CN103944593B - Bi-stable stochastic resonance array processing method and system based on independent receiving units - Google Patents
Bi-stable stochastic resonance array processing method and system based on independent receiving units Download PDFInfo
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Abstract
The invention relates to the field of signal processing and provides a bi-stable stochastic resonance array processing method based on independent receiving units. The bi-stable stochastic resonance array processing method based on the independent receiving units comprises the following steps that A, signals are input into M independent bi-stable systems which are arranged in parallel in the receiving units; B, the input signals are computed in the bi-stable systems, wherein the computing equation is seen in the text; C, results output by the M independent bi-stable systems which are arranged in parallel are added and are averaged, and then a signal is output. The multiple bi-stable systems form a parallel array, the structure is simple, and the method is easy to implement; the stochastic resonance phenomenon of the array is more obvious than that of a single bi-stable system, restraint to the noise is more remarkable, the signal to noise ratio is improved greatly, and the practicability is high; compared with a self-adaption system or other complex systems, a bi-stable stochastic resonance array processing system based on the independent receiving units has the advantages of being high in processing speed, not high in requirement for hardware and capable of lowering cost.
Description
Technical field
The invention belongs to field of signal processing, more particularly to based on the bistable-state random resonance array of individual reception unit at
Reason method and system.
Background technology
People always want to obtain the signal useful to oneself, but these signals are can often drown out in substantial amounts of noise.
In field of signal processing, noise is typically considered the harmful signal to useful signal generation severe jamming of a class.At signal
The basic goal of reason is exactly in order that useful signal and noise separation, or to strengthen useful signal, suppresses noise.People's analysis is made an uproar
The formation of sound, study noise correlation properties, try every means disinthibite, burbling noise, it is desirable to reach enhancing useful signal
Purpose, specifically how process the small-signal being submerged in noise, even more as its difficulty height causes numerous researcheres
Pay attention to.
Common signal processing method is divided into time domain approach and frequency domain method, mainly has Power estimation theory, higher order statistical point
Analysis, theoretical sef-adapting filter, blind signal analysis, neutral net, wavelet theory, Sampling Integral and time domain average etc..These
Prior art typically has following features：1st, reduce interference by suppressing noise：Wavelet transformation decomposes many chis signals and associated noises
In degree, then the wavelet coefficient for belonging to noise is removed under each yardstick, retain and strengthen the wavelet coefficient for belonging to signal, most
The signal after wavelet noise is reconstructed afterwards；2nd, eliminated by burbling noise and disturbed：Time domain average is from the signal of noise jamming
The process of extracting cycle signal, also referred to as coherent detection.Intercept signal is gone by interval of certain cycle to mechanical signal, then
It is average after the Signal averaging that will be intercepted, the aperiodic component and random disturbances in signal can be so eliminated, retains the week for determining
Phase composition；3rd, signal gain is improved by Mathematical treatment：The methods such as such as blind signal analysis, neutral net and adaptive-filtering, lead to
Effective mathematic(al) manipulation is crossed, signal to noise ratio or detection probability etc. is improved；4th, useful signal is extracted by single accidental resonance unit：
Signal further realizes the process side that signal to noise ratio increases by the increase noise in system after single receiving unit is received
Method；5th, useful signal is extracted by the accidental resonance array processing method of dependent reception device：The technology is by one is passed
The signal that sensor is received is distributed to a series of stochastic resonance system and is processed.And then obtain larger signal gain.
Although existing and various suppression noises that are will releasing, the method for strengthening useful signal is provided to multi-signal environment
Support, but generally speaking the above method has its application conditions and limitation, still come with some shortcomings part：Complex structure
Degree：Sef-adapting filter and neural network structure are complicated, high cost；Processing speed has much room for improvement：Adaptive filter algorithm is multiple
It is miscellaneous, it is computationally intensive, and the selection of parameter also needs to test to determine, application is inconvenient.Sampling Integral device need to be by sacrifice
Time increases accumulative frequency to realize；The universal performance of architecture：Various neural network architectures be only applicable to a class or
A few class problems, poor universality；The scope of application is restricted：Neutral net is large-scale (either statically or dynamically) system of nonlinearity
System, the complexity of its height make it impossible to Accurate Analysis its property indices.Which greatly limits the suitable of neutral net
Use scope.Recursion type structural self adaptive algorithm it is non-linear, the Exact Analysis of adaptive process astringency wait to inquire into, actual
Using still by a definite limitation.During Practical Calculation is considered in the research of power spectrum, data can only take limited, compose also always with limited
Resolution shows, and from from the point of view of Physical Experiment and numerical computations, the very long solution of a cycle and a Chaotic Solution are
It is difficult to what is distinguished；Processing gain is limited：Stochastic resonance system is although simple to operate, but conventional stochastic resonance system is to signal
Gain is less, it is impossible to improve output signal-to-noise ratio by a relatively large margin.
The content of the invention
The present invention provides a kind of stable state accidental resonance array processing method double based on individual reception unit, it is intended to solve with
Gain of the machine resonator system to signal is less, and complex structure, processing speed are slow, can not improve asking for output signal-to-noise ratio by a relatively large margin
Topic.
The present invention is achieved in that a kind of bistable-state random resonance array processing method based on individual reception unit,
The bistable-state random resonance array processing method is comprised the following steps：
A, the individual separate bistable systems of M that the signal input parallel arranged of noise will be mixed with；
B, the signal to being input in bistable system carry out calculating process, wherein the equation for calculating process is：
C, the result of the M of parallel arranged independent bistable system output is added and average output signal again；
Wherein, in equation：In, A0Cos (Ω t) --- system is input into
Sinusoidal signal, ξiThe system input zero-mean white Gauss noise of (t) --- i-th array element；xiThe system of (t) --- i-th array element
Output；U (x) --- system potential function,A, b are systematic parameter.
The present invention further technical scheme be：Step A is comprised the following steps：
A1, transmitting terminal launch sinusoidal signal；
A2, M bistable system keeps at a certain distance away to put constitutes the separate receiving units of M；
A3, M receiving unit receives the sinusoidal signal for being mixed with Gaussian noise respectively.
The present invention further technical scheme be：Step C is comprised the following steps：
C1, the result of parallel arranged M independent bistable system output is summed up into process；
C2, will plus and process result carry out signal output after average computation process.
The present invention further technical scheme be：With the increase of number M of the bistable system, output signal-to-noise ratio
Increase, its signal to noise ratio increase be not more and more obvious.
The present invention further technical scheme be：Bistable system number M is odd number and the bistable system
When number is M-1, output difference is less than 10-16。
The present invention further technical scheme be：Bistable system number M is even number and the bistable system
When number is M+1, input sinusoidal signal frequency is identical, and input signal amplitude increases, and input signal-to-noise ratio is lifted, then system output noise
Than being lifted.
The present invention further technical scheme be：Bistable system number M is even number and the bistable system
When number is M+1, input sinusoidal signal amplitude is identical, and frequency input signal is less than 0.05 more than 0.01, produces accidental resonance and exports
Signal to noise ratio is between 0.26-0.33；Frequency input signal persistently increases, output signal-to-noise ratio increasingly level off to one do not rely on
The fixed value of frequency.
Another object of the present invention is to provide a kind of bistable-state random resonance ARRAY PROCESSING based on individual reception unit
System, the bistable-state random resonance array processing system include：
Signal input receiver module, for separate double of M of the signal input parallel arranged by noise is mixed with
Steady-state system；
Processing module being calculated, calculating process being carried out for the signal to being input in bistable system, wherein calculating is processed
Equation be：
Plus with average output module, for adding and putting down again the result of the M of parallel arranged independent bistable system output
Equal output signal；
Wherein, in equation：In, A0Cos (Ω t) --- system is input into
Sinusoidal signal, ξiThe system input zero-mean white Gauss noise of (t) --- i-th array element；xiThe system of (t) --- i-th array element
Output；U (x) --- system potential function,A, b are systematic parameter.
The present invention further technical scheme be：The signal input receiver module includes：
Signal transmitter unit, launches sinusoidal signal for transmitting terminal；
Receiving unit Component units, put composition M separate for M bistable system is kept at a certain distance away
Receiving unit；
Signal receiving unit, receives the sinusoidal signal for being mixed with Gaussian noise respectively for M receiving unit.
The present invention further technical scheme be：It is described plus and average output module include：
Plus and processing unit, for the result of parallel arranged M independent bistable system output is summed up process；
Average calculation unit, for the result for adding and process is carried out signal output after average computation process.
The invention has the beneficial effects as follows：Multiple bistable systems are collectively constituted into parallel array, simple structure, it is easy to real
It is existing；Array is become apparent from than the Stochastic Resonance Phenomenon of single bistable system, more significantly for the suppression of noise, can be significantly
Signal to noise ratio is improved, it is practical；Relative to the system that self adaptation etc. is complicated, the system processing speed is fast, and the requirement to hardware
It is not high, it is possible to decrease cost.
Description of the drawings
Fig. 1 is the bistable-state random resonance array processing method stream based on individual reception unit provided in an embodiment of the present invention
Cheng Tu；
Fig. 2 is the parallel array system of M bistable system composition provided in an embodiment of the present invention；
Fig. 3 be element number of array provided in an embodiment of the present invention for 1 and even number when output signal-to-noise ratio；
Fig. 4 be element number of array provided in an embodiment of the present invention be odd number when output signal-to-noise ratio；
Signal to noise ratio when Fig. 5 is array number M=20 unlike signal amplitudes provided in an embodiment of the present invention；
Signal to noise ratio when Fig. 6 is array number M=21 provided in an embodiment of the present invention during unlike signal amplitude；
Fig. 7 is the asynchronous SNR of array number M=20 frequency input signals provided in an embodiment of the present invention；
Fig. 8 is the asynchronous SNR of array number M=21 frequency input signals provided in an embodiment of the present invention；
Fig. 9 is frequency input signal provided in an embodiment of the present invention close to signal to noise ratio when 0；
Figure 10 is array number M=20 provided in an embodiment of the present invention, signal to noise ratio when parameter b changes；
Figure 11 is signal to noise ratio when array number M=21 parameters b provided in an embodiment of the present invention change；
Figure 12 is array number M=20 provided in an embodiment of the present invention, signal to noise ratio when systematic parameter a changes；
Figure 13 is array number M=21 provided in an embodiment of the present invention, signal to noise ratio when systematic parameter a changes.,
Specific embodiment
Fig. 1 shows a kind of bistable-state random resonance array processing method based on individual reception unit of present invention offer
Flow chart, details are as follows for which：
In step S1, transmitting terminal in systems sends and needs sinusoidal signal.
In step S2, M bistable system is spaced a distance and is put so as to formed M it is separate and
The individual reception unit that will not be interfered with each other.
In step S3, in signal processing system, M receiving unit receives the sinusoidal signal for being mixed with Gaussian noise respectively；
Wherein M independent receiving unit is in the processing system with parallel forming array form.
In step S4, the mixed signal to being input in each bistable system is processed into calculating, by the letter for processing
Number output, wherein in calculation processes, the equation of employing：In equation
In formula, A0Cos (Ω t) --- system is input into sinusoidal signal, ξiThe white Gauss of system input zero-mean of (t) --- i-th array element
Noise；xiThe system output of (t) --- i-th array element；U (x) --- system potential function,A, b are
System parameter.
In step S5, each result of the M of parallel arranged independent bistable system output is added up respectively
Plus process with calculating.
In step S6, the accumulative signal for adding and calculating process is carried out into meansigma methodss process, the signal that meansigma methodss were processed
The output signal that output composition system was processed.
Each bistable system comes with sensor to receive signal, realizes that the signal that each unit is received is identical, and
Noise is then statistically independent identically distributed mutually.Accidental resonance is capable of achieving by the intensity for changing additive noise
With the increase of number M of the bistable system, output signal-to-noise ratio also increases, and its signal to noise ratio increases more and more not
Substantially.
When bistable system number M is M-1 with the bistable system number for odd number, output difference is less than 10-16。
When bistable system number M is M+1 with the bistable system number for even number, sinusoidal signal frequency is input into
Identical, input signal amplitude increases, and input signal-to-noise ratio is lifted, then system output signal-to-noise ratio is lifted.
When bistable system number M is M+1 with the bistable system number for even number, sinusoidal signal amplitude is input into
Identical, frequency input signal is less than 0.05 more than 0.01, and generation accidental resonance output signal-to-noise ratio is between 0.26-0.33；Input
Signal frequency persistently increases, output signal-to-noise ratio increasingly level off to one be independent of the fixed value with frequency.
In an array the number of bistable system system is exported with impact, wherein, systematic parameter a=1, b=1,
Input sinusoidal signal frequency is 1Hz, and it is bistable-state random resonance system number that signal amplitude is 0.3, M.By can be with analogous diagram
Find out, it is when bistable system number M is odd number (M ＞ 1), defeated when array system output is M-1 with bistable system number
Go out curve approximation coincidence.And according to emulation data, the output difference in the case of two kinds is less than 10-16。
As shown in Figure 3 and Figure 4, this is systematic parameter a=1, b=1, and input sinusoidal signal frequency is 1Hz, and signal amplitude is
0.3, when bistable-state random resonance system number is respectively 1,2,10,30,50 and Output simulation figure when 1,3,11,31,51.From
It can be seen that with the increase of input noise intensity, each curve all occurs first increasing to the feelings that peak value reduces again in two figures
Condition, illustrates to generate Stochastic Resonance Phenomenon.And the increase of number M with bistable system, output signal-to-noise ratio also increases, but
The effect of increase is not more and more obvious.
In bistable system, input signal amplitude has on system output and affects, wherein, when bistable system in array
Number M when being 20 and 21, parameter a=1, b=1, input sinusoidal signal frequency is 1Hz, signal amplitude respectively 0.01,
0.05th, 0.1,0.2,0.3 when, as shown in Figure 5 and Figure 6.For Fig. 5 and Fig. 6, the frequency of system input sinusoidal signal is fixed, is changed
Become the amplitude of input signal, during amplitude A=0.05, highest output signal-to-noise ratio is 0.08676, now D (noise variance)=0.13；
During amplitude A=0.1, highest output signal-to-noise ratio is 0.347, now D=0.13；During amplitude A=0.2, highest output signal-to-noise ratio is
1.388, now D=0.13；During amplitude A=0.3, highest output signal-to-noise ratio is 3.12, and now D=0.13 is can be seen that for not
Same input signal amplitude, input noise variance when producing accidental resonance are basically unchanged.Be input into during accidental resonance due to producing
Noise is basically unchanged, therefore the difference of input signal-to-noise ratio comes from the difference of input signal amplitude.
As Fig. 5 and Fig. 6 can be seen that that is, input signal-to-noise ratio is lifted if input signal amplitude increases, then system output is believed
Make an uproar than lifting identical multiple.
In bistable system, frequency input signal has on system output and affects, wherein, as shown in Figure 7 and Figure 8, this is
When number M of bistable system in array is 20 and 21, parameter a=1, b=1, input sinusoidal signal amplitude are A=0.1, are believed
Number frequency is respectively output signal-to-noise ratio curve when 0.01,0.05,0.1,10,100,5000.By more than, two figures can be seen that and work as
When frequency input signal is less (more than 0.01 be less than 0.05), produce accidental resonance when output signal-to-noise ratio 0.26 and 0.33 it
Between.And making frequency input signal persistently increase, then output signal-to-noise ratio when system reaches accidental resonance can be seen close to 0.35.
Go out, as frequency constantly increases, output signal-to-noise ratio increasingly levels off to a fixed value for not relying on frequency.
And it is constant to work as other conditions, frequency input signal is less than 0.01, level off to 0 when analogous diagram it is as shown in Figure 9.From figure
As can be seen that when frequency input signal close to 0 i.e. close to direct current signal when, output signal-to-noise ratio curve is in the range of very little
Drastically raise, and rapid falling, define an impulse.Now periodic modulation acts on very little, and particle is between potential barrier
Transition presents irregular saltus step, at this moment there is no Stochastic Resonance Phenomenon.
Systematic parameter on system output with affect, wherein, when input signal amplitude be A0=0.1, frequency f=1Hz,
During observation M=20 and M=21, different system parameter is for the impact of output.Parameter a=1, b are 0.001,0.1,0.3,0.5,1
With analogous diagram when 2.2 as shown in Figure 10 and Figure 11.It can be seen that when b is near 0.1, not producing random
Covibration.When b continues to increase, Stochastic Resonance Phenomenon is gradually produced.Noise variance when accidental resonance is produced is with the increasing of b
It is gradually reduced greatly, but the peak value of output signal-to-noise ratio but gradually increases.Therefore from from image, the crest of output signal-to-noise ratio curve
It is moved to the left, and crest is gradually uprised.As b is further increased, crest becomes sharp, noise intensity when producing accidental resonance
Minor variations will cause the strong variations of output signal-to-noise ratio.When b continues to increase, Stochastic Resonance Phenomenon fades away.
When input signal amplitude be A0=0.1, frequency f=1Hz, observe in element number of array M=20 and M=21, no
Homologous ray parameter is for the impact of output.Parameter b=1, the such as Figure 12 of analogous diagram when a is 0.001,0.1,0.3,0.5,1 and 1.5
With shown in Figure 13.For shown in Figure 12 and Figure 13, when parameter a very little, the not generation of Stochastic Resonance Phenomenon, with a by
When gradually increasing near 0.5, Stochastic Resonance Phenomenon is occurred in that, but its output signal-to-noise ratio curve ratio is more sharp, accidental resonance is existing
As not substantially, when a is increased near 1, system produces obvious accidental resonance.With the increase of a, when producing accidental resonance
Constantly increase is that crest is moved to right to noise intensity.After a is more than 1.5, output signal-to-noise ratio curve gradually tends to 0.
For, shown in Fig. 3-13, each system all generates the phenomenon of accidental resonance.Signal to noise ratio is with the increasing of noise intensity
Greatly, first it is gradually increased to peak value to be gradually reduced again.Each array system in for each figure, the output during number N ＞ 1 of array
Apparently higher than system during N=1, signal to noise ratio illustrates that the method can improve the output signal-to-noise ratio of bistable-state random resonance system.
When N is odd number (N ＞ 1), curve approximation when output signal-to-noise ratio curve and array number are N-1 is equal, illustrates which is defeated
It is approximately equalised to go out characteristic.
Why more conventional stochastic resonance system snr gain has raising by a larger margin to the present invention, mainly due to
Using mutually independent acceptance and the array element that processes so that the signal section that each unit is received is identical, noise then phase
It is mutually independent.Specifically, obtain for the array processing system of above-mentioned M array element, its output signal-to-noise ratio is：
Wherein
Wherein,AndThe definition of Euler integral of the second kind is：WhereinX in formulai(t)=± xm--- the system output of i-th array element.
The above results can theoretically obtain the signal to noise ratio for exporting.As a result show according to single bistable accidental resonance system
System and traditional array stochastic resonance system, its snr gain are greatly improved.
Another object of the present invention is to provide a kind of bistable-state random resonance ARRAY PROCESSING based on individual reception unit
System, the bistable-state random resonance array processing system include：
Signal input receiver module, for separate double of M of the signal input parallel arranged by noise is mixed with
Steady-state system；
Processing module being calculated, calculating process being carried out for the signal to being input in bistable system, wherein calculating is processed
Equation be：
Plus with average output module, for adding and putting down again the result of the M of parallel arranged independent bistable system output
Equal output signal；
Wherein, in equation：In, A0Cos (Ω t) --- system is input into
Sinusoidal signal, ξiThe system input zero-mean white Gauss noise of (t) --- i-th array element；xiThe system of (t) --- i-th array element
Output；U (x) --- system potential function,A, b are systematic parameter.
The signal input receiver module includes：
Signal transmitter unit, launches sinusoidal signal for transmitting terminal；
Receiving unit Component units, put composition M separate for M bistable system is kept at a certain distance away
Receiving unit；
Signal receiving unit, receives the sinusoidal signal for being mixed with Gaussian noise respectively for M receiving unit.
It is described plus and average output module include：
Plus and processing unit, for the result of parallel arranged M independent bistable system output is summed up process；
Average calculation unit, for the result for adding and process is carried out signal output after average computation process.
In signal processing system, with the increase of number M of the bistable system, output signal-to-noise ratio also increases, its
Signal to noise ratio increase is not more and more obvious.
When bistable system number M is M-1 with the bistable system number for odd number, output difference is less than 10-16。
When bistable system number M is M+1 with the bistable system number for even number, sinusoidal signal frequency is input into
Identical, input signal amplitude increases, and input signal-to-noise ratio is lifted, then system output signal-to-noise ratio is lifted.
When bistable system number M is M+1 with the bistable system number for even number, sinusoidal signal amplitude is input into
Identical, frequency input signal is less than 0.05 more than 0.01, and generation accidental resonance output signal-to-noise ratio is between 0.26-0.33；Input
Signal frequency persistently increases, and output signal-to-noise ratio increasingly levels off to a fixed value for not relying on frequency.
Presently preferred embodiments of the present invention is the foregoing is only, not to limit the present invention, all essences in the present invention
Any modification, equivalent and improvement made within god and principle etc., should be included within the scope of the present invention.
Claims (9)
1. a kind of bistable-state random resonance array processing method based on individual reception unit, it is characterised in that the bistable state
Accidental resonance array processing method is comprised the following steps：
A, the individual separate bistable systems of M that the signal input parallel arranged of noise will be mixed with；
B, the signal to being input in bistable system carry out calculating process, wherein the equation for calculating process is：
C, the result of the M of parallel arranged independent bistable system output is added and average output signal again；
Wherein, in equation：In, A0Cos (Ω t) --- the sinusoidal letter of system input
Number, ξiThe system input zero-mean white Gauss noise of (t) --- i-th array element；xiThe system output of (t) --- i-th array element；U
(x) --- system potential function,A, b are systematic parameter；
Step A is comprised the following steps：
A1, transmitting terminal launch sinusoidal signal；
A2, M bistable system keeps at a certain distance away to put constitutes the separate receiving units of M；
A3, M receiving unit receives the sinusoidal signal for being mixed with Gaussian noise respectively.
2. bistable-state random resonance array processing method according to claim 1, it is characterised in that step C includes
Following steps：
C1, the result of parallel arranged M independent bistable system output is summed up into process；
C2, will plus and process result carry out signal output after average computation process.
3. bistable-state random resonance array processing method according to claim 2, it is characterised in that：With the bistable state
The increase of number M of system, output signal-to-noise ratio also increase, and its signal to noise ratio increase is not more and more obvious.
4. bistable-state random resonance array processing method according to claim 3, it is characterised in that：The bistable system
When number M is M-1 with the bistable system number for odd number, output difference is less than 10-16。
5. bistable-state random resonance array processing method according to claim 4, it is characterised in that：The bistable system
When number M is M+1 with the bistable system number for even number, input sinusoidal signal frequency is identical, and input signal amplitude increases,
Input signal-to-noise ratio is lifted, then system output signal-to-noise ratio is lifted.
6. bistable-state random resonance array processing method according to claim 5, it is characterised in that：The bistable system
When number M is M+1 with the bistable system number for even number, input sinusoidal signal amplitude is identical, and frequency input signal is more than
0.01 is less than 0.05, and generation accidental resonance output signal-to-noise ratio is between 0.26-0.33；Frequency input signal persistently increases, output
Signal to noise ratio increasingly levels off to a fixed value for not relying on frequency.
7. a kind of bistable-state random resonance array processing system based on individual reception unit, it is characterised in that the bistable state with
Machine resonance array processing system includes：
Signal input receiver module, for M separate bistable state of the signal input parallel arranged by noise is mixed with
System；
Processing module is calculated, and calculating process is carried out for the signal to being input in bistable system, wherein calculating the side of process
Cheng Wei：
Plus with average output module, for the result of the M of parallel arranged independent bistable system output being added and average defeated again
Go out signal；
Wherein, in equation：In, A0Cos (Ω t) --- the sinusoidal letter of system input
Number, ξiThe system input zero-mean white Gauss noise of (t) --- i-th array element；xiThe system output of (t) -- i-th array element；U
(x) --- system potential function,A, b are systematic parameter.
8. bistable-state random resonance array processing system according to claim 7, it is characterised in that the signal input connects
Receiving module includes：
Signal transmitter unit, launches sinusoidal signal for transmitting terminal；
Receiving unit Component units, put for M bistable system is kept at a certain distance away and constitute M separate reception
Unit；
Signal receiving unit, receives the sinusoidal signal for being mixed with Gaussian noise respectively for M receiving unit.
9. bistable-state random resonance array processing system according to claim 8, it is characterised in that described plus and average defeated
Going out module includes：
Plus and processing unit, for the result of parallel arranged M independent bistable system output is summed up process；
Average calculation unit, for the result for adding and process is carried out signal output after average computation process.
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