Estimation of Large Truck Volume Using Single Loop Detector Data

Transcription

1 Estmaton of Large Truck Volume Usng Sngle Loop Detector Data Yunlong Zhang*, Ph.D., P.E. Assstant Professor Department of Cvl Engneerng Texas A&M Unversty 3136 TAMU College Staton TX, Phone: (979) Emal: Zhru Ye Department of Cvl Engneerng Texas A&M Unversty 3136 TAMU College Staton, TX Phone (979) Emal: Yuanchang Xe Department of Cvl Engneerng Texas A&M Unversty 3116 TAMU College Staton, TX Phone (979) Emal: July, 2007 *Correspondng Author Word Count: (10 Tables and Fgures)*250 = 6676

2 Estmaton of Large Truck Volume Usng Sngle Loop Detector Data Yunlong Zhang, Zhru Ye, and Yuanchang Xe ABSTRACT Ths paper presents a methodology to estmate the volume of large trucks by usng sngle loop outputs. An Unscented Kalman Flterng (UKF) algorthm s used to generate speed estmaton based on sngle loop data, and the mean effectve vehcle length of each tme nterval s thus obtaned wth the loop outputs and speed data provded. We nvestgated the bmodal vehcle length dstrbuton and further separated t nto short and long vehcle dstrbutons. Based on the estmated mean effectve vehcle lengths and vehcle length dstrbutons, an algorthm s proposed to estmate large truck volume. Data collected from Texas Transportaton Insttute s vehcle detecton test beds are used for ths study. The results show that the proposed method produces good performances n large truck volume estmaton under varous traffc condtons. Key Words: Trucks; Volume Estmaton; Sngle Loop Detectors 2

3 INTRODUCTION Truck traffc has been ncreasng steadly on Amerca s hghways due to the growng economy and ncreased nternatonal trade. Trucks have dfferent characterstcs from passenger cars and thus are a key consderaton n many stages of a hghway project. Trucks are crtcal to transportaton plannng, pavement desgn, geometrc desgn, and traffc operatons. Wth the rapd growth of truck volumes on hghways, safety wth respect to trucks has also receved more and more attenton. Vehcle classfcaton nformaton can be obtaned from vehcle detecton equpment wth a specfc classfcaton mechansm. Vsual, axle, and presence sensors are three common types of detectors used for truck dentfcaton. The presence sensors, such as loop detectors, are the most wdely used detectors n the U.S. due to ther cost-effectveness. Dual-loop (double loop) detectors can measure vehcle length nformaton and act as a crude vehcle classfer (1). For sngle loop detectors, however, the vehcle length and classfcaton nformaton s not avalable n the output. Snce sngle loops are a very common type of detector n the feld that provde onlne traffc data, an effectve estmaton method for vehcle length and truck traffc based on sngle loop output would be very useful for real-tme traffc management and control Research n the estmaton of large truck volume from sngle loop outputs has attracted more and more attenton n recent years. A study n the state of Washngton (2) proposed a pattern dscrmnaton method to estmate large truck volume usng sngle loop data. One assumpton used n that study s that vehcle speeds n each fve-mnute tme perod are 3

4 consstent and speed varance can be gnored. The developed method s hence sutable for stable traffc condtons wthout large speed varatons. Another study n Calforna ( 3 ) used lane-to-lane speed correlaton to estmate large truck volume usng data from sngle loop detectors. They assumed that the percentage of large trucks n the leftmost lane can be gnored, and vehcle speeds over dfferent lanes tend to be synchronzed. However, due to wde ranges of traffc and geometrc condtons, varatons of speeds and truck lane dstrbuton can be very sgnfcant. The assumptons made n the pror studes may not be vald for some types or locatons of hghways or for some traffc condtons. Ths drawback lmts the applcaton scope and may affect the effectveness of the approach. Most recently, an Artfcal Neural Network (ANN) was proposed for vehcle classfcaton usng sngle loop outputs (4). Four length-based vehcle classfcaton categores were used n ths study. The results showed that ths method performs well for two categores wth the shortest and the largest vehcle lengths. The performance of an ANN s drectly related to the tranng dataset that s used, and overpredcton based on lmted tranng data s often assocated wth ANNs. Ths paper provdes a new methodology to estmate the volume of large trucks from sngle loop detector outputs. In ths study, a Large Truck (LT) or a long vehcle s defned as a truck wth a length greater than or equal to m (40 feet) as n the studes of Wang and Nhan (2) and Kwon et al. (3). An accurate sngle loop speed estmaton algorthm usng an Unscented Kalman Flter (UKF) s employed to generate speed data, and the Mean Effectve Vehcle Length (MEVL), whch s equal to the sum of average vehcle length and sngle loop detector length, can then be calculated at each tme nterval. The paper then nvestgates the overall 4

5 vehcle length dstrbuton as well as short and long vehcle length dstrbutons. An algorthm s then proposed to estmate LT volumes based on the MEVL and vehcle length dstrbutons. Fnally, estmaton results are presented and evaluated wth data collected from two vehcle detecton test beds. DATA FOR THE STUDY The data we used are collected from two freeway locatons, State Hghway 6 (SH6) near the FM 60 (Unversty Drve) Brdge n College Staton, Texas, and Interstate Hghway 35 (IH-35) near the 47 th street ext n Austn, Texas. Texas Transportaton Insttute (TTI) has two test beds at those locatons. SH6 has two lanes n each drecton whle IH-35 has four at the test bed locaton. Data are collected usng Peek ADR 6000 detectors, each of whch ncludes two nductve loops embedded n the pavement. Ths relatvely new ADR 6000 detector adopts the nductve loop technology and generates accurate outputs of vehcle presence tme, speed, count, vehcle length, and vehcle classfcaton (5). Count and occupancy data, whch are typcal outputs of sngle loop detectors, can be extracted from vehcle presence tmes (the duraton a vehcle passng a sngle loop) wth a certan tme nterval for speed and vehcle length estmaton purposes. Vehcle classfcaton, vehcle length, and speed data are also avalable for every tme nterval from the detector outputs and are used to compare wth estmaton results to assess the performances of the estmaton algorthms. 5

6 Traffc volume on SH6 s moderate, wth daly volume around 13,000 vehcles for the rght lane, and 10,000 vehcles for the left lane. Most vehcles were travelng at hgh speeds at ths locaton. Traffc volume s hgh on IH-35, wth an average daly volume over 27,000 vehcles for the rghtmost lane, and about 15,000 vehcles for the leftmost lane. Congeston repeatedly occurred durng mornng and afternoon peak hours. Durng those congested perods, vehcles traveled at very low speeds and many experenced stop and go stuatons. The rghtmost lanes of both locatons are selected for ths study because they experenced the worst traffc condtons and contaned the hghest LT percentages. Data were collected for one weekday from each test bed (January 27, 2004 on northbound SH6 and October 27, 2004 on southbound IH-35) and compled nto 30-second tme ntervals, whch s a common type of tme nterval used by sngle loop detectors. Large Truck Classfcatons As has been mentoned before, whether a vehcle s a LT or not s determned by ts length n ths paper. Thus, n the LT volume estmaton usng sngle loop outputs, vehcles are smply classfed nto two types: short vehcles (less than m) and large trucks (greater than or equal to m). Ths way of classfcaton s dfferent from the Vehcle Classfcaton Scheme F (6), whch classfes vehcles nto 15 types wth 13 types explctly defned based on the number of axles, axle spacng, and other features of vehcles. In the Scheme F that are used by most state DOTs, classes 5 to 13 are classfed as trucks. Trucks of class 5 (sngle-unt trucks) have two axles and those of classes 6 to 13 have three axles or more. 6

7 Wth data collected from Peek systems, we are able to dscover the dfference between LTs and trucks. We conducted a comparson of LTs (based on length) and trucks wth three axles and up, usng two-day data collected from the test beds. Results of the comparson are shown n Table 1. It s found that the percentages of LTs based on vehcle length are only slghtly less than those of trucks wth three or more axles based on the Scheme F. Therefore, based on our data, the LT classfcaton based on vehcle length n ths study s reasonable and the LT results can be used to represent all trucks excludng sngle unt trucks from the Scheme F classfcaton method. METHODOLOGY In order to determne LT volume from sngle loop detector data, the most crtcal parameter to be determned n ths study s the MEVL n a tme nterval. Snce both vehcle lengths and speeds are unknown, one way to obtan the MEVL s to employ some algorthms to frst estmate the average speed at each tme nterval. Speed Estmaton Usng the UKF For tme nterval wth duratont, assume N vehcles pass over a loop detector, vehcle j has speed s j, and the effectve vehcle length (EVL), defned as the vehcle length plus sngle loop length, s L j. The occupancy s then defned by 7

8 O 1 T N = j=1 L s j j + ε (1) where ε s a zero-mean nose of occupancy. Daley (7) has statstcally transformed ths equaton to an aggregated level. Assume perfect measurement ( ε = 0 ) for a loop detector, Equaton 1 s transformed to N O T s = L 1 / s [ 2 2 σ s ] + 1 (2) where s s the mean speed, σ 2 s s the speed varance and L s the MEVL at th tme nterval. A number of research efforts have been conducted to estmate speeds usng sngle loop outputs (8; 9; 10). However, most prevous studes of speed estmaton cannot produce very accurate estmates under varous traffc condtons due to varous smplfcatons and lnear assumptons. As descrbed n Equaton 2, the problem of speed estmaton s a nonlnear system. An Extended Kalman Flterng (EKF) technque was proposed to solve ths problem through lnearzaton (7). However, ths flterng technque has ts weaknesses n dealng wth nonlnear systems (11, 12). Partcularly, ts nablty to make good predctons of the system state, observatons, and assocated covarance matrces when the system and/or observaton models are nonlnear affects predcton accuracy.. Recently, Ye et al. (13) proposed a UKF method for speed estmaton. Ths method s able to generate hghly accurate speed estmates under both normal and congested traffc condtons. The speed estmaton s not the man focus of ths paper and t can be also 8

9 ndependent from the LT estmaton methodology proposed n ths paper. However, to make ths paper self-suffcent, the UKF s brefly dscussed here. The fundamental part of the UKF s the Unscented Transformaton (UT) (12). It uses a determnstc algorthm to sample a set of weghted sgma ponts, whch are appled to parameterze the means and covarances of probablty dstrbutons. For a d-dmensonal random varable x wth mean x and covarance P xx, ( 2d + 1) weghted sgma ponts are drawn to approxmate the random varable. The ( 2d + 1) sgma ponts { χ,..., χ } are determned by 0 2 d χ = x, W = κ/(d+ κ) 0 0 χ = x + ( ( d + κ) P ), W = 1/[2( d + κ)], = 1,..., d xx where χ = x ( ( d + κ) P ), W = 1/[2( d + κ)], = 1,..., d + d xx +d κ R provdes an extra degree of freedom to fne-tune the hgher order moments of the approxmaton, P xx s the covarance of random varable x, ( ( d + κ) P xx ) s the th row or column of the matrx root of ( d + κ P, and W s the weght assocated wth the th sgma ) xx pont. After sgma ponts are selected, the UKF wll undergo two steps at each tme nterval: the tme update step and the measurement update step. The tme update step predcts the state and covarance, and the measurement step corrects the state and covarance wth consderaton of the most recent observaton. The operaton process of the UKF s shown n Fgure 1. The calculated sgma ponts are used n both tme update and measurement update steps to approxmated mean, covarance and cross-varance of both state varable s and measurement varable N /O. For more detals about the UKF algorthm, refer to (13). 9

10 Estmaton of the MEVL As the mean speed s s estmated usng the UKF at each tme nterval, the MEVL for the tme nterval ( L )s obtaned by rearrangng Equaton 2: O T s L = N 1 / s [ 2 2 σ s ] + 1 (3) O and N are occupancy and count for the th tme nterval and are drectly from the sngle loop output. Once the MEVL s determned, t wll be used for further LT volume estmaton. Estmaton of LT Volume Vehcle Length Dstrbuton In the study by Wang and Nhan (2), a large sample of vehcle lengths was collected from dual-loop detectors and t was found that there were two peaks n the dstrbuton of vehcle length. After separatng vehcle lengths less than m (40ft) from the lengths greater than m, two vehcle length dstrbutons were obtaned and each ft a normal dstrbuton very well. In ths paper, a sample of vehcle lengths from IH-35 was chosen for the study of vehcle length dstrbuton. The Kernel densty of vehcle lengths s shown n the part a) of Fgure 2. The densty plot dsplays a bmodal dstrbuton of vehcle lengths. Small vehcle lengths are hghly concentrated around 5 m and long vehcle lengths are dstrbuted around 20 m. In order to nvestgate the dstrbutons of small and long vehcles, the sample was separated nto two groups, usng m as the separaton pont. To examne f both samples ft normal dstrbutons, 10

11 normal probablty plots were utlzed. Parts b) and c) of Fgure 2 show the Q-Q plots of short and long vehcle lengths. A Q-Q plot can be used to determne graphcally f a dataset comes from a normal dstrbuton. Obvously, the dstrbuton of short vehcle lengths s hghly rght skewed and the dstrbuton of long vehcle lengths s left skewed. The dstrbutons of both short and long vehcle lengths are not normally dstrbuted. The methodology of LT volume estmaton n ths paper does not hnge upon the normal dstrbuton assumptons. No matter what knd of dstrbuton vehcle lengths ft for, we assume that the mean values of short and long vehcle lengths are u 1 and u 2. It s also assumed that the short vehcle length dstrbuton X and the long vehcle length dstrbuton Y are ndependent. Then the average vehcle length at each tme nterval wll be subjected to a dstrbuton wth the expectaton u = p1 * u1 + p2 * u2, where p 1 and p 2 denote the proportons of short and long vehcles. At th tme nterval, assume that N vehcle are detected, and suppose that n 1 vehcles are short vehcles and n 2 vehcles are LTs. Then, X 1, X 2,..., X n form a random 1 sample from the dstrbuton X, and Y 1, Y2,..., Yn form the other random sample from the 2 dstrbuton Y. To compute the average vehcle length ( τ ), we smply take the expectaton X + X + X + Y + Y + + Y τ = E N n1 u1 + n2 u2 = E N n1 n2 = u1 + u2 N N 1 2 n1 1 2 n2 where n 1 +n 2 =N, and the average vehcle length ( τ ) equals to the MEVL mnus sngle loop (4) length. 11

12 Two samples of hstorcal vehcle length data from IH-35 and SH6 are gathered to generate vehcle length dstrbutons of both short vehcles and LTs. Mean length ( u 1 ) of short vehcles s around 4.88 m at SH6 and 4.72 m at IH-35; mean LT length ( u 2 ) s about m at SH6 and m at IH-35. IH 35 s an urban freeway whle SH6 s a rural area. The truck percentages are sgnfcantly dfferent as shown n Table 1. However, u 1 and u 2 are about the same. Further nvestgaton showed that at both locatons, u 1 and u 2 for dfferent tme perods pretty much stay the same even though truck volumes and percentage may vary sgnfcantly between tme perods. Therefore, u 1 and u 2 are treated as known parameters n our method and can be determned based on samples from hstorcal vehcle length data from a smlar hghway n the area. Estmaton of LT Volume Gven the MEVL value estmated n the prevous secton and the number of vehcles at a certan tme nterval, we can calculate the number of LTs durng ths tme perod by rearrangng Equaton 4: n 2 = N( τ u1) ( u u ) 2 1 (5) where u 1 and u 2 are mean short vehcle and LT lengths correspondng to a specfc hghway or locaton. Note that n 2 s rounded to the nearest nteger. 12

13 RESULTS AND DISCUSSIONS One set of weekday data from each TTI s test bed, as descrbed n the second secton, s processed and analyzed. The UKF algorthm s frstly used to generate speed nformaton. Then the average vehcle length at each tme nterval s calculated through Equaton 3. Comparsons between estmated and observed speed data, of 30 second tme ntervals n a day are shown n parts a) and b) of Fgures 3 and 4. The results demonstrate that the UKF does well n speed estmaton under both normal and congested condtons. The Root Mean Square Error (RMSE) s used for the evaluaton of speed estmaton. The RMSE s square root of Mean Square Error (MSE), whch can capture both the varance of errors and the bas of estmates. The RMSE values are shown n parts b) of Fgures 3 and 4. The estmated MEVL and vehcle length estmaton errors for all 30 seconds ntervals are shown n parts c) and d) of Fgures 3 and 4. It should be noted that the estmaton errors of the MEVL shown n the part d) s of Fgures 3 and 4 have some larger values and varatons durng nghttme and durng daytme when traffc congeston exsts, ndcatng potental estmaton accuracy ssues for both tme perods. The observed average vehcle lengths between mdnght and 6 a.m. are generally longer than m from the part c) s of Fgures 3 and 4, a result of very hgh percentage of LTs n early mornng hours when few passenger cars are on the road. Wth speed and MEVL estmated, the LT volume at each tme nterval s obtaned. For better llustraton, LT volume data are aggregated nto 1-hour ntervals. Fgure 5 shows both observed and estmated LT volumes. The estmaton curves capture the observaton curves very 13

14 well durng most hours of the day. A summary of hourly-based estmaton results of LT volume for the entre day s descrbed n Table 2. In ths table, two Measurements of Effectveness (MOEs) are used: the Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). They are defned as MAE = MAPE = = 1 24 nˆ = 1 ( ) est. nˆ n ( ) est ( ) obs.. n ( ) n obs. ( ) obs. (6) where ( ) ˆ est. n s the estmated LT volume durng th hour and n s the observed LT volume. ( ) obs. The overall estmated LT percentages are very close (wthn 0.5%) to observed percentages wth slght underestmatons. By comparng the estmated LT percentages wth truck percentages that are computed based on vehcle classfcatons and shown n Table 1, the estmaton errors are less than 1% for both data sets. To further explore the factors affectng estmaton results, the effects of LT percentage and traffc volume level are nvestgated usng the SH6 data. Frstly, a study of estmaton errors under dfferent traffc volume levels s conducted. Part a) of Fgure 6 llustrates hourly traffc volumes throughout the experment whle part c) of ths fgure shows hourly Absolute Percentage Errors (APEs). Based on parts a) and c) of ths fgure, t s observed that APE values durng nghttme when traffc volume s relatvely low are generally not much smaller than those durng daytme when traffc volume s relatvely hgh, ndcatng that overall traffc volume does not seem to affect LT estmaton accuracy. Secondly, hourly-based LT percentages 14

15 are also calculated from the observed dataset and shown n the part b) of Fgure 6. The LT percentages are very hgh between mdnght and 6 a.m., and the maxmum percentage s close to 40%. Nevertheless, the relatve larger estmaton errors n the part c) are not generated durng those hgh LT percentage hours. Thus, the LT percentage tself does not show sgnfcant effects on the LT volume estmaton ether accordng to our experment. From Fgure 6(c), there are perods of tme durng the day when there are more fluctuatons n APE. For example, at the 22:00 hour, the APE reaches 20%. However, a closer lookng at Fgure 5 reveals that the estmaton error for the hour s only three LTs, 18 estmated versus 15 observed, and obvously acceptable. In addton, the fluctuatons llustrated n Fgure 6(c) are centered around the MAPE lne, ndcatng no system error trend wth respect to any partcular factor. Ths seems to ndcate that the estmaton results are not sgnfcantly affected by ether LT percentage or overall traffc volume. To further nvestgate the performance of the algorthm under varous traffc condtons, partcularly under congested condtons, data of two consecutve days (November 9 and 10, 2004) from IH-35 ste were analyzed. The ste has regular AM and PM recurrent congeston perods. Fgure 7 presents LT estmaton results along wth speed estmaton results and Fgure 8 llustrate the LT estmaton error dstrbuton. For ths analyss, LTs are estmated at 15-mnutes nterval, an nterval commonly used n real-tme traffc flow predcton. It can be seen that agan MAPE lne centers around zero, ndcatng no systematc estmaton errors. A closer look nto the error dstrbuton of the LT estmaton at 15-mnute nterval n Fgure 8 show that there are only 6 ntervals that have error over 15 LTs per nterval, or 1 LT per mnute on average. About 90% of 15

16 the ntervals have errors smaller than 10 Lts per nterval. About 80% of the ntervals have errors of less than 8 LTs, or about 1 LT every 2 mnutes. That s certanly good accuracy for practcal applcatons. From Fgure 7, wth the excepton of early mornng perods durng whch overall traffc s very lght but LT percentage s very hgh, LT estmaton accuracy dd not seem to show any trend wth respect to overall traffc volume, LT volume, or LT percentage. Durng the early mornng perods (when LT% s at the hghest), LT estmaton accuracy s the best. The worst estmaton accuracy occurred durng the perods of congeston. A further nvestgaton reveal that for the AM peak on the frst day and both the AM peak and PM peak on the second day the speed estmaton results are not as good as the rest of the perods. Concdently, those are the same three perods that have sgnfcant LT estmaton errors. Ths ndcates that traffc congeston s a factor nfluencng the LT volume estmaton results. Traffc congeston affects speed estmaton and consequently contrbutes to the accuracy of LT estmaton. CONCLUSIONS Ths paper frstly uses an accurate speed estmaton method to estmate speed and mean effectve vehcle length based on sngle loop detector outputs. A vehcle length sample s selected to nvestgate length dstrbutons, ncludng short and long vehcle length dstrbutons. Ths paper does not assume that ether short or long vehcle length dstrbuton ft a normal dstrbuton and proposes an algorthm for LT volume estmaton based on vehcle length estmaton results. Data collected from two Texas Transportaton Insttute s vehcle detecton test beds are used for ths 16

17 study. The estmated large truck volumes are compared wth feld data. The results show that the proposed method has good performances under varous traffc condtons. Fnally, the factors that nfluence the estmaton accuraces are explored. It s found that whle LT percentage and traffc volume generally do not sgnfcantly affect estmaton accuracy, traffc congeston s a factor affectng the results of large truck volume estmaton for the congested perods manly due to the fact that speed estmaton under congested flow condtons are typcally less accurate. Real tme large truck volume can be easly estmated usng ths proposed method and provde useful nformaton for traffc management and control n an Intellgent Transportaton System (ITS). The results can also be valuable to detaled and more relable analyses such as level of servce (LOS) analyss of a freeway segment or safety study of a locaton at a gven demand level. It should be ponted out that the UFK speed estmaton method s used n the paper for the purpose of provdng relable speed nputs for the LT estmaton methodology. Any accurate speed estmaton method usng sngle loop data can work wth the LT estmaton methodology proposed n ths paper. Ths study uses ADR sensor that provdes more relable and accurate measures of flow and occupancy than a normal sngle loop detector. ADR data are also used as ground truth data for valdaton. Actual sngle loop detectors have more measurement error such as mssng data or erroneous readngs. Because of ths, further nvestgaton and valdaton wth actual sngle loop and ground truth data are needed n the future. 17

18 ACKNOWLEDGEMENT The authors would lke to acknowledge TTI for ther support. Specal thanks go to Dan R. Mddleton for provdng detector data. REFERENCES 1 Cofman, B., and Ergueta, E. Improved Vehcle Redentfcaton and Travel Tme Measurement on Congested Freeways. In Proceedngs of the 81st Annual Meetng Transportaton Research Board, Washngton D.C., Wang, Y., and Nhan, N. L. Dynamc Estmaton of Freeway Large Truck Volume Based on Sngle-loop Measurements. Journal of Intellgent Transportaton Systems, Vol (8), No. 3,,2004, pp Kwon, J., Varaya, P., and Skabardons, A. Estmaton of Truck Traffc Volume from Sngle Loop Detector Usng Lane-to-Lane Speed Correlaton. In Transportaton Research Record: Journal of the Transportaton Research Record, No. 1232, Natonal Research Councl, Washngton, D.C., 2002, pp Zhang, G., Wang, Y., and We, H. Artfcal Neural Network Method for Vehcle Classfcaton Usng Sngle-Loop Outputs.. In Proceedngs of the 85th Annual Meetng of the Transportaton Research Board, Washngton D.C., Mddleton, D.R., and R.T. Parker. Summary Report on Evaluaton of Vehcle Detecton Systems. PSR S. Texas Transportaton Insttute, College Staton, TX. January Wyman, J.H., Gary, A. B., and Robert, I. S. Feld Evaluaton of FHWA Vehcle Classfcaton Categores. Mane Department of Transportaton. Fnal Report for Contract DTFH ME-03 for USDOT, Daley, D.J. A Statstcal Algorthm for Estmatng Speed from Sngle Loop Volume and Occupancy Measurements. Transportaton Research Part B, 33B(5), 1999, pp Athol, P. Interdependence of Certan Operatonal Characterstcs wthn a Movng Traffc Stream. Hghway Research Record 72, HRB, Natonal Research Councl, Washngton D.C., 1965, pp

19 9 Hall, F. An nterpretaton of Speed-flow-concentraton Relatonshps Usng Catastrophe Theory. Transportaton Research Part A, Vol.21A, No.3, 1987, pp Ln, W., Dahlgren, J., and Huo, H. Enhancement of Vehcle Speed Estmaton wth Sngle Loop Detectors. Transportaton Research Record 1870, Natonal Research Councl, Washngton, D.C., 2004, pp Juler, S., and Uhlmann, J. A General Method for Approxmatng Nonlnear Transformatons of Probablty Dstrbutons. Oxford Unversty: Oxford, Juler, S., and Uhlmann, J. A New Extenson of the Kalman Flter to Nonlnear Systems. Internatonal Symposum of Aerospace/Defense Sensng, Smulaton, and Controls, Orlando, FL, 1997, pp Ye, Z., Zhang, Y., and Mddleton, D. An Unscented Kalman Flter Method for Speed Estmaton Usng Sngle Loop Detector Data. In Transportaton Research Record: Journal of the Transportaton Research Record, No. 1968, Natonal Research Councl, Washngton, D.C., 2006, pp

20 LIST OF TABLES TABLE 1 Comparson of Truck Classfcaton Results Based on Scheme F and LTs TABLE 2 Results of Hourly-Based Estmaton of LT Volume LIST OF FIGURES FIGURE 1 Operaton process of the UKF FIGURE 2 Vehcle length dstrbutons FIGURE 3 Speed and vehcle length nformaton of SH6 (Jan. 27, 2004) FIGURE 4 Speed and vehcle length nformaton of IH-35 (Oct. 27, 2004) FIGURE 5 Observed and estmated LT volumes FIGURE 6 Hourly-based traffc volumes, LT percentages and estmaton errors on SH FIGURE 7 Speed and LT Volume Estmaton Results for IH-35 (Nov. 9-10, 2004) FIGURE 8 IH-35 LT Estmaton Error Dstrbuton (Nov. 9-10, 2004)

21 TABLE 1 Comparson of Truck Classfcaton Results Based on Scheme F and LTs Daly Traffc Volume (Veh.) Trucks (Based on Scheme F) Number of Percentage Trucks (%) (Veh.) LT (Based on Length) Number of Percentage LT (%) (Veh.) IH SH

22 TABLE 2 Results of Hourly-Based Estmaton of LT Volume Traffc Number of LT Total LT MAE of MAPE of Volume Real Estmated Error LT LT (veh.) (veh.) (veh.) (veh.) (veh.) (%) SH (6.26%) 795 (6.10%) IH (11.50%) 3064 (11.07%)

23 Intal estmates of state and covarance Calculate sgma ponts Tme Update 1) Project the state ahead 2) Project the error covarance ahead Measurement Update 1) Compute the Kalman gan 2) Update estmate wth measurement 3) Update the error FIGURE 1 Operaton process of the UKF. 23

24 FIGURE 2 Vehcle length dstrbutons. a) Kernel densty of vehcle lengths. b) Q-Q plot of short vehcle lengths. c) Q-Q plot of long vehcle lengths. 24

25 FIGURE 3 Speed and vehcle length nformaton of SH6 (Jan. 27, 2004). a) Observed speed. b) Estmated speed usng the UKF. c) Observed vehcle lengths. d) Estmaton error of vehcle length. 25

26 FIGURE 4 Speed and vehcle length nformaton of IH-35 (Oct. 27, 2004). a) Observed speed. b) Estmated speed usng the UKF. c) Observed vehcle lengths. d) Estmaton error of vehcle length. 26

27 FIGURE 5 Observed and estmated LT volumes. a) Hourly-based LT volumes on SH6. b) Hourly-based LT volumes on IH

28 FIGURE 6 Hourly-based traffc volumes, LT percentages and estmaton errors on SH6. a) Traffc volume. b) LT percentages. c) APE. 28

29 FIGURE 7 Speed and LT Volume Estmaton Results for IH-35 (Nov. 9-10, 2004). 29

30 LT Estmaton Error Dstrbuton Frequency Estmaton Error (vehs/15 mnutes) Error (LTs/15-mn) <= % <= % <= % >15 6 ntervals Max Error/Interval 22 FIGURE 8 IH-35 LT Estmaton Error Dstrbuton (Nov. 9-10, 2004). 30