through the optimal FIR of one M rank of design Filter (hereinafter referred to as M rank FIR filter), the filter are guaranteeing that frequency is ωlWeak harmonic signal undistorted transmission Under the premise of, keep the energy of strong Chaotic Background minimum, i.e., can convert following optimization for the test problems of weak harmonic signal and ask Topic:
Wherein,It is that detection sequence rejects frequency as ωlHarmonic components g (ωl) after autocorrelation matrix, that is, remove Frequency is ωlHarmonic signal outside, the covariance matrix of remaining strong Chaotic Background signal, w is the weight of M rank FIR filter. Then,It is exactly the energy of the Chaotic Background of M rank FIR filter output.a(ωl) it is signal frequency vector, wHa (ωl) be exactly frequency be ωlOutput signal of the harmonic signal after wave filter, wHa(ωl)=1 indicates the weak harmonic signal It is undistorted after wave filter, to guarantee the accurate recovery to weak harmonic signal.In order to realize weak harmonic signal of the invention Detection, by L frequency point (ω1=ωlow,ω2=ωlow+Δω,…,ωl=ωlow+(l-1)Δω,…,ωL= ωhigh) SINR estimation: the energy of the weak harmonic signal corresponding to filtered each frequency point is carried out respectively Divided by the energy of Chaotic Background corresponding to the frequency point If frequency point to be detected is not echo signal (weak harmonic signal), SINR very little, if it is echo signal, then corresponding to SINR will Much larger than other frequency points, so that it is determined that the frequency of echo signal, completes weak harmonic signal detection.
Method of Lagrange multipliers is applied to formula (9), construction cost function K (w) obtains:
Gradient is asked about weight w to cost function K (w), and it is enabled to be equal to 0, it may be assumed that
It obtains:
Wherein, coefficientThe weight of M rank FIR filter can be calculated by (12) w。
Formula (9) can be write as:
Wherein, it is ω that β, which is measured frequency to be checked,lWeak harmonic signal complex magnitude.
J (w, β) can be opened up:
J (w, β)=| β-wHg(ωl)|2+wHRw-wHg(ωl)gH(ωl)w (14)
It can be obtained by formula (14), make the smallest β of objective function are as follows:
It is ω that frequency, which can be obtained, by formula (15)lWeak harmonic signal complex magnitude
Based on SINR (ω corresponding to L frequency pointl), frequency can be drawn -- output Signal to Interference plus Noise Ratio (SINR) figure, according to Frequency -- output Signal to Interference plus Noise Ratio (SINR) figure detects weak harmonic signal, and obtains the frequency of weak harmonic signalIt is i.e. maximum The corresponding frequency of SINR (ω) is
Again willSubstitution formula (8) can accurately obtain frequency in sequence to be detectedWeak harmonic signal amplitude and phase Position, according to the frequency of the weak harmonic signal detected, amplitude and phase can the weak harmonic signal of recovery and rebuilding.
By the method for the present invention and neural network method (bibliography " Xing H Y, Xu W.The neural networks Method for detecting weak signals under chaotic background.2007. [a row letter man of virtue and ability, xuwei Neural network method [J] Acta Physica Sinica of Detection of Weak Signals, 2007,56 (7): 3771-3776. in Chaotic Background] ") it carries out Contrast verification, simulating scenes are as follows:
In signal x (n) to be detected, weak harmonic signal is s (n)=β ej2πfn, the normalized frequency of fixed weak harmonic signal F=0.06Hz, the amplitude of weak harmonic signal | β |=0.05.
(1) uniform Chaotic Background
When uniform Chaotic Background, the Chaotic Background c of sequence to be detected in formula (1)1(n) and the Chaotic Background c of reference sequences2 (n) it is all generated by Lorenz system, since the initial value of the two sequences is different, the two sequences are completely uncorrelated.It should The state equation of system are as follows:
Wherein a=10, b=28, c=8/3, step-length 0.01, the initial value x of x, y, z0=y0=z0=0.1.c1(n) it is Continuous 3000 points intercepted at random in Lorenz chaos system x-component, c2It (n) is in Lorenz chaos system x-component Continuous 1000 points of meaning interception.
(2) non-homogeneous Chaotic Background
When non-homogeneous Chaotic Background, the Chaotic Background c of sequence to be detected in formula (1)1(n) mixed for the Lorenz in formula (16) Continuous 3000 points intercepted at random in the x-component of ignorant system, the Chaotic Background c of reference sequences2It (n) is Rossler chaos Continuous 1000 points intercepted at random in system x-component.The state equation of the Rossler system are as follows:
Wherein parameter a=0.2, b=0.4, c=5.7, step-length 0.1, the initial value x of x, y, z0=y0=z0=0.1.
Here, c1(n) and c2(n) be the sequence generated by different chaos system, thus with different dynamic characteristics and Different space geometry structures.
1. the Testing of Feeble Signals under uniform Chaotic Background
(1) white Gaussian noise is free of
IfWherein, s (n)=β ej2πfn,c1(n) and c2(n) by Lorenz chaos system generates.
Figure1It is sequence x to be detected1(n) time domain waveform (Fig. 1-a) and spectrogram (Fig. 1-b), from figure, weak harmonic wave No matter signal is all covered under Lorenz chaos noise background in the time domain or on frequency spectrum, can not be examined by time domain and frequency domain It measures.
Separately below with the method for the present invention and neural network method under the uniform Chaotic Background without white Gaussian noise Emulation.Wherein, neural network method is, first with the x of 1000 points2(n) training neural network, then with trained nerve net Network prediction and reconstruction x1(n) the Chaotic Background c in1(n), to realize the detection and recovery of weak harmonic signal.
Fig. 2 be at SINR=-47.01dB (| β |=0.05), it is weak under the uniform Chaotic Background without white Gaussian noise Harmonic signal testing result.In Fig. 2-b, by the weak harmonic signal ratio maximum that the method for the present invention detected at f=0.06Hz The high 17dB or more of valve, and in the neural network method of Fig. 2-a, weak harmonic signal is only 10dB higher than maximum secondary lobe；Fig. 2 shows Under uniform Chaotic Background without white Gaussian noise, the mentioned method detection performance of the method for the present invention is better than neural network method.
Definition output Signal to Interference plus Noise Ratio are as follows: the ratio of main lobe and maximum secondary lobe.With the method for the present invention and neural network method pair Harmonic signal is detected, and detection performance is as shown in Figure 3.Fig. 3 is the difference letter when weak signal harmonic frequency is fixed as 0.06Hz It is dry to make an uproar than the ratio of lower main lobe and maximum secondary lobe.Ratio is greater than zero, can detecte weak harmonic signal, conversely, cannot then detect. From figure 3, it can be seen that the method for the present invention can detecte out weak harmonic signal more than -55dB, and neural network method is in -50dB It is above just to can detecte out weak harmonic signal.And when detectable, the output Signal to Interference plus Noise Ratio of the method for the present invention compares neural network method High 8~17dB.
(2) there is white Gaussian noise
It is 0 that mean value is first added into weak harmonic signal, the white Gaussian noise that variance is 0.0125, at this time signal-to-noise ratio (SNR) For -10dB, addition Lorenz Chaotic Background signal in the weak harmonic signal of white noise is then mixed with to this.Sequence to be detected at this time It can indicate are as follows:
Wherein, w (n) is the white Gaussian noise of addition.It is equally compared with neural network method, with reference to Fig. 4.
Fig. 4 is the testing result of SNR=-10dB and SINR=-47.01dB.From Fig. 4-b, the method for the present invention is having height It remains to effectively detect weak harmonic signal when this white noise；And in Fig. 4-a, neural network method is due to dialogue noise-sensitive, not Weak harmonic signal can be detected.
2. the signal detection under non-homogeneous Chaotic Background
In order to be compared with neural network method, using the non-homogeneous Chaotic Background in the case of false reference sequences, and it is Guarantee neural network method does not fail, and under non-homogeneous Chaotic Background does not introduce white Gaussian noise.If:
Wherein, weak harmonic signal s (n)=β e2πfn,c1(n) it is generated by Lorenz chaos system, c2(n) by Rossler Chaos system generates.
In emulation, sequence x is first used2(n) 1000 points training neural network, then with trained neural network prediction with Rebuild x1(n) continuous Chaotic Background c in1(n) weak harmonic signal is detected, testing result is as shown in Figure 5.
Fig. 5 is the method for the present invention knot compared with neural network method under SINR=-47.01dB (| β |=0.05) Fruit.In Fig. 5-b, the method for the present invention is 17dB or more higher than highest secondary lobe at frequency f=0.06Hz.In Fig. 5-a, neural network At frequency f=0.06Hz, weak harmonic signal is submerged under strong Chaotic Background method, can not detect the weak harmonic signal.
3. the restoration and reconstruction of weak harmonic signal
Neural network method can only detect the frequency of weak harmonic signal, can not accurately estimate the amplitude and phase of the signal Position, thus can not the restoration and reconstruction weak harmonic signals.The method of the present invention then can be based on the frequency of the weak harmonic signal detectedSubstituted into the complex magnitude that formula (8) calculate weak harmonic signal.In order to guarantee that neural network method is effective, we use and are free of Simulating scenes under the uniform Chaotic Background of white Gaussian noise.In Fig. 2-b, it can be easy to estimate the frequency of weak harmonic signal The complex magnitude of weak harmonic signal can be obtained in frequency substitution formula (8) by f=0.6006Hz, goes out to detect so as to accurate reconstruction Harmonic signal out.
Fig. 6 is that the harmonic signal that the method for the present invention and neural network method recover compares: as seen from Figure 6, mind The signal recovered through network method has biggish distortion about original signal；The method of the present invention has then accurately recovered humorous Wave, performance are better than neural network method.
To sum up, with neural network method, the present invention has following three major advantages:
(1) under uniform Chaotic Background, the detection performance of the present invention (not using reference sequences) is better than neural network algorithm The detection performance of (using reference sequences)；Under non-homogeneous Chaotic Background, the present invention can detecte out weak harmonic signal, and neural Network algorithm failure；
(2) in practical engineering application, it can be also usually mixed with white Gaussian noise under Chaotic Background, at this point, neural network method Due to failing to noise-sensitive, the present invention then can detecte out the weak harmonic signal under the Chaotic Background for being mixed with Gaussian noise；
(3) neural network method cannot accurately restore harmonic signal.And the present invention is detecting the same of the frequency of weak harmonic wave When can also accurately estimate the amplitude and phase of weak harmonic signal, can the accurate restoration and reconstruction weak harmonic signals.
The above description is merely a specific embodiment, any feature disclosed in this specification, except non-specifically Narration, can be replaced by other alternative features that are equivalent or have similar purpose；Disclosed all features or all sides Method or in the process the step of, other than mutually exclusive feature and/or step, can be combined in any way.

Claims (3)

1. the weak harmonic signal detection method under a kind of strong Chaotic Background, characterized in that it comprises the following steps:
Data processing is done to the sequence to be detected { x (n), n=1,2 ..., N } that length is N, is converted to matrix y (n):
L is indicated to weak harmonic wave The division number of the frequency range of signal, M=N-L+1；
The autocorrelation matrix of sequence to be detected is calculated based on y (n)Wherein subscript H indicates that conjugation turns It sets；
With [ωlow,ωhigh] indicate the frequency range of weak harmonic signal in sequence to be detected, with fixed step sizeBy frequency range [ωlow,ωhigh] it is divided into L aliquot, obtain the frequencies omega of L different valuesl=ωlow + (l-1) Δ ω, wherein l=1,2 ..., L；
According to formulaCalculate frequencies omegalCorresponding harmonic components g (ωl), wherein j indicates empty Number unit, e indicate the nature truth of a matter；
According to formulaCalculate frequencies omegalCorresponding Chaotic Background autocorrelation matrix
According to formulaCalculate frequencies omegalCorresponding signal frequency vector a (ωl)；
According to formulaCalculate frequencies omegalCorresponding output Signal to Interference plus Noise Ratio SINR (ωl)；
Remember maximum SINR (ωl) corresponding to frequency beBy frequencyFrequency as the weak harmonic signal in sequence to be detected.
2. the method as described in claim 1, which is characterized in that calculate output Signal to Interference plus Noise Ratio SINR based on M rank FIR filter (ωl), the wherein weight of M rank FIR filterAre as follows:It is filtered through M rank FIR filter Frequency is ωlWeak harmonic signal energyIt is ω divided by frequencylChaotic Background energyObtain frequencies omegalCorresponding output Signal to Interference plus Noise Ratio SINR (ωl), wherein
3. the weak harmonic signal under a kind of strong Chaotic Background detects method for reconstructing, characterized in that it comprises the following steps:
Based on method of any of claims 1 or 2, the frequency of the weak harmonic signal in sequence to be detected is determined
According to the frequency of weak harmonic signalAccording to formulaCalculate answering for weak harmonic signal AmplitudeThe complex magnitudeIncluding amplitude and phase, according to the frequency of acquired weak harmonic signalAmplitude, phase Bit recovery reconstructs weak harmonic signal.
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