CN106209706B - The detection method of weak harmonic signal under a kind of Chaotic Background - Google Patents
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Abstract
The invention belongs to chaotic signal detection technique field, in particular to the detection method of weak harmonic signal under a kind of Chaotic Background.The present invention is based on the fast algorithms of spreading kalman EKF, according to the feature that the second-order statistics of Chaotic Background are constant, weak harmonic signal test problems are converted into minimum variance test problems first, measurement equation and state equation are established on this basis, to avoid matrix inversion, and filter weights are iterated to calculate out with EKF method, signal output Signal to Interference plus Noise Ratio SINR is calculated on the basis of filter weights, and Signal to Interference plus Noise Ratio is exported according to signal to detect weak harmonic signal.The present invention utilizes the undistorted problem of Extended Kalman filter solution by iterative method minimum variance, obtains optimal filter weight vector value, to reduce algorithm computation complexity while accurately detecting harmonic signal；Steady with algorithm, computation complexity is low and the good advantage of detection performance.
Description
Technical field
The invention belongs to chaotic signal detection technique field, in particular to the detection of weak harmonic signal under a kind of Chaotic Background
Method.
Background technique
Testing of Feeble Signals in Chaotic Background is one of hot spot of current research, is received significant attention.Studies have shown that very much
Engineering problem can be attributed to the abnormal signal inspection in the problem of Testing of Feeble Signals in strong Chaotic Background, such as mechanical concussion
It surveys (see document " B.Li, P.L.Zhang, Z.J.Wang, S.S.Mi, and P.Y.Liu.Morphological covering
based generalized dimension for gear fault diagnosis.Nonlinear Dynamics 67,
2561-2571. "), the investigation of chaotic communication system security performance, the weak target signal inspection in ocean clutter no.4 (2012):
It surveys (see document " J. Hu, W.W.Tung, and J.B.Gao.Detection of low observable targets
within sea clutter by structure function based multifractal analysis.Antennas
and Propagation,IEEE Transactions on.2006Jan；54 (1): 136-43. ") etc., in these engineering problems
In, background clutter may be regarded as strong chaotic signal, and echo signal is often very faint.Therefore, the faint mesh in strong Chaotic Background
The research for marking signal detection problem has very strong practical meaning in engineering.
The weak harmonic signal detection method under strong Chaotic Background mainly divides two major classes at present: based on Takens phase-space reconstruction
Detection method and detection method based on optimal filter.Detection method based on Takens phase-space reconstruction is mainly using mixed
The geometry of the ignorant phase space feature different from echo signal is detected, wherein neural network method is of greatest concern (see text
Offer " a row letter man of virtue and ability, neural network method [J] Acta Physica Sinica of Detection of Weak Signals in xuwei Chaotic Background, 2007,56 (7):
3771-3776").Neural network method is the one-step prediction model that Chaotic Background signal is obtained based on neural metwork training, is passed through
The Chaotic Background that original signal subtracts reconstruct obtains one-step prediction error to realize the detection of weak harmonic signal.However, due to chaos
System itself is a dissipative system, therefore the above method carries out Chaotic Background to be easy to appear prediction error when prediction reconstructs,
Cause occur biggish deviation when target echo detection.In view of the above-mentioned problems, 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) " propose optimal filter side
Method, this method feature constant according to the second-order statistics of Chaotic Background, Testing of Feeble Signals problem is converted on frequency domain
The design problem of optimal filter.However, this method is related to matrix inversion calculating, it is understood that there may be the unstable problem of algorithm；
Meanwhile this method operand is larger, limits the engineer application of the algorithm.
Summary of the invention
For above-mentioned there are problem or deficiency, high for solution annual reporting law computation complexity, detection performance is low, and algorithm is unstable
Technical problem, the present invention provides a kind of weak harmonic signal detection methods based under Chaotic Background.
This is based on the weak harmonic signal detection method under Chaotic Background, comprising the following steps:
Step 1, building data matrix, convert optimization for the Weak Signal test problems under strong Chaotic Background and ask
Topic.
The N sections of signals containing only strong Chaotic Background noise are randomly selected as reference sequences, i.e. yzAs reference unit, it is used to
Estimate CHAOTIC INTERFERENCE covariance matrix, N is even number；By yxIt is placed on detection unit.Detection unit and reference unit collectively as
The row vector of data matrix, then the matrix one shares N+1 row cell data.Wherein, the frequency domain data y=[y of detection unit1,
y2,...,yM]T, reference unit data yi, (i=1,2 ..., N) it is yi=[yi1,yi2,...,yiM]T.M is the sampling of signal
Points, i.e. frequency channel number.The format of data matrix is as shown in Figure 1.
The sequence to be detected (Sequence to be Detected): yx(n)=cx(n)+s (n), wherein yx(n) it is
Sequence to be detected includes chaotic signal cx(n) and harmonic signal s (n).Usual chaotic signal is very strong, and harmonic signal is very weak,
Lead to detection difficult.
The reference sequences (Reference Sequence): yz(n)=cz(n), harmonic signal is free of, only includes chaos
Signal cz(n)。
Step 2 calculates CHAOTIC INTERFERENCE covariance matrix
Step 3, calculating frequency channel are ωlThe signal frequency guiding vector s (ω of (l=1 ..., M)l)
Step 4 establishes state equation and measurement equation:
State equation are as follows:
W (n)=α w (n-1)+vs(n) (3)
Wherein, α≤1 is a constant, vs(n) it is process noise vector, is set as zero mean Gaussian white noise, covariance
Matrix are as follows:I is unit matrix, and subscript s indicates to correspond to state transition equation, W (n) indicates filter
Value when recurrence weight vector state n.
Measurement equation are as follows:
Measurement equation shown in formula (4) is written as matrix form are as follows:
Z=h (w (n))+vm(n) (5)
Wherein, h2(w (n))=ε2wH(n)w(n)-wH(n)ssHw(n)+wH(n)s+sHW (n), ε are constant value 10-3
~10-5The order of magnitude, s is signal guide vector set, v1It (n) is residual error, v2It (n) is constraint error；Minimize v1(n) make
Filter output reaches minimum, minimizes v2(n) guarantee the undistorted output of frequency signal to be detected, v1(n) and v2(n) it models
For two independent zero mean Gaussian white noises, covariance matrix are as follows:
Wherein,Value work as with filter output phase, andValue meets constraint condition, and representative value is 10-12。
Step 5 calculates Jacobin matrix Hw(n, w (n)) and two Hessian matrixes
Jacobin matrix Hw(n, w (n)) are as follows:
It is respectively as follows:
Step 6, the initialization weight vector for setting recurrence weight vector w are estimated as w (0), initialize covariance matrix accordingly
For P (0 | 0).What then weight vector was estimated is updated to
Step 7 successively calculates prediction measurement matrixFilter gain weight vector G (n) is new to cease covariance square
Battle array S (n), measurement prediction covariance matrix P (n | n-1) and update covariance vector P (n | n).
P (n | n-1)=α2P(n-1|n-1)+Q (14)
P (n | n)=P (n | n-1)-G (n) S (n) GH(n) (15)
Formula (11)~formula (15) is substituted into formula (10) iterate until convergence, the filter weight vector obtained at this time
For optimal filter weight vector
Step 8 calculates output signal-to-noise ratio:
The output SINR that each frequency channel signals are calculated separately according to formula (16) is detected according to the energy of output SINR
Frequency where echo signal out.
The present invention is based on spreading kalman extended Kalman filter (EKF), are united according to the second order of Chaotic Background
The constant feature of characteristic is counted, weak harmonic signal test problems are converted into minimum variance test problems first, are built on this basis
Vertical measurement equation and state equation, to avoid matrix inversion, and iterate to calculate out filter weights with EKF method, are filtering
Signal output Signal to Interference plus Noise Ratio SINR is calculated on the basis of device weight, and Signal to Interference plus Noise Ratio is exported according to signal to detect that weak harmonic wave is believed
Number.
It can allow echo signal is undistorted to pass through by designing one, noise signal passes through the filter that is inhibited.Filter
When wave device exports, target inband energy is much larger than noise signal energy, and energy will converge at echo signal frequency, according to
Frequency-output Signal to Interference plus Noise Ratio figure finds out the highest point of energy to judge echo signal existence, completes to echo signal
Detection.
There are stable second-order statistics according to chaotic signal, make and join of the Chaotic Background signal of no weak harmonic signal
Signal is examined, a filter is designed, is filtered out strong Chaotic Background signal while retaining weak harmonic signal, to detect this
Weak harmonic signal:
Wherein, w is the coefficient of the filter of design, and s is desired signal guide vector.Indicate filter handle
Strong Chaotic Background signal is filtered out, wHS=1 indicates that weak harmonic signal is undistorted after the filter.
||wc||2=wHRw, wherein the second-order statistics of R expression Chaotic Background signal.Due to the second order of chaotic signal
Statistical property is constant, and the Chaotic Background signal in signal to be detected is estimated using the reference signal containing only Chaotic Background signal.
In formula (17), constraint condition wHThe meaning of s=1 is to guarantee the undistorted transmission of weak harmonic signal.In practical work
In Cheng Yingyong, there is errors to a certain extent by desired signal guide vector s and actual signal steering vector d:
D=s+ δ (18)
Wherein, δ is the deviation between detection steering vector s and true steering vector d used, | | δ | |≤ε.
Formula (18) illustrates that true steering vector d is included in a neighborhood of expectation steering vector s used when detectionIt is interior,It is defined as follows:
In formula (19) as e=δ, u=d.Since δ is unknown, d may beIn any one vector, so we
Assuming that such a constraint condition: for being included inIn institute's directed quantity, the absolute value of the output of filter is all not less than
1, it may be assumed that
Using constraint condition shown in formula (20), then optimization problem described in formula (17) becomes following form:
For optimization problem described in formula (21), since true steering vector d is included inIn, so inequality is about
Beam condition ensure that echo signal to be detected by that will not decay after filter.But the constraint condition only makes the optimization problem
It is non-linear, non-convex.Therefore, next we will continue to derive constraint condition.Firstly, formula (21) optimization is asked
The constraint condition of topic is equivalent to following formula:
Utilize Cauchy-Schwarz inequality and condition | | e | |≤ε can be obtained:
|wHs+wHe|≥|wHs|-|wHe|≥|wHs|-ε||w|| (23)
When ε is sufficiently small, i.e., | wHS | > ε | | w | | when have:
|wHs+wHE |=| wHs|-ε||w|| (24)
So formula (24) can be converted are as follows:
And then optimization problem shown in formula (21) can further indicate that are as follows:
Formula (21) is simplified the problem of formula (17), and is converted to a convex optimization problem.For optimal filter
Target equation wHRw, mean square error (the mean square being denoted as between optimal filter output and 0 signal
Error, MSE), it may be assumed that
MSE=E [| 0-yHw(n)|2]=wHRw (27)
Then, following optimization problem further is converted by former optimization problem formula (17):
Wherein, restrictive condition h (w (n))=1 is stated are as follows:
h2(w (n))=ε2wH(n)w(n)-wH(n)ssHw(n)+wH(n)s+sHW (n)=1 (29)
Since optimization problem is nonlinear, so the solution of optimal weight vector is carried out using spreading kalman, according to formula
(28) and formula (29) its state equation (3) and measurement equation (5), are derived.
There are state equation and measurement equation, Kalman filter is recycled to solve weight vector w.Because of measurement equation right and wrong
Linear, so using second order EKF below, h () is subjected to second order Taylor series expansion at w (n), obtains Jacobin square
Battle array Hw(n,w(n))。
To Hw(n, w (n)) asks first derivative and second dervative respectively, obtains two Hessian matrixes
According to step 6, step 7 iterates, to update filter weights until it converges on optimal filter power
Value.After obtaining optimal filter weight, the output SINR of filter is calculated by step 8.According to output SINR, from Chaotic Background
The middle detection for realizing weak harmonic signal.By derivation process above it is found that the computation complexity of formula (7) Jacobin matrix is O
(M2)；The computation complexity of formula (10) weight vector iteration is O (M)；Formula (11) prediction matrixComputation complexity be O
(M2)；Formula (12) filter weight vector G (n) gain is O (M2)。
New breath covariance matrix S (n) computation complexity of formula (13) is O (M2), it is to traditional new breath covariance matrix
Optimization.
Update covariance vector P (n | n) computation complexity of formula (15) is O (M2), it is that covariance vector is updated to tradition
Optimization.Traditional update covariance vector are as follows:
Its computation complexity is O (M3).After optimization, the computation complexity of algorithm entirety can be reduced.
Thus, the computation complexity for the extended Kalman filter that the present invention is mentioned is O (M2).And according to document
“S.A.Vorobyov,A.Gershman,and Z.Q.Luo,“Robust adaptive beamforming using
worst-case performance optimization:A solution to the signal mismatch
Problem, " derivation of IEEE Trans.Signal Process., vol.51, no.2, pp.313-324, Feb.2003 ",
The computation complexity of SOCP is O (M3).Therefore, the fast algorithm computation complexity of the extended Kalman filter mentioned herein is excellent
In the computation complexity of SOCP.
In conclusion the present invention has algorithm steady, computation complexity is low, the good technical effect of detection performance.
Detailed description of the invention
Fig. 1 is data matrix format chart of the invention；
Fig. 2-a is neural network method testing result；Fig. 2-b is SOCP method testing result；Fig. 2-c is the present embodiment inspection
Survey result；
Fig. 3 is output Signal to Interference plus Noise Ratio figure of the embodiment from existing two kinds of detection methods under different input Signal to Interference plus Noise Ratio.
Specific embodiment
The present invention is further elaborated with reference to the accompanying drawings and examples.
Here Chaotic Background signal, the nonlinear state equation of the system are generated with Lorenz system are as follows:
Wherein σ=10, r=28, b=8/3, step-length 0.01, initial value x0=y0=z0=0.1.
In the Lorenz chaotic signal of generation, the Chaotic Background signal data conduct that 5 segment length are 2000 is randomly selected
Signal of the weak harmonic signal as detection unit is added into paragraph 1 data for the strong Chaotic Background of this experiment, remaining 4 segment data
As the reference unit signal containing only Chaotic Background signal.Harmonic signal s (n)=α ej2πfnIt indicates, wherein fixed harmonic wave
The normalized frequency f=0.06Hz of signal, the amplitude of harmonic signal | α |=0.05.
Neural network algorithm is respectively adopted, the optimal filter algorithm based on SOCP and the EKF fast algorithm mentioned herein
It is detected respectively, testing result is as shown in Figure 2:
Fig. 2 be at SINR=-47.01dB (α=0.05), using neural network algorithm, the optimal filter based on SOCP
The signal detecting result of device algorithm and the EKF fast algorithm mentioned herein under strong Chaotic Background.In Fig. 2-a, using nerve net
Network algorithm, harmonic signal are only 6dB higher than maximum secondary lobe.And in Fig. 2-b and Fig. 2-c, using the optimal filter based on SOCP
Algorithm and herein mentioned EKF fast algorithm, at f=0.06Hz, harmonic signal is 12dB higher than maximum secondary lobe.As seen from Figure 1,
Mentioned EKF fast algorithm performance is suitable better than neural network algorithm, and the optimal filter algorithm performance based on SOCP herein.
Definition output Signal to Interference plus Noise Ratio are as follows: the ratio of main lobe and maximum secondary lobe.Fig. 3 provides neural network algorithm, is based on SOCP
Optimal filter algorithm and herein the comparison figure of mentioned EKF fast algorithm detection performance.
Fig. 3 is the ratio of main lobe and maximum secondary lobe under different Signal to Interference plus Noise Ratio when harmonic frequency is fixed as 0.06Hz.Ratio
Greater than zero, then illustrate that harmonic signal is easy to be correctly detected, conversely, being then not easy to be correctly detected.By simulation result it is found that originally
Invention performance is better than neural network algorithm performance；Input SINR be less than -40dB when, the present invention and be based on SOCP optimal filter
Device algorithm performance is suitable, and when inputting SINR greater than -40dB, inventive can be better than based on SOCP optimal filter algorithm
Energy.But computation complexity of the present invention, which is far below, is based on SOCP optimal filtering algorithm.Therefore, the present invention has stronger Practical Project to anticipate
Justice.
Claims (2)
1. a kind of weak harmonic signal detection method based under Chaotic Background, comprising the following steps:
Step 1, building data matrix, convert optimization problem for the Weak Signal test problems under strong Chaotic Background:
The N sections of signals containing only strong Chaotic Background noise are randomly selected as reference sequences, i.e. yzAs reference unit, for estimating
CHAOTIC INTERFERENCE covariance matrix, N are even number, by yxIt is placed on detection unit；Detection unit and reference unit are collectively as data
The row vector of matrix, then the matrix one shares N+1 row cell data；Wherein, the frequency domain data y=[y of detection unit1,y2,...,
yM]T, reference unit data yi, (i=1,2 ..., N) it is yi=[yi1,yi2,...,yiM]T, M is the sampling number of signal, i.e. frequency
Rate port number；
The sequence Sequence to be Detected:y to be detectedx(n)=cx(n)+s (n), wherein yxIt (n) is to be detected
Sequence includes chaotic signal cx(n) and harmonic signal s (n)；
The reference sequences Reference Sequence:yz(n)=cz(n) harmonic signal is free of, only includes chaotic signal cz
(n)；
Step 2 calculates CHAOTIC INTERFERENCE covariance matrix
Step 3, calculating frequency channel are ωlThe signal frequency guiding vector s (ω of (l=1, L, M)l)
Step 4 establishes state equation and measurement equation:
State equation are as follows:
W (n)=α w (n-1)+vs(n) (3)
Wherein, α≤1 is a constant, vs(n) it is process noise vector, is set as zero mean Gaussian white noise, covariance matrix
Are as follows:I is unit matrix, and subscript s indicates to correspond to state transition equation, W (n) indicates filter recurrence
Value when weight vector state n；
Measurement equation are as follows:
Measurement equation shown in formula (4) is written as matrix form are as follows:
Z=h (w (n))+vm(n) (5)
Wherein, h2(w (n))=ε2wH(n)w(n)-wH(n)ssHw(n)+wH(n)s+sHW (n), ε are constant value 10-3~10-5
The order of magnitude, s is signal guide vector set, v1It (n) is residual error, v2It (n) is constraint error；Minimize v1(n) make filter
Output reaches minimum, minimizes v2(n) guarantee the undistorted output of frequency signal to be detected, v1(n) and v2(n) two are modeled as
Independent zero mean Gaussian white noise, covariance matrix are as follows:
Wherein,Value work as with filter output phase,Value meets constraint condition；
Step 5 calculates Jacobin matrix Hw(n, w (n)) and two Hessian matrixes
Jacobin matrix Hw(n, w (n)) are as follows:
It is respectively as follows:
Step 6, the initialization weight vector for setting recurrence weight vector w are estimated as w (0), and initializing covariance matrix accordingly is P (0
| 0), then what weight vector was estimated is updated to
Step 7 successively calculates prediction measurement matrixFilter gain weight vector G (n) is new to cease covariance matrix S
(n), prediction covariance matrix P (n | n-1) and update covariance vector P (n | n) is measured:
P (n | n-1)=α2P(n-1|n-1)+Q (14)
P (n | n)=P (n | n-1)-G (n) S (n) GH(n) (15)
Formula (11)~formula (15) is substituted into formula (10) iterate until convergence, the filter weight vector obtained at this time are most
Excellent filter weight vector
Step 8 calculates output signal-to-noise ratio:
The output SINR that each frequency channel signals are calculated separately according to (16) detects target according to the energy of output SINR
Frequency where signal.
2. as described in claim 1 based on the weak harmonic signal detection method under Chaotic Background, it is characterised in that: the step 4
InValue is 10-12。
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