CN102185661B - Noise enhancement distributed detection method and system based on Bayes criterion of gradient method - Google Patents

Abstract

The invention relates to a noise enhancement distributed detection method and a system based on the Bayes criterion of the gradient method. A multi-path observation vector is preliminary judged by a sensor and then is transmitted to a fusion center via a transmission channel for a final judgment. Before the final judgment, the noise is added under the Bayes criterion of the gradient method. Through adding the noise to the final judgment under the Bayes criterion of the gradient method, the performance of the distributed detection is enhanced. In the meanwhile, the distributed detection method is still effective even the channels and the fusion center of a distributed system are not independent, so the distributed detection method is suitable for various non-ideal distributed systems, and can improve the detection performance of the non-ideal distributed systems.

Description

Strengthen distribution detection method and system based on the noise under the gradient method bayesian criterion

Technical field

The present invention relates to a kind of noise and strengthen the Distributed Detection method and system, relate in particular to a kind of based on the enhancing distribution detection method of the noise under the gradient method bayesian criterion and system.

Background technology

In the distributed multi-sensor treatment system, each transducer carries out certain preliminary treatment earlier to the observation data that obtains, and the data with compression send other transducer to then, are aggregated into fusion center at last.The compressibility preliminary treatment of data has been reduced requirement to communication bandwidth.The distributed multi-sensor structure can reduce performance requirement, the reduction cost to single-sensor.The signal processing mode that disperses can increase calculated capacity.Along with this distributed detection system is used more and more widely, how further to optimize distributed detection system and become the problem that receives much concern.Existing optimisation technique is generally carried out from the following aspects:

The optimization of local decision rule: distributed detection system is at first done a preliminary judgement for the information that is transferred to each transducer, delivers to fusion center again.The suboptimization criterion by improving the decision rule of each local detectors, improves the detectability of system exactly.

The optimization of fusion criterion: fusion center forms total judgement according to the compressed information that receives.If utilize bayesian criterion to optimize the Distributed Detection problem, generally make the cost function minimum of fusion center, and then seek optimum fusion criterion, the detection mistake of fusion center is minimized.

Distributed network structure design: at different distributed network structure and the signal transmission forms of user's request design, improve the input ability of system, finally reach customer objective.

At present prior art mostly be the local observed value of hypothesis be condition independently, and the output of the local sensor that receives of fusion center is without any loss, then under Niemann Pierre Si criterion, can draw the decision rule of the local sensor that optimum likelihood ratio detects.Channel at local sensor and fusion center is under the independent non-ideality, and optimum local likelihood ratio detects as can be known.The optimal policy of a large amount of local detectors is based in various degree, and the knowledge of channel statistical grows up.

In view of this, prior art and research are conceived to ideal situation more: the channel of local detector and fusion center is to carry out under the independent situation.Yet, along with the fast development of radio communication and wireless sensor network, produce the more actual constraints channel model different with needing exploitation.For example because limited bandwidth and a large amount of users, so the interference of interchannel also can not be left in the basket as receiving signal, so it is the function of the output of part local sensor.For example: Gauss's interference channel model.Therefore, in many methods, likelihood ratio detects rule and still is used widely in local sensor.But for distributed detection system, even adopt the optimum fusion rule at fusion center, the performance of whole system remains suboptimal.

Summary of the invention

The technical problem that the present invention solves is: make up a kind of based on the enhancing distribution detection method of the noise under the gradient method bayesian criterion and system, overcome in the prior art for distributed detection system, when the channel of local detector and fusion center non-when separate, the technical problem that its performance is low relatively.

Technical scheme of the present invention is: provide a kind of and strengthen the distribution detection method based on the noise under the gradient method bayesian criterion, comprise and carry out the transducer that signal is handled, carry out the transmission channel of signal transmission, the fusion center that multiple signals are judged, described multichannel observation data constitutes the multichannel observation vector respectively, described detection method comprises the steps: that described multichannel observation vector carries out final decision by described transmission channel to described fusion center behind described transducer preliminary judgement, add noise before carrying out final decision under the bayesian criterion of gradient method, the probability density function of described noise is:

The probability density function of expression noise,

N wherein ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain.

Further technical scheme of the present invention is: described noise is used for described transducer at the preliminary judgement previous crops.

Further technical scheme of the present invention is: described noise final decision previous crops behind preliminary judgement is used for described fusion center.

Further technical scheme of the present invention is: described noise is used for described transducer at the preliminary judgement previous crops, and the final decision previous crops is used for described fusion center behind preliminary judgement simultaneously.

Technical scheme of the present invention is: make up a kind of based on the enhancing of the noise under gradient method bayesian criterion distributed detection system, comprise and carry out the transducer that signal is handled, carry out the transmission channel of signal transmission, the fusion center that multiple signals are judged, the noise module that adds noise, described multichannel observation data constitutes the multichannel observation vector respectively, described multichannel observation vector carries out final decision by described transmission channel to described fusion center behind described transducer preliminary judgement, described noise module adds noise in signal under the bayesian criterion of gradient method before carrying out final decision, and the probability density function of described noise is:

Wherein The probability density function of expression noise, The probability density function of expression noise, N wherein ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain.

Further technical scheme of the present invention is: described noise module adds noise contributions in described transducer before preliminary judgement.

Further technical scheme of the present invention is: described noise module adds noise contributions in described fusion center before the final decision behind preliminary judgement.

Further technical scheme of the present invention is: described noise module adds noise contributions in described transducer before preliminary judgement, adds noise contributions simultaneously before the final decision in described fusion center behind preliminary judgement.

Technique effect of the present invention is: the present invention is a kind of to strengthen distribution detection method and system based on the noise under the gradient method bayesian criterion, multichannel observation vector of the present invention carries out final decision by described transmission channel to described fusion center behind described transducer preliminary judgement, before carrying out final decision, adding noise under the bayesian criterion of gradient method by adding noise under the bayesian criterion in gradient method before carrying out final decision, the present invention adds noise and judges, improved the performance of Distributed Detection, simultaneously, independently situation is still effectively mutually at each passage of distributed system and fusion center, be applicable to various imperfect distributed systems, make it to detect performance and improve.

Description of drawings

Fig. 1 is schematic flow sheet of the present invention.

Fig. 2 is Pe of the present invention and the change curve chart of Δ Pe in iterative process.

Fig. 3 is structural representation of the present invention.

Embodiment

Below in conjunction with specific embodiment, technical solution of the present invention is further specified.

As shown in Figure 1, the specific embodiment of the present invention is: provide a kind of and strengthen the distribution detection method based on the noise under the gradient method bayesian criterion, comprise and carry out the transducer 1 that signal is handled, carry out the transmission channel 2 of signal transmission, the fusion center 3 that multiple signals are judged, described multichannel observation data constitutes the multichannel observation vector respectively, described detection method comprises the steps: that described multichannel observation vector is transferred to described fusion center 3 by described transmission channel 2 and carries out final decision behind described transducer 1 preliminary judgement, add noise before carrying out final decision under the bayesian criterion of gradient method, the probability density function of described noise is:

Wherein

The probability density function of expression noise,

The probability density function of expression noise, N wherein ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain.Specifically, noise can be considered as DC level this moment.

As shown in Figure 1, specific implementation process of the present invention is as follows: y ₁, y ₂..., y _MBe the vector of the observation data formation of M transducer 1, by every road signal is increased noise n ₁, n ₂..., n _M, be sent to each transducer 1, by the processing of transducer, tentatively be judged as u ₁, u ₂..., u _M, through being transferred to fusion center 3, fusion center 3 increases suitable noise w earlier according to the data that receive and judges that again final decision is u ₀

One, the multichannel observation data constitutes the multichannel observation vector respectively.

As shown in Figure 1, at first obtain observation data y from phenomenon ₁, y ₂..., y _M, multichannel observation data y ₁, y ₂..., y _MConstitute the multichannel observation vector.

As shown in Figure 1, in distributed detection system, noise both can act on the transducer 1, can act on fusion center 3 again, but also the two acted on simultaneously.Introduce the situation of noise contributions below.

Two, under bayesian criterion, can make systematic function reach optimum form of noise.

In distributed detection system, M transducer is as the response of associated electromagnetic field or sound field, and signal comes from different signal sources.Based on " 0 " " 1 " signal that transducer receives, make the judgement of dualism hypothesis, (H at fusion center ₀) only there is noise, (H in the representative sensor ₁) the representative input signal that is transferred to transducer comprises noise and signal.

u _nRepresent the output of n local sensor, its value is 0 or 1, has 2 ^MPlanting may.R representative hypothesis H ₁The subclass of setting up namely " has signal to exist ".The false alarm probability that then obtains and detection probability are:

$P_i\left(n\right)={\mathrm{\Σ}}_{u_n\∈R}\mathrm{Pr}\left(u_n\right|H_i),i=\mathrm{0,1}---\left(A2.1\right)$

Pr (u _n| H _i) representative hypothesis H ₁Set up time series u _nArrive the probability of fusion center.Sequence u _nCan be assigned to R territory or its supplementary set R according to Chair-Varshney fusion criterion or other judgement fusion criterion ₀The territory.u _NkRepresent sequence u _nK element.By separate getting between transducer

$\mathrm{Pr}\left(u_n\right|H_i)={\mathrm{\Π}}_{k=1}^M\left\{(1-u_{\mathrm{nk}})\right[1-P_{\mathrm{ki}}]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}\}---\left(A2.2\right)$

P wherein _KiBe the detection probability of i=1 in k the transducer or the false alarm probability of i=0.

At first, suppose noise n in each transducer _kIndependent mutually, the probability density function of noise is f _N(n) satisfy condition

f _N(n)≥0 for all n (A2.3)

${\∫}_N{f}_N\left(n\right)\mathrm{dn}=1---(A2.4)$

The noise probability density function is f in each local sensor _Nk(n _k), satisfy condition

f _Nk(n _k)≥0 for all n _k (A2.5)

${\∫}_{\mathrm{Nk}}{f}_{\mathrm{Nk}}\left(n_k\right)d{n}_k=1---\left(A2.6\right)$

After the process noise strengthens in each transducer be

$\mathrm{Pr}\left(u_n\right|H_i)={\mathrm{\Π}}_{k=1}^M\left\{(1-u_{\mathrm{nk}})\right[1-{\∫}_N{P}_{\mathrm{ki}}\left(n_k\right)f_{\mathrm{Nk}}\left(n_k\right)d{n}_k]+$

$u_{\mathrm{nk}}{\∫}_N{P}_{\mathrm{ki}}\left(n_k\right)f_{\mathrm{Nk}}\left(n_k\right)d{n}_k\}---\left(A2.7\right)$

It is equivalent to

$\mathrm{Pr}\left(u_n\right|H_i)={\mathrm{\Π}}_{k=1}^M{\∫}_N\left\{(1-u_{\mathrm{nk}})\right[1-P_{\mathrm{ki}}\left(n_k\right)]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}\left(n_k\right)\}{f}_{\mathrm{Nk}}\left(n_k\right)d{n}_k$

(A2.8)

Because the n in each transducer _kSeparate, so

$\mathrm{Pr}\left(u_n\right|H_i)={\∫}_N{\mathrm{\Π}}_{k=1}^M\left\{(1-u_{\mathrm{nk}})\right[1-P_{\mathrm{ki}}\left(n_k\right)]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}\left(n_k\right)\}{f}_{\mathrm{Nk}}\left(n_k\right)\mathrm{dn}$

$={\∫}_N\left({\mathrm{\Π}}_{k=1}^M\right\{(1-u_{\mathrm{nk}})[1-P_{\mathrm{ki}}\left(n_k\right)]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}\left(n_k\right)\left\}\right)\left({\mathrm{\Π}}_{k=1}^M{f}_{\mathrm{Nk}}\left(n_k\right)\right)\mathrm{dn},---\left(A2.9\right)$

Wherein

Obtained by (A2.1),

$P_i\left(f_N\right)={\mathrm{\Σ}}_{u_n\∈R}\mathrm{Pr}\left(u_n\right|H_i)$

$={\∫}_N\left({\mathrm{\Σ}}_{u_n\∈R}{\mathrm{\Π}}_{k=1}^M\right\{(1-u_{\mathrm{nk}})[1-P_{\mathrm{ki}}\left(n_k\right)]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}\left(n_k\right)\left\}\right){\mathrm{\Π}}_{k=1}^M{f}_{\mathrm{Nk}}\left(n_k\right)\mathrm{dn}.---\left(A2.10\right)$

We stipulate

$P_i\left(n\right)={\mathrm{\Σ}}_{u_n\∈R}{\mathrm{\Π}}_{k=1}^M\left\{(1-u_{\mathrm{nk}})\right[1-P_{\mathrm{ki}}\left(n_k\right)]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}\left(n_k\right)\}---\left(A2.11\right)$

$f_N\left(n\right)={\mathrm{\Π}}_{k=1}^M{f}_{\mathrm{Nk}}\left(n_k\right)---\left(A2.12\right)$

Then (A2.10) formula becomes

$P_i\left(f_N\right)={\∫}_N{P}_i\left(n\right)f_N\left(n\right)\mathrm{dn}---\left(A2.13\right)$

As seen, the noise n in the transducer _kWhen separate, f _N(n) be the Joint Distribution of probability density.

In fact, the noise n in each transducer _kNon-when independent, we still can obtain the conclusion of (A2.13) formula.Joint probability density still is f _N(n).But work as n _kNon-when independent, (A2.7) formula is false, so (A2.8) (A2.9) (A2.10) also is false.But false alarm probability or detection probability in k the transducer that noise strengthens still are P _Ik(n _k), so (A2.11) formula is set up.We make P ₁(n) maximum is to find the most effective n.Yet n is random process, and the function of random process still is random process, asks P so the problem of maximizing has become ₁(n) expectation E (P ₁(n)) Zui Da problem, i.e. (A2.13) formula.We can expand to the problem that non-independent distribution formula detects, and expression formula is constant.This means no matter whether local sensor is independent, and false alarm probability or detection probability that noise strengthens all are the functions of accidental resonance noise.When in the channel loss being arranged, the independent distribution formula detects and has transposition error.That is to say that it is α that channel k can be expressed as the transposition error probability _kAnd β _kBinary channel.

Consider the influence of channel errors α and β, we obtain the detection probability P of equivalence _K1With false alarm probability P _K0For

$P_{\mathrm{ki}}^c\left(n\right)=(1-{\mathrm{\β}}_k)P_{\mathrm{ki}}\left(n\right)+(1-P_{\mathrm{ki}}\left(n\right)){\mathrm{\α}}_k---\left(A2.14\right)$

So P _i(n) equivalent expression is

$P_i\left(n\right)={\mathrm{\Σ}}_{u_n\∈R}{\mathrm{\Π}}_{k=1}^M\left\{(1-u_{\mathrm{nk}})\right[1-P_{\mathrm{ki}}^c\left(n\right)]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}^c\left(n\right)\}$

$={\mathrm{\Σ}}_{u_n\∈R}{\mathrm{\Π}}_{k=1}^M\left\{(1-u_{\mathrm{nk}})\right[1-((1-{\mathrm{\β}}_k)P_{\mathrm{ki}}\left(n_k\right)+(1-P_{\mathrm{ki}}\left(n_k\right)){\mathrm{\α}}_k)]+u_{\mathrm{nk}}((1-$

${\mathrm{\β}}_k)P_{\mathrm{ki}}\left(n_k\right)$

$+(1-P_{\mathrm{ki}}\left(n_k\right)){\mathrm{\α}}_k)\}---\left(A2.15\right)$

As seen, it still is the function of n.

Be p at prior probability ₁And p ₀Situation under, C _IjH is worked as in representative _jFor true time is judged to H _iCost function (i, j=0,1).For example: when satisfying C ₁₀＞C ₀₀And C ₀₁＞C ₁₁During condition, the mistaken verdict cost is higher than correct judgement cost.Overall risk R is expressed as

R(f _N)＝C ₀₀(1-P _FA(f _N))p ₀+C ₁₀P _FA(f _N)p ₀+C ₀₁(1-P _D(f _N))p ₁+C ₁₁P _D(f _N)p ₁

(A2.16)

P wherein _FA(f _N)=P ₀(f _N), P _D(f _N)=P ₀(f _N).In order to find the optimum noise under the bayesian criterion, we need solve following problem:

$f_{N_{\mathrm{opt}}}=\arg \mathrm{mi}{n}_{f_N\left(n\right)\∈F}R\left(f_N\right)---\left(A2.17\right)$

Satisfy restrictive condition

$f_{N_{\mathrm{opt}}}\≥0\mathrm{for\; all\; n}---\left(A2.18\right)$

${\∫}_N{f}_{N_{\mathrm{opt}}}\left(n\right)\mathrm{dn}=1---\left(A2.19\right)$

The expression formula of Distributed Detection (A2.17) is (A2.19) (A2.18), and is identical with single channel noise enhancing input problem.Therefore, we obtain similar theorem by similar proof: the optimum or approaching optimum probability density function for the independent noise n in the local sensor that makes the Distributed Detection best performance under bayesian criterion is

$f_{N_{\mathrm{opt}}}\left(n\right)=\mathrm{\δ}(n-n_0)---\left(A2.20\right)$

Three, obtain optimum noise relevant parameter.

In the priori Probability p ₁And p ₀Under the known situation, C _IjH is worked as in representative _jFor true time is judged to H _iCost function (i, j=0,1).For example: when satisfying C ₁₀＞C ₀₀And C ₀₁＞C ₁₁During condition, the mistaken verdict cost is higher than correct judgement cost.Overall risk R is expressed as

R＝C ₀₀(1-P _FA)p ₀+C ₁₀P _FAp ₀+C ₀₁(1-P _D)p ₁+C ₁₁P _Dp ₁

(A3.1)

C in particular cases in the error probability minimum ₀₀=C ₁₁=0, C ₀₁=C ₁₀=1, p ₀=p ₁=0.5, (A3.1) becomes behind the adding noise

Pe(n)＝0.5P _FA(n)+0.5(1-P _D(n))

(A3.2)

Wherein, Pe (n) is error probability.

u _nRepresent the output of n local sensor, its value is 0 or 1, has 2 ^MPlanting may.R representative hypothesis H ₁The subclass of setting up namely " has signal to exist ".The false alarm probability that then obtains and detection probability are

$P_i\left(n\right)={\mathrm{\Σ}}_{u_n\∈R}\mathrm{Pr}\left(u_n\right|H_i),i=\mathrm{0,1}---\left(A3.3\right)$

Wherein, Pr (u _n| H _i) representative hypothesis H ₁Set up time series u _nArrive the probability of fusion center.

Fusion criterion hypothetical sequence u _nLikelihood ratio function at R or its supplementary set R ' is

$\frac{\mathrm{Pr}\left(u_n\right|H_1)}{\mathrm{Pr}\left(u_n\right|H_0)}\≥\mathrm{\η}\⇒u_n\∈R---\left(A3.4\right)$

Perhaps

$\frac{\mathrm{Pr}\left(u_n\right|H_1)}{\mathrm{Pr}\left(u_n\right|H_0)}<\mathrm{\&eta;}\&DoubleRightArrow;u_n\&Element;R^{\&prime;}---\left(A3.5\right)$

Can also use other fusion criterion.u _NkRepresent sequence u _nK element.Because the independence between transducer gets

$\mathrm{Pr}\left(u_n\right|H_i)={\mathrm{\&Pi;}}_{k=1}^M\left\{(1-u_{\mathrm{nk}})\right[1-P_{\mathrm{ki}}]+u_{\mathrm{nk}}{P}_{\mathrm{ki}}\}---\left(A3.6\right)$

In order to make Pe (n) reach minimum by changing noise n.At any n ₀Near the point, error Pe (n) can be similar to is expressed as n-n ₀Binary function.

$\mathrm{Pe}\left(n\right)=\mathrm{Pe}\left(n_0\right)+g\&CenterDot;(n-n_0)+\frac{1}{2}{(n-n_0)}^{\&prime;}\&CenterDot;H\&CenterDot;(n-n_0)---\left(A3.7\right)$

Wherein g is at n ₀Gradient vector (the g of point ₁, g ₂..., g _M)

$g_k=\frac{\&PartialD;\mathrm{Pe}\left(n\right)}{\&PartialD;n_k}|n=n_0---\left(A3.8\right)$

H is at n ₀The extra large gloomy matrix of point, its matrix element is

$H_{\mathrm{mk}}=\frac{{\&PartialD;}^2\mathrm{Pe}\left(n\right)}{\&PartialD;n_m\&PartialD;n_k}|n=n_0---\left(A3.9\right)$

At noise n ₀Test set in, (A3.8) formula equal sign the right is minimum to have obtained a new set by making.To find the solution M system of linear equations for this reason.

${\mathrm{\&Sigma;}}_{m=1}^M{H}_{\mathrm{km}}(n_m-n_{0m})=-g_k,1\&le;k\&le;M---\left(A3.10\right)$

The new set of noise is

n＝n ₀-h，h＝H ^-1g. (A3.11)

Error change value is

$\mathrm{\&Delta;Pe}=-\frac{1}{2}g\&CenterDot;h=-\frac{1}{2}{\mathrm{\&Sigma;}}_{k=1}^M{\mathrm{\&Sigma;}}_{m=1}^M\left(H^{-1}\right)g_k{g}_m---\left(A3.12\right)$

Value at k the element of n point gradient g is

$g_k=\frac{\&PartialD;\mathrm{Pe}\left(n\right)}{\&PartialD;n_k}=-0.5\frac{\&PartialD;P_1\left(n\right)}{\&PartialD;n_k}+0.5\frac{\&PartialD;P_0\left(n\right)}{\&PartialD;n_k},1\&le;k\&le;M---\left(A3.13\right)$

(A3.6) (A3.7) must by (A3.3)

$\frac{\&PartialD;P_i\left(n\right)}{\&PartialD;n_k}={\mathrm{\&Sigma;}}_{u_n\&Element;R}(1-{2u}_{\mathrm{nk}})p_{\mathrm{ki}}\left(n_k\right)\mathrm{Pr}\left(u_n^k\right|H_i),i=\mathrm{0,1}.---\left(A3.14\right)$

P wherein _Ki(n _k) be n _kProbability density function, u _NkN the sequence u that is _nDisregard k element.

$\mathrm{Pr}\left(u_n^k\right|H_i)={\mathrm{\&Pi;}}_{r\&NotEqual;k}\left\{(1-u_{\mathrm{nr}})\right[1-P_{\mathrm{ri}}\left(n_r\right)]+u_{\mathrm{nr}}{P}_{\mathrm{ri}}\left(n_r\right)\}---\left(A3.15\right)$

As infructescence u _n Remove k element 0 or 1, so can equivalence be expressed as sequence

And sequence

If two sequences all are positioned at the R territory, (A3.14) sum term of formula is by every generation of cancelling each other, and one is 1-2u _Nk=1, another is 1-2u _Nk=-1.When

In the R territory,

When non-R territory, sum term only comprises u _n, (A3.14) formula is transformed to R _kDomain representation is

$\frac{\&PartialD;P_i\left(n\right)}{\&PartialD;n_k}=-P_{\mathrm{ki}}\left(n_k\right){\mathrm{\&Sigma;}}_{\mathrm{ki}},i=\mathrm{0,1}---\left(A3.16\right)$

Wherein

∑ _Ki, i=0,1 depends on fusion criterion and all quantization level except k element.(A3.15) k the element representation of gradient g is in the formula

g _k＝0.5P _k1(n _k)∑ _k1-0.5P _k0(n _k)∑ _k0 (A3.18)

Suppose that the zero income equation that these elements are equivalent to local smallest error function is

$\frac{p_{k1}\left(n_k\right)}{p_{k0}\left(n_k\right)}=\frac{{\mathrm{\&Sigma;}}_{k0}}{{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="110407092448.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="k"\; filenames="110407092448.png"\; state="\{\{state\}\}">k</figure-callout>\; </figure-callout>}1}},1\&le;k\&le;M---\left(A3.19\right)$

The diagonal entry of the gloomy matrix in sea is

$H_{\mathrm{kk}}=0.5{\mathrm{<figure-callout\; id="1"\; label="P\; k"\; filenames="110407092448.png"\; state="\{\{state\}\}">P</figure-callout>}}_k^1\left(n_k\right){\mathrm{\&Sigma;}}_{k1}-0.5{\mathrm{<figure-callout\; id="0"\; label="P\; k"\; filenames="110407092443.png"\; state="\{\{state\}\}">P</figure-callout>}}_k^0\left(n_k\right){\mathrm{\&Sigma;}}_{k0}---\left(A3.20\right)$

For off diagonal element, we differentiate (A3.15) formula substitution (A3.14) formula

$\frac{{\&PartialD;}^2{P}_i\left(n\right)}{\&PartialD;n_k\&PartialD;n_m}=-{\mathrm{\&Sigma;}}_{u_n\&Element;R}(1-2u_{\mathrm{nk}})(1-2u_{\mathrm{nm}})P_{\mathrm{ki}}\left(n_k\right)P_{\mathrm{mi}}\left(n_m\right)\mathrm{Pr}\left\{u_n^{\mathrm{km}}\right|H_i\}---\left(A3.21\right)$

Wherein

N the sequence u that is _nRemove k and m element, so

$H_{\mathrm{km}}=-0.5\frac{{\&PartialD;}^2{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="110407092448.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}{\&PartialD;n_k\&PartialD;n_m}+0.5\frac{{\&PartialD;}^2{\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="110407092443.png"\; state="\{\{state\}\}">P</figure-callout>}}_0}{\&PartialD;n_k\&PartialD;n_m}---\left(A3.22\right)$

Can obtain calculating any testing site n ₀Gradient g and the method for Hai Sen matrix H, new testing site can be tried to achieve by (A3.11) formula.This process lasts till the change amount in (A3.12) | Δ Pe| is lower than ∈, and wherein ∈ belongs to Pe (n ₀), value is ∈=0.0001

Here note 2 differences: at first, error Pe (n) minimum value is not unique, at the set R of these minimum values _MIn the non-positive definite of extra large gloomy matrix H, (A3.12) the Δ Pe in the formula may on the occasion of, so just can not determine next testing site n with (A3.11) formula ₀Therefore current some n ₀The right side of substitution (A3.19) formula, the left side of solving equation obtains new quantization level:

${\mathrm{<figure-callout\; id="0"\; label="n\; k"\; filenames="110407092443.png"\; state="\{\{state\}\}">n</figure-callout>}}_k\&LeftArrow;{\mathrm{\&Lambda;}}_k^{-1}({\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="110407092443.png"\; state="\{\{state\}\}">k</figure-callout>}0}/{\mathrm{\&Sigma;}}_{k1}),1\&le;k\&le;M---\left(A3.23\right)$

Wherein

Be the contrary of k likelihood ratio,

Consider that from integral body we should make up a Jacobi type method and find the solution (A3.19) formula like this, but its convergence effect is very slow.In the example of next joint, (A3.23) formula produces and shrinks sequence of mapping by taking the logarithm or Bessel function contrary, and finally obtains a testing site n during again for negative at C ₀If but when data be non-negative, it is suboptimal separating when 1 or M-1 quantization level are zero.(A3.11) formula will cause some n _kBecome negative, for avoiding this result, we take following step.We calculate the quantity in each stage with the vector h in (A3.11) formula

$r={\min }_{h_k>0}({\mathrm{<figure-callout\; id="0"\; label="n\; k"\; filenames="110407092443.png"\; state="\{\{state\}\}">n</figure-callout>}}_k/h_k),1\&le;k\&le;M---\left(A3.25\right)$

If r＜1 replaces with (A3.11) formula

${\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="110407092443.png"\; state="\{\{state\}\}">n</figure-callout>}}_0\&LeftArrow;n_0-\frac{1}{2}\mathrm{rh}---\left(A3.26\right)$

Otherwise (A3.11) formula will be for next step.

The factor is in order to guarantee the new value n of all quantization level _0kNon-vanishing.The quantized value r of long run test point is that 0 situation also may take place, and will recomputate with new initial condition in this case.

Irregular Δ Pe＞0 and r＜1 situation only occurs once in a while in the starting stage.Gloomy matrix is regularly positive in the sea, in case the n point has advanced trench around minimum value, (A3.11) formula makes it arrive the valley point fast.The algorithm of this Pe of making (n) cost minimization sees Table I (the equation expression formula of corresponding this joint of numeral in the bracket).

For example: make numerical value n Rayleigh distributed

p _k0(nk)＝exp(-(θ _k-n _k))U(θ _k-n _k)，p _k1(n _k)＝a _kexp(-a _k(θ _k-n _k))U(θ _k-n _k)， (A3.27)

$a_k=\frac{1}{1+S_k}---\left(A3.28\right)$

S wherein _kBe the signal to noise ratio of k transducer, U () is unit step function, θ _kBe threshold value,

$U\left(x\right)=\left\{\begin{array}{cc}1,& x\&GreaterEqual;0,\\ 0,& x<0\end{array}\right.---\left(A3.29\right)$

Complementary cumulative distribution is

q _k0(n _k)＝exp(-(θ _k-n _k))U(θ _k-n _k)， (A3.30)

q _k1(n _k)＝exp(-a _k(θ _k-n _k))U(θ _k-n _k)，(A3.31)

(A3.26) the contrary of likelihood ratio is in the formula

${\mathrm{\&Lambda;}}_k^{-1}\left(x\right)={(1-a_k)}^{-1}\ln (x/a_k).---\left(A3.32\right)$

This example assumes M=7, S _k=[7,14,21,28,35,42,49], threshold value is θ _k=[8,16,24,32,40,48,56] are namely as x＞θ _kThe time, be judged to H ₁, through after 67 iteration, C=0.0563 becomes C=0.0006 as can be seen from Figure 2, and optimum noise is υ=[3.1013,5.5130,13.7036,21.7963,29.8510,37.8872,45.9128].N thus ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain.

Detailed process is as follows:

0: initialization n ₀=0

1: with μ _nSequence (A3.5) is categorized into R or R ' by (A3.4)

2: according to (A3.18) compute gradient g, (A3.21) calculate extra large gloomy matrix H according to (A3.20)

3: calculate _MThe vectorial h=H of unit ^-1g

4: calculate according to (A3.12)

If ΔPe≥0

Calculate new n according to (A3.23);

Got back to for the 0th step;

Else

Calculate r according to (A3.25)

5：If r≥1

Calculate new n according to (A3.11);

Else

Calculate new n according to (A3.26);

End if

6：If|ΔPe|＜∈Pe

Finish, quit a program.

Else

Got back to for the 0th step.

End if

End if

As shown in Figure 1, preferred implementation of the present invention is: described noise only acts on described transducer before preliminary judgement.Only act at noise under the situation of transducer, find under bayesian criterion, can make systematic function reach optimum form of noise, the optimum or approaching optimum probability density function for the independent noise n in the local sensor that makes the Distributed Detection best performance under bayesian criterion is

$f_{N_{\mathrm{opt}}}\left(n\right)=\mathrm{\&delta;}(n-n_0)$

Wherein

The probability density function of expression noise,

N wherein ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain, detailed process is with above-mentioned process.

As shown in Figure 1, preferred implementation of the present invention is: described noise module adds noise contributions in described fusion center before the final decision behind preliminary judgement, and concrete processing procedure coexists and only acts on described transducer before the preliminary judgement.

As shown in Figure 1, preferred implementation of the present invention is: described noise is used for described transducer at the preliminary judgement previous crops, and the final decision previous crops is used for described fusion center behind preliminary judgement simultaneously.At this moment, described noise each passage of distributed system and fusion center mutually independently situation still effectively, concrete processing procedure coexists and only acts on described transducer before the preliminary judgement.

As shown in Figure 3, the specific embodiment of the present invention is: make up a kind of based on the enhancing of the noise under gradient method bayesian criterion distributed detection system, comprise and carry out the transducer 1 that signal is handled, carry out the transmission channel 2 of signal transmission, the fusion center 3 that multiple signals are judged, the noise module 4 that adds noise, described multichannel observation data constitutes the multichannel observation vector respectively, described detection method comprises the steps: that described multichannel observation vector is transferred to described fusion center 3 by described transmission channel 2 and carries out final decision behind described transducer 1 preliminary judgement, described noise module adds noise in signal under the bayesian criterion of gradient method before carrying out final decision, and the probability density function of described noise is:

Wherein

The probability density function of expression noise, N wherein ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain.

Specific implementation process is the same with the implementation process that strengthens the distribution detection method based on the noise under the gradient method bayesian criterion.

As shown in Figure 3, preferred implementation of the present invention is: described noise module 4 adds noise contributions in described transducer 1 before preliminary judgement.Specific implementation process is the same with the implementation process that strengthens the distribution detection method based on the noise under the gradient method bayesian criterion.

As shown in Figure 3, preferred implementation of the present invention is: described noise module 4 adds noise contributions in described fusion center 3 before the final decision behind preliminary judgement.Specific implementation process is the same with the implementation process that strengthens the distribution detection method based on the noise under the gradient method bayesian criterion.

As shown in Figure 3, preferred implementation of the present invention is: described noise module 4 adds noise contributions in described transducer 1 before preliminary judgement, adds noise contributions simultaneously before the final decision in described fusion center 3 behind preliminary judgement.Specific implementation process is the same with the implementation process that strengthens the distribution detection method based on the noise under the gradient method bayesian criterion.

Above content be in conjunction with concrete preferred implementation to further describing that the present invention does, can not assert that concrete enforcement of the present invention is confined to these explanations.For the general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, can also make some simple deduction or replace, all should be considered as belonging to protection scope of the present invention.

Claims (8)

1. one kind strengthens the distribution detection method based on the noise under the gradient method bayesian criterion, it is characterized in that, comprise and carry out the transducer that signal is handled, carry out the transmission channel of signal transmission, the fusion center that multiple signals are judged, the multichannel observation data constitutes the multichannel observation vector respectively, described detection method comprises the steps: that described multichannel observation vector carries out final decision by described transmission channel to described fusion center behind described transducer preliminary judgement, add noise before carrying out final decision under the bayesian criterion of gradient method, the probability density function of described noise is: fN _Pt(n)=δ (n-n ₀), wherein, fN _Opt(n) probability density function of expression noise,

N wherein ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain.

2. strengthen the distribution detection method according to claim 1 is described based on the noise under the gradient method bayesian criterion, it is characterized in that described noise is used for described transducer at the preliminary judgement previous crops.

3. strengthen the distribution detection method according to claim 1 is described based on the noise under the gradient method bayesian criterion, it is characterized in that, described noise final decision previous crops behind preliminary judgement is used for described fusion center.

4. strengthen the distribution detection method according to claim 1 is described based on the noise under the gradient method bayesian criterion, it is characterized in that described noise is used for described transducer at the preliminary judgement previous crops, the final decision previous crops is used for described fusion center behind preliminary judgement simultaneously.

5. one kind strengthens distributed detection system based on the noise under the gradient method bayesian criterion, it is characterized in that, comprise and carry out the transducer that signal is handled, carry out the transmission channel of signal transmission, the fusion center that multiple signals are judged, the noise module that adds noise, the multichannel observation data constitutes the multichannel observation vector respectively, described multichannel observation vector carries out final decision by described transmission channel to described fusion center behind described transducer preliminary judgement, described noise module adds noise in signal under the bayesian criterion of gradient method before carrying out final decision, and the probability density function of described noise is: fN _Pt(n)=δ (n-n ₀), wherein, fN _Opt(n represents the probability density function of noise,

N wherein ₀By being target with bayes cost minimum or error probability minimum, utilize gradient method to pass through repeatedly iteration, finally when the error probability variation equals or approaches zero, stop iteration and obtain.

6. strengthen distributed detection system according to claim 5 is described based on the noise under the gradient method bayesian criterion, it is characterized in that described noise module adds noise contributions in described transducer before preliminary judgement.

7. strengthen distributed detection system according to claim 5 is described based on the noise under the gradient method bayesian criterion, it is characterized in that, described noise module adds noise contributions in described fusion center before the final decision behind preliminary judgement.

8. strengthen distributed detection system according to claim 5 is described based on the noise under the gradient method bayesian criterion, it is characterized in that, described noise module adds noise contributions in described transducer before preliminary judgement, add noise contributions simultaneously before the final decision in described fusion center behind preliminary judgement.

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