CN101592730A - Sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment - Google Patents

Sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment Download PDF

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CN101592730A
CN101592730A CNA2009100994389A CN200910099438A CN101592730A CN 101592730 A CN101592730 A CN 101592730A CN A2009100994389 A CNA2009100994389 A CN A2009100994389A CN 200910099438 A CN200910099438 A CN 200910099438A CN 101592730 A CN101592730 A CN 101592730A
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李建龙
徐博侯
潘翔
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Zhejiang University ZJU
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Abstract

A kind of sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment may further comprise the steps: 1) spatial beams forms: at first be poised for battle the reception spacing wave and carry out wave beam formation processing, to obtain the spatial gain of battle array; 2) time scale conversion: the time shaft to each wave beam territory signal elongates, to reduce the frequency of medium-high frequency feeble signal; 3) wave beam territory PSR handles; 4) PSR aftertreatment; 5) time scale inverse transformation is to recover the frequency of time domain signal in each wave beam territory under the former sampling rate.If be applied to active probe, then 1) increases matched filter processing afterwards.The present invention can realize that linear signal disposal route and nonlinear PSR processing are independent of each other on handling property, satisfy the processing requirements of low frequency and medium-high frequency feeble signal simultaneously, significantly promote to handle the feeble signal ability, and utilize aftertreatment to eliminate to greatest extent because the signal waveform distortion that the PSR Nonlinear Processing is caused.

Description

Sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment
Technical field
The present invention relates to a kind of sensor array beam territory feeble signal disposal route.
Background technology
Utilizing sensor array to carry out the weak target detection is a difficulty and the problem that presses for solution.As in the shallow sea or immediate offshore area, utilize active sonar to carry out the target detection of burying under the strong reverberation background; Utilize passive sonar to carry out remote Detection of Weak Signals etc.Usually, traditional time domain linear signal processing method such as frequency band select filtering, matched filtering etc. to can be used to suppress noise/reverberation, mix ratio thereby improve signal to noise ratio (S/N ratio)/letter.Yet studies show that since the eighties in last century, may there be great potential in the nonlinear kinetics system in the signal Processing field, cause that wherein (Stochastic Resonance, SR) system have become research one of focus for the accidental resonance of the extensive interest of numerous scholars.The SR development is from the eighties in last century, and the research field that relates to comprises physics, signal Processing, biology etc.As a kind of nonlinear signal processing theory, SR makes nonlinear system, signal and noise produce synergy (resonance) by increasing noise, thereby the raising system is to the response of useful signal, and it appears in some nonlinear system, also is the difference of nonlinear system and linear system.
Parameter-induced stochastic resonance (Parameter-induced SR, PSR) at the SR that realizes being different from the method that resonates traditional adjusting noise, thereby it is by the natural frequency of regulating system parameter change system itself, make nonlinear system, signal and noise produce resonance effects, thereby the system output signal energy is increased, noise is inhibited, and obtains high output signal-to-noise ratio.Consider and regulate the difficult realization of noise intensity in the practical application, especially when noisiness the unknown or system's input noise intensity have surpassed resonance point and need reduce noise intensity and could realize SR, PSR has more actual application value [Li Jianlong and Xu Bohou, " Parameter-inducedstochastic resonance with a periodic signal ", Chinese Physics, vol.15 (12), pp.2867-2871,2006 (Chinese: Li Jianlong, Xu Bohou, " parameter-induced stochastic resonance under the periodic signal situation ", China's physics, Vol.15 (12), pp.2867-2871,2006); Li Jianlong, " Evidence ofparameter-induced aperiodic stochastic resonance with fixed noise ", Chinese Physics, Vol.16 (2), pp.340-345,2007 (Chinese: Li Jianlong, " aperiodic parameters under the steady noise situation is regulated accidental resonance ", Chinese physics, Vol.16 (2), pp.340-345,2007) .].Because thereby SR has utilized the co of nonlinear system to make system's output in order, signal to noise ratio (S/N ratio) improves, this is the unexistent signal Processing mechanism of general linear wave filter, therefore has weak signal and handles advantage, can be used as the useful of linear signal disposal route and replenishes.
PSR be used for sensor array handle existing a small amount of document study [Ye Qinghua, the Huanghai Sea is peaceful, He Xinyi, Zhang Chunhua, " utilizing the feeble signal DOA estimation of accidental resonance technology ", acoustic journal, Vol.29 (4), pp.369-372,2004; Pacify the good Chen Lijun, Lu Jiren, " wave beam based on the accidental resonance method under the sea noise background forms ", acoustic technique, Vol.25 (2), pp.98-102,2006], and obtained effect preferably.Weak point is, (1) prior art is placed on the array element territory to the SR Nonlinear Processing and carries out, cause signal waveform distortion and each array element signals phase place of after nonlinear system is handled, causing inconsistent, thereby influence follow-up linear signal processor and (form (Beamforming as spatial beams, BF), time domain matched filtering etc.) performance, make follow-up linear processor performance descend; (2) prior art is not carried out corresponding aftertreatment to output signal after Nonlinear Processing, and promptly inversion procedure to recover original signal waveform to greatest extent, reduces the spinoff that signal distortion produces subsequent treatment; (3) according to the adiabatic approximation theory, SR nonlinear properties disposal system is better to the low frequency signal handling property, and therefore for high-frequency signal, the performance of prior art can descend.
Summary of the invention
In order to eliminate existing array element territory SR disposal route to follow-up linear processor Effect on Performance, overcome processing requirements, the more weak deficiency of processing medium-high frequency feeble signal ability that existent method can not satisfy low frequency and medium-high frequency feeble signal simultaneously simultaneously, the invention provides a kind of linear signal processing is independent of each other with the nonlinear properties disposal route, and can satisfy the requirement that low frequency and high frequency weak signal are handled simultaneously, significantly promote the sensor array beam territory feeble signal disposal route of handling the feeble signal ability based on parameter-induced stochastic resonance and aftertreatment.
The technical solution adopted for the present invention to solve the technical problems is:
A kind of sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment, described sensor array beam territory feeble signal disposal route may further comprise the steps:
1) spatial beams forms:
If source signal/echo is expressed as after each sensor receives:
r(n)=v(φ s)s(n)+w(n), (1)
R (n)=[r wherein 1(n) r 2(n) ... r M(n)], noise/reverberation w (n)=[w 1(n) w 2(n) ... w M(n)], M is the sensor number, and s (n) is for passive source or initiatively launch echoed signal, v (φ s) be the battle array response vector, φ sBe azimuth of target;
At first this M dimension space signal is carried out wave beam and form processing, to obtain the spatial gain of battle array; Be located at and carry out wave beam formation on I the direction, obtain I wave beam and be expressed as:
x i(n)=c Hi)r(n),i=1,2,…,I, (2)
C (φ wherein i) be that battle array is driven to φ iThe weight vector of direction, this weight vector designs according to different wave beam formation methods, and subscript H represents conjugate transpose;
2) time scale conversion:
To each wave beam territory signal x i(n) time shaft elongates, and after the time scale conversion, wave beam territory signal indication is x i(τ), τ=Ln wherein, L is the change of scale multiple;
3) wave beam territory PSR handles:
Adopt most typical bistable state nonlinear system:
dy ( τ ) dτ = ay - by 3 + x i ( τ ) , - - - ( 3 )
Wherein systematic parameter a and b are positive number, x i(τ) be system's input, y (τ) is system's output;
Thereby natural frequency by regulating system parameter a and b change system itself;
At first, the signal to noise ratio (S/N ratio)/letter of definition output mixes than for weighing the objective function of PSR handling property index, establishing objective function being
Figure A20091009943800071
, then systematic parameter a and b regulate by following formula:
Figure A20091009943800072
Wherein parameter a and b need the input x according to system i(τ) carry out the self-adaptation adjustment, when objective function was maximum, a and b were the optimized parameter of nonlinear system;
4) PSR aftertreatment:
Input signal x in the non-linear Langevin equation (3) i(τ) form, be expressed as x by two parts i(τ)=s i(τ)+w i(τ), (3) formula both sides got all be worth:
y ‾ · ( τ ) = a y ‾ ( τ ) - b y ‾ ( τ ) 3 + s ‾ i ( τ ) , - - - ( 5 )
Y (τ)=E[x (τ) wherein], s i(τ)=E[s i(τ)]; Work as condition | y &OverBar; &CenterDot; ( &tau; ) | < < s &OverBar; i ( &tau; ) When satisfying, must the signal inversion formula be:
s i(τ)≈by(τ) 3-ay(τ). (6)
The calculating of average y (τ) with τ constantly the averaged amplitude value of adjacent spaces estimate, therefore, the signal s that inverting obtains i(τ) be the level and smooth in short-term of actual signal, except the minimum signal sampling point of amplitude, i.e. their amplitude s i(τ) → 0, most points can both satisfy condition | y &OverBar; &CenterDot; ( &tau; ) | < < s &OverBar; i ( &tau; ) ; For the minimum amplitude output signal that does not satisfy condition, recover original waveform by interpolation, smoothing technique;
5) time scale inverse transformation:
Carry out the time scale inverse transformation, i.e. n=τ/L is to recover the time-domain signal s in each wave beam territory under the former sampling rate i(n).
As preferred a kind of scheme: under the active target detection event, in described step 1) and step 2) between increase wave beam territory matched filter processing.
Technical conceive of the present invention is: at first the sensor received signal is carried out spatial beams and form; Then in the wave beam territory, carry out matched filter processing (for passive detection, not carrying out this processing) earlier, its output is carried out carrying out the PSR Nonlinear Processing again after the time scale conversion, aftertreatment is carried out in output to nonlinear system at last, with the signal waveform distortion that reduces to cause owing to Nonlinear Processing.Carry out after wherein the PSR Nonlinear Processing being placed on wave beam formation and matched filtering, eliminating the influence of nonlinear effect to the linear signal processor, and the time scale conversion can be handled the PSR that low frequency signal is had a greater advantage to high frequency weak signal.Instance processes shows that a whole set of disposal route of associating PSR can significantly promote the ability that feeble signal is handled.
Simultaneously, the PSR system can be used as the useful of linear signal processor and replenishes because the difference of signal Processing mechanism has the unexistent advantage of linear signal processor, brings into play both and handles advantage in conjunction with the feeble signal of being brought; Utilize the time scale conversion to reduce the signal frequency of input PSR system, give full play to the processing power of PSR nonlinear properties disposal route faint low frequency signal; After the PSR system, be connected in series post-processing approach such as corresponding signal inverting, interpolation, because the signal waveform that the nonlinear effect of PSR causes distorts, help processing such as follow-up further detection, estimation with basic recovery.
Beneficial effect of the present invention mainly shows: can eliminate because the performance of linear processors such as the wave beam formation that nonlinear effect causes, matched filtering descends; Can satisfy the processing requirements of low frequency and high frequency weak signal simultaneously, significantly promote the feeble signal processing power; Adopt optimal system as nonlinear processor, to obtain best feeble signal handling property; Aftertreatment can eliminate to greatest extent because the signal waveform distortion that Nonlinear Processing caused.
Description of drawings
Fig. 1 is a sensor array target detection PSR wave beam territory feeble signal processing flow chart.
Fig. 2 is a PSR system handles process flow diagram.
Fig. 3 be through conventional wave beam form (Conventional Beamforming, CBF) and matched filtering (Matched Filtering, MF) the comparison synoptic diagram of gained beam pattern after the beam pattern after the processing and CBF, MF and the PSR Combined Treatment.
Fig. 4 is the synoptic diagram of the result of two target correspondences.
Fig. 5 is a synoptic diagram of going up the Data Processing in Experiment result.
Fig. 6 is waveguide Data Processing in Experiment result's a synoptic diagram.
Embodiment
Below in conjunction with accompanying drawing the present invention is further described.
With reference to Fig. 1~Fig. 6, a kind of sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment, the sonar battle array or the land/sensor array feeble signals such as airborne radar battle array that are used for are under water handled.The technical scheme of a whole set of disposal route is as follows:
1) spatial beams forms
If source signal (passive detection)/echo (active probe) can be expressed as after each sensor receives
r(n)=v(φ s)s(n)+w(n), (1)
R (n)=[r wherein 1(n) r 2(n) ... r M(n)] noise/reverberation w (n)=[w 1(n) w 2(n) ... w M(n)], M is the sensor number, and s (n) is for passive source or initiatively launch echoed signal, v (φ s) be the battle array response vector, φ sBe azimuth of target.At first this M dimension space signal is carried out wave beam and form processing, to obtain the spatial gain of battle array.Be located at and carry out wave beam formation on I the direction, obtaining I wave beam can be expressed as
x i(n)=c Hi)r(n),i=1,2,…,I, (2)
C (φ wherein i) be that battle array is driven to φ iThe weight vector of direction, this weight vector can design according to different BF methods, and subscript H represents conjugate transpose.
2) wave beam territory matched filter processing
Wave beam territory MF handles and represents that as frame of broken lines among Fig. 1 this processing method generally is used under the active target detection event, and the purpose of processing is to improve signal to noise ratio (S/N ratio)/letter to mix ratio, increases range resolution.Also place MF the array element territory to handle during some is handled, and then carry out the BF spatial manipulation,, therefore do not influence final handling property because both all belong to linear process.
3) time scale conversion
After above-mentioned linear process, because echo is faint, signal to noise ratio (S/N ratio)/letter mixes ratio still may be very low, and PSR can further improve the mixed ratio of signal to noise ratio (S/N ratio)/letter.According to the adiabatic approximation theory, PSR has better handling property in lower frequency region usually, therefore, wave beam territory signal need carry out the time scale conversion before entering the PSR system handles, with the echo of upper frequency, by the time scale conversion, be reduced to lower frequency region.Shown in Fig. 1 (handling A), the main path of time scale conversion is to each wave beam territory signal x i(n) time shaft elongates, and after the time scale conversion, beam signal is expressed as x i(τ), τ=Ln wherein, L is the change of scale multiple.
4) wave beam territory PSR handles
Place PSR wave beam formation and two kinds of linear signal processors of matched filtering afterwards mainly based on following consideration: the system response time of (1) PSR nonlinear system is influenced by signal amplitude and noise intensity, both inconsistent all will cause the system response time difference, if handle in the array element territory, the time delay of the output signal of each array element correspondence is changed, form effect thereby influence follow-up wave beam; (2) owing to be subjected to system's non-linear effects, the PSR system output signal can produce distortion, thereby influences the matched filter processing performance.
PSR can realize that patent of the present invention adopts most typical bistable state nonlinear system in all kinds of nonlinear kinetics system
dy ( &tau; ) d&tau; = ay - by 3 + x i ( &tau; ) , - - - ( 3 )
Wherein systematic parameter a and b are positive number, x i(τ) be system's input, y (τ) is system's output.PSR is different from the SR of traditional adjusting noise on the method that realizes resonance, thereby it is by the natural frequency of regulating system parameter a and b change system itself, make nonlinear system, signal and noise produce resonance effects, obtain high output signal-to-noise ratio, be applicable to the feeble signal processing.Consider that regulating noise intensity difficult realization, especially noisiness the unknown or system's input noise intensity in the practical application need reduce noise intensity above resonance point, PSR has more actual application value.
The PSR treatment scheme as shown in Figure 2.At first, according to the difference of application background, should define the objective function of weighing the nonlinear system output performance, use background for patent of the present invention, generally signal to noise ratio (S/N ratio)/the letter of definable output mixes than the objective function for measurement PSR handling property index.If objective function is , then systematic parameter a and b can regulate by following formula
Figure A20091009943800112
Wherein parameter a and b need the input x according to system i(τ) carry out the self-adaptation adjustment, when objective function (signal to noise ratio (S/N ratio)/letter mixes ratio) was maximum, a and b were the optimized parameter of nonlinear system.When PSR realized under some situation, system may be in suboptimum state [Li Jianlong and Xu Bohou, " Parameter-induced stochastic resonancewith a periodic signal ", Chinese Physics, vol.15 (12), pp.2867-2871,2006 (Chinese: Li Jianlong, Xu Bohou, " parameter-induced stochastic resonance under the periodic signal situation ", Chinese physics, Vol.15 (12), pp.2867-2871,2006); Li Jianlong, " Evidence of parameter-induced aperiodic stochasticresonance with fixed noise ", Chinese Physics, Vol.16 (2), pp.340-345,2007 (Chinese: Li Jianlong, " aperiodic parameters under the steady noise situation is regulated accidental resonance ", China's physics, Vol.16 (2), pp.340-345,2007) .], patent of the present invention still adopts optimal system as nonlinear processor, to obtain best feeble signal handling property.
5) PSR aftertreatment
After PSR handles, still need use other amplitude area detectors to detect in most of practical application and estimate, or carry out processing such as Target Recognition, patent of the present invention is used one than simple but effective post-processing technology (comprising signal inverting and local interpolation processing), with the restoring signal waveform, be beneficial to follow-up further processing.
Input signal x in the nonlinear system (3) i(τ) form, be expressed as x by two parts i(τ)=s i(τ)+w i(τ), (3) formula both sides are got all be worth
y &OverBar; &CenterDot; ( &tau; ) = a y &OverBar; ( &tau; ) - b y &OverBar; ( &tau; ) 3 + s &OverBar; i ( &tau; ) , - - - ( 5 )
Y (τ)=E[x (τ) wherein], s i(τ)=E[s i(τ)].Work as condition | y &OverBar; &CenterDot; ( &tau; ) | < < s &OverBar; i ( &tau; ) When satisfying, can get the signal inversion formula and be
s i(τ)≈by(τ) 3-ay(τ). (6)
In the reality, the available τ of the calculating of average y (τ) averaged amplitude value of adjacent spaces constantly estimates, therefore, and the signal s that inverting obtains i(τ) be the level and smooth in short-term of actual signal, except the minimum signal sampling point of amplitude, i.e. their amplitude s i(τ) → 0, most points can both satisfy condition | y &OverBar; &CenterDot; ( &tau; ) | < < s &OverBar; i ( &tau; ) . For the minimum amplitude output signal that does not satisfy condition, can pass through interpolation, technology such as level and smooth is recovered original waveform.
6) time scale inverse transformation
Through 1) and 2) linear process, can obtain spatial gain and temporal gain, and then utilize 3)-5) wave beam territory PSR Nonlinear Processing, further promoted the feeble signal handling property, and the signal waveform distortion that makes nonlinear system handle generation is recovered, this moment each wave beam territory signal all with τ as time scale, for not influencing subsequent treatment, shown in Fig. 1 treatments B, needing 5) afterwards signal carries out the time scale inverse transformation, be n=τ/L, to recover the time-domain signal s in each wave beam territory under the former sampling rate i(n).
The example explanation: establishing transmits is the 1.2kHz-1.5kHz linear FM signal, pulsewidth 500ms, and receiving battle array is 16 yuan of linear arrays, signal to noise ratio (S/N ratio)-20dB, 20 ° of echo incident angles.What Fig. 3 showed is the comparison of gained beam pattern after the beam pattern after conventional wave beam formation (CBF) and matched filtering (MF) processing and CBF, MF and PSR Combined Treatment, dotted line and dot-and-dash line are represented the result that two kinds of method single random number simulations produce respectively among the figure, and solid line correspondence assembly average separately, as seen from the figure, after increasing PSR and corresponding aftertreatment, secondary lobe significantly reduces (reducing about 10dB).
Fig. 3 is the impact analysis of PSR to target Bearing Estimation.Dotted line and dot-and-dash line are that the emulated data that each time produces is at random handled the gained result, add the labelled notation solid line for not utilize PSR to handle each time gained result's average, and the rectangle marked solid line is an average of utilizing PSR and each time of aftertreatment gained result.
What Fig. 4 showed is the result of two target correspondences, wherein target 1 echo signal to noise ratio (S/N ratio) is-20dB, and the incident orientation angle is 15 °, and target 2 echo signal to noise ratio (S/N ratio)s are-23dB, incident angle is 25 °, as can be seen from the figure, CBF and MF handle can only estimate one of them target azimuth, and secondary lobe is very high, and after increasing PSR and aftertreatment, secondary lobe obviously reduces, and two target azimuths all can estimate, has shown DOA estimation ability preferably.
Comparative result when Fig. 4 is two targets.Target 1 echo signal to noise ratio (S/N ratio)-20dB, 15 ° of incident angles, target 2 echo signal to noise ratio (S/N ratio)-23dB, 25 ° of incident angles.Add the labelled notation solid line for not utilize PSR to handle each time gained result's average, the rectangle marked solid line is to utilize PSR to handle each time gained result's average.
Be the validity of further verification algorithm, Fig. 5 is marine Data Processing in Experiment result, and used reception battle array is 16 yuan of linear arrays, and target is positioned at about 20 ° of orientation, and used broadband signal frequency range is 1.2kHz-1.5kHz during data processing.By among the figure to two kinds of algorithms more as can be known, PSR can effectively reduce secondary lobe equally.-60 ° of places, orientation are two passive sources that fall within the frequency band that initiatively transmits among the figure, are used for other experiment purposes.
Fig. 5 is marine Data Processing in Experiment result.Add the labelled notation solid line and do not handle the gained result for utilizing PSR, the rectangle marked solid line is handled the gained result for utilizing PSR.
To burying the ability of the faint Echo Processing of target, carried out the waveguide experimental verification for verifying this algorithm.The laboratory waveguide is about 14m, wide 1.22m, and depth of water 1.42m, acoustic absorbant is posted in waveguide on four sides, and the bottom is covered with the fine sand of 0.2m.Target is embedded in 1cm under the sand bed, and distance receives battle array 8m.Used object detection method is launched focusing at first utilizing the time reversal technology in the experiment, and the guiding sound wave incides target, then echo is carried out collectiong focusing, the echoed signal that each array element is received becomes focus beam territory signal behind collectiong focusing (multi-path delay compensation), but list of references [Yan Liming, Li Jianlong, Pan Xiang are introduced in concrete detection method and experiment, Zhao Hangfang, Zhu Hengnian, " handle time reversal and be used to bury target detection ", acoustic journal, 2008 (6), pp.64-69].Fig. 6 is an experimental data after the wave beam territory focuses on, and utilizes PSR and the comparison that does not utilize PSR to handle, and as seen from the figure, after the focus beam territory increased PSR and handles, 8m buries at the place target-echo intensity obviously to be increased.
Fig. 6 is waveguide Data Processing in Experiment result.Target is embedded in 1cm under the sand bed, and distance receives battle array 8m.Dotted line is handled the gained result for utilizing PSR, solid line be the time reversal connection pinching burnt wave beam territory increase PSR and handle after the gained result.

Claims (2)

1, a kind of sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment, it is characterized in that: described sensor array beam territory feeble signal disposal route may further comprise the steps:
1) spatial beams forms:
If source signal/echo is expressed as after each sensor receives:
r(n)=v(φ s)s(n)+w(n), (1)
R (n)=[r wherein 1(n) r 2(n) ... r M(n)], noise/reverberation w (n)=[w 1(n) w 2(n) ... w M(n)], M is the sensor number, and s (n) is for passive source or initiatively launch echoed signal, v (φ s) be the battle array response vector, φ sBe azimuth of target;
At first this M dimension space signal is carried out wave beam and form processing, to obtain the spatial gain of battle array; Be located at and carry out wave beam formation on I the direction, obtain I wave beam and be expressed as:
x i(n)=c Hi)r(n),i=1,2,…,I, (2)
C (φ wherein i) be that battle array is driven to φ iThe weight vector of direction, this weight vector designs according to different wave beam formation methods, and subscript H represents conjugate transpose;
2) time scale conversion:
To each wave beam territory signal x i(n) time shaft elongates, and after the time scale conversion, wave beam territory signal indication is x i(τ), τ=Ln wherein, L is the change of scale multiple;
3) wave beam territory PSR handles:
Adopt most typical bistable state nonlinear system:
dy ( &tau; ) d&tau; = ay - b y 3 + x i ( &tau; ) , - - - ( 3 )
Wherein systematic parameter a and b are positive number, x i(τ) be system's input, y (τ) is system's output;
Thereby natural frequency by regulating system parameter a and b change system itself;
At first, the signal to noise ratio (S/N ratio)/letter of definition output mixes than for weighing the objective function of PSR handling property index, establishing objective function being
Figure A2009100994380003C1
Then systematic parameter a and b regulate by following formula:
Wherein parameter a and b need the input x according to system i(τ) carry out the self-adaptation adjustment, when objective function was maximum, a and b were the optimized parameter of nonlinear system;
4) PSR aftertreatment:
Input signal x in the nonlinear system (3) i(τ) form, be expressed as x by two parts i(τ)=s i(τ)+w i(τ), (3) formula both sides got all be worth:
y &OverBar; &CenterDot; ( &tau; ) = a y &OverBar; ( &tau; ) - b y &OverBar; ( &tau; ) 3 + s &OverBar; i ( &tau; ) , - - - ( 5 )
Y (τ)=E[x (τ) wherein], s i(τ)=E[s i(τ)]; Work as condition | y &OverBar; &CenterDot; ( &tau; ) | < < s &OverBar; i ( &tau; ) When satisfying, must the signal inversion formula be:
s i(τ)≈by(τ) 3-ay(τ). (6)
The calculating of average y (τ) with τ constantly the averaged amplitude value of adjacent spaces estimate, therefore, the signal s that inverting obtains i(τ) be the level and smooth in short-term of actual signal, except the minimum signal sampling point of amplitude, i.e. their amplitude s i(τ) → 0, most points can both satisfy condition | y &OverBar; &CenterDot; ( &tau; ) | < < s &OverBar; i ( &tau; ) ; For the minimum amplitude output signal that does not satisfy condition, recover original waveform by interpolation, smoothing technique;
5) time scale inverse transformation:
Carry out the time scale inverse transformation, i.e. n=τ/L is to recover the time-domain signal s in each wave beam territory under the former sampling rate i(n).
2, the sensor array beam territory feeble signal disposal route based on parameter-induced stochastic resonance and aftertreatment as claimed in claim 1, it is characterized in that: under the active target detection event, in described step 1) and step 2) between increase wave beam territory matched filter processing.
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