Multi-sensor information modeling and fusion method based on complex network and evidence distance

Abstract

The invention provides a multi-sensor information modeling and fusion method based on a complex network and an evidence distance. The accuracy of a traditional evidence fusion method is mainly improved. According to the scheme of the invention, modeling is carried out on an obtained BPA by using a complex network, and an evidence distance between nodes is calculated; direct node weights and indirect node weights of all nodes are calculated, and weights of all evidence bodies are obtained through comprehensive calculation; calculating a weighted average value of all evidence bodies, and modifying the original evidence body by adding a weight factor; and finally, fusing all the modified evidence bodies for (P-1) times through a Dempster combination rule to obtain a final result. According to the sensor conflict information modeling and fusion method based on the complex network and the evidence distance, how to solve the conflict information fusion problem in the evidence theory from the angle of sensor information relevance is considered, and the loss of effective information in the multi-sensor information fusion process is correspondingly reduced. Tests prove that the method is high in accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of uncertainty management in multi-source information fusion, and mainly relates to a multi-sensor information modeling and fusion method based on complex networks and evidence distance. Background Art

[0002] In modern warfare, due to the diversification and complexity of offensive weapons and attack means, a single target recognition system can no longer meet the requirements of high-intensity combat state detection, while multi-target sensors can more accurately identify and analyze complex situations. However, multi-sensor recognition means that evidence fusion of multiple recognition results is required. In traditional evidence fusion methods, many uncertain factors are simply treated as deterministic factors, which will lead to poor accuracy of reliability analysis results; in addition, traditional evidence fusion methods often produce counter-intuitive fusion effects when dealing with highly conflicting evidence, and have great defects in terms of application scope and flexibility; moreover, most traditional evidence fusion methods do not consider the correlation between information sources and cannot truly and comprehensively describe the reliability of information sources.

[0003] Therefore, when fusing multi-target sensor information, how to reasonably and comprehensively consider the reliability of information sources and correspondingly improve the accuracy of target recognition is an urgent problem to be solved in multi-target sensor information fusion. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, improve the accuracy of traditional evidence fusion methods, and improve the flexibility of application of traditional evidence fusion methods, the present invention provides a multi-sensor information modeling and fusion method based on complex networks and evidence distance. The main technical problem to be solved by the present invention is: how to improve the existing multi-target sensor information fusion method and thereby improve the accuracy of multi-target sensor information fusion.

[0005] The multi-sensor information modeling and fusion method based on complex networks and evidence distance includes the following steps:

[0006] Step 1: Construct an identification framework for sensor information sources; construct a basic belief assignment (BBA) based on the identification framework; use complex network theory to construct a bipartite graph based on the basic belief assignment (BBA); each basic belief assignment (BBA) corresponds to a node in the bipartite graph, and different nodes are connected by bipartite edges;

[0007] The identification framework Θ is: for information fusion of P sensor information sources, the sensor has N judgment results, where θ 1 …θ N represents N judgment results; Θ is a non-empty set; the identification framework includes N pairwise mutually exclusive events, that is, Θ = {θ 1 , θ 2 …θN}; The power set of the identification framework Θ contains 2 N elements, and the power set 2 Θ of the identification framework Θ is:

[0008]

[0009] Among them, represents the empty set, that is, a set that does not contain any elements;

[0010] The basic belief assignment BBA is: within the identification framework, the mass function m of the evidence body is a mapping of the power set 2 Θ on the interval [0, 1]

[0011]

[0012] And the mass function m of the evidence body satisfies the following relationship:

[0013]

[0014] Among them, when the condition m(A)>0 holds, the propositional subset A is called a focal element; and m(A) is the value of the mass function of the evidence body of the propositional subset A, that is, m(A) is the basic belief assignment BBA, or m(A) is the basic probability assignment BPA;

[0015] If the judgment results of any sensor on the target have two types, that is, N = 2, Θ = {θ 1 , θ 2}, then the basic belief assignment BBA of the sensor is expressed as:

[0016] m(θ 1 ) = 0.2

[0017] m(θ 2 ) = 0.6

[0018] m(Θ) = 0.2 Equation (4)

[0019] Step 2: Calculate the direct node weights of the nodes in the bipartite graph;

[0020] Step 3: Calculate the indirect node weights of the nodes in the bipartite graph;

[0021] Step 4: Calculate the node weights of the nodes in the bipartite graph;

[0022] Step 5: Calculate the weighted evidence body in the bipartite graph;

[0023] Step 6: Update the mass function of the evidence body to an optimized evidence body with low conflict;

[0024] Step 7: Use the Dempster combination rule to fuse the optimized evidence bodies with low conflicts, that is, obtain the evidence body after data fusion, and perform evaluation and judgment based on the evidence body after data fusion.

[0025] Further, the step of calculating the direct node weight of the nodes in the bidirectional graph is as follows:

[0026] Step 2.1: Calculate the evidence distance dj(m i , m j ) between any two nodes;

[0027] Use Equation (5) to calculate the evidence distance between the mass function m i of the evidence body and the mass function m j of the evidence body. The identification frameworks of m i and m j both contain N elements, and i, j = 1…P:

[0028]

[0029] where is the vector corresponding to the mass function m i of the evidence body, is the vector corresponding to the mass function m j of the evidence body, the vector corresponding to the mass function m i of the evidence body and the vector corresponding to the mass function m j of the evidence body are arranged in the order of 2 Θ ; D is a 2 N ×2 N matrix, where:

[0030]

[0031] where x, y = 1,..., 2 N ; A x is the focal element of m i , A y is the focal element of m j ; |·| is the cardinality of a subset; d xy is the element in matrix D;

[0032] Step 2.2: Calculate the direct node strength S i of each node;

[0033] Use Equation (7) to calculate the direct node strength S i of each node, i = 1…P:

[0034]

[0035] where rel ik = 1 - dj(m i , m k ), rel ik represents the correlation between two basic belief assignments (BBAs), i.e., the correlation between node i and node k;

[0036] Step 2.3: Normalize the direct node strength to obtain the direct node weight wd i ;

[0037] The direct node weight wd i is:

[0038]

[0039] The direct node weight wd i is obtained by normalizing the direct node strength S i .

[0040] Furthermore, the steps for calculating the indirect node weights of nodes in the bipartite graph are as follows:

[0041] Step 3.1: Solve for the secondary node strength S' of each remaining node after the j-th node is separately removed from the bipartite graph ji ;

[0042] The secondary node strength S' of each remaining node after the j-th node is separately removed from the bipartite graph ji is:

[0043]

[0044] where j = 1...P, i ≠ j;

[0045] Step 3.2: Solve for the secondary node weight wd' of each remaining node after the j-th node is separately removed from the bipartite graph ji ;

[0046] The secondary node weight wd' of each remaining node after the j-th node is separately removed from the bipartite graph ji is:

[0047]

[0048] where i = 1...P, i ≠ j;

[0049] Step 3.3: Solve for the node vector

[0050] The node vector is the direct node weight wd of the remaining nodes after the j-th node is separately removed from the bipartite graph iA vector composed of;

[0051] Node vector where \(i = 1,\cdots,P\), \(i\neq j\);

[0052] Step 3.4: Solve the secondary node vector

[0053] Node vector is the secondary node weight \(wd'\) of the remaining nodes after separating node \(j\) from the bipartite graph alone ji A vector composed of;

[0054] Secondary node vector where \(i = 1,\cdots,P\), \(i\neq j\);

[0055] Step 3.5: Solve the modulus value of the node vector Modulus value of

[0056] Solve the node vector using Equation (11) Modulus value of

[0057]

[0058] where \(i = 1,\cdots,P\), \(i\neq j\);

[0059] Step 3.6: Normalize the secondary node vector into the quasi-node vector

[0060] Use Equation (12) to normalize the secondary node weight \(wd'\) of the remaining nodes after separating node \(j\) from the bipartite graph alone ji Composed secondary node vector Normalize into the quasi-node vector

[0061]

[0062] where:

[0063]

[0064] where \(i = 1,\cdots,P\), \(i\neq j\);

[0065] Step 3.7: Calculate the relative indirect node strength \(IS_r\) of node \(j\) j ;

[0066] The relative indirect node strength \(IS_r\) of node \(j\) j is:

[0067]

[0068] where j = 1…P;

[0069] Step 3.8: Calculate the absolute indirect node strength IS of node j j ;

[0070] The absolute indirect node strength IS of node j j is:

[0071] IS j = wd j ×ISr j Equation (15)

[0072] where j = 1…P; the absolute indirect node strength IS j is the indirect node strength;

[0073] Step 3.9: Calculate the indirect node weight wid j ;

[0074] The indirect node weight wid j is:

[0075]

[0076] Normalize the indirect node strength IS j to obtain the indirect node weight wid j .

[0077] Furthermore, the specific steps for calculating the node weight of a node in the bidirectional graph are:

[0078] The node weight w of node j j is:

[0079]

[0080] where j = 1...P.

[0081] Furthermore, the specific steps for calculating the weighted evidence body in the bidirectional graph are;

[0082]

[0083] where A is any subset of the power set 2 Θ ; in the formula, m k (A) represents the credibility assignment of the mass function of the k-th evidence body to the target A, and w k is the node weight of the k-th node.

[0084] Furthermore, the specific steps for updating the evidence body mass function to an optimized evidence body with low conflict are:

[0085] The optimized mass function m′ with low conflicti is:

[0086]

[0087] where m i is the evidence body mass function.

[0088] Furthermore, the steps of fusing the optimized evidence bodies with low conflict using Dempster's combination rule are:

[0089] Suppose there are two independent evidence body mass functions m i and m j , then m i and m j are evidence-fused through Dempster's combination rule:

[0090]

[0091] where B and C represent proposition subsets, that is, the focal elements of the two evidence body mass functions m i and m j respectively, and m i (B) is the value of the evidence body mass function of the proposition subset B, and m j (C) is the value of the evidence body mass function of the proposition subset C; k is the normalization factor, that is, the conflict coefficient, and the conflict coefficient measures the conflict degree between m i and m j , and the normalization factor k is:

[0092]

[0093] where k = 0 indicates that there is no conflict between m i and m j , and k = 1 indicates that there is a complete contradiction between m i and m j ; in particular, Dempster's combination rule is only applicable to two BPAs that satisfy the condition k < 1.

[0094] The beneficial effects of the present invention are:

[0095] The present invention proposes a sensor conflict information modeling and fusion scheme based on complex networks and evidence distance. First, the scheme makes a simple and objective judgment on the target according to the recognition results of different sensors, constructs an identification framework and obtains the basic belief assignment (BBA); then uses complex networks to model the BBA, calculates the evidence distance between nodes, and calculates the direct node strength and direct node weight of the nodes according to the evidence distance; then calculates the indirect node weight of the nodes, and the weight of the nodes can be obtained from the direct node weight and indirect node weight of the nodes; then calculates the weighted evidence body in the complex network, and modifies the original evidence body by adding a weight factor; finally, uses the Dempster combination rule for (P - 1) times of fusion.

[0096] Compared with the prior art, the scheme of the present invention starts from the perspective of the relevance of sensor information, effectively solves the problem of conflict information fusion in the evidence theory, and can significantly reduce the loss of effective information in the process of multi - sensor information fusion. At the same time, through evidence distance and weighted average, the subjectivity of the relevance evaluation between tasks is reduced; the confidence of different sensors in the recognition target is modeled by using complex networks, avoiding counter - intuitive results. The modified sensor recognition information is fused by using the Dempster combination rule, overcoming the limitations of a single sensor and greatly improving the accuracy of target recognition; the improved complex network algorithm enhances flexibility, reduces subjectivity, and can output more accurate evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 is a flowchart for the implementation of the sensor conflict information modeling and fusion method based on complex networks and evidence distance;

[0098] Figure 2 is a schematic diagram of complex network modeling. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0099] The multi - sensor information modeling and fusion method based on complex networks and evidence distance includes the following steps:

[0100] Step 1: Construct an identification framework for P sensor information sources;

[0101] Suppose information fusion is performed on P sensor information sources, and the sensors have N judgment results, that is, the reliability levels of N judgment results; where if θ 1 …θ N represents N judgment results, then the identification framework is Θ; Θ is a non - empty set; the identification framework contains N pairwise - exclusive events, that is, Θ = {θ 1 , θ 2 …θ N}; and the power set of the identification framework Θ contains 2 N elements, which are represented as follows:

[0102]

[0103] Among them, represents the empty set, that is, a set that does not contain any elements;

[0104] Step 2: Construct the basic belief assignment (BBA);

[0105] The basic belief assignment is Basic belief assignment;

[0106] Within the frame of discernment, define the mass function of the evidence body; the mass function of the evidence body represents uncertain information, and the mass function m of the evidence body is a mapping on the power set 2 Θ in the interval [0, 1] As shown in Equation (2):

[0107]

[0108] And the mass function m of the evidence body satisfies the following relational expressions:

[0109]

[0110] Among them, when the condition m(A)>0 holds, the proposition subset A is called a focal element; and m(A) is the value of the mass function of the evidence body of the proposition subset A, that is, m(A) is the basic belief assignment BBA, or m(A) is the basic probability assignment BPA; BBA is Basic belief assignment; BPA is Basic probability assignment;

[0111] If the judgment results of any sensor for the target have two types, that is, N = 2, Θ = {θ 1 , θ 2}, assuming that the credibility assignment of the sensor for the target θ 1 is 0.2, the credibility assignment for the target θ 2 is 0.6, and the credibility assignment for the target Θ is 0.2, then the basic belief assignment BBA of the sensor is expressed as:

[0112] m(θ 1 ) = 0.2

[0113] m(θ 2 ) = 0.6

[0114] m(Θ) = 0.2 Equation (4)

[0115] Step 3: Use complex network theory to model the basic belief assignment (BBA) as a bidirectional graph, where each BBA corresponds to a node and different nodes are connected by bidirectional edges;

[0116] Step 4: Calculate the evidence distance dj(m i ,m j );

[0117] Use Equation (5) to calculate the evidence distance between the mass functions m i and m j of the evidence bodies. The frames of discernment of m i and m j both contain N elements, and i, j = 1…P:

[0118]

[0119] where is the vector corresponding to the mass function m i of the evidence body, is the vector corresponding to the mass function m j of the evidence body. The vectors corresponding to the mass functions m i and m and the vector corresponding to the mass function m j are all arranged in the order of 2 . D is a 2 Θ ×2 N matrix, where: N where x, y = 1,..., 2

[0120]

[0121] where A N , A x is the focal element of m i , A y is the focal element of m j ; |·| is the cardinality of a subset;

[0122] Step 5: Calculate the direct node strength S i of each node;

[0123] Use Equation (7) to calculate the direct node strength S i of each node, i = 1…P:

[0124]

[0125] where rel ik = 1 - dj(m i , m k ), relik Represents the correlation between two basic belief assignments BBA, that is, the correlation between node i and node k;

[0126] Step 6: Normalize the direct node strength to obtain the direct node weight wd i ;

[0127] Normalize the direct node strength S i using Equation (8) to obtain the direct node weight wd i :

[0128]

[0129] Step 7: Solve for the sub-node strength S′ of the remaining nodes after the j-th node is separately stripped from the bidirectional graph ji ;

[0130] The sub-node strength S′ of the remaining nodes after the j-th node is separately stripped from the bidirectional graph ji is:

[0131]

[0132] where j = 1…P, i≠j;

[0133] Step 8: Solve for the sub-node weight wd′ of the remaining nodes after the j-th node is separately stripped from the bidirectional graph ji ;

[0134] The sub-node weight wd′ of the remaining nodes after the j-th node is separately stripped from the bidirectional graph ji :

[0135]

[0136] where i = 1…P, i≠j;

[0137] Step 9: Solve for the node vector

[0138] The node vector is the vector composed of the direct node weights wd of the remaining nodes after the j-th node is separately stripped from the bidirectional graph i ;

[0139] The node vector where i = 1…P, i≠j;

[0140] Step 10: Solve for the sub-node vector

[0141] The node vector is the sub-node weight wd′ of the remaining nodes after the j-th node is separately stripped from the bidirectional graphji The vector formed

[0142] The secondary node vector where i = 1…P, i≠j;

[0143] Step 11: Solve for the node vector The modulus value of

[0144] Use Equation (11) to solve for the modulus value of the node vector The modulus value of

[0145]

[0146] where i = 1…P, i≠j;

[0147] Step 12: Normalize the secondary node vector into the quasi-node vector

[0148] Use Equation (12) to separately strip node j from the bipartite graph and then use the secondary node weights wd′ of the remaining nodes ji The secondary node vector formed Normalize it into the quasi-node vector

[0149]

[0150] where:

[0151]

[0152] where i = 1…P, i≠j;

[0153] Step 13: Calculate the relative indirect node strength ISr of node j j ;

[0154] The relative indirect node strength ISr of node j j is:

[0155]

[0156] where j = 1…P;

[0157] Step 14: Calculate the absolute indirect node strength IS of node j j ;

[0158] The absolute indirect node strength IS of node j j is:

[0159] IS j = wd j ×ISr jEquation (15)

[0160] where j = 1…P; the absolute indirect node strength IS j is the indirect node strength;

[0161] Step 15: Normalize the indirect node strength IS j to obtain the indirect node weight wid j ;

[0162] The indirect node weight wid j is:

[0163]

[0164] Step 16: Calculate the node weight w of node j j ;

[0165] The node weight w of node j j is:

[0166]

[0167] where j = 1…P;

[0168] Step 17: Calculate the weighted evidence body m in the bidirectional graph avg ;

[0169] The weighted evidence body m in the bidirectional graph avg is:

[0170]

[0171] where A is any subset of the power set 2 Θ ;

[0172] Step 18: Update the evidence body mass function m i to the optimized evidence body mass function m' with low conflict i ;

[0173] The optimized mass function m' with low conflict i is:

[0174]

[0175] Step 19: Use Dempster's combination rule to fuse the updated P optimized evidence body mass functions m' i for P - 1 times to obtain the final result, that is, the value of the evidence body mass function after data fusion, and then make corresponding evaluation and judgment based on this.

[0176] Specifically, the following are the specific steps for performing P-1 times of fusion using the Dempster combination rule in step 19 to obtain the final result:

[0177] Suppose there are m i and m j two independent bodies of evidence mass functions. Then m i and m j can perform evidence fusion through the Dempster combination rule:

[0178]

[0179] where B and C represent subsets of propositions, that is, the focal elements of the mass functions of the two bodies of evidence m i and m j respectively, and m i (B) is the value of the mass function of the body of evidence for the subset of proposition B, and m j (C) is the value of the mass function of the body of evidence for the subset of proposition C; k is the normalization factor, that is, the conflict coefficient, and the conflict coefficient measures the degree of conflict between m i and m j . The normalization factor k is:

[0180]

[0181] where k = 0 indicates that there is no conflict between m i and m j , and k = 1 indicates that there is a complete contradiction between m i and m j ; in particular, the Dempster combination rule is only applicable to two BPAs that satisfy the condition k < 1.

[0182] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0183] Embodiment 1: A method for modeling and fusing sensor conflict information based on complex networks and evidence distance, characterized by including the following steps:

[0184] Step 1: Assume that there are P sensor informants and N judgment results (reliability levels) in the conflict information fusion; where if θ 1 …θ N represent these N judgment results, then the frame of discernment can be defined as a non-empty set Θ, and this frame of discernment contains N pairwise mutually exclusive events, that is, Θ = {θ 1 , θ 2 …θ N}; and the power set of the frame of discernment Θ contains 2 N elements, which are expressed as follows:

[0185]

[0186] Among them, represents the empty set, that is, a set that contains no elements.

[0187] Step 2: Construct the BBA (Basic belief assignment), which is specifically as follows:

[0188] Within the frame of discernment, define the mass function of the evidence body to represent uncertain information. The mass function m of the evidence body is a mapping on the power set 2 Θ in the interval [0, 1], and its formal expression is as follows:

[0189]

[0190] And this function m satisfies the following relational expressions:

[0191]

[0192] Among them, when the condition m(A)>0 holds, the proposition subset A is called a focal element. And m(A) is the mass function value of the proposition subset A, also known as the basic belief assignment BBA, or the basic probability assignment BPA (Basic probability assignment).

[0193] Specifically, if the recognition result (judgment result) of a certain sensor for a certain target has two types, that is, N = 2, Θ = {θ 1 , θ 2}, assuming that the credibility assignment of this sensor to the target θ 1 is 0.2, the credibility assignment to the target θ 2 is 0.6, and the credibility assignment to the target Θ is 0.2, then the specific BBA representation form of this sensor can be shown as follows:

[0194]

[0195] Step 3: Use complex network theory to model the known BBA as a bidirectional graph. Each BBA corresponds to a node, and different nodes are connected by bidirectional edges.

[0196] Step 4: Use the following formula to calculate the evidence distance between two mass functions m i and m j (whose frame of discernment contains N elements, and i, j = 1…P), that is, the evidence distance between node i and node j:

[0197]

[0198] Among them is the mass function of the evidence body mi The corresponding vector is the evidence body mass function m j The corresponding vector, the evidence body mass function m i The corresponding vector and the evidence body mass function m j The corresponding vector The elements of are all arranged in the order of 2 Θ in; D is a 2 N ×2 N matrix, where:

[0199]

[0200] where x, y = 1,..., 2 N ; A x , A y are the focal elements of m i , m j respectively; |·| is the cardinality of a subset.

[0201] Step 5: Calculate the direct node strength S of each node using the following formula i (i = 1…P):

[0202]

[0203] where rel ik = 1 - dj(m i , m k ), representing the correlation between two BBAs (i.e., node i and node k).

[0204] Step 6: Normalize the direct node strength S i using the following formula to obtain the direct node weight wd i :

[0205]

[0206] Step 7: Solve the sub-node strength S′ of the remaining nodes after each node (node j, j = 1…P) is separately stripped from the complex network using the following formula ji (i = 1…P, i ≠ j):

[0207]

[0208] Step 8: Solve the sub-node weight wd′ of the remaining nodes after each node (node j, j = 1…P) is separately stripped from the complex network using the following formula ji :

[0209]

[0210] Step 9: The direct node weight wd of the remaining nodes after separately stripping node j (j = 1…P) from the complex network i forms a node vector

[0211] Step 10: The secondary node weight wd′ of the remaining nodes after separately stripping node j (j = 1…P) from the complex network ji forms a node vector

[0212] Step 11: Solve for the modulus value of the node vector using the following formula

[0213]

[0214] where i = 1…P, i ≠ j.

[0215] Step 12: Normalize the secondary node vector ji formed by the secondary node weight wd′ of the remaining nodes after separately stripping node j (j = 1…P) from the complex network into a quasi-node vector

[0216]

[0217] where:

[0218]

[0219] where i = 1…P, i ≠ j.

[0220] Step 13: Calculate the relative indirect node strength ISr of node j (j = 1…P) using the following formula j :

[0221]

[0222] Step 14: Calculate the absolute indirect node strength IS of node j (j = 1…P) using the following formula j (i.e., the indirect node strength):

[0223] IS j = wd j × ISr j Equation (15)

[0224] Step 15: Normalize the indirect node strength IS j using the following formula to obtain the indirect node weight wid j :

[0225]

[0226] Step 16: Calculate the node weight w of node j (j = 1…P) using the following formula j :

[0227]

[0228] Step 17: Calculate the weighted evidence body m in the complex network using the following formula avg :

[0229]

[0230] where A is an arbitrary subset of the power set 2 Θ of.

[0231] Step 18: Modify the original evidence body m i to m′ i so that there is no longer a high conflict between the evidence bodies:

[0232]

[0233] Step 19: Use Dempster's combination rule to fuse the modified P new evidence bodies m′ i (P - 1) times to obtain the final result, that is, the mass function value after data fusion, and then make corresponding evaluation and judgment based on this.

[0234] Specifically, the specific steps for the S7 to use Dempster's combination rule to fuse (P - 1) times to obtain the final result are as follows:

[0235] Suppose there are m i and m j two sets of independent mass functions, then m i and m j can be evidence - fused through Dempster's combination rule:

[0236]

[0237] where B and C represent subsets of propositions, that is, the focal elements of the two mass functions m i and m j respectively, and m i (B) is the mass function value of the subset of proposition B, and m j (C) is the mass function value of the subset of proposition C. In addition, k in the formula is the normalization factor, called the conflict coefficient, which can measure m i and m jThe degree of conflict between them is defined as follows:

[0238]

[0239] Among them, k = 0 means that there is no conflict between m i and m j , while k = 1 indicates that there is a complete contradiction between m i and m j . Note that Dempster's combination rule is only applicable to two BPAs that satisfy the condition k < 1.

[0240] Embodiment 2: A method for modeling and fusing sensor conflict information based on complex networks and evidence distance, characterized by comprising the following steps:

[0241] Step 1: Assume that the identification framework is Θ = {θ 1 , θ 2 , θ 3}, and based on this identification framework, there are three mass functions m 1 , m 2 and m 3 , that is, N = 3, P = 3;

[0242] Step 2: Assume the specific BBAs of the three mass functions are as follows:

[0243] m 1 : m 1 (θ 1 ) = 0.8, m 1 (θ 2 ) = 0, m 1 (θ 3 ) = 0.2

[0244] m 2 : m 2 (θ 1 ) = 0, m 2 (θ 2 ) = 0.8, m 2 (θ 3 ) = 0.2

[0245] m 3 : m 3 (θ 1 ) = 0.8, m 3 (θ 2 ) = 0, m 3 (θ 3 ) = 0.2

[0246] Step 3: Use complex network theory to model the known BBAs as a bidirectional graph, with each BBA corresponding to a node, and different nodes are connected by bidirectional edges.

[0247] Step 4: From Equation (5), we can obtain the evidence distance dj(m i , m j ) among each node. The specific data obtained is as follows:

[0248] dj(m 1 , m 2 ) = 0.8, dj(m 1 , m 3 ) = 0., dj(m 2 , m 3 ) = 0.8

[0249] Step 5: From Equation (7), obtain the direct node strength S of each node i . The specific data is as follows:

[0250] S 1 = 1.2, S 3 = 0.4, S 3 = 1.2

[0251] Step 6: From Equation (8), obtain the direct node weight wd of each node i . The specific data obtained is as follows:

[0252] wd 1 = 0.4286, wd 2 = 0.1428, wd 3 = 0.4286

[0253] Step 7: Calculate the sub-node strength S′ of the remaining nodes after stripping a single node using Equation (9) ji . Taking the stripping of Node 1 as an example, the specific data is as follows:

[0254] S′ 12 = 0.2, S′ 13 = 0.2

[0255] Step 8: Normalize S′ ji using Equation (10) to obtain the sub-node weight wd′ ji . Taking the stripping of Node 1 as an example, the specific data is as follows:

[0256] wd′ 12 = 0.5, wd′ 13 = 0.5

[0257] Step 9: Compose the direct node weights wd i of the remaining nodes after stripping a certain node from the complex network into a node vector . Taking the stripping of Node 1 as an example, the specific data is as follows:

[0258]

[0259] Step 10: Combine the sub-node weights wd' of the remaining nodes after stripping a certain node from the complex network ji to form a sub-node vector Taking the stripping of Node 1 as an example, the specific data is as follows:

[0260]

[0261] Step 11: Based on the node vector calculated in Step 9 calculate its modulus value according to Equation (11) Taking the node vector obtained by stripping Node 1 as an example, the specific data is as follows:

[0262]

[0263] Step 12: Normalize the sub-node vector to a quasi-node vector by Equation (12) Taking the quasi-node vector obtained by stripping Node 1 as an example, the specific data is as follows:

[0264]

[0265] Step 13: Calculate the relative indirect node strength ISr of each node by Equation (14) j , and the specific data is as follows:

[0266] ISr 1 = 10.5627×10 -2 , ISr 2 = 0, ISr 3 = 10.5627×10 -2

[0267] Step 14: Obtain the indirect node strength IS of each node by Equation (15) j , and the specific data is as follows:

[0268] IS 1 = 4.5272×10 -2 , IS 2 = 0, IS 3 = 4.5272×10 -2

[0269] Step 15: Calculate the indirect node weights of each node by Equation (16), and the specific data is as follows:

[0270] wid 1 = 0.5, wid 2 = 0, wid 3 = 0.5

[0271] Step 16: Calculate the weights of each node according to Equation (17), and the specific data are as follows:

[0272] w 1 = 0.5, w 2 = 0, w 3 = 0.5

[0273] Step 17: Based on the node weights in Step 16, calculate the weighted evidence body m in the complex network using Equation (18), avg , such as m avg (θ 1 ) = m 1 (θ 1 ) × w 1 + m 2 (θ 1 ) × w 2 + m 3 (θ 1 ) × w 3 = 0.8 × 0.5 + 0 × 0 + 0.8 × 0.5 = 0.8, and the specific data are as follows:

[0274] m avg (θ 1 ) = 0.8, m avg (θ 2 ) = 0, m avg (θ 3 ) = 0.2

[0275] Step 18: Modify the original evidence body using Equation (19) to make there no longer a high conflict between evidence bodies, and the specific data are as follows:

[0276] m′ 1 (θ 1 ) = 0.8, m′ 1 (θ 2 ) = 0, m′ 1 (θ 3 ) = 0.2

[0277] m′ 2 (θ 1 ) = 0.4, m′ 2 (θ 2 ) = 0.4, m′ 2 (θ 3 ) = 0.2

[0278] m′ 3 (θ 1 ) = 0.8, m′ 3 (θ 2 ) = 0, m′ 3 (θ 3 ) = 0.2

[0279] Step 19: Based on the Dempster combination rule, fuse the new three bodies of evidence to obtain the final result, that is, the mass function values after data fusion are as follows:

[0280] m(θ 1 ) = 0.9697, m(θ 2 ) = 0, m(θ 3 ) = 0.0303

[0281] Compare the results obtained by the above method with the results obtained by only using the Dempster combination rule, and the data obtained are as follows:

[0282] Dempster combination rule: m(θ 1 ) = 0, m(θ 2 ) = 0, m(θ 3 ) = 1

[0283] Our results: m(θ 1 ) = 0.9697, m(θ 2 ) = 0, m(θ 3 ) = 0.0303

[0284] As can be seen from the above, m 1 , m 2 and m 3 have a low level of support for θ 3 . At this time, the fusion result of the Dempster combination rule fully supports 3 , but completely does not support θ 1 and θ 2 . Such a fusion result is obviously counterintuitive; on the contrary, for the method proposed in this paper, the obtained fusion result distributes most of the beliefs to θ 1 , and m(θ 3 ) =

[0285] 0.0303, avoiding counterintuitive results. In addition, if another body of evidence m 4 is added, the fusion result of the Dempster combination rule still fully supports θ 3 , which is still a counterintuitive result. However, in the method proposed in this paper, with the addition of m 4 , the level of support for θ 1 is further improved, while the level of support for θ 3 is further reduced, which is in line with the actual situation. This further proves the feasibility and effectiveness of this method. The specific data are as follows:

[0286] m 4 : m 4 (θ 1 ) = 0.8, m4 (θ 2 ) = 0, m 4 (θ 3 ) = 0.2

[0287] Dempster combination rule: m(θ 1 ) = 0, m(θ 2 ) = 0, m(θ 3 ) = 1

[0288] Our results: m(θ 1 ) = 0.9922, m(θ 2 ) = 0, m(θ 3 ) = 0.0078

[0289] Example 3: A method for modeling and fusing sensor conflict information based on complex network and evidence distance, characterized in that the method for modeling and fusing sensor conflict information based on complex network and evidence distance is as described in claims 1 and 2, and includes the following steps:

[0290] Step 1: Let P = 5, N = 3, and construct the identification framework as Θ = {A, B, C}; for the different recognition results generated by five different sensor signal sources, including radar, infrared system, ultrasonic sensor, image sensor, and pressure sensor, the proposed method for modeling and fusing sensor conflict information based on complex network and evidence distance is used for evidence fusion. For example, m 1 is the basic evidence function obtained according to the recognition result of the radar for the target. Similarly, m 2 is the basic evidence function obtained according to the recognition result of the infrared system for the target, m 3 is the basic evidence function obtained according to the recognition result of the ultrasonic sensor for the target, m 4 is the basic evidence function obtained according to the recognition result of the image sensor for the target, m 5 is the basic evidence function obtained according to the recognition result of the pressure sensor for the target.

[0291] Step 2: Based on the recognition results of the 5 sensors, the BBA regarding the recognition results can be obtained (see Table 1);

[0292] Step 3: According to the above 5 BBAs, use complex network theory to model the known BBAs as a bidirectional graph;

[0293] Step 4: From Equation (5), we can obtain the evidence distance dj(m i , m j ) (see Table 2);

[0294] Step 5: Obtain the direct node strength S of each node from Equation (7)i , the specific data are as follows:

[0295] S 1 = 2.7646, S 2 = 1.0710, S 3 = 2.6338, S 4 = 2.7123, S 5 = 2.8465

[0296] Step 6: From Equation (8), we can obtain the direct node weights wd of each node i , the specific data are as follows:

[0297] wd 1 = 0.2298, wd 2 = 0.0890, wd 3 = 0.2190, wd 4 = 0.2255, wd 5 = 0.2367

[0298] Step 7: Calculate the sub-node strength S′ of the remaining nodes after a certain node is peeled off from the complex network according to Equation (9) ji , taking the peeled-off node one as an example, the specific data are as follows;

[0299] S′ 12 = 0.7365, S′ 13 = 1.8909, S′ 14 = 1.9552, S′ 15 = 1.9165

[0300] Step 8: Obtain the sub-node weights wd′ of the remaining nodes from Equation (10) ji , taking the peeled-off node one as an example, the specific data are as follows:

[0301] wd′ 12 = 0.1133, wd′ 13 = 0.2910, wd′ 14 = 0.3008, wd′ 15 = 0.2949

[0302] Step 9: Combine the direct node weights wd of the remaining nodes after a certain node is peeled off from the complex network i to form a node vector , taking the peeled-off node one as an example, the specific data are as follows:

[0303]

[0304] Step 10: Combine the sub-node weights wd′ of the remaining nodes after a certain node is peeled off from the complex network ji to form a sub-node vector Taking the stripping node 1 as an example, the specific data is as follows:

[0305]

[0306] Step 11: Based on the node vectors calculated in Step 9 Calculate its modulus value according to Equation (11) Taking the node vectors obtained by stripping node 1 as an example, the specific data is as follows:

[0307]

[0308] Step 12: Standardize the secondary node vectors to the quasi-node vectors by Equation (12) Taking the quasi-node vectors obtained by stripping node 1 as an example, the specific data is as follows:

[0309]

[0310] Step 13: Calculate the relative indirect node strength ISr of each node j , the specific data is as follows:

[0311] ISr 1 = 3.0000×10 -4 ,ISr 2 = 2.4090×10 -4 ,ISr 3 = 15.0333×10 -4

[0312] ISr 4 = 14.0910×10 -4 ,ISr 5 = 3.7326×10 -4

[0313] Step 14: Obtain the indirect node strength IS of each node j , the specific data is as follows:

[0314] IS 1 = 0.6894×10 -4 ,IS 2 = 0.2144×10 -4 ,IS 3 = 3.2923×10 -4

[0315] IS 4 = 3.1775×10 -4 ,IS 5 = 0.8835×10 -4

[0316] Step 15: Calculate the indirect node weights of each node according to Equation (16), and the specific data are as follows:

[0317] wid 1 = 0.0835, wid 2 = 0.0260, wid 3 = 0.3987, wid 4 = 0.3848, wid 5 = 0.1070

[0318] Step 16: Calculate the weights of each node according to Equation (17), and the specific data are as follows:

[0319] w 1 = 0.0869, w 2 = 0.0104, w 3 = 0.3952, w 4 = 0.3929, w 5 = 0.1146

[0320] Step 17: Based on the node weights in Step 16, calculate the weighted evidence body m in the complex network using Equation (18) avg , such as m avg (A) = w 1 × m 1 (A) + w 2 × m 2 (A) + w 3 × m 3 (A) + w 4 × m 4 (A) + w 5 × m 5 (A) = 0.0869 × 0.52 + 0.0104 × 0 + 0.3952 × 0.56 + 0.3929 × 0.64 + 0.1146 × 0.59 ≈ 0.5856, and the specific data obtained are as follows:

[0321] m avg (A) = 0.5856, m avg (B) = 0.0533, m avg (C) = 0.1343, m avg (A,B) = 0.2248

[0322] Step 18: Modify the original evidence body according to Equation (19), and the modified BBA is shown in Table 3;

[0323] Step 19: Based on the Dempster combination rule, fuse the new five evidence bodies to obtain the final result, that is, the mass function values after data fusion are as follows:

[0324] m(A) = 0.9906, m(B) = 0.0073, m(C) = 0.0014, m(A,B) = 0.0007

[0325]

[0326] Table 1 Basic belief assignments (BBAs) of five sensors to three possible recognition targets

[0327]

[0328] Table 2 Evidential distances between nodes

[0329]

[0330] Table 3 Modified BBAs.

Claims

1. A multi-sensor information modeling and fusion method based on complex networks and evidence distance, characterized in that: The method includes the following steps: Step 1: constructing an identification framework of sensor information sources; constructing a basic belief assignment BBA based on the identification framework; using complex network theory to construct a bidirectional graph based on the basic belief assignment BBA; each basic belief assignment BBA corresponds to a node in the bidirectional graph, and different nodes are connected by bidirectional edges; The identification framework θ is: information fusion is performed on P sensor information sources. The sensor has N kinds of judgment results, among which θ1…θ N represents N kinds of judgment results; Θ is a non-empty set; the identification framework includes N mutually exclusive events, that is, Θ = {θ1, θ2…θ N }; The power set of the identification frame Θ contains 2 N elements, the power set of the identification frame Θ2 Θ for: in, represents the empty set, that is, a set that contains no elements; The basic belief assignment BBA is: within the identification framework, the evidence body mass function m is the power set 2 Θ Mapping on the interval [0,1] And the evidence body mass function m satisfies the following relationship: Among them, when the condition m(A)>0 holds, the proposition subset A is called a focal element; and m(A) is the mass function value of the body of evidence of the proposition subset A, that is, m(A) is the basic belief assignment BBA, or m(A) is the basic probability assignment BPA; If any sensor has two judgment results for the target, that is, N = 2, θ = {θ1, θ2}, then the basic belief assignment BBA of the sensor is expressed as: m(θ1)=0.2 m(θ2)=0.6 m(θ)=0.2 Formula (4) Step 2: Calculate the direct node weights of the nodes in the bidirectional graph; Step 3: Calculate the indirect node weights of the nodes in the bidirectional graph; Step 4: Calculate the node weights of the nodes in the bidirectional graph; Step 5: Calculate the weighted evidence body in the bidirectional graph; Step 6: Update the evidence body mass function to a low-conflict optimized evidence body; Step 7: Use the Dempster combination rule to fuse the low-conflict optimized evidence body, that is, obtain the evidence body after data fusion, and make evaluation and judgment based on the evidence body after data fusion.

2. The multi-sensor information modeling and fusion method based on complex network and evidence distance according to claim 1 is characterized in that: The steps of calculating the direct node weights of nodes in the bidirectional graph are: Step 2.1: Calculate the evidence distance dj(m) between any two nodes i ,m j ); Use formula (5) to calculate the evidence body mass function m i and the evidence body mass function m j Evidence distance, m i and m j The identification framework contains N elements, and i,j=1…P: in is the evidence body mass function m i The corresponding vector, is the evidence body mass function m j The corresponding vector, the evidence mass function m i The corresponding vector and the evidence body mass function m j The corresponding vector The elements are all in 2 Θ Arrange in order; D is a 2 N ×2 N A matrix where: Where x, y = 1,...,2 N ; A x is m i The focal element, A y is m j The focal element of |·| is the cardinality of a subset; d xy is the element in matrix D; Step 2.2: Calculate the direct node strength S of each node i ; Use formula (7) to calculate the direct node strength S of each node i , i=1…P: Among them, rel ik =1-dj(m i ,m k ),rel ik represents the correlation between two basic belief assignments BBA, that is, the correlation between node i and node k; Step 2.3: Normalize the direct node strength to obtain the direct node weight wd i ; Direct node weight wd i for: Direct node weight wd i To convert the direct node strength S i Normalized to get.

3. The multi-sensor information modeling and fusion method based on complex network and evidence distance according to claim 1 is characterized in that: The steps to calculate the indirect node weight of a node in a bidirectional graph are: Step 3.1: Calculate the sub-node strength S′ of each node remaining after the j-th node is stripped from the bidirectional graph ji ; The sub-node strength S′ of each remaining node after the jth node is stripped from the bidirectional graph ji for: Where j = 1…P, i≠j; Step 3.2: Calculate the secondary node weight wd′ of each remaining node after the jth node is stripped from the bidirectional graph ji ; The sub-node weights wd′ of the remaining nodes after the jth node is stripped from the bidirectional graph ji : Where i = 1…P, i≠j; Step 3.3: Solve for the node vector Node Vector is the direct node weight wd of the remaining nodes after node j is stripped from the bidirectional graph i The vector composed of Node Vector Where i = 1…P, i≠j; Step 3.4: Solve for the secondary node vector Node Vector is the secondary node weight wd′ of the remaining nodes after node j is removed from the bidirectional graph ji The vector composed of Secondary node vector Where i = 1…P, i≠j; Step 3.5: Solve for the node vector The modulus value Use equation (11) to solve the node vector The modulus value Where i = 1…P, i≠j; Step 3.6: Sub-node vector Normalized to quasi-node vector Use formula (12) to separate node j from the bidirectional graph and calculate the secondary node weight wd′ of the remaining nodes ji The secondary node vector Normalized to quasi-node vector in: Where i = 1…P, i≠j; Step 3.7: Calculate the relative indirect node strength ISr of node j j ; The relative indirect node strength ISr of node j j for: Where j = 1…P; Step 3.8: Calculate the absolute indirect node strength IS of node j j ; The absolute indirect node strength IS of node j j for: IS j =wd j ×ISr j Formula (15) where j = 1…P; absolute indirect node strength IS j It is the indirect node strength; Step 3.9: Calculate the indirect node weight wid j ; Indirect node weight wid j for: Indirect node strength IS j Normalize to get the indirect node weight wid j .

4. The multi-sensor information modeling and fusion method based on complex network and evidence distance according to claim 1 is characterized in that: The specific steps of calculating the node weights of nodes in the bidirectional graph are: The node weight w of node j j for: Where j=1…P.

5. The multi-sensor information modeling and fusion method based on complex network and evidence distance according to claim 1 is characterized in that: The specific steps of calculating the weighted evidence body in the bidirectional graph are: Where A is the power set 2 Θ Any subset of k (A) represents the credibility distribution of the mass function of the k-th evidence body for the target A, w k is the node weight of the kth node.

6. The multi-sensor information modeling and fusion method based on complex network and evidence distance according to claim 1 is characterized in that: The specific steps to update the evidence body mass function to a low-conflict optimized evidence body are: Low-conflict optimized mass function m′ i for: Among them, m i is the mass function of the evidence body.

7. The multi-sensor information modeling and fusion method based on complex network and evidence distance according to claim 1 is characterized in that: The steps to fuse the low-conflict optimized evidence bodies using the Dempster combination rule are: Assume there is m i and m j Two independent evidence mass functions, then m i and m j Evidence fusion through Dempster combination rule: Among them, B and C represent proposition subsets, that is, two evidence bodies, mass functions m respectively. i and m j The focal element, and m i (B) is the mass function value of the evidence body of proposition subset B, m j (C) is the mass function value of the evidence body of proposition subset C; k is the normalization factor, i.e., the conflict coefficient, which measures m i and m j The degree of conflict between them, the normalization factor k is: Where k = 0 means m i and m j There is no conflict between them, and k = 1 means m i and m j There is a complete contradiction between them; in particular, Dempster's combination rule only applies to two BPAs that satisfy the condition k<1.

8. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that When the processor executes the computer program, the multi-sensor information modeling and fusion method based on complex network and evidence distance according to any one of claims 1-7 is implemented.

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