Research of Data Fusion Method of Multi-Sensor Based on Correlation Coefficient of Confidence Distance

Transcription

1 Send Orders for Reprints to 340 The Open Cybernetics & Systemics Journa, 015, 9, Open Access Research of Data Fusion Method of Muti-Sensor Based on Correation Coefficient of Confidence Distance Xinhua Jiang, Heru Xue *, Chen Wang and Yanqing Zhou Coege of Computer and Information Engineering, Inner Mongoia Agricutura University, Hohhot, , P.R. China Abstract: Because of the sensor or environment probem, the muti-sensor detection data can resut in data mutation for the individua sensor. To obtain consistent, stabe and accurate tested target description, the paper adopts confidence distance matrix, distance correation coefficient and p-vaue significant test to get The number of optima fusion number of muti-sensor, and uses maximum ikeihood estimation to study the muti-sensor data fusion. The resuts show that the agorithm mentioned by the paper is superior to the muti-sensor consistency data fusion means and is fairy practica. Keyword: Confidence distance, correation coefficient, maximum ikeihood estimation, p-vaue test, support. 1. INTRODUCTION The detecting accuracy of singe sensor is difficut to improve [1], and the faiure and error of sensor can cause a decine at the respect of accuracy in the whoe system. So independent muti-sensor which has ow precision is adopted to achieve the same target detection, and improve the effectiveness and robustness of the detection system. In mutisensor detection process, because of various orientations which the senor ocated, the difference of sensor and the effect of random factors in practica environment, the target vaue measured by each senor wi have deviation []. Then, to reduce the errors that happen probaby in the system processing, there is a question how to consistenty accuratey describe the measured target in the detection system. It is an effective method for the measured target to adopt the data fusion to impement muti-sensor consistency description. The key of data fusion is judging the data obtained by the every sensor of system, determining the credibiity of the data, so as to decide on which data of sensor to do fusion [3]. Finay, the optima fusion resut for many target detection is acquired. Data fusion methods invove signa processing, estimation theory, uncertainty theory, pattern recognition and optimization technique and so on [4], in accordance with, using the principe of statistics. From the principe of statistics, using the actua coected data from the every sensor to cacuate the confidence distance matrix, and adopting threshod to get reation matrix, which measure the correation degree among sensors [5-8]. The confidence matrix can obtained the support degree to determine the optima number of sensors. That threshod using to judge the mutua support between sensors exists a ot of fuzziness, and chooses subjectivey the threshod to ead to the inaccuratey fusion resuts [9-11]. Once data oss or disturb, the fusion resut is not stabe [1, 13]. Determining the confidence distance threshod, the paper empoys the confidence distance correation coefficient p-vaue significant test to examine the reated degree between sensors, ensures the optima fusion number of muti-sensor under different confidence eves, and uses the maximum ikeihood estimation to compute the fina fusion resuts. Through the anaysis of the confidence interva ength and the measured vaues of each sensor which incude standard deviation, root mean square error and residua sum of square, the fina fusion resuts is confirmed. The muti-sensor data fusion mean mentioned by the paper is more scientific basis and practice, have an effective and reiabe fusion resut. The cacuation process is simper.. THE COMPUTATION OF CONFIDENCE DISTANCE AMONG MULTI-SENSOR MEASURED VALUE Suppose there are n sensors that measure the same parameter from different orientation. X i {x i1,x i,,x im }is the data of the i th sensor. i can vaue 1,,,n, and 1,, m is the m vaues of the ith sensor. Due to the factors of the sensor, measurement environment and measurement system stabiity, the actua vaues are errors with the measurements. In the actua measurement, the effect of a kinds of random factors wi resut in the measurement resut X i to Gauss distribution. So measuring expectation of the sensor i can be described by Gauss probabiity density function as P i (x). P i (x x i ) 1 exp( 1 ( x x i ) ) (1) i i i can vaue 1,, n. n is the number of sensors. On the definition of statistics, confidence needs sampe statistic average μ, variance and confidence intervas [-, +]. For Gauss distribution N(μ,), the confidence eve c X/ Bentham Open

2 Research of Data Fusion Method of Muti-Sensor The Open Cybernetics & Systemics Journa, 015, Voume μ c N(μ,) dx () μ+ To refect the support degree of the data vaue between sensor i and j, paper [11] adopts the confidence distance to measure d ij. x d ij j p i (x x i ) dx (3) x i x d ji i p j (x x j ) dx (4) x j d ij is the data confidence distance measure of the i th and j th sensor. It refects the mutua support degree of two sensors data. d ij can use the error function erf() to obtain directy. d ij erf ( x j x i i ) (5) d ji erf ( x x i j ) (6) j For n sensors measure a target at the same time, the confidence measure distance d ij (i,j1,,,n) consists a mutisensor confidence distance matrix D nn. d 11 d 1... d d D nn 1 d... d n d n1 d n... d nn 3. CONFIRMATION OF OPTIMAL FUSION NUMBER OF MULTI-SENSOR Taking advantage of the confidence distance matrix soves the mutua support degree of each sensor. Generay, the d ij threshod vaue is given through the experience or the previous measure resut, and sets up: 1, d ij (8) 0, d ij > stands for the mutua support of i and j sensor. If confidence distance d ij is ess than, then is equa to 1 is regarded as the good correation of i th and j th sensor. It cas that the i th sensor supports the j th. If is equa to 0, it considers that the i th sensor does not support the the j th. If and r ji is equa 1, the i th sensor and j th sensor is mutua support. If is arger than a certain extent, the data is vaid, or the data is invaid. When muti-sensor measure the same parameter, the effective sensor set is fusion set. The sensor number of fusion set is caed the optima fusion number. wi be inevitaby infuence the resut of data fusion. The optima fusion number reduces and the data oss if chooses impropery. The different eads to the different fusion resuts. Form the computation of d ij, the vaue of d ij is between -1 and 1. That d ij absoute vaue is greater shows the measurement deviation between two sensors. otherwise, the smaer vaue means the simiar measured vaue of two sensors. Those refect that the support degree of two sensors is high. (7) Under the condition of sensor norma, the measured vaue can consistenty refect the rea vaues of measured object. The confidence distance matrix D wi not appear sharp peaks and fat tai. So the support degree of two sensors is determined through probabiity correation coefficient or reated index. The most common method for correation coefficient is product moment method which is caed Pearson correation coefficient. It uses the rate of the product covariance and standard deviation of two variabes to indicate the correation. For i and j sensor, confidence distance correation coefficient can be defined as foows: di d j di d j di d j di d j (d ik d i )(d jk d j ) (d ik d i ) (d jk d j ) m d i d d j i d j m d i ( d i ) * m d j ( d j (9-1) ) (9-) d i is the confidence distance mean between i sensor and other sensors. is between -1 and 1. Confidence distance correation coefficient for n sensors can make up a n*n matrix R nn. r 11 r 1... r r R nn 1 r... r n (10) r n1 r n... r nn Reated significant degree between senor measurements can be determined through testing confidence distance correation coefficient. The paper uses the specified and different confidence eve to examine the correation coefficient significant p-vaue test and ensure the optima number of mutisensor fusion by the correation coefficient significance. Confidence distance correation coefficient significant p- vaue for n sensors makes a n*n matrix P nn. p 11 p 1... p p P nn 1 p... p n p n1 p n... p nn (11) Matrix P is the symmetric matrix. p ij is the correation significance p-vaue of i and j sensors. When p ij is not ess than, i sensor is no significant correation with j sensor. When p ij is ess than, i sensor is significant correation with j sensor. The optima fusion number is composed of reated and significant sensor. 4. MULTI-SENSOR DATA FUSION Suppose the optima fusion number of n sensors is {x1,x,x3,,xl}. Adopting maximum ikeihood estimation method cacuates the data fusion resuts for L sensors. The formua (1) is estabishing a ikeihood function. p( Ê ) p( x ) (1) k 1 k

3 34 The Open Cybernetics & Systemics Journa, 015, Voume 9 Jiang et a. To get ogarithmic ikeihood function of formua (1): H( ) n pê ( ) n px ( ) (13) k 1 According to the theory of maximum ikeihood estimation, sensor fusion resut shoud satisfy the equation (14): k H() n p(x k ) 0 (14) To sove the equation (14) can get the foow vaue: μ 1 1 x k (x k μ) The fina soution: x k k 1 k (15) (16) ˆ is the fusion data resut of the optima fusion number {x1,x,x3,,xl}. 5. DATA FUSION EXPERIMENTS 5.1. Experimenta Data Sources In this paper, the temperature of the experimenta data coected from oat panting environment in a sunight greenhouse, many temperatures and humidity of wireess sensors were distributed in greenhouse, and temperature and humidity data of each sensor is coected every 15 minutes. The temperature experimenta data in Tabe 1 were coected from the 10 temperature and humidity sensors distributed different ocations in Greenhouse, and acquisition time was eary Apri 10:00 to 1:30 in northern region. From Tabe 1 it can be seen the variance of the 9 th sensor changes sighty arger than other from the coumn of variance of measured data, from the actua position of the sensor in the greenhouse, the 9 th sensor was in the area of ess sunight than other sensor. 5.. Data Fusion Experiment First, using the formua (5) and (6) to cacuate and obtain the confidence measure vaue distance matrix D of the 10 sensors, D is a symmetric matrix. Tabe 1. The monitoring temperature data of 10 sensors. Sensor Monitoring Vaue x i Mean Variance e e e e D e e

4 Research of Data Fusion Method of Muti-Sensor The Open Cybernetics & Systemics Journa, 015, Voume R P By the formua (9) to cacuate the sensors confidence distance correation coefficient matrix R. The correation coefficient matrix R is cacuated according to the experimenta data obtained by samping, there must inevitaby be error, in order to infer the existence of correation between each of the sensors, the method of hypothesis testing used in the experiments to test significant of correation coefficient. By cacuating significant p-vaue of the correation coefficient data of each sensor, we get a significant test matrix P of correation coefficient of the 10 sensors, and matrix P is a 10*10 symmetric. Tabe. Confidence Leve The number of optima fusion of different confidence eve. The Number of Optima Fusion Resut of Data Fusion 0.05 x1,x,x3,x4,x x1,x,x3,x x,x Experiments seected the confidence eve 0.05, 0.05 and 0.01, and got the number of optima fusion through cacuating significant correation test, and used formua (16) to cacuate fusion resuts of the data of different confidence eve, the resuts shown in Tabe Anaysis of Fusion Resuts To use formua (16) to cacuate the fusion resuts of monitoring data at confidence eve 0.05, 0.05 and As shown in Tabe 3, the confidence eve is 0.05, 0.05 and 0.01, and the ength of the confidence interva of fusion resuts are respectivey 0.9, and , but the three confidence interva ength difference is not very obvious under the confidence eves. The root mean square error and residua sum of squares are cacuated and obtained by the fusion resuts in Tabe and the 100 monitoring resuts of 10 sensors in Tabe 1 under different confidence eve, from resuts of the root mean square error RMSE and the residua sum of squares RSS, we can get the RMSE and RSS vaues under 0.05 smaer than 0.05 and 0.01, the distribution of each sensors monitoring data concentrated with respect to the fusion resuts of under the eve of Tabe 3. Maximum ikeihood fusion resuts. Confidence Leve Resut of Data Fusion Confidence Interva Standard Deviation Root Mean Square Error (RMSE) Residua Sum of Squares (RSS) [9.066,9.966] [9.7587, ] [9.58,30.587]

5 344 The Open Cybernetics & Systemics Journa, 015, Voume 9 Jiang et a. Tabe 4. Fusion resuts of 10 sensors on different monitoring time points. Confidence Leve Fusion Resuts of Each Sensors on T time T1 T T 3 T 4 T 5 T 6 T7 T 8 T 9 T 10 RMSE RSS In order to further prove the fusion resut at the confidence eve of 0.05 is more precise than the fusion resuts of the eves of 0.05 and 0.01, in this paper, we cacuated respectivey the fusion resuts of monitoring data of 10 sensors on each monitoring time point T under eve of 0.05, 0.05 and 0.01 by using the maximum ikeihood estimation, the fusion resuts as shown in Tabe 4. The root mean square error RMSE and the residua sum of squares RSS in Tabe 4 are cacuated by the fusion resuts with T1-T10 monitoring times and the corresponding fusion resut in Tabe under different confidence eve. Through the above anaysis, we seected resut as the utimate fusion resut, which is cacuated by monitoring data of 10 sensors in Tabe 1 under the confidence eve CONCLUSION In the muti-sensor detection system, data fusion is the purpose of using some agorithms to process comprehensivey information and data from muti-sensor, and get more reiabe and effective concusion than a singe sensor. Mutisensor data fusion method presented in this paper is based on the monitoring data of each sensor, and then cacuated the confidence distance between the monitoring data of sensors, and then tested the significant of correation degree of confidence distance by the p-vaue test, and determined the optima number of fusion of muti-sensor. The agorithms used in this paper avoid the subjective factors in determining the threshod of the fusion of the sensors, and have more adequate scientific basis. To use the maximum ikeihood estimation method at different confidence eve to obtain the fina fusion resuts, and using the confidence interva ength, root mean square error (RMSE) and the residua sum of squares (RSS) under different confidence eve and anayze the fusion resuts, and finay get the optima fusion resuts. To some extent, by experiments the data fusion methods used in this paper is simpe and effective, and practica. CONFLICT OF INTEREST The authors confirm that this artice content has no confict of interest. ACKNOWLEDGEMENTS This work was supported in part by a grant from The Natura Science Foundation of the Inner Mongoia Autonomous Region (014MS063), and Nationa Natura Science Foundation of China ( ), and Technoogy Innovation Team of Inner Mongoia Agricutura University (NDPYTD010-9). REFERENCES [1] J. Feng, C. Hegao, Data fusion in sensor mode, Journa of Transducer Technoogy, vo. 18, no. 6, pp , [] Y. Yongxu, C. Xuhui, The appication of fuzzy set theory in muti-sensors information fusion, Computer Appication and Software, vo. 8, no. 11, pp. 1-14, 011. [3] Z. Yanong, W. Junyong, Overview of the muti-senor data fusion technoogy, Ship Eectronic Engineering, vo. 4, no., pp , 013. [4] L. Jueshi, J. Jing and C. Huaxi, An agorithom of muti-sensor information fusion based on the combination of rough set and neura network, Computer Appication and Software, vo. 6, no., pp , 34, 009. [5] F. Zhengnan and S. Wenfu, Anaysis of correation coefficient significance test, Physica Experiment of Coege, vo., no. 3, pp , 90, 009. [6] W. Xu, C. Chang, Y.S. Hung, PCW Fung, Asymptotic properties of order statistics correation coefficient in the norma cases, IEEE Trans Signa Process, vo. 56, no. 6, pp , 008. [7] X. Wei-chao, A review on correation coefficients, Journa of Guangdong University of Technoogy, vo. 9, no. 3, pp. 1-17, 01. [8] Z. Shun-zhong, W. Shu-mei, Anaysis on correation coefficients matrix and mutivariabe inear correation, Coege Mathematics, vo. 7, no. 1, pp , 011. [9] H. Jiang and S. You-chao, Appication study of muti-sourced reiabiity data fusion method based on bayes theory, Aircraft DE- SIGN, vo. 3, no. 6, pp. 5-55, 01. [10] W. Xiao-jun, C. Qi-ying, C. Bao-xiang and L. Tong-ming, Study on mutisensor data fusion methods based on bayes estimation, Systems Engineering-Theory & Practice, vo. 0, no. 7, pp , 000. [11] C. Zengfu, Mathematica method of muti-sensor data fusion, Journa of Mathematics in Practice and Theory, vo., pp , [1] T. Guoping, A robust method for the data fusion, Journa of Data Acquisition & Processing, vo. 13, no. 1, pp , [13] L. Yi, L. Baichuan and L. Xue, Muti-sensor data fusion based on muti-scae kaman fiter, Journa of Chong Qing Jiao Tong University(Natura Science), vo. 31, no., pp , 01. Received: September 16, 014 Revised: December 3, 014 Accepted: December 31, 014 Jiang et a.; Licensee Bentham Open. This is an open access artice icensed under the terms of the Creative Commons Attribution Non-Commercia License ( icenses/by-nc/3.0/) which permits unrestricted, non-commercia use, distribution and reproduction in any medium, provided the work is propery cited.