Generation of Road Reference Heading using GPS Trajectories for

Accurate Lane Departure Detection

Shahnewaz Chowdhury, Md. Touhid Hossain and M. I. Hayee

Department of Electrical Engineering, University of Minnesota Duluth, Duluth, MN 55812, U.S.A.

Keywords: Lane Departure Warning System, Road Reference Heading, GPS Trajectory.

Abstract: Lane departure warning system (LDWS) has significant potential to reduce crashes on roads. Most existing

commercial LDWSs use image processing techniques with or without Global Positioning System (GPS)

technology and/or high-resolution digital maps to detect unintentional lane departures. However, the

performance of such systems is compromised in unfavourable weather or road conditions e.g., fog, snow, or

irregular road markings. Previously, the authors proposed and developed an LDWS using a standard GPS

receiver without any high-resolution digital maps. The previously developed LDWS relies on a road reference

heading (RRH) of a given road extracted from an open-source low-resolution mapping database to detect an

unintentional lane departure. This method can detect true lane departures accurately but occasionally gives

false alarms i.e., it issues lane departure warnings even if a vehicle is within its lane. The false alarms occur

due to the inaccuracy of RRH originated from inherent lateral error in open-source low-resolution maps. To

overcome this problem, now authors propose a novel algorithm to generate an accurate RRH for a given road

using a vehicle’s past trajectories on that road. The newly proposed algorithm to generate an accurate RRH

for any given road has been integrated with the previously developed LDWS and extensively evaluated in the

field to detect unintentional lane departures. The field test results show that the newly developed RRH

generation algorithm significantly improves the performance of the previously developed LDWS by

accurately detecting all true lane departures while practically reducing the frequency of false alarms to zero.

1 INTRODUCTION

Lane departure warning system (LDWS) has

significant potential to reduce accidents. According to

the American Association of State Highway and

Transportation Officials (AASHTO), almost 60% of

fatal accidents are caused by an unintentional lane

drifting of a vehicle on major roads (AASHTO:

Driving down lane-departure crashes: A national

priority, 2008). A recent study which compared

crashes with and without an LDWS found that an in-

vehicle LDWS was helpful in reducing crashes of all

severities by 18%, with injuries by 24%, and with

fatalities by 86% (J Cicchino, 2018). Systems which

predict the driver’s attentive state and intent of lane

change (D. D. Salvucci, 2004, N. Kuge et al. 1998, J.

McCall et al. 2004) and provide map-based route

guidance and/or warning about unintentional lane

departure (F. Heimes et al. 2002, W. Kwon et al.

2002), are also useful to reduce major road crashes.

Most available LDWSs rely on image processing

technology using a camera or an optical scanning

device to estimate a vehicle’s lateral shift within a

lane to detect an unintentional lane departure

(Xiangjing An et al. 2006, Pei-Yung Hsiao et al.

2006, B. Yu et al. 2008, Y. C. Leng et al. 2010, P.

Lindner et al. 2009). Although advanced image

processing techniques work well in diminished

lighting scenarios (McCall et al. 2006, Daimler,

2018) the performance of image processing based

LDWSs deteriorates in unfavourable weather and

road conditions e.g., fog and snow-covered or worn-

out road marking signs. To overcome these problems

and improve performance, Global Positioning System

(GPS) technology is integrated within vision based

LDWS. However, such systems use differential GPS

technology and/or inertial navigation sensors as well

as high-resolution digital maps to estimate a vehicle’s

lateral shift in its lane making such systems more

complex and expensive to implement (

Clanton, 2009).

Previously, the authors proposed a novel method

to accurately detect an unintentional lane departure

using a standard GPS receiver and commonly

available open-source low-resolution digital maps

584

Chowdhury, S., Hossain, M. and Hayee, M.

Generation of Road Reference Heading using GPS Trajectories for Accurate Lane Departure Detection.

DOI: 10.5220/0010465405840593

In Proceedings of the 7th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2021), pages 584-593

ISBN: 978-989-758-513-5

(Faizan et al. 2019). The previously proposed method

estimates vehicle’s lateral shift by comparing

vehicle’s heading acquired by standard GPS receiver

to a road reference heading (RRH) extracted from an

open-source digital map. Although this system works

well to successfully detect unintentional lane

departure, occasionally, it generates false alarms i.e.,

it wrongfully issues lane departure warnings even if

the vehicle is within its lane (Faizan et al. 2019). The

false alarms occur due to inherent error in open-

source digital maps which resulted in an error in the

corresponding RRH of the given road extracted from

such maps. The authors now propose another method

to generate an accurate RRH for any given road using

a vehicle’s past GPS trajectories on that road without

relying on open-source digital maps.

Previously, many techniques have been proposed

to process GPS trajectories to generate a routable road

network or create a complete digital road map using

graph and structured learning theory and/or statistical

analysis (Cao et al. 2009, Guo et al. 2007, Chen et al.

2008, Guo et al. 2010, Shi et al. 2009, Huang et al.

2018). In this paper, a novel algorithm is proposed to

generate an accurate RRH from a vehicle’s past GPS

trajectories to improve the performance of the

previously proposed lane departure detection method

(16). The test results show that the newly proposed

algorithm significantly improves the performance of

the previously proposed lane departure detection

method by accurately detecting all true lane

departures while practically reducing the frequency

of false alarms to zero.

The rest of the paper is organized as follows.

Section 2 describes the system architecture of the

proposed lane departure system using RRH generated

from a vehicle’s past trajectories. The details of the

newly proposed RRH generation algorithm are

provided in Section 3, and the field test results are

discussed in Section 4. The conclusions are given in

Section 5.

2 SYSTEM ARCHITECTURE

The newly proposed algorithm generates RRH for

any given road using a vehicle’s one or more past

trajectories on that road acquired by a standard GPS

receiver. Once an RRH for a given road is generated,

it can be used to detect any future unintentional lane

departure of a vehicle as illustrated in Figure 1a,

where the dashed line represents a vehicle’s past

trajectory which can be used to generate RRH for the

road to detect an unintentional lane departure e.g., as

represented by a dotted line in Figure 1a.

The architecture of the proposed system combining

the previously developed lane departure detection

method and the newly proposed RRH generation

algorithm is shown in Figure 1b where the GPS

receiver acquires longitude and latitude of a moving

vehicle’s position in real-time to be used by both

processors. The Processor 1 uses a sufficient length of

a GPS trajectory on a given road to generate an RRH

for that road using the newly developed algorithm.

Figure 1: (a) Conceptual diagram showing how a past trajectory (black dashed line) of a given vehicle can serve to generate

RRH to detect its unintentional lane departure in future (black dotted line), and (b) the system architecture of LDWS using

the newly proposed algorithm to generate RRH from a vehicle’s past GPS trajectories.

Generation of Road Reference Heading using GPS Trajectories for Accurate Lane Departure Detection

585

On the other hand, Processor 2 works in real-time

to detect unintentional lane departure using the

previously proposed lane departure detection method

except that it uses the RRH generated by Processor 1

using one or more past GPS trajectories as opposed to

the RRH extracted from an open-source low-

resolution map as was used in . The Processor 2 can

detect an unintentional lane departure of any vehicle

on a given road if the vehicle has been driven on that

road at least once before so that the necessary RRH

for that road has already been generated by Processor

1. Please note that the proposed algorithm is suitable

to be integrated into smartphone Apps e.g., Waze,

Google Maps, or Apple Maps to take advantage of the

vast database of multiple GPS trajectories of a

broader road network. This can enable any vehicle to

detect an unintentional lane departure on any road

even if the vehicle is driven on that road for the first

time.

3 RRH GENERATION

ALGORITHM

Any typical road segment may consist of a

combination of straight and curve road sections.

Usually, a road is not curved abruptly, therefore, a

transition section exists between a straight and a

curve section. The proposed algorithm to generate a

vehicle’s trajectory into a useful RRH works in three

stages. In the first stage, all straight, curve, and

transition sections of any road are identified from the

given GPS trajectory on that road. In the second stage,

each identified section is characterized with a set of

optimized parameters defining road reference

heading value at each point on that road section. In

the third stage, all individual road sections are

combined to obtain a composite RRH for that road.

3.1 Identification of Various Sections

The heading for a straight road section remains

constant while it changes uniformly for a curve

section. Similarly, the differential heading for a

straight section is zero while it has a non-zero

constant value for a curve section with larger values

for sharper curves. A typical vehicle trajectory

acquired by a standard GPS receiver consists of its

position coordinates at fixed time intervals (typically

every 100 msec). Any two consecutive position

coordinates of a moving vehicle on a given road can

be used to obtain heading and differential heading of

the road at that point.

The proposed algorithm uses differential heading

to identify various sections present in a given road by

first identifying all straight sections where differential

heading remains zero followed by curve sections

where differential heading is a non-zero constant. The

transition sections are identified at the end.

To illustrate the section identification process,

heading and differential heading calculated from a

typical GPS trajectory versus distance are shown in

Figure 2a and 2b, respectively. The GPS trajectory

was acquired using a standard GPS receiver with a

UBlox LEA-6 chipset on a 4.2 km section of

Interstate I-35 while driving at 70 MPH. The heading

at each point of the given road, calculated from a

vehicle’s GPS trajectory, exhibits a high-frequency

noise over distance caused by inherent GPS error

which is further accentuated in differential heading

values as shown in Figure 2b. This high-frequency

noise can be reduced by moving average method

using more than two consecutive GPS points for

heading and differential heading calculation. For the

proposed algorithm, a 9-point moving average was

used to reduce the standard deviation of differential

heading to 0.03

3.1.1 Identification of Straight Sections

Although the average differential heading of a

straight section is zero, the instantaneous differential

heading at any point of a straight section fluctuates

around zero due to GPS noise. This fluctuation

remains within the boundaries of ±0.09

or three

times the standard deviation of differential heading as

shown in Figure 2b. The proposed algorithm

identifies straight sections by comparing the

differential heading with a threshold of ±0.09

shown by dashed red line in Figure 2b. Whenever the

differential heading exceeds the threshold of ±0.09

in either direction, the crossing points are marked as

the beginning and ending points of the straight

sections of the road. All such points are shown by

vertical blue dashed lines in Figure 2, identifying a

total of four straight sections from the given trajectory

which are marked as S1, S2, S3, and S4.

There is no lane change present in the trajectory

of Figure 2. However, in reality, a vehicle may

change lanes while traveling on a multiple lane road.

The lane changes present in any given trajectory may

wrongfully be considered as road curvature on that

road. However, the differential heading during any

typical lane change does not exceed the threshold of

±0.09

. Therefore, the proposed algorithm can

correctly identify all straight sections of the road even

if lane changes are present in each trajectory.

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586

3.1.2 Identification of Curve Sections

There is usually a curve and two transition sections

present between any two consecutive straight

sections. To identify a curve section between any two

consecutive straight sections, the proposed algorithm

calculates a path average differential heading

(PADH) between the ending point of the first and

beginning point of the second of the two consecutive

straight sections.

The value of calculated PADH will be slightly

smaller than the true PADH value of the curve section

alone because this is calculated for the curve section

including the two adjoining transition sections on

each side of the curve as illustrated in Figure 3, where

a zoomed-in portion of the trajectory of Figure 2 is

reproduced showing only the first curve section

surrounded by two straight sections (S1 and S2) and

corresponding transition sections. To identify the

beginning and ending points of a curve section alone,

a set of two points between two consecutive straight

sections (one on each side) are identified where the

differential heading value is closest to the calculated

PADH.

The beginning and ending points of a curve

section identified this way will still not be the true

beginning and ending points of the curve because the

PADH value used to identify these points was

calculated for the curve section including the two

transition sections. Therefore, a second iteration of

the same routine is performed by calculating a new

PADH value between the two points identified in the

first iteration. The new PADH value calculated in the

second iteration is more likely to be closer to the true

PADH value of the curve section alone because it is

calculated for the curve section including only the

extreme ends of the transition sections on both sides.

This process can be repeated, however, beyond two

iterations, the beginning and ending points of a curve

section do not change significantly. Using this

method, all curve sections can be identified in any

given GPS trajectory. A total of three curve sections

(C1, C2, and C3) were identified in the given GPS

trajectory of Figure 2. Please note that the proposed

algorithm can correctly identify all curve sections in

a given trajectory even when a lane change is present

for the same reason as explained for straight section.

3.1.3 Identification of Transition Sections

After identifying the beginning and ending points of all

straight and curve sections, all remaining portions of

the trajectory are marked as transition sections. The

beginning and ending points of any transition section

will be the ending and beginning points of adjoining

straight and curve sections as shown for the transition

sections T1 and T2 in Figure 3. Similarly, all transition

sections in any given trajectory are identified.

Figure 2: (a) Vehicle heading and (b) differential heading vs. distance for a vehicle’s trajectory acquired by a standard GPS

receiver on a 4.2 km segment of Interstate I-35. The picture of Google Map of the relevant portion of the road is shown on

the top.

Generation of Road Reference Heading using GPS Trajectories for Accurate Lane Departure Detection

587

Figure 3: (a) Vehicle heading and (b) differential heading vs. distance for a small portion of the trajectory of Figure 2. This

portion includes a part of first straight section, S1, T1, C1, T2, and a part of S2.

3.2 Characterization of Various

Sections

After identifying all individual sections of the road

from a given trajectory, each section is characterized

separately with a proper set of parameters to define

RRH at each point of the given road section. Each

straight section is characterized with a path average

heading (PAH) as heading remains the same for the

entire length of a straight section. Similarly, heading

of a curve section changes uniformly with distance,

therefore, it is characterized with a path average

heading slope (PAHS) and an initial heading (IH) i.e.,

the heading at the beginning point of the curve section

to completely define RRH at each point of the curve

section. For a transition section, heading neither

remains the same as in a straight section nor does it

change uniformly with distance as in a curve section

suggesting that a transition section should be

characterized as a second-order polynomial.

However, the length of a typical transition section is

usually too small to characterize it as a second-order

polynomial. Furthermore, the incremental accuracy

of RRH with a second-order characterization is

negligibly small. Therefore, the proposed algorithm

characterizes each transition section just like a curve

section i.e., with IH and PAHS values. Please note

that the PAHS value of a transition section is different

from the PAHS value of the adjoining curve section.

3.2.1 Characterization of Straight Sections

Each straight section is initially characterized with a

PAH value, between the beginning and ending points

of a straight section, calculated using equation 1,

where h

is the vehicle heading between any given

point n and its previous point, and d

is the distance

between the two points.

𝑃𝐴𝐻=

∑







∑



(1)

However, the initially assigned value of PAH for

any given straight section may not be the optimal

value. To find the optimal value of PAH for a straight

section, the heading error between the vehicle

heading and PAH should be minimized. The value of

PAH is varied in small increments around its initially

assigned value and root mean square of heading error

(RMSHE) is calculated for each value of PAH using

equation 2, where h

ref

is the RRH i.e., PAH for a

straight section.

𝑅𝑀𝑆𝐻𝐸 =



〈

ℎ



−ℎ







〉

(2)

The RMSHE for the first straight section (S1) of

Figure 2 is shown in Figure 4a for varying values of

PAH. The RMSHE remains almost flat for a wide

range of PAH values suggesting that optimal value of

PAH is not very sensitive to small changes. Although

minimizing RMSHE would result in an optimized

-0.1

0.1

0.2

0.3

0.4

1400 1500 1600 1700 1800 1900 2000 2100

Differential Heading (deg)

Distance(m)

230

240

250

260

270

280

1400 1500 1600 1700 1800 1900 2000 2100

Heading (deg)

PADH of curve &

transition sections

PADH of curve section

only

VEHITS 2021 - 7th International Conference on Vehicle Technology and Intelligent Transport Systems

588

value of h

ref

for a given straight section, the objective

at hand is to minimize ALS for each section because

ALS is to be used to detect unintentional lane

departure (Faizan et al. 2019). Therefore, the absolute

value of ALS (|ALS|) is also calculated by varying

PAH value for each straight section using equation 3.

|𝐴𝐿𝑆| = 

∑

𝑑



𝑠𝑖𝑛 (ℎ



−ℎ



) (3)

Figure 4: (a) RMSHE and |ALS| vs. PAH for the straight

section S1 showing optimal value of PAH, and (b) a surface

plot of |ALS| vs. IH and PAHS for the curve section C1

showing optimal combination of IH and PAHS values.

The calculated value of |ALS| for different PAH

values around its initially assigned value for the

section S1 is also shown in Figure 4a, along with

RMSHE values, revealing a clear minimum. The

optimal value of PAH (239.50

) not only minimizes

|ALS| but also falls within the flat minimum range of

RMSHE. The same general trend was true for all

straight sections of the trajectory. Using this method,

any straight section can be characterized with an

optimal value of PAH.

Please note that the heading can change

significantly as opposed to differential heading

during a lane change present in a trajectory.

Therefore, the optimal value of PAH can be adversely

affected for a straight section if a lane change is

present. The proposed algorithm can detect the

location and span length of such a lane change and

optimize the PAH value excluding the lane change

portion of the section.

3.2.2 Characterization of Curve Sections

As described earlier, each curve section is

characterized with two parameters, i.e., IH and

PAHS. An initial value of IH is assigned as the

heading at the beginning point of any curve section

and the initial value of PAHS is assigned using

equation 4, where h

is the heading between any given

point n and its previous point, and h

n-1

is the heading

between point n-1 and its previous point.

𝑃𝐴𝐻𝑆 =

(∑

















)

∑



(4)

After initial values are assigned to both IH and

PAHS for a curve section, they are optimized by

minimizing |ALS| by varying both IH and PAHS

values in small increments around their initially

assigned values. The optimization process is

illustrated in Figure 4b, where |ALS| is plotted versus

IH and PAHS as a surface plot for the curve section

C1. Please note that the resulting optimal values of IH

and PAHS are 243.30

and 0.066425 deg/m,

respectively, and are noticeably different from their

corresponding initially assigned values (243.26

and

0.066475 deg/m). Using the same method, all other

curve sections are optimized. Please note that the

optimization of a curve section in the presence of a

lane change is performed the same way as described

for straight section.

3.2.3 Characterization of Transition

Sections

As discussed earlier, each transition section is

characterized as it is a curve section. Therefore, it

should be initially assigned with two parameters, i.e.,

IH and PAHS, and their optimization process should

be like that of a curve section. However, if both

parameters are optimized independently then there is

a possibility of an abrupt change of heading at corner

points where transition section adjoins a straight or a

curve section. This is because the end points of any

transition section are the same as the beginning and/or

ending points of adjoining straight and/or curve

sections. Therefore, the characterization of transition

section is more straightforward. The optimized

heading at the ending point of the preceding straight

or curve section is considered as the IH value of the

transition section. Similarly, an optimal value of

PAHS for a transition section is calculated using the

optimized values of heading at the two end points of

the transition section.

Generation of Road Reference Heading using GPS Trajectories for Accurate Lane Departure Detection

589

Figure 5: Screen shot of a typical output file containing optimized parameters of each section in the composite RRH.

3.3 Combining All Sections to Generate

a Composite RRH

After identifying and characterizing each section with

an optimal set of parameters, all sections are

combined to generate a composite RRH for that road.

The typical output file generated by the algorithm is

shown in Figure 5, where each row represents an

individual section of the road defined by its beginning

and ending points (in terms of latitude and longitude),

the optimized parameter values, and the section type.

Please note that an “N” indicates that the

corresponding parameter is not applicable to that

section. This file has the necessary information to

completely define the RRH at any point along the

road and can be used to detect an unintentional lane

departure in real-time using previously proposed lane

departure detection method.

A composite RRH generated from a single

trajectory may not be accurate for all future

trajectories because usually, a vehicle will take a

slightly different trajectory in each new trip on the

same road. However, multiple composite RRHs

obtained from different vehicle trajectories for a

given road can be combined to obtain an average

composite RRH. The combination of two or more

composite RRHs generated from different individual

GPS trajectories is achieved in two steps. First, every

optimized parameter of each straight and curve

section is combined using a simple average method.

Second, the beginning and ending points of each

straight and curve section are combined by averaging

the latitude and longitude values of the beginning and

ending points, separately.

After combining all straight and curve sections,

transition sections are automatically combined

because the beginning and ending points of all

transition sections are the same as the beginning and

ending points of adjoining straight and/or curve

sections as described earlier. Using the same

averaging method, each additional composite RRH

generated from a future vehicle trajectory can be

added to an already existing average composite RRH

to improve its accuracy over time.

The proposed algorithm was applied to many

vehicle trajectories on the same road segment of

Interstate I-35 and a composite RRH was generated

from each trajectory. Three such composite RRHs

generated from three different trajectories on the

same road and the average composite RRH are shown

in Figure 6a where heading versus distance is plotted

across the entire 4.2 km length.

The difference in heading values of multiple

composite RRH is not visible in Figure 6a because of

the large variation of heading over the span of the

road segment. To highlight the difference in different

composite RRH values, a zoomed-in portion of

Figure 6a marked by a red dashed circle is shown in

Figure 6b. The zoomed-in portion includes the right-

side portion of S2, entire T2, and the left side portion

of C2 sections of the road where the difference in

heading values of each composite RRH is more

pronounced showing the averaging effect.

4 FIELD TESTS AND RESULTS

The main purpose of the proposed algorithm is to

generate an average composite RRH from multiple

vehicle trajectories for a given road to accurately

detect unintentional lane departure in real-time using

the previously developed lane departure detection

method by calculating ALS at any given point on the

road using equation 5, where h

ref,k

is the RRH value at

the current point, n, of the road.

VEHITS 2021 - 7th International Conference on Vehicle Technology and Intelligent Transport Systems

590

𝐴𝐿𝑆=

∑

𝑑



sin (ℎ



−ℎ

,

)





(5)

When a vehicle unintentionally drifts away from

its lane, ALS starts to increase in value (positive or

negative), and once its value increases beyond a

certain threshold (±1m), an unintentional lane

departure is detected initiating a warning for the

driver. Please note that ALS will also increase in

value if a vehicle intentionally changes its lane. An

intentional lane change can be distinguished from an

unintentional lane departure by the presence or

absence of turn signal.

In case of an intentional lane change, the increase

in ALS begins to saturate upon completion of lane

change because the vehicle starts to travel again in

parallel to the RRH of the road. As a result of normal

driving behaviour, this phenomenon i.e., the

saturation of ALS can also occur in case of an

unintentional wandering within a lane while ALS

values remain within the ±1m threshold. This

phenomenon is used to reset the value of ALS to zero

whenever its value begins to saturate.

The accuracy of the lane departure detection

method depends upon the accuracy of the composite

RRH for that road. To evaluate its accuracy, field tests

were performed by driving a test vehicle multiple

times on the same 4.2 km segment of Interstate I-35

for which an average composite RRH was already

generated using the newly proposed algorithm. The

test vehicle was driven at about speed limit (70 MPH)

on this 4-lane freeway and many back-and-forth lane

changes were made intentionally during the field

tests. For safety reasons, intentional lane changes

were made to test the accuracy of lane departure

detection using the composite RRH generated by the

newly proposed algorithm.

For each trip, ALS was calculated in real-time to

detect any lane departure. The vehicle heading for one

such test trip vs. distance is plotted along with the

RRH of the road segment in Figure 7a showing that

vehicle heading deviates from the RRH during each

lane change as expected. The corresponding ALS vs.

distance is plotted in Figure 7b showing that ALS

exceeds ±1m threshold during each lane change. A

total of ten right and left lane changes were made in

this trip and all lane changes were detected accurately

and in a timely manner. A digital mask for lane

departure detection warning signal is plotted as a

dashed red line showing the start and end of each lane

change in Figure 7b. Lane departure warning signal

becomes active when ALS exceeds the ±1m threshold

and is deactivated when the vehicle heading becomes

parallel to RRH of the road. In multiple field tests,

more than 100 lane changes were made, and each lane

change or lane departure was accurately and timely

detected. Furthermore, nowhere else along the

trajectory, ALS exceeded the threshold i.e., no false

alarm was observed.

To test the frequency of the false alarms, the test

vehicle was also driven multiple times on the same

road segment without making any lane changes. In

more than 10 trips on the 4.2 km long route, no false

alarm was observed as indicated in Figure 7c, where

ALS is plotted vs. distance for four such test trips.

Figure 6: (a) Heading of average composite RRH and three individual composite RRH obtained from three different vehicle

trajectories of 4.2 km segment of Interstate I-35, and (b) zoomed portion of (a) highlighted by red dashed circle.

230

245

260

275

0 600 1200 1800 2400 3000 3600 4200

Heading (deg)

(b)

264

266

268

270

272

2100 2140 2180 2220 2260 2300

Heading (deg)

Distance (m)

Composite RRH 1

Composite RRH 2

Composite RRH 3

Avg. Composite RRH

Generation of Road Reference Heading using GPS Trajectories for Accurate Lane Departure Detection

591

Figure 7: (a) Vehicle heading and RRH vs travelled distance for one test trial, (b) ALS versus travelled distance of the

corresponding test trial trajectory, and (c) ALS versus distance on the same 4.2 km segment of Interstate I-35 for four typical

trial trajectories with no lane change.

Furthermore, ALS value along any point on the road

remained below ±0.3m which is well below the ±1m

threshold, showing that the composite RRH generated

from past vehicle trajectories significantly improves

the accuracy of previously proposed lane departure

detection method by practically reducing the

frequency of false alarms to zero with a lot of margins

to spare.

5 CONCLUSIONS

In this paper, a novel algorithm is proposed to

generate an accurate RRH for any given road from a

vehicle’s past trajectories on that road. The newly

proposed algorithm can be applied to large tracts of a

vehicle trajectory to generate an accurate RRH for

that road regardless of whether a lane change is made

during acquisition of the trajectory. The newly

proposed algorithm was implemented to obtain RRH

for multiple roads and integrated with the previously

developed LDWS to test its ability to accurately

detect unintentional lane departures. Field test results

show that the newly proposed algorithm accurately

detects any unintentional lane departure as well as

minimizes the number of false alarms to almost zero

which was the prime objective while designing the

newly proposed algorithm. Successful development

of the proposed algorithm will pave the way for

integration of the algorithm into one of the popular

smartphone Apps.

ACKNOWLEDGEMENTS

The authors wish to acknowledge those who made

this research possible. The study was funded by the

Minnesota Department of Transportation (MnDOT)

and Minnesota Local Research Board (LRRB).

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