- Email: [email protected]
Outlier Handover Location Correction of Mobile Probe
JOURNAL OF TRANSPORTATION SYSTEMS ENGINEERING AND INFORMATION TECHNOLOGY Volume 11, Issue 5, October 2011 Online English edition of the Chinese language journal RESEARCH PAPER
Cite this article as: J Transpn Sys Eng & IT, 2011, 11(5), 42í47.
Outlier Handover Location Correction of Mobile Probe YUAN Yueming, GUAN Wei* MOE Key Laboratory for Urban Transportation Complex System Theory and Technology, Beijing Jiaotong University, Beijing 100044, China
Abstract: In this paper, handover location technique is employed for positioning mobile probes. In view of low location accuracy of handover location technique, an outlier handover location correction approach was presented that solved the problem in two phases, travel speed correction of outlier handover link and outlier handover location reposition. In the first phase, a two-layer data fusion model based on the definition of bridge handover link was proposed for recalculating the travel speeds of outlier handover links. In the second phase, the problem of outlier handover location reposition was solved by genetic algorithm. Based on the empirical data, absolute errors of travel speeds of handover links determined by the corrected results are analyzed and compared with results without outlier handover location correction. Evaluation results demonstrate that the proposed approach is feasible and effective, which can be used in the application of traffic information extraction. Key Words: intelligent transportation system; outlier handover location correction; mobile probe; handover location technique
1
Introduction
Mobile probes are a new means of collecting traffic information for road traffic administration departments, and have already been one of hot topics in intelligent transportation systems (ITS)[1–6]. Existing literature reveals that the handset-based location technique and the handover location technique are two promising techniques for positioning mobile probes[3–6]. Owing to lack of enough GPS-enabled mobile phones in many cities in China, the handover location technique was employed in this study for positioning mobile probes. In a cellular network, a handover is designed to be performed as a mobile phone in-use moves from one cell to another, so that mobile phone subscribers will always have high-quality services from the cellular network[7]. The mechanism of the handover location technique is to position mobile probes through pattern matching methods, which is not the same as that of the GPS location technique based on distance measurements[8]. Therefore, the handover location technique will generally produce handover locations with a lower level of accuracy than that produced with GPS. In such circumstances, speed estimations must be impacted by handover location errors of mobile probes, and sometimes will
not be precise enough to be used for ITS applications. In order to improve traffic speed estimation accuracy using handover locations of mobile probes, it becomes essential to add a preprocessing procedure for handling those handover locations that may bring about great negative impacts on speed estimations because of their large location errors. In this paper, owing to space limitations, only the problem of outlier handover location correction in the preprocessing procedure is studied in this paper.
2
Problem statements and modeling ideas
Assuming that a probe mobile repeatedly travels K times on the test section, naturally K handover location datasets can be obtained. In this work, the following variables are used to depict handover locations in one field test run: k: serial number of the field test run, k 1,2, , K ; hok(i): ith handover in the kth field test run, i 1,2, , n k ; Cell kf (i ) : From cell ID; Cell kt (i ) : To cell ID;
linkk(i): matched road link ID; x k (i) : average location of hok(i) in its matched road link; 'x k (i ) : upper location bias limit of the average location of hok(i);
Received date: Jul 13, 2011; Revised date: Sep 8, 2011; Accepted date: Sep 13, 2011 *Corresponding author. E-mail: [email protected] Copyright © 2011, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(10)60140-7
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
'x k (i ) : lower location bias limit of the average location of hok(i); tk(i): timestamps of hok(i). Further, a conception called handover link is proposed, which is defined as a road section joining two handovers in one field test run. According to the orders of two handovers connected by a handover link adjacent or not in one field test run, two types of handover links are introduced, called adjoining handover link and bridging handover link, respectively. As shown in Fig. 1, the road sections connected by hok(1), hok(2) and hok(2), hok(3) are adjoining handover links; the road section connected by hok(1) and hok(3) is bridging handover link. To avoid confusion, handover links discussed hereinafter mean only adjoining handover links. On the basis of the obtained handover location datasets in multiple field test runs, it is easy to further generate handover link dataset of each field test run, which are depicted by the following variables: hlk(i): ith handover link of kth field test run, i 1,2, , n k 1 ; hok(i): from handover of hlk(i); hok(i+1): to handover of hlk(i); dˆ k (i ) : length of hlk(i); 'tk(i): travel time of hlk(i); vˆ k (i ) : traffic speed of hlk(i), vˆ k (i ) = dˆ k (i ) /'tk(i). The characteristic variable 'tk(i) (i=1, 2, ···, nk–1, k=1, 2, ···, K) of handover link hlk(i) is calculated by subtracting the timestamp of hok(i) from that of hok(i+1); hence, 'tk(i) of hlk(i) being precise can be out of the question. On the contrary, the characteristic variable dˆ k (i ) of hlk(i) is obtained by calculating the distance between the average locations of hok(i) and hok(i+1), thus dˆ k (i ) of hlk(i) cannot be precise and sometimes may have large estimation error due to large location error of hok(i) or hok(i+1). Therefore, low handover location accuracy is a main factor that impacts on the estimation of the traffic speed of handover link. The larger the errors of handover locations, the greater the impacts on speed estimations. In this paper, a new outlier handover location correction approach instead of the statistical analysis approach is proposed, which consists of two phases, traffic speed correction of outlier handover link and outlier handover location reposition. In the first phase, handover links with great traffic speed estimation errors are called outlier handover links, and the main modeling idea is to re-estimate their speeds by means of their neighbouring bridging handover links. In the second phase, the major objective is to finally generate accurate enough speed estimations of handover links with the help of the intermediate results obtained in the first phase; thus, the main modelling idea is to optimally reposition outlier handover locations (locations of handovers connected by outlier handover links) via developing an optimization model.
3
Outlier handover location correction of mobile probes
3.1 Development of bridging handover link Given the ith handover link in the kth handover link dataset, there are three kinds of bridging handover links for traffic speed correction of outlier handover link: (1) lbhl kj (i ) [hl k (i j ), , hl k (i )] (2) rbhl kj (i ) [hl k (i ), , hl k (i j )] (3) mbhl kj (i) [hl k (i j ), , hl k (i), , hl k (i j )] where lbhl kj (i) is a bridging handover link that contains j+1 handover links and handover link hlk(i) is the last one in the j+1 handover links; rbhl kj (i ) is a bridging handover link that also contains j+1 handover links and hlk(i) is the first one in the j+1 handover links; mbhl kj (i ) is a bridging handover link that contains 2j+1 handover links and hlk(i) is in the middle of the 2j+1 handover links. 3.2 Traffic speed correction of outlier handover link It is generally believed that traffic speeds of neighbouring handover links have spatial and temporal correlations, thus a two-layer data fusion model is developed for traffic speed correction of outlier handover link. With the help of three kinds of bridging handover links, two data fusion models established respectively from the standpoints of spatial and temporal correlation are developed in the first layer. In the second layer, results from spatial and temporal correlated data fusion models are assumed to be independent, and their arithmetic mean values are fused to be the final speed estimations of outlier handover links. Fig. 2 shows the data fusion flow chart of traffic speed correction of outlier handover links.
Fig. 1 Sketch map of handover link
Fig. 2 Data fusion flow chart of traffic speed correction of outlier handover link
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
Given handover link dataset {hlk} of the kth field test run, if the ith handover link is outlier handover link, the steps for its traffic speed correction are explained as follows: Initialization: set the threshold values of spatial and temporal correlation ȗs and ȗt; Develop spatial correlated bridging handover link datasets associated with hlk(i).
BHLs
r,s ª ) ) rbhlkj (1)º « » « » l,s m, s r,s « lbhl j (i ) mbhlkj (i ) rbhlkj (i ) »» k « « » « » jl,s ( 1 ) ) ) lbhl n k k ¬ ¼
(4)
in which the spatial correlated bridging handover links’ lengths should be less than ȗs; for instance, the maximum number of handover links in bridging handover link m, s mbhl kj (i) can be determined by m, s jmax
arg min
¦
i j m, s
ic i j
dˆk (ic) ] s m, s
v~sr (hlk (i )) v~sm (hlk (i ))
¦ ¦ ¦
l,s j max
l,s
a
l,s jl,s 1 j r,s j max
a
v(lbhlkj (i ))
r,s jr,s 1 j m, s j max
a
(6)
r,s
v(rbhlkj (i ))
m, s j m, s 1 j
v(mbhlkj
m, s
(i ))
(7) (8)
where {a j l , s } , {a j r ,s } , {a j m ,s } are weight coefficients satisfying normalizing condition; Follow the same way to re-estimate the traffic speed of hlk(i), using three kinds of bridging handover links in BHLt, and obtain corrected traffic speeds of hlk(i) [v~tl (hlk (i )), v~tr (hlk (i )), v~tm (hlk (i ))] ; Fusing the corrected traffic speeds of hlk(i) obtained in the fifth step by weighted average approach v~s ( hlk (i )) Kl v~sl (hlk (i )) K m v~sm (hlk (i )) K r v~sr (hlk (i )) (9) where Ș=[0.3, 0.3, 0.4]. Follow the same way to fuse the corrected traffic speeds of hlk(i) obtained in the sixth step, and obtain v~t (hlk (i)) . Calculate the final corrected traffic speed of hlk(i) based on v~s ( hlk (i )) and v~t ( hlk (i )) : v~ (hlk (i )) (v~s (hlk (i )) v~t (hlk (i ))) / 2 (10) 3.3 Outlier handover location reposition The problem of outlier handover location reposition is to seek corrections of outlier handovers locations, which can ensure final speed estimation errors of outlier handover links after correction are within the permissive range. As a matter of
1 2
min Q
(5)
Develop temporal correlated bridging handover link datasets associated with hlk(i), in which the temporal correlated bridging handover links’ travel times should be less than ȗt; Calculate lengths, travel times and speeds of bridging handover links in BHLs and BHLt; Re-estimate the traffic speed of hlk(i) using three kinds of bridging handover links in BHLs:
v~sl (hlk (i ))
fact, repositioning an outlier handover location will simultaneously change the speeds of the two handover links (one is the outlier handover link and the other is its neighbouring handover link) attached to it. Wrong corrections of outlier handover locations may enhance the speed estimation accuracy of outlier handover links, but in turn reduce the speed estimation accuracy of their neighbouring handover links. Therefore, all handover links travelled by a mobile probe in one field test run are treated as a whole in this paper. Moreover, the basic correction criterion is to obtain the desired level of accuracy of traffic speed estimations whether it is outlier handover links or not. A common correction criterion to solve the problem of outlier handover location reposition is the least square method, which can be established by the following optimization model: nk 1
¦ (v (i) v~ (i)) k
k
2
(11)
i 1
s.t. 0 d v k (i) d V , i 1, , n k 1 'xk (ic) i
(12)
d 'xk (ic) d 'xk (i c), ic 1, , nk (13)
ic 1 i, ® ¯i c 1, i c (1, nk ]
(14)
where v~k (i) is the traffic speed of the ith handover link in the kth field test run obtained in the first phase; vk (i )
vˆk (i )
'xk (i 1) 'xk (i) , i 't k (i )
1, , nk 1
The object function in Eq. (11) is a residual sum of the squares of speed estimations, given the kth handover link dataset of mobile probe; the constraint condition in Eq. (12) means that handover links’ speed estimations should be less than the speed limit and greater than zero; the constraint condition in Eq. (13) means that the corrections of handover locations should be between upper and lower location bias limits; the constraint condition in Eq. (14) is the relationship between i and i’. Although the least square method is easy to implement, it is incapable of outputting solutions to the problem with the desired level of accuracy. In order to assure estimated traffic speeds of handover links after correction as accurate as possible, the characteristic variable {vˆk (i )}(i 1, , nk 1) is regarded as a stochastic variable and propose an integrated object function together with the constraint conditions in Eqs. (12)–(14) to solve the problem of outlier handover location reposition. nk 1
min J
p1 (vk (i ))
¦ p (v (i)) log p (v~ (i)) OV 1
i 1
k
2
2 'v
(15)
k
where Ȝ is a penalty coefficient and Ȝ=0.75; the first term on the right side of Eq. (15) is a difference measurement between the empirical distribution functions of handover links’ speeds after the first phase and the second phase, which is called Kullback–Leibler distance[9,10]; V '2v is the variance of speed estimation errors after outlier handover location reposition.
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
To solve the proposed optimization model, a genetic algorithm-based approach is proposed: (1) Initialization: input the kth handover location dataset and the intermediate results obtained in the first phase; set the population size, maximum generation, crossover rate and mutation rate; set t=0, choose the initial population of N real-coded individuals at random and evaluate the fitness of each individual in the initial population; (2) Carry on crossover operation based on a partial discrete crossover operator and evaluate the fitness of new individuals; (3) Carry on mutation operation based on real uniform mutation operator and evaluate the fitness of new individuals; (4) Select N best-fit individuals in the parent and offspring and put into the next population P(t+1); (5) If termination condition is met, stop and output final solutions to the problem; or else, set t=t+1 and to Step (2).
4
Empirical analysis
A preliminary empirical study has been conducted by means of repeated field tests runs on a stretch of inner-suburban freeway in Beijing. The length of the experimented freeway is about 8 km, including four freeway links, an on-ramp link and an off-ramp link, as shown in Table 1. In the course of the field test runs, a GPS equipment is also employed to simultaneously record driving data of the test car, which served as ground truth data for evaluation. In this paper, threshold values ȗs, ȗt in the first phase are equal to L/2 and T /2, respectively, where L and T are the total lengths of the surveyed route and the average travel time of testing car moving on the whole surveyed route; parameters for the genetic algorithm-based approach in the second phase, population size, maximum generation, crossover rate and mutation rate, are 20, 80, 0.8 and 0.2. The absolute error between speed estimation of a handover link after correction and its ground truth data is used as the evaluation statistic for assessing our proposed approach, and mean absolute error, Į trimmed mean absoluter error (Į=0.1), median absolute error and median absolute deviation of absolute error are used as the evaluation indexes. Table 2 shows the evaluation results of our proposed approach, in which the benchmark approach is to seek solutions of outlier handover location reposition through solving the optimization models (11) to (14) in the second phase. As shown in Table 2, our proposed approach is superior to the benchmark approach in reducing traffic speed estimation errors owing to handover location errors. Figure 3 shows the empirical distribution functions of the mean absolute errors of all field test runs determined by the benchmark approach and our proposed approach. 85% percentile of two empirical distribution functions of the benchmark approach and our proposed approach are 4.35 m/s and 3.91 m/s, so it can be suggested that our proposed
approach produces 10.11% improvement on speed estimation accuracy. On the other hand, the range of two empirical distribution functions of the benchmark approach and our proposed approach are 4.07 m/s and 3.31 m/s, which suggests that our proposed approach has 18.67% increase in speed estimation reliability. For empirical distribution functions of the other three evaluation indexes, we conducted the same analysis as above and eventually arrived at the same conclusions. Therefore, it can be concluded that our proposed approach can achieve better improvement on accuracy and reliability of handover links’ speed estimations than the benchmark approach. Table 1 Surveyed road links Surveyed road link
Road link ID
Road type
Length (m)
Link 1
111611
Freeway
2 437.17
Link 2
111717
Freeway
644.33
Link 3
111718
Freeway
376.40
Link 4
110991
Freeway
4 347.05
Link 5
99646
On-ramp road
336.43
Link 6
110995
Off-ramp road
388.39
Table 2 Evaluation results Indexes (m/s) Mean
Raw data 6.5991
Benchmark approach 3.0741
Proposed approach 2.9390
Į trimmed mean
4.6544
2.9018
2.7253
Median Median absolute deviation
3.2771
2.6221
2.1859
6.2073
1.8818
2.0255
Fig. 3 Empirical distribution functions of mean absolute error
Fig. 4 Probability density function of time consumption of mobile probe outlier handover location correction
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
Table 3 performance evaluations of real time Į
n (d=1.5 m/s) 2.95
n (d=3 m/s) 0.74
Time consuming (min) 0.67
Time consuming (min) 0.17
1.5
6.65
1.66
1.51
0.38
2
11.80
2.95
2.68
0.67
2.5
18.43
4.61
4.19
1.05
3
26.54
6.64
6.03
1.51
3.5
36.13
9.03
8.21
2.05
4
47.19
11.80
10.73
2.68
1
1.71
0.43
0.39
0.10
ı (m/s) 1
0.99
0.95
1.5
3.84
0.96
0.87
0.22
2
6.83
1.71
1.55
0.39
2.5
10.67
2.67
2.43
0.61
3
15.37
3.84
3.49
0.87
3.5
20.92
5.23
4.75
1.19
4
27.32
6.83
6.21
1.55
Maintaining timeliness of traffic data is also an essential condition for successfully making use of mobile probes, thus time consumption of the proposed approach was also studied to clarify whether the proposed approach can satisfy requirements of accuracy, reliability and timeliness. Probability dense function of time consumption of the proposed approach is shown in Fig. 4, whose mean and standard deviation are 13.64 s and 2.07 s. According to the minimum sample size model n=( zĮ/2ı/d)2 (zĮ/2 is bilateral standard normal distribution value in 1-Į conference level, ı is standard deviation of speed, d is permissive error[11]), Table 3 shows the required minimum sample size and their total time consumption under different combinations of confidence level, permissive error and standard deviation of speed. If the temporal period of speed estimation is 10 min, our proposed approach can separately finish 13 cases and 14 cases in time under 99% and 95% confidence level. In conclusion, the proposed approach is effective for handling outlier handover location correction.
5
Conclusions
Traffic speed estimations are greatly impacted by low accuracies of handover locations, so outlier handover location correction is an essential procedure to enhance speed estimation accuracy using handover locations. In this paper, a two-phase outlier handover location correction approach is proposed. Evaluation results based on empirical analysis show that our proposed approach is feasible and effective, which could be practically advantageous to handling outlier correction of handover data. However, our proposed approach cannot simultaneously satisfy requirements of accuracy, reliability and timeliness under high confidence level, high standard deviation of speed estimations and low permissive error. Therefore, it is suggested that the temporal period of
speed estimation should be increased to 15 min in the future application or an improved outlier handover correction approach utilizing multiple sources of information should be developed. Future studies should be focused on (1) validating the proposed approach using more data from mobile operators or simulation and (2) developing a robust traffic information extraction approach based on handover locations after correction.
Acknowledgements This research was funded in part by the National Nature Science Foundation of China (No. 60874078), the Program for New Century Excellent Talents in University of China (NCET-08-0718), the Ph.D. Program Foundation of China Ministry of Education (20070004020), the National Basic Research Program of China (2006CB70557) and the National Science and Technology Infrastructure Program of China (2006BAG01A01).
References [1]
Rose G. Mobile phones as traffic probes: practices, prospects and issues. Transport Reviews, 2006, 26(3): 275–291.
[2]
Smith B L, Fontaine M D, Beaton J, et al. Private-sector provision of congestion data. University of Virginia Center for Transportation Studies, 2007.
[3]
Qiu Z J, Jin J, Cheng P, et al. State of the art and practice: cellular probe technology applied in advanced traveler information system. 86th Annual Transportation Research Board Meeting, Washington, D.C., January, 2007.
[4]
Wunnava S V, Ken K, Babij T, et al. Travel time estimation using cell phones (TTECP) for highways and roadways. Florida International University, 2007.
[5] Gundlegard D, Karlsson J M. Handover location accuracy for travel time estimation in GSM and UMTS. IET Intelligent Transportation Systems, 2009, 3(1): 87–94. [6] Herrera J C, Work D B, Herring R, et al. Evaluation of traffic data obtained via GPS-enabled mobile phones: The Mobile Century field experiment. Transportation Research Part C, 2010, 18(4): 568–583. [7]
Li B. Research on handoff schemes in cellular mobile systems. Xi’an: Xidian University, 2001.
[8]
Yang F, Hui Y. The map matching method based on cell phone handover pattern. System Engineering, 2007, 25(11): 6–13.
[9]
Lin H H. Measurement error and uncertainty evaluation. Beijing: China Machine Press, 2009.
[10]
Haykin S. Neural networks: a comprehensive foundation. 2nd ed. New Jersey: Prentice Hall, 1998.
[11]
Smith B L, Zhang H, Fontaine M D, et al. Wireless location technology-based traffic monitoring critical assessment and evaluation of an early-generation system. Journal of Transportation Engineering, 2004, 130(5): 576–584.
Cite this article as: J Transpn Sys Eng & IT, 2011, 11(5), 42í47.
Outlier Handover Location Correction of Mobile Probe YUAN Yueming, GUAN Wei* MOE Key Laboratory for Urban Transportation Complex System Theory and Technology, Beijing Jiaotong University, Beijing 100044, China
Abstract: In this paper, handover location technique is employed for positioning mobile probes. In view of low location accuracy of handover location technique, an outlier handover location correction approach was presented that solved the problem in two phases, travel speed correction of outlier handover link and outlier handover location reposition. In the first phase, a two-layer data fusion model based on the definition of bridge handover link was proposed for recalculating the travel speeds of outlier handover links. In the second phase, the problem of outlier handover location reposition was solved by genetic algorithm. Based on the empirical data, absolute errors of travel speeds of handover links determined by the corrected results are analyzed and compared with results without outlier handover location correction. Evaluation results demonstrate that the proposed approach is feasible and effective, which can be used in the application of traffic information extraction. Key Words: intelligent transportation system; outlier handover location correction; mobile probe; handover location technique
1
Introduction
Mobile probes are a new means of collecting traffic information for road traffic administration departments, and have already been one of hot topics in intelligent transportation systems (ITS)[1–6]. Existing literature reveals that the handset-based location technique and the handover location technique are two promising techniques for positioning mobile probes[3–6]. Owing to lack of enough GPS-enabled mobile phones in many cities in China, the handover location technique was employed in this study for positioning mobile probes. In a cellular network, a handover is designed to be performed as a mobile phone in-use moves from one cell to another, so that mobile phone subscribers will always have high-quality services from the cellular network[7]. The mechanism of the handover location technique is to position mobile probes through pattern matching methods, which is not the same as that of the GPS location technique based on distance measurements[8]. Therefore, the handover location technique will generally produce handover locations with a lower level of accuracy than that produced with GPS. In such circumstances, speed estimations must be impacted by handover location errors of mobile probes, and sometimes will
not be precise enough to be used for ITS applications. In order to improve traffic speed estimation accuracy using handover locations of mobile probes, it becomes essential to add a preprocessing procedure for handling those handover locations that may bring about great negative impacts on speed estimations because of their large location errors. In this paper, owing to space limitations, only the problem of outlier handover location correction in the preprocessing procedure is studied in this paper.
2
Problem statements and modeling ideas
Assuming that a probe mobile repeatedly travels K times on the test section, naturally K handover location datasets can be obtained. In this work, the following variables are used to depict handover locations in one field test run: k: serial number of the field test run, k 1,2, , K ; hok(i): ith handover in the kth field test run, i 1,2, , n k ; Cell kf (i ) : From cell ID; Cell kt (i ) : To cell ID;
linkk(i): matched road link ID; x k (i) : average location of hok(i) in its matched road link; 'x k (i ) : upper location bias limit of the average location of hok(i);
Received date: Jul 13, 2011; Revised date: Sep 8, 2011; Accepted date: Sep 13, 2011 *Corresponding author. E-mail: [email protected] Copyright © 2011, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(10)60140-7
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
'x k (i ) : lower location bias limit of the average location of hok(i); tk(i): timestamps of hok(i). Further, a conception called handover link is proposed, which is defined as a road section joining two handovers in one field test run. According to the orders of two handovers connected by a handover link adjacent or not in one field test run, two types of handover links are introduced, called adjoining handover link and bridging handover link, respectively. As shown in Fig. 1, the road sections connected by hok(1), hok(2) and hok(2), hok(3) are adjoining handover links; the road section connected by hok(1) and hok(3) is bridging handover link. To avoid confusion, handover links discussed hereinafter mean only adjoining handover links. On the basis of the obtained handover location datasets in multiple field test runs, it is easy to further generate handover link dataset of each field test run, which are depicted by the following variables: hlk(i): ith handover link of kth field test run, i 1,2, , n k 1 ; hok(i): from handover of hlk(i); hok(i+1): to handover of hlk(i); dˆ k (i ) : length of hlk(i); 'tk(i): travel time of hlk(i); vˆ k (i ) : traffic speed of hlk(i), vˆ k (i ) = dˆ k (i ) /'tk(i). The characteristic variable 'tk(i) (i=1, 2, ···, nk–1, k=1, 2, ···, K) of handover link hlk(i) is calculated by subtracting the timestamp of hok(i) from that of hok(i+1); hence, 'tk(i) of hlk(i) being precise can be out of the question. On the contrary, the characteristic variable dˆ k (i ) of hlk(i) is obtained by calculating the distance between the average locations of hok(i) and hok(i+1), thus dˆ k (i ) of hlk(i) cannot be precise and sometimes may have large estimation error due to large location error of hok(i) or hok(i+1). Therefore, low handover location accuracy is a main factor that impacts on the estimation of the traffic speed of handover link. The larger the errors of handover locations, the greater the impacts on speed estimations. In this paper, a new outlier handover location correction approach instead of the statistical analysis approach is proposed, which consists of two phases, traffic speed correction of outlier handover link and outlier handover location reposition. In the first phase, handover links with great traffic speed estimation errors are called outlier handover links, and the main modeling idea is to re-estimate their speeds by means of their neighbouring bridging handover links. In the second phase, the major objective is to finally generate accurate enough speed estimations of handover links with the help of the intermediate results obtained in the first phase; thus, the main modelling idea is to optimally reposition outlier handover locations (locations of handovers connected by outlier handover links) via developing an optimization model.
3
Outlier handover location correction of mobile probes
3.1 Development of bridging handover link Given the ith handover link in the kth handover link dataset, there are three kinds of bridging handover links for traffic speed correction of outlier handover link: (1) lbhl kj (i ) [hl k (i j ), , hl k (i )] (2) rbhl kj (i ) [hl k (i ), , hl k (i j )] (3) mbhl kj (i) [hl k (i j ), , hl k (i), , hl k (i j )] where lbhl kj (i) is a bridging handover link that contains j+1 handover links and handover link hlk(i) is the last one in the j+1 handover links; rbhl kj (i ) is a bridging handover link that also contains j+1 handover links and hlk(i) is the first one in the j+1 handover links; mbhl kj (i ) is a bridging handover link that contains 2j+1 handover links and hlk(i) is in the middle of the 2j+1 handover links. 3.2 Traffic speed correction of outlier handover link It is generally believed that traffic speeds of neighbouring handover links have spatial and temporal correlations, thus a two-layer data fusion model is developed for traffic speed correction of outlier handover link. With the help of three kinds of bridging handover links, two data fusion models established respectively from the standpoints of spatial and temporal correlation are developed in the first layer. In the second layer, results from spatial and temporal correlated data fusion models are assumed to be independent, and their arithmetic mean values are fused to be the final speed estimations of outlier handover links. Fig. 2 shows the data fusion flow chart of traffic speed correction of outlier handover links.
Fig. 1 Sketch map of handover link
Fig. 2 Data fusion flow chart of traffic speed correction of outlier handover link
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
Given handover link dataset {hlk} of the kth field test run, if the ith handover link is outlier handover link, the steps for its traffic speed correction are explained as follows: Initialization: set the threshold values of spatial and temporal correlation ȗs and ȗt; Develop spatial correlated bridging handover link datasets associated with hlk(i).
BHLs
r,s ª ) ) rbhlkj (1)º « » « » l,s m, s r,s « lbhl j (i ) mbhlkj (i ) rbhlkj (i ) »» k « « » « » jl,s ( 1 ) ) ) lbhl n k k ¬ ¼
(4)
in which the spatial correlated bridging handover links’ lengths should be less than ȗs; for instance, the maximum number of handover links in bridging handover link m, s mbhl kj (i) can be determined by m, s jmax
arg min
¦
i j m, s
ic i j
dˆk (ic) ] s m, s
v~sr (hlk (i )) v~sm (hlk (i ))
¦ ¦ ¦
l,s j max
l,s
a
l,s jl,s 1 j r,s j max
a
v(lbhlkj (i ))
r,s jr,s 1 j m, s j max
a
(6)
r,s
v(rbhlkj (i ))
m, s j m, s 1 j
v(mbhlkj
m, s
(i ))
(7) (8)
where {a j l , s } , {a j r ,s } , {a j m ,s } are weight coefficients satisfying normalizing condition; Follow the same way to re-estimate the traffic speed of hlk(i), using three kinds of bridging handover links in BHLt, and obtain corrected traffic speeds of hlk(i) [v~tl (hlk (i )), v~tr (hlk (i )), v~tm (hlk (i ))] ; Fusing the corrected traffic speeds of hlk(i) obtained in the fifth step by weighted average approach v~s ( hlk (i )) Kl v~sl (hlk (i )) K m v~sm (hlk (i )) K r v~sr (hlk (i )) (9) where Ș=[0.3, 0.3, 0.4]. Follow the same way to fuse the corrected traffic speeds of hlk(i) obtained in the sixth step, and obtain v~t (hlk (i)) . Calculate the final corrected traffic speed of hlk(i) based on v~s ( hlk (i )) and v~t ( hlk (i )) : v~ (hlk (i )) (v~s (hlk (i )) v~t (hlk (i ))) / 2 (10) 3.3 Outlier handover location reposition The problem of outlier handover location reposition is to seek corrections of outlier handovers locations, which can ensure final speed estimation errors of outlier handover links after correction are within the permissive range. As a matter of
1 2
min Q
(5)
Develop temporal correlated bridging handover link datasets associated with hlk(i), in which the temporal correlated bridging handover links’ travel times should be less than ȗt; Calculate lengths, travel times and speeds of bridging handover links in BHLs and BHLt; Re-estimate the traffic speed of hlk(i) using three kinds of bridging handover links in BHLs:
v~sl (hlk (i ))
fact, repositioning an outlier handover location will simultaneously change the speeds of the two handover links (one is the outlier handover link and the other is its neighbouring handover link) attached to it. Wrong corrections of outlier handover locations may enhance the speed estimation accuracy of outlier handover links, but in turn reduce the speed estimation accuracy of their neighbouring handover links. Therefore, all handover links travelled by a mobile probe in one field test run are treated as a whole in this paper. Moreover, the basic correction criterion is to obtain the desired level of accuracy of traffic speed estimations whether it is outlier handover links or not. A common correction criterion to solve the problem of outlier handover location reposition is the least square method, which can be established by the following optimization model: nk 1
¦ (v (i) v~ (i)) k
k
2
(11)
i 1
s.t. 0 d v k (i) d V , i 1, , n k 1 'xk (ic) i
(12)
d 'xk (ic) d 'xk (i c), ic 1, , nk (13)
ic 1 i, ® ¯i c 1, i c (1, nk ]
(14)
where v~k (i) is the traffic speed of the ith handover link in the kth field test run obtained in the first phase; vk (i )
vˆk (i )
'xk (i 1) 'xk (i) , i 't k (i )
1, , nk 1
The object function in Eq. (11) is a residual sum of the squares of speed estimations, given the kth handover link dataset of mobile probe; the constraint condition in Eq. (12) means that handover links’ speed estimations should be less than the speed limit and greater than zero; the constraint condition in Eq. (13) means that the corrections of handover locations should be between upper and lower location bias limits; the constraint condition in Eq. (14) is the relationship between i and i’. Although the least square method is easy to implement, it is incapable of outputting solutions to the problem with the desired level of accuracy. In order to assure estimated traffic speeds of handover links after correction as accurate as possible, the characteristic variable {vˆk (i )}(i 1, , nk 1) is regarded as a stochastic variable and propose an integrated object function together with the constraint conditions in Eqs. (12)–(14) to solve the problem of outlier handover location reposition. nk 1
min J
p1 (vk (i ))
¦ p (v (i)) log p (v~ (i)) OV 1
i 1
k
2
2 'v
(15)
k
where Ȝ is a penalty coefficient and Ȝ=0.75; the first term on the right side of Eq. (15) is a difference measurement between the empirical distribution functions of handover links’ speeds after the first phase and the second phase, which is called Kullback–Leibler distance[9,10]; V '2v is the variance of speed estimation errors after outlier handover location reposition.
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
To solve the proposed optimization model, a genetic algorithm-based approach is proposed: (1) Initialization: input the kth handover location dataset and the intermediate results obtained in the first phase; set the population size, maximum generation, crossover rate and mutation rate; set t=0, choose the initial population of N real-coded individuals at random and evaluate the fitness of each individual in the initial population; (2) Carry on crossover operation based on a partial discrete crossover operator and evaluate the fitness of new individuals; (3) Carry on mutation operation based on real uniform mutation operator and evaluate the fitness of new individuals; (4) Select N best-fit individuals in the parent and offspring and put into the next population P(t+1); (5) If termination condition is met, stop and output final solutions to the problem; or else, set t=t+1 and to Step (2).
4
Empirical analysis
A preliminary empirical study has been conducted by means of repeated field tests runs on a stretch of inner-suburban freeway in Beijing. The length of the experimented freeway is about 8 km, including four freeway links, an on-ramp link and an off-ramp link, as shown in Table 1. In the course of the field test runs, a GPS equipment is also employed to simultaneously record driving data of the test car, which served as ground truth data for evaluation. In this paper, threshold values ȗs, ȗt in the first phase are equal to L/2 and T /2, respectively, where L and T are the total lengths of the surveyed route and the average travel time of testing car moving on the whole surveyed route; parameters for the genetic algorithm-based approach in the second phase, population size, maximum generation, crossover rate and mutation rate, are 20, 80, 0.8 and 0.2. The absolute error between speed estimation of a handover link after correction and its ground truth data is used as the evaluation statistic for assessing our proposed approach, and mean absolute error, Į trimmed mean absoluter error (Į=0.1), median absolute error and median absolute deviation of absolute error are used as the evaluation indexes. Table 2 shows the evaluation results of our proposed approach, in which the benchmark approach is to seek solutions of outlier handover location reposition through solving the optimization models (11) to (14) in the second phase. As shown in Table 2, our proposed approach is superior to the benchmark approach in reducing traffic speed estimation errors owing to handover location errors. Figure 3 shows the empirical distribution functions of the mean absolute errors of all field test runs determined by the benchmark approach and our proposed approach. 85% percentile of two empirical distribution functions of the benchmark approach and our proposed approach are 4.35 m/s and 3.91 m/s, so it can be suggested that our proposed
approach produces 10.11% improvement on speed estimation accuracy. On the other hand, the range of two empirical distribution functions of the benchmark approach and our proposed approach are 4.07 m/s and 3.31 m/s, which suggests that our proposed approach has 18.67% increase in speed estimation reliability. For empirical distribution functions of the other three evaluation indexes, we conducted the same analysis as above and eventually arrived at the same conclusions. Therefore, it can be concluded that our proposed approach can achieve better improvement on accuracy and reliability of handover links’ speed estimations than the benchmark approach. Table 1 Surveyed road links Surveyed road link
Road link ID
Road type
Length (m)
Link 1
111611
Freeway
2 437.17
Link 2
111717
Freeway
644.33
Link 3
111718
Freeway
376.40
Link 4
110991
Freeway
4 347.05
Link 5
99646
On-ramp road
336.43
Link 6
110995
Off-ramp road
388.39
Table 2 Evaluation results Indexes (m/s) Mean
Raw data 6.5991
Benchmark approach 3.0741
Proposed approach 2.9390
Į trimmed mean
4.6544
2.9018
2.7253
Median Median absolute deviation
3.2771
2.6221
2.1859
6.2073
1.8818
2.0255
Fig. 3 Empirical distribution functions of mean absolute error
Fig. 4 Probability density function of time consumption of mobile probe outlier handover location correction
YUAN Yueming et al. / J Transpn Sys Eng & IT, 2011, 11(5), 42í47
Table 3 performance evaluations of real time Į
n (d=1.5 m/s) 2.95
n (d=3 m/s) 0.74
Time consuming (min) 0.67
Time consuming (min) 0.17
1.5
6.65
1.66
1.51
0.38
2
11.80
2.95
2.68
0.67
2.5
18.43
4.61
4.19
1.05
3
26.54
6.64
6.03
1.51
3.5
36.13
9.03
8.21
2.05
4
47.19
11.80
10.73
2.68
1
1.71
0.43
0.39
0.10
ı (m/s) 1
0.99
0.95
1.5
3.84
0.96
0.87
0.22
2
6.83
1.71
1.55
0.39
2.5
10.67
2.67
2.43
0.61
3
15.37
3.84
3.49
0.87
3.5
20.92
5.23
4.75
1.19
4
27.32
6.83
6.21
1.55
Maintaining timeliness of traffic data is also an essential condition for successfully making use of mobile probes, thus time consumption of the proposed approach was also studied to clarify whether the proposed approach can satisfy requirements of accuracy, reliability and timeliness. Probability dense function of time consumption of the proposed approach is shown in Fig. 4, whose mean and standard deviation are 13.64 s and 2.07 s. According to the minimum sample size model n=( zĮ/2ı/d)2 (zĮ/2 is bilateral standard normal distribution value in 1-Į conference level, ı is standard deviation of speed, d is permissive error[11]), Table 3 shows the required minimum sample size and their total time consumption under different combinations of confidence level, permissive error and standard deviation of speed. If the temporal period of speed estimation is 10 min, our proposed approach can separately finish 13 cases and 14 cases in time under 99% and 95% confidence level. In conclusion, the proposed approach is effective for handling outlier handover location correction.
5
Conclusions
Traffic speed estimations are greatly impacted by low accuracies of handover locations, so outlier handover location correction is an essential procedure to enhance speed estimation accuracy using handover locations. In this paper, a two-phase outlier handover location correction approach is proposed. Evaluation results based on empirical analysis show that our proposed approach is feasible and effective, which could be practically advantageous to handling outlier correction of handover data. However, our proposed approach cannot simultaneously satisfy requirements of accuracy, reliability and timeliness under high confidence level, high standard deviation of speed estimations and low permissive error. Therefore, it is suggested that the temporal period of
speed estimation should be increased to 15 min in the future application or an improved outlier handover correction approach utilizing multiple sources of information should be developed. Future studies should be focused on (1) validating the proposed approach using more data from mobile operators or simulation and (2) developing a robust traffic information extraction approach based on handover locations after correction.
Acknowledgements This research was funded in part by the National Nature Science Foundation of China (No. 60874078), the Program for New Century Excellent Talents in University of China (NCET-08-0718), the Ph.D. Program Foundation of China Ministry of Education (20070004020), the National Basic Research Program of China (2006CB70557) and the National Science and Technology Infrastructure Program of China (2006BAG01A01).
References [1]
Rose G. Mobile phones as traffic probes: practices, prospects and issues. Transport Reviews, 2006, 26(3): 275–291.
[2]
Smith B L, Fontaine M D, Beaton J, et al. Private-sector provision of congestion data. University of Virginia Center for Transportation Studies, 2007.
[3]
Qiu Z J, Jin J, Cheng P, et al. State of the art and practice: cellular probe technology applied in advanced traveler information system. 86th Annual Transportation Research Board Meeting, Washington, D.C., January, 2007.
[4]
Wunnava S V, Ken K, Babij T, et al. Travel time estimation using cell phones (TTECP) for highways and roadways. Florida International University, 2007.
[5] Gundlegard D, Karlsson J M. Handover location accuracy for travel time estimation in GSM and UMTS. IET Intelligent Transportation Systems, 2009, 3(1): 87–94. [6] Herrera J C, Work D B, Herring R, et al. Evaluation of traffic data obtained via GPS-enabled mobile phones: The Mobile Century field experiment. Transportation Research Part C, 2010, 18(4): 568–583. [7]
Li B. Research on handoff schemes in cellular mobile systems. Xi’an: Xidian University, 2001.
[8]
Yang F, Hui Y. The map matching method based on cell phone handover pattern. System Engineering, 2007, 25(11): 6–13.
[9]
Lin H H. Measurement error and uncertainty evaluation. Beijing: China Machine Press, 2009.
[10]
Haykin S. Neural networks: a comprehensive foundation. 2nd ed. New Jersey: Prentice Hall, 1998.
[11]
Smith B L, Zhang H, Fontaine M D, et al. Wireless location technology-based traffic monitoring critical assessment and evaluation of an early-generation system. Journal of Transportation Engineering, 2004, 130(5): 576–584.