Journal of Sensors

Volume 2016 (2016), Article ID 3954573, 11 pages

http://dx.doi.org/10.1155/2016/3954573

## Decision-Making Algorithm for Multisensor Fusion Based on Grey Relation and DS Evidence Theory

College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Received 12 May 2016; Accepted 22 September 2016

Academic Editor: Biswajeet Pradhan

Copyright © 2016 Fang Ye et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Decision-making algorithm, as the key technology for uncertain data fusion, is the core to obtain reasonable multisensor information fusion results. DS evidence theory is a typical and widely applicable decision-making method. However, DS evidence theory makes decisions without considering the sensors’ difference, which may lead to illogical results. In this paper, we present a novel decision-making algorithm for uncertain fusion based on grey relation and DS evidence theory. The proposed algorithm comprehensively takes consideration of sensor’s credibility and evidence’s overall discriminability, which can solve the uncertainty problems caused by inconsistence of sensors themselves and complexity of monitoring environment and simultaneously ensure the validity and accuracy of fusion results. The innovative decision-making algorithm firstly obtains the sensor’s credibility through the introduction of grey relation theory and then defines two impact factors as sensor’s credibility and evidence’s overall discriminability according to the focal element analyses and evidence’s distance analysis, respectively; after that, it uses the impact factors to modify the evidences and finally gets more reasonable and effective results through DS combination rule. Simulation results and analyses demonstrate that the proposed algorithm can overcome the trouble caused by large evidence conflict and one-vote veto, which indicates that it can improve the ability of target judgment and enhance precision of uncertain data fusion. Thus the novel decision-making method has a certain application value.

#### 1. Introduction

In practical applications, single sensor is difficult to meet the requirements like target accuracy and identification performance. Thus, there is a broad application of decision-making algorithm on data fusion about target’s attributes, characteristics, and types through comprehensive processing of information obtained from multisensor. Currently, data decision-making technology [1–3] based on multisensor is highly valued by scholars at home and abroad. In addition, a lot of theorems and algorithms emerge in the area of data decision-making. However, due to constraints on the attributes as well as the types of data, there is still no unified theoretical framework or unique algorithm for classification issue of multisensor data decision-making.

For multisensor decision-making field, the traditional algorithms are statistical method [4], empirical reasoning [5], voting method [6], Bayesian inference [7], template method [5], and adaptive neural network [8], among others. These typical methods all can settle the decision fusion of multisensor information to some extent, whereas they all have some defects. Statistical method, empirical reasoning, and voting method are too simple to achieve the reliable decision results for multisensor information fusion. Bayesian inference needs the prior knowledge of environment to finish the reasoning, which cannot be guaranteed in actual applications. And template method would waste time and energy of system when selecting the suitable template according to certain rules. Although adaptive neural network can fulfill a reasonable decision fusion, it is usually not adopted in practical applications because of its large computation complexity. DS evidence theory [9, 10] is favored for its ability of dealing with uncertainty, integration of measurement information, and reasonable theoretical derivation. Thus, DS evidence theory has become the mainstream method in multisensor decision-making field.

As a wildly used decision-making algorithm for uncertain data fusion, DS evidence theory is able to deal with the uncertainty and imprecision of multisensor information fusion. Hence, DS evidence theory can properly handle the inconsistency of sensor conditions and complexity of monitoring environment. With its introduction and perfection put forward by Dempster and Shafer, respectively, DS evidence theory occupies a lot in the development of intelligent computing and identification theory for multisensor information fusion. Along with its development, DS evidence theory has been widely applied in various fields, like pattern recognition [11], target identification [12], cognitive radio network [13], fault diagnosis [14], signal recognition [15], and decision-making [16], among others. Although there are some problems of DS evidence theory itself, these problems can be effectively solved through rigorous theoretical derivation, scientific improvements, and combination with other methods. For example, a new entropy, named as Deng entropy, is proposed in [17] to handle the uncertain measure of BPA, which is the generalization of Shannon entropy. The new entropy provides a promising way to measure the uncertainty of multisensor fusion system. Besides, Deng entropy is applied in [18] to realize the measurement of information volume of the evidence. This improvement makes the application of DS evidence theory with more validity and robustness. Due to limit space, the classic modified methods [19–31] are exhibited in references and partially taken as compared methods in Section 5.2.

In this paper, systematic research is implemented on DS evidence theory, and the multisensor decision-making algorithm is realized by the combination of DS evidence theory and grey relation analysis [32, 33]. The proposed decision-making algorithm for uncertain data fusion firstly utilizes sensors’ report generator to settle the acquisition processing of sensor’s credibility by the introduction of grey relation theory. Then, the sensor’s credibility is consecutively adjusted by two different processes of consistency and conflict analysis in focal elements. At the same time, the novel method defines the evidence’s overall discriminability according to the concept of evidence’s distance function. Finally, the original evidences are modified by two impact factors as sensor’s credibility and evidence’s overall discriminability, which can ensure getting more reasonable and effective decision-making results after evidences combine.

This paper is organized as follows. The theoretical theorem and derivation of DS evidence theory and grey relation theory are briefly introduced in the next section. And the implementation diagram and flow chart of uncertain data fusion system are given in Section 3. Then, Section 4 highlights the implementation method and specific steps of the new decision-making algorithm for uncertain data fusion, and Section 5 presents the simulation results and comparative analyses. Concluding remarks are given in the last section of this paper.

#### 2. Theoretical Foundations

DS evidence theory and grey relation theory are separately presented in this section, which are the foundations of the novel decision-making algorithm in this paper.

##### 2.1. DS Evidence Theory

DS evidence theory, also called Dempster-Shafer theory, is an effective data decision-making method to deal with the uncertainty of multisensor information fusion system. Relative to probability theory [5], DS evidence theory can settle imprecise data and has a more extensive application area. Similar to Bayesian inference [7], DS evidence theory uses the prior probability to represent the evidence interval of posterior probability, which can quantify the credible degree and plausibility degree of propositions. DS evidence theory is briefly comprised by the following four key points.

###### 2.1.1. Frame of Discernment and the Power Set

In DS model, the frame of discernment (FoD) denoted by indicates a set of mutually exclusive and exhaustive hypotheses, which represents all interested propositions. And FoD is defined as the form of function set as where is the th hypothesis belonging to and is the number of hypotheses.

On the basis of FoD, we can derive as the power set, which is composed of propositions of (all subsets of FoD). where is the empty set, which belongs to any propositions.

###### 2.1.2. Basic Probability Assignment

The basic probability assignment (BPA) is a mass function defined on , which should satisfy the following demands:. is called the mass function of proposition that represents the basic belief degree and initial support degree strictly assigned to proposition [17].

Due to the lack of further knowledge, cannot be subdivided. Any proposition satisfying that is called the focal element, and the set of all focal elements is named as the core of BPA.

###### 2.1.3. Belief Function and Plausibility Function

DS evidence theory designates two uncertain measurements as the belief function (Bel) and plausibility function (Pl). Similar to the definition of BPA, Bel and Pl can be defined, respectively, as , where Bel() is interpreted as the low probability of , while Pl() is interpreted as the upper probability of . The relationship between Bel() and Pl() is derived as follows: where is the complement set of .

According to the relationship between Bel() and Pl(), DS evidence theory also divides the evidence interval into supporting interval, uncertainty interval, and rejecting interval, which are shown in Figure 1.