CN104408324B - Multiple sensor information amalgamation method based on D S evidence theories - Google Patents

Abstract

Based on the multiple sensor information amalgamation method of D S evidence theories, it is related to the multiple sensor information amalgamation method of evidence theory, belongs to information fusion field.There is veto by one vote and the probabilistic problem of composite result to solve the computationally intensive of traditional evidence fusion method in combining evidences in invention.Based on the multiple sensor information amalgamation method of D S evidence theories, evidence collection E={ e are obtained_i, i=1,2 ..., l }；According to the framework of identification Θ={ θ of setting₁, θ₂..., θ_nBy evidence e_iIt is proof data m to arrange_i(A)；It is ranked up from small to large by the radix of A, forms Jiao metaset K={ C in order₁, C₂..., C_J, to proof data m_i(C_j) BPA determinizations are carried out, obtain m '_i(C_j)；By w_i(C_j(the m ' of)=1_i(C_j)‑m_i(C_j)) obtain fusion weighting function w_i(C_j)；PressCombining evidences are carried out, the composite result of all evidence collection is obtained, as the output decision-making of sensor.The present invention is applied to multi-sensor information fusion.

Description

Multiple sensor information amalgamation method based on D-S evidence theory

Technical field

The present invention relates to the multiple sensor information amalgamation method of evidence theory, belong to information fusion field.

Background technology

Multi-sensor information fusion is that the information obtained to different data sources or different sensors carries out comprehensive and treatment, Redundancy that may be present and contradictory information between multi-sensor information are eliminated or constrained, the uncertainty of raw information is reduced, with Formed to system environments relatively complete consistent description or judgement.This is improving the decision science of intelligence system, reaction correctly Property and target positioning accuracy, the accuracy of Information locating play conclusive effect, so as to reduce the decision-making of whole system Risk.Multi-sensor information fusion automatic target detection, aircraft navigation, tactical Situation and threat estimating, fault detect with The aspects such as positioning suffer from being widely applied.

The method of multi-sensor information fusion mainly includes probability theory method, D-S evidence theory method, Fuzzy Set Theory With neural net method etc..Wherein D-S evidence theory can merge the attribute information in different levels, while can at utmost connect By unascertained information, fault-tolerant ability is strong, so obtained the attention of people.

D-S evidence theory is that Dempster was proposed first in 1976, and by Shafer specifications into a full theoretical body System.It by object to be identified the constituted definition space of all possible set is identification framework that D-S evidence theory is And the power set of Θ is denoted as 2^Θ.For 2^ΘIn any hypothesis set A, have Basic probability assignment function m (A), be m:2^Θ→ [0,1] and meet following condition：

Wherein φ is empty set, and m is basic probability assignment (the Basic Probability on identification framework Θ Assignment, BPA).In evidence theory, various evidence bodies are merged using the evidence fusion rule of Dempster.If m₁ And m₂It is two BPA functions of evidence, the rule for merging two evidences is defined as follows：

The fusion rule proposed using Dempster more than the multiple sensor information amalgamation method of evidence theory is currently based on, i.e., Formula (1).The rule only considers that evidence ignores proposition reliability attribute in evidence to the common portion of proposition reliability, so as to cause The irrationality of composite result, although the fusion rule has good evidence focusing power, but it cannot be processed differs The limiting case (there is veto by one vote phenomenon) of cause, does not differentiate the probabilistic size of subset where evidence yet.Some are learned Person is improved for the veto by one vote problem in Dempster fusion rules, although can process the situation of evidences conflict, But it is all or part of to there is problems with：1. algorithm focusing power is weak, and composite result increased the uncertainty of evidence, unfavorable Judge in decision-making；2. some algorithm parameters need artificial determination；3. amount of calculation is larger, there are calculating explosion issues.

Relevant document：R.Yager.On the Dempster-Shafer framework and new combination Rules.Information sciences [J], 1987,41 (2)；Wait on the sunny side on some amendment of Combination Rules of Evidence Theory Extra large university of communications's journal [J], 1999,33 (3)；A kind of new composite formula [J] electronics based on evidence theory of grandson's congruence Report, 2000,28 (8)；A kind of combined method of effective treatment conflicting evidence of the such as Deng Yong are infrared with millimeter wave journal [J], and 2004, 23(1)；A kind of synthetic method bullets arrows for processing conflicting evidence of the such as Wang Xiaoxia and guidance journal [J], 2008,27 (5)

In the case where amount of calculation is reduced as far as possible, how while veto by one vote problem in eliminating combining evidences, make conjunction There is the certainty of maximum into result, the key issue of multi-sensor information fusion can be correctly carried out as evidence theory, while Original evidence data are only depended in calculating process, it is not necessary to carry out artificial parameter setting.

The content of the invention

There is veto by one vote to solve the computationally intensive of traditional evidence fusion method in combining evidences in the present invention Problem and the probabilistic problem of composite result, and then propose the multiple sensor information amalgamation method based on D-S evidence theory.

Multiple sensor information amalgamation method based on D-S evidence theory, comprises the following steps：

The acquisition of step one, original evidence：

By the l each sensor source (from the angle of data acquisition, sensor being referred to as sensor source) of sensor when An evidence source is done, is obtained by l bar evidences e_iThe evidence collection E={ e of composition_i, i=1,2 ..., l }；According to the framework of identification of setting Θ={ θ₁, θ₂..., θ_nBy evidence e_iIt is proof data m to arrange_i(A), i=1,2 ..., l；

Θ={ θ₁, θ₂..., θ_nFor proposition mutual exclusion and complete collection are collectively referred to as framework of identification, n is the proposition of framework of identification Number,Represent the event or target pointed by proof data；

Step 2, burnt metaset are extracted and sequence：

Meet proof data m by all in evidence collection E_i(A) A of ＞ 0 is extracted, and is entered from small to large by the radix of A Row sequence, forms Jiao metaset K={ C in order₁, C₂..., C_J, C₁, C₂..., C_JIt is burnt unit, a total J burnt unit；For orderly Jiao unit C in burnt metaset K_j, j=1,2 ..., J, C_jCorresponding proof data is m_i(C_j)；

Step 3, BPA determinizations：

For a certain Jiao unit C in orderly Jiao's metaset K_j, with Jiao unit C_jCorresponding proof data m_i(C_j), it is substantially general to it Rate distributes (Basic Probability Assignment) being determined, i.e. BPA determinizations, obtains m_i′(C_j)；Determinization Formula is：

|C_j| represent Jiao unit C_jRadix；B and C in formula_jRepresent Jiao unit in Jiao's metaset K in order, a certain Jiao unit C_jIt is to work as Jiao unit of preceding calculating, B is except C_jIn addition in order in Jiao's metaset K other are burnt first；|C_j|=1, that is, work as | C_j| when=1, exclude the current Jiao unit C for calculating_jAfter, remaining all burnt units are calculated successively in orderly Jiao's metaset K, A burnt unit is once taken to be calculated, after the completion of all of burnt unit calculates, summation；The purpose of BPA determinizations is carried out, is handle Part (burnt unit's radix is more than 1) is not known in BPA functions to be evenly distributed in Jiao unit that radix is 1；

Step 4, the reliability of burnt unit and synthetic weight：

M obtained by different evidences_i′(C_j) its source of value is different, causes its reliability difference being merged, it is necessary to calculate it Weight in journey；

I-th evidence is calculated for Jiao unit C that radix is 1_jFusion weighting function w_i(C_j), such as following formula：

w_i(C_j)=1- (m_i′(C_j)-m_i(C_j)), | C_j|=1

Step 5, combining evidences：

According to fusion weighting function w_i(C_j) and m_i′(C_j), carry out combining evidences by formula (2)

D represents Jiao unit that radix is 1 in formula；

To all Jiao unit C_jCombining evidences are carried out with above formula, the composite result of all evidence collection is obtained, as biography The output decision-making of sensor.

Beneficial effect of the present invention：

With comprising the n framework of identification Θ={ θ of proposition₁, θ₂..., θ_nAs a example by, it is provided with l datas, i.e. evidence collection E= {e_i, i=1,2 ..., l }, burnt metaset is K={ C₁, C₂..., C_J}.The meter of traditional evidence fusion method (such as Dempster methods) With the increase of burnt unit's number, index increases (referring to the fusion formula of " background technology " part), i.e. amount of calculation for O to calculation amount (J^l).The amount of calculation of the inventive method is concentrated mainly on step 3 and step 5, and the amount of calculation of step 3 is O (Jl), step 5 Amount of calculation be O (Jl), total amount of calculation is the multiple of burnt unit's number and the product Jl of evidence number, and amount of calculation is smaller.Burnt unit's number J Bigger with evidence number l, the amount of calculation that the inventive method is saved is more considerable.By taking Jiao unit number J=10 and evidence number l=5 as an example, tradition Evidence fusion method amount of calculation is O (10⁵)；The amount of calculation of the inventive method is O (10*5).

The present invention eliminates the veto by one vote problem in combining evidences in the case where amount of calculation is greatly decreased.For depositing In Jiao unit of wall scroll evidence negative, can be synthesized according to Jiao unit weight in each evidence, veto by one vote phenomenon is disappeared Removing solid capacity is 100%.Uncertain regardless of original evidence, the determinization for evidence of the invention is more than 90%.

Brief description of the drawings

Fig. 1 is multi-sensor information fusion flow chart；

Fig. 2 proof data flow graphs.

Specific embodiment

Specific embodiment one：With reference to Fig. 1 and Fig. 2 explanation present embodiments, the multisensor letter based on D-S evidence theory Breath fusion method, comprises the following steps：

The acquisition of step one, original evidence：

By the l each sensor source (from the angle of data acquisition, sensor being referred to as sensor source) of sensor when An evidence source is done, is obtained by l bar evidences e_iThe evidence collection E={ e of composition_i, i=1,2 ..., l }；According to the framework of identification of setting Θ={ θ₁, θ₂..., θ_nBy evidence e_iIt is proof data m to arrange_i(A), i=1,2 ..., l；

Θ={ θ₁, θ₂..., θ_nFor proposition mutual exclusion and complete collection are collectively referred to as framework of identification, n is the proposition of framework of identification Number,Represent the event or target pointed by proof data；

Step 2, burnt metaset are extracted and sequence：

Meet proof data m by all in evidence collection E_i(A) A of ＞ 0 is extracted, and is entered from small to large by the radix of A Row sequence, forms Jiao metaset K={ C in order₁, C₂..., C_J, C₁, C₂..., C_JIt is burnt unit, a total J burnt unit；For orderly Jiao unit C in burnt metaset K_j, j=1,2 ..., J, C_jCorresponding proof data is m_i(C_j)；

Step 3, BPA determinizations：

For a certain Jiao unit C in orderly Jiao's metaset K_j, with Jiao unit C_jCorresponding proof data m_i(C_j), it is substantially general to it Rate distributes (Basic Probability Assignment) being determined, i.e. BPA determinizations, obtains m_i′(C_j)；Determinization Formula is：

|C_j| represent Jiao unit C_jRadix；B and C in formula_jRepresent Jiao unit in Jiao's metaset K in order, a certain Jiao unit C_jIt is to work as Jiao unit of preceding calculating, B is except C_jIn addition in order in Jiao's metaset K other are burnt first；|C_j|=1, that is, work as | C_j| when=1, exclude the current Jiao unit C for calculating_jAfter, remaining all burnt units are calculated successively in orderly Jiao's metaset K, A burnt unit is once taken to be calculated, after the completion of all of burnt unit calculates, summation；The purpose of BPA determinizations is carried out, is handle Part (burnt unit's radix is more than 1) is not known in BPA functions to be evenly distributed in Jiao unit that radix is 1；

Step 4, the reliability of burnt unit and synthetic weight：

M obtained by different evidences_i′(C_j) its source of value is different, causes its reliability difference being merged, it is necessary to calculate it Weight in journey；

I-th evidence is calculated for Jiao unit C that radix is 1_jFusion weighting function w_i(C_j), such as following formula：

w_i(C_j)=1- (m_i′(C_j)-m_i(C_j)), | C_j|=1

Step 5, combining evidences：

According to fusion weighting function w_i(C_j) and m_i′(C_j), carry out combining evidences by formula (2)

D represents Jiao unit that radix is 1 in formula；

To all Jiao unit C_jCombining evidences are carried out with above formula, the composite result of all evidence collection is obtained, as biography The output decision-making of sensor.

Specific embodiment two：Fusion weighting function w described in step 4_i(C_j) following condition should be met：

(1) fusion weighting function w_i(C_j) nonnegativity, i.e. w should be met_i(C_j) >=0,

(2) fusion weighting function w_i(C_j) boundedness, i.e. w should be met_i(C_j)≤1, j=1,2 ..., J；

(3) fusion weighting function w_i(C_j) proposition C should be embodied_jReally qualitative extent, for Jiao unit C in original evidence_jWith C_qIf, C_jReally qualitative extent is higher than Jiao unit C_q, then should have w_i(C_j)≥w_i(C_q), wherein q is the index that burnt unit counts, meaning It is identical with j, i.e. q=1,2 ..., J；w_i(C_q) it is C_qFusion weighting function.

Other steps and parameter are identical with specific embodiment one.

Specific embodiment three：Fusion weighting function w described in step 4_i(C_j) meet following condition：

Work as m_i′(C_j)=m_i(C_j) when, w_i(C_j)=1；

Work as m_i(C_j)=0 and m_i′(C_j)=1, w_i)C_j)=0.

Fusion weighting function w_i(C_j) effectively reflect the reliability of evidence.

Other steps and parameter are identical with specific embodiment one or two.

Embodiment

With the stability of three groups of proof validation the inventive method and the degree of accuracy.Embodiment stresses the card of the inventive method Omitted according to the effect of fusion, the step of obtain evidence by sensor information source, proof data directly gives.

Conflicting evidence of first group of evidence involved by Zadeh antinomys.Evidence collection includes two evidence E={ e₁, e₂, its Framework of identification is Θ={ θ₁, θ₂, θ₃, its corresponding BPA is respectively

m₁({θ₁)=0.99, m₁({θ₂)=0.01, m₁({θ₃)=0；

m₂({θ₁)=0, m₂({θ₂)=0.01, m₂({θ₃)=0.99；

The synthetic method proposed with Dempster obtains result for m ({ θ₂)=1, and m (A)=0, A ≠ { θ₂}.This Obvious counterintuitive.

It is calculated as with of the invention：

According to step one, original evidence is obtained, evidence has been provided in the present embodiment.

According to step 2, orderly Jiao metaset K={ { θ are obtained₁, { θ₂, { θ₃}}。

According to step 3, determinization BPA is obtained

m′₁({θ₁)=0.99, m '₁({θ₂)=0.01, m '₁({θ₃)=0；

m′₂({θ₁)=0, m '₂({θ₂)=0.01, m '₂({θ₃)=0.99；

According to step 4, synthetic weight is calculated

According to step 5, composite result is obtained

It can be seen that the present invention can well process conflicting evidence, veto by one vote problem, simultaneously synthesizing rear determinization letter are eliminated Cease is 100%.

Second group of evidence uses the example of " failure evidence ".So-called failure evidence, i.e., propose fusion rule in Dempster Under then, the fusion results of the evidence collection are only determined by half-proof, and other evidences are invalid.

If framework of identification isEvidence collection isIts corresponding BPA is

m₁({θ₅)=0.35, m₁({θ₅, θ₆)=0.65；

m₂({θ₂)=0.8, m₂({θ₅)=0.2, m₄=m₃=m₂。

Use the result and m of Dempster fusion rules₁It is identical, i.e. m₂And later evidence in fusion entirely without Effect.It is calculated as using the present invention：

According to step one, original evidence is obtained, evidence has been provided in the present embodiment.

According to step 2, orderly Jiao metaset K={ { θ are obtained₁, { θ₂, { θ₃, { θ₄, { θ₅, { θ₆, { θ₅, θ₆, Θ }；

According to step 3, determinization BPA is obtained

m′₁({θ₅)=0.675, m '₁({θ₆)=0.325；

m′₂({θ₂)=0.8333, m '₂({θ₁)=m '₂({θ₃)=m '₂({θ₄)=m '₂({θ₅)=m '₂({θ₆)= 0.0333；

m_i' (A)=m '₂(A), i=3,4.

According to step 4, synthetic weight is calculated

w₁({θ₅)=w₁({θ₆)=0.675, w₁(A)=1, A ≠ { θ₅, { θ₆}；

w_i(B)=0.9667, | B |=1, i=2,3,4.

According to step 5, composite result is obtained

m({θ₂)=0.6196, m ({ θ₅)=0.1545, m ({ θ₆)=0.0884, m ({ θ₁)=m ({ θ₃)=m ({θ₄)=0.0248, m (Θ)=0.0631.

It can be seen that the present invention can carry out effective information fusion for the evidence of the lower failure of Dempster rules, one is eliminated Ticket vetos problem, and simultaneously synthesizing rear determinization information is about 94%.

The 3rd group of burnt unit of evidence example nested successively.If framework of identificationEach evidence only one of which is burnt Unit, and nested successively, i.e. m₁Jiao unit be { θ₁, m₂Jiao unit be { θ₁, θ₂, m₃Jiao unit be { θ₁, θ₂, θ₃, and its BPA letter Number meets：

m_i({θ₁, θ₂..., θ_i)=1, i=1,2,3

It is m ({ θ for the result under Dempster composition rules₁)=1, do not square with the fact.

It is calculated as using the present invention：

According to step one, original evidence is obtained, evidence has been provided in the present embodiment.

According to step 2, orderly Jiao metaset K={ { θ are obtained₁, { θ₁, θ₂, { θ₁, θ₂, θ₃}}；

According to step 3, determinization BPA is obtained

m′₁({θ₁)=1；

m′₂({θ₁)=1/2, m '₂({θ₂)=1/2；

m′₃({θ₁)=1/3, m '₃({θ₂)=1/3, m '₃({θ₃)=1/3；

According to step 4, synthetic weight is calculated

w₁(A)=1, | A |=1；

w₂({θ₁)=0.5, w₂({θ₂)=0.5, w₂({θ₃)=1；

w₃({θ₁)=2/3, w₃({θ₂)=2/3, w₃({θ₃)=2/3.

According to step 5, composite result is obtained

m({θ₁)=0.6795, m ({ θ₂)=0.2179, m ({ θ₃)=0.0833, m (Θ)=0.0193,

It can be seen that when the present invention is nested for burnt unit, eliminating veto by one vote problem, simultaneously synthesizing rear determinization information It is 98%.

Claims (3)

1. the multiple sensor information amalgamation method of D-S evidence theory is based on, it is characterised in that comprised the following steps：

The acquisition of step one, original evidence：

L each sensor source of sensor is regarded into an evidence source, is obtained by l bar evidences e_iThe evidence collection E=of composition {e_i, i=1,2 ..., l }；According to the framework of identification Θ={ θ of setting₁,θ₂,…,θ_nBy evidence e_iIt is proof data m to arrange_i (A), i=1,2 ..., l；

Θ={ θ₁,θ₂,…,θ_nFor proposition mutual exclusion and complete collection are collectively referred to as framework of identification, n is the proposition number of framework of identification,Represent the event or target pointed by proof data；

Step 2, burnt metaset are extracted and sequence：

Meet proof data m by all in evidence collection E_i(A) A of ＞ 0 is extracted, and is arranged from small to large by the radix of A Sequence, forms Jiao metaset K={ C in order₁,C₂,…,C_J, C₁,C₂,…,C_JIt is burnt unit, a total J burnt unit；For burnt unit in order Jiao unit C in collection K_j, j=1,2 ..., J, C_jCorresponding proof data is m_i(C_j)；

Step 3, BPA determinizations：

For a certain Jiao unit C in orderly Jiao's metaset K_j, with Jiao unit C_jCorresponding proof data m_i(C_j), to its basic probability assignment Being determined, i.e. BPA determinizations, obtain m '_i(C_j)；Determinization formula is：

$m_i^{\′}\left(C_j\right)=\left\{\begin{array}{c}{\mathrm{\Σ}}_B{m}_i\left(B\right)\frac{|C_j\∩B|}{\left|B\right|},\left|C_j\right|=1\\ 0,\left|C_j\right|\≠1\end{array}\right.---\left(1\right)$

|C_j| represent Jiao unit C_jRadix；B and C in formula_jRepresent Jiao unit in Jiao's metaset K in order, a certain Jiao unit C_jIt is current meter Jiao unit of calculation, B is except C_jIn addition in order in Jiao's metaset K other are burnt first；Work as | C_j|= When 1, the current Jiao unit C for calculating is excluded_jAfter, remaining all burnt units are calculated successively in orderly Jiao's metaset K, once A burnt unit is taken to be calculated, after the completion of all of burnt unit calculates, summation；

Step 4, the reliability of burnt unit and synthetic weight：

I-th evidence is calculated for Jiao unit C that radix is 1_jFusion weighting function w_i(C_j), such as following formula：

w_i(C_j)=1- (m '_i(C_j)-m_i(C_j)),|C_j|=1

Step 5, combining evidences：

According to fusion weighting function w_i(C_j) and m '_i(C_j), carry out combining evidences by formula (2)

$m\left(C_j\right)=\left\{\begin{array}{c}{\mathrm{\Σ}}_i\frac{w_i\left(C_j\right)}{{\mathrm{\Σ}}_p{w}_p\left(C_j\right)}{m}_i^{\′}\left(C_j\right),\left|C_j\right|=1\\ 1-{\mathrm{sum}}_{\left|D\right|=1}m\left(D\right),C_j=\mathrm{\Θ}\end{array}\right.---\left(2\right)$

D represents Jiao unit that radix is 1 in formula；

To all Jiao unit C_jCombining evidences are carried out with above formula, the composite result of all evidence collection is obtained, as sensor Output decision-making.

2. the multiple sensor information amalgamation method based on D-S evidence theory according to claim 1, it is characterised in that step Fusion weighting function w described in rapid four_i(C_j) following condition should be met：

(1) fusion weighting function w_i(C_j) nonnegativity, i.e. w should be met_i(C_j)≥0,

(2) fusion weighting function w_i(C_j) boundedness, i.e. w should be met_i(C_j)≤1, j=1,2 ..., J；

(3) fusion weighting function w_i(C_j) proposition C should be embodied_jReally qualitative extent, for Jiao unit C in original evidence_jAnd C_q, such as Fruit C_jReally qualitative extent is higher than Jiao unit C_q, then should have w_i(C_j)≥w_i(C_q), wherein q is the index that burnt unit counts, meaning and j phases Together, i.e. q=1,2 ..., J；w_i(C_q) it is C_qFusion weighting function.

3. the multiple sensor information amalgamation method based on D-S evidence theory according to claim 1 and 2, it is characterised in that Fusion weighting function w described in step 4_i(C_j) meet following condition：

As m '_i(C_j)=m_i(C_j) when, w_i(C_j)=1；

Work as m_i(C_j)=0 and m '_i(C_jDuring)=1, w_i(C_j)=0.