Advanced Curve Speed Warning System using Standard GPS

Technology and Road-level Mapping Information

Shahnewaz Chowdhury, Muhammad Faizan and M. I. Hayee

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

Keywords: Advance Curve Warning System, Super-elevation, Friction Factor, Advisory Speed Limit.

Abstract: Lane departure and advance curve warning are critical among several Advanced Driver-Assistance Systems

(ADAS) functions, which have significant potential to reduce crashes. Generally, lane departure and advance

curve speed warning systems either use different image processing techniques or GPS technology with digital

maps of lane-level resolution. However, these systems are expensive to implement as well as have some

limitations such as harsh weather or irregular lane markings can negatively influence their performance.

Previously we proposed a lane departure detection which uses a standard GPS receiver without any lane-level

resolution maps. Now, we have added another feature in this algorithm to detect an upcoming curve in advance

and warn the driver about its advisory speed at a safe distance so that driver can adjust vehicle speed

accordingly before reaching the curve. We have implemented our algorithm in a prototype system and

demonstrated in the field. We have performed extensive field tests and the test results show that each time

vehicle approaches a curve, our algorithm issues a warning and correctly determines the advisory speed for

the curve to warn the driver at a safe distance before the curve starts.

1 INTRODUCTION

An increasing number of modern vehicles include

different Advanced Driver-Assistance Systems

(ADAS) to assist in driver’s safety (C. Maag et al.

2012). Lane departure detection and advanced curve

speed warning are two important ADAS features

which can prevent high-speed accidents on highways

and freeways when a vehicle is about to

unintentionally drift away from its lane on a straight

or a curve road. According to American Association

of State Highway and Transportation Officials

(AASHTO) almost 60% of the 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).

Similarly, in a Minnesota crash study, it was reported

that 25 to 50 percent of the severe road departure

crashes in Minnesota occur on curves, even though

curves account for only 10 percent of the total system

mileage (Preston, H., and T. Schoenecker, 1999).

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 all useful to reduce major

road crashes. Majority of these crashes involve

crossing of an edge line, center line, or otherwise

leaving the intended lane or trajectory (FHA:

Roadway Departure Strategic Plan, 2013). According

to a recent study which compared crashes with and

without a lane departure warning system, it was found

that such a warning system was helpful in reducing

crashes of all severities by 18%, with injuries by 24%,

and with fatalities by 86% without considering for

driver demographics (J Cicchino, 2018).

Most available lane departure warning systems

typically use a single camera and a processor to

identify the imminent lane departure (Xiangjing An

et al. 2006, Pei-Yung Hsiao et al. 2006, B. Yu et al.

2008, Y. C. Leng et al. 2010), while other modern

systems use optical scanning and Light Detection and

Ranging (LIDAR) sensors (P. Lindner et al. 2009).

Similarly, majority of the curve speed warning

systems use a standard GPS receiver, a speed sensor,

and access to the digital maps of lane-level resolution

to detect the curve ahead (S. Glaser et al. 2007, R.

Yoneda et al. 2013, S. Rogers et al. 2003). Some

curve speed warning systems are also equipped with

Bluetooth Low Energy (BLE) technology along with

464

Chowdhury, S., Faizan, M. and Hayee, M.

Advanced Curve Speed Warning System using Standard GPS Technology and Road-level Mapping Information.

DOI: 10.5220/0009396804640472

In Proceedings of the 6th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2020), pages 464-472

ISBN: 978-989-758-419-0

the GPS receiver to transmit the curve information to

the onboard unit (Qin Xiao et al. 2015).

In advance curve speed warning systems, once a

curve ahead is detected and its degree of curvature is

estimated, a safe distance and an advisory speed is

calculated. The safe distance for a given curve is

defined as the distance required for a vehicle to

reduce its current speed to the advisory speed of a

curve. Some available systems also impose the speed

control mechanism to the vehicle in order to achieve

a safe speed in case the driver could not achieve it (S.

Glaser et al. 2007). If a vehicle is moving on a straight

section with speed higher than the advisory speed of

a curve, it is beneficial to warn the driver well in

advance so that the driver can adjust the speed

according to the advisory speed of the curve ahead.

Based upon the advisory speed and the current speed

of the vehicle, the proposed method will warn the

driver about advisory speed of a given curve at a safe

distance before the curve starts.

Although, useful, majority of the existing

commercial systems with lane departure or advanced

curve speed warning features require GPS

technology, inertial navigation sensor, and access to

digital maps of lane-level resolution (Daimler

Chrysler AG, 2018) making such systems more

complex and expensive to implement in most

common vehicles.

We have proposed a novel algorithm for lane

departure detection and advanced curve speed

warning which uses only standard GPS receiver

without any lane-level maps. Although absolute

position accuracy of a standard GPS receiver is larger

than the lane width (LW), its relative accuracy is

much better (< LW), providing an opportunity to

potentially detect lateral lane drift of a vehicle (J. M.

Clanton et al. 2009, S. Glaser et al. 2007). Previously,

the authors developed a methodology to accurately

identify the relative lanes of the surrounding vehicles

on a road by utilizing the relative accuracy of a

standard GPS receiver (S. Hussain et al. 2018). Using

that concept, the authors also proposed an algorithm

to detect an unintentional lane drift of a vehicle

(Muhammad Faizan et al. 2019). The proposed

algorithm compares vehicle’s trajectory to the

reference direction of a given road to determine the

lateral shift of a vehicle for potential lane departure

detection. The reference direction of a given road is

obtained from a standard digital mapping database

containing only road level maps without lane-level

resolution, which are commonly available in any

navigational system.

The authors now propose an added feature for

advanced curve speed warning system using the same

road level resolution maps which were used for lane

departure warning system. Based upon this feature,

the prototype system was updated, and field tested. In

this system, both lane departure and advanced curve

speed warning system work simultaneously and warn

the driver accordingly. The advanced curve speed

warning system detects a curve ahead and calculates

the degree of curvature and a safe distance using road

geometry for a possible curve ahead warning. If a

vehicle is moving on a straight section with speed

higher than the advisory speed of a curve, it will warn

the driver well in advance so that the driver can adjust

the speed according to the advisory speed of the curve

ahead. Based upon the advisory speed and the current

speed of the vehicle, the proposed method will warn

the driver about advisory speed of a given curve at a

safe distance before the curve starts.

The rest of the paper is organized as follows.

Section 2 describes the detail of the proposed

algorithm and methodology for the advanced curve

speed warning system. Section 3 summarizes the field

tests and results followed by conclusions in Section

Figure 1: Conceptual diagram showing advance curve speed warning system.

Starting

Point of curve

Safe Distance

Advanced Curve Speed Warning System using Standard GPS Technology and Road-level Mapping Information

465

2 ADVANCE CURVE

DETECTION ALGORITHM

Our proposed advance curve detection algorithm

utilizes reference road direction to detect a possible

curve ahead and warn the driver about the advisory

speed for a given curve at a safe distance before the

curve starts as shown in Figure 1. The safe distance is

assumed to be the distance needed to reduce a

vehicle's speed from its current speed to the advisory

speed of the curve by applying normal braking with

safe deceleration rate. Usually, before applying

brakes, a driver needs a buffer time called reaction

time to adjust to the warning. Therefore, driver’s

reaction time will also be included in determining

safe distance. There are three crucial parts of

advanced curve speed algorithm. First to determine

the advisory speed of a given curve and second to

determine safe distance using vehicle's current speed

and advisory speed for the curve, and a safe

deceleration rate. The third element is the constituents

of the advisory speed warning itself which is issued if

the vehicle’s current speed is higher than the advisory

speed. In the following these three aspects of the

proposed algorithm are explained in detail.

2.1 Advisory Speed for the Curve

We have explored two methods for determining

advisory speed for a given curve. Although, various

vehicles have different capacity to handle speed on

curves, we have assumed just one advisory speed for

all vehicles. To estimate the advisory speed, both

methods obtain specific information from the same

digital map database as we previously used for the

lane departure warning system. In the first method, an

advisory speed is determined using the shape points

for a given curve which we previously used to

determine the reference road direction. However, in

the second method an advisory speed value for a

given curve is directly acquired from the same

mapping database. These two methods are further

described below.

2.1.1 Calculated Advisory Speed

Our proposed algorithm uses reference road direction

to determine the degree of curvature for any given

curved section of the road segment. The degree of

curvature is then used to calculate the advisory speed

for that curved section. Our proposed methodology to

determine the degree of curvature needed to calculate

advisory speed for our proposed system is

schematically shown in Figure 2 where the heading

between two consecutive shape points for a given

road is shown versus distance. The beginning and

ending points of the curved section of the road are

also shown along with the safe distance.

Our previously developed lane departure

detection algorithm can detect the beginning and

ending points of a curve ahead. By determining the

beginning and ending points of a curve, we can

calculate the total length of the curve (L) as well as

the differential heading which is the difference of

initial

heading (h1) at the beginning of the curve and

Figure 2: Schematic diagram showing methodology to determine beginning and ending points of a curve ahead. This will be

needed to determine advisory speed.

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

466

Figure 3: The friction factor vs. degree of curvature.

Figure 4: An Estimated advisory speed vs. Super-elevation values.

final heading (h2) at the end of the curve. Finally, the

degree of curvature (D) which is defined as the

change of heading (in degrees) over 100 ft, is

calculated using equation 1 (AASHTO: A Policy on

Geometric Design of Highways and Streets), where L

is the curve length in feet.

D =

||



(1)

Once the degree of curvature is calculated, it is

used to determine the advisory speed (V) which not

only depends on degree of curvature but also rely on

other factors including super-elevation (e) and road

friction factor (f), and can be calculated using

equation 2 (AASHTO: A Policy on Geometric Design

of Highways and Streets).

=



(

.

)



(



)

()



(2)

Both super-elevation and friction values can be

estimated empirically. According to MnDOT road

design manual, the specific degree of curvature

corresponds to a specific limiting friction factor value

for a given road (S. Glaser et al. 2007). It contains

specific friction factor values for a few discrete values

of degree of curvature ranging from 2 to 21 degrees

(S. Glaser et al. 2007). We have curved fitted the

specified friction factor values to generate a generic

formula to determine friction factor value for a given

degree of curvature as shown in Figure 3 where

friction factor values are plotted versus degree of

curvature.

Although friction factor value is fixed for a given

degree of curvature, the super-elevation value for a

given road can vary between 0 to 6 percent for the

same degree of curvature. There is a possibility that

roads with the same degree of curvature can have

different super-elevation values or vice versa. Most of

the highways and freeways in Minnesota use 6

percent of super-elevation value (maximum

recommended) but a few highways especially the old

ones use a smaller super-elevation value.

Figure 4

shows calculated advisory speed versus super-

elevation values for two curved road segments (Rice

Lake Road and Interstate I-35 near Duluth,

Advanced Curve Speed Warning System using Standard GPS Technology and Road-level Mapping Information

467

Minnesota). The calculated advisory speed of Rice

Lake road ranges from 56 to 71 mph. However, the

actual posted advisory speed for that curved section

is 55 mph. This indicates that a super-elevation value

of 0% is used to calculate the posted advisory speed

for the Rice Lake Road. On the other hand, for the

Interstate section I-35, the actual posted speed is 70

mph while the calculated advisory speed ranges from

58 to 76 mph. Which implies that the 4% super-

elevation value was used to calculate the posted

advisory speed for that segment. Without having the

super-elevation information in advance, we cannot

reliably calculate an advisory speed for a given road.

Although the safest value of super-elevation is 0%

resulting in the least or safest advisory speed for any

given curve. Therefore, we used a super-elevation

value of 0% to calculate advisory speed in our

prototype system. In the cases of two roads (Rice

Lake and I-35), the calculated advisory speed for the

Rice Lake Road was close to the posted speed but

much less for the I-35 curved section which was

actually designed for a higher speed. An advisory

speed using one fixed value of super-elevation i.e.,

0% could vary from the actual posted advisory speed

for any given road. To mitigate this factor and to warn

the driver appropriately, it is best to obtain the actual

posted advisory speed from the digital map database

as explained below.

2.1.2 Acquired Advisory Speed

This method directly extracts posted advisory speed

from the digital mapping database which also has

road level information including advisory speed.

After extracting the advisory speed directly from the

mapping database, our algorithm compares it with the

calculated advisory speed. To be on the safe side, we

used the lower advisory speed whether it is from the

mapping database or from the calculation method for

issuing the warning. After determining the advisory

speed, next step is to find the safe distance before

issuing the warning.

2.2 Safe Distance

Safe distance is calculated using vehicle's current

speed, the advisory speed of the given curve, and a

safe deceleration rate. The current speed of the

vehicle is calculated from the GPS coordinates and

advisory speed is determined as explained above. As

for as the safe deceleration rate is concerned,

according to AASHTO, approximately 90% of

motorists brake with the deceleration rate of more

than 3.4 m/s

(S. Glaser et al. 2007). This rate enables

drivers to reduce their speed safely without losing

control. Therefore, 3.4 m/s

is used as a safe

deceleration rate to calculate safe distance for our

algorithm. Using current speed, advisory speed, and

safe deceleration rate (a), the safe distance is

calculated by using Equation 3.













(3)

However, Equation 3 does not accommodate

driver’s reaction time. Therefore, an adjustment is

made to include the driver’s reaction time in

calculating safe distance using Equation 4, where T is

the reaction time for the driver. According to

AASHTO, a person can take 0.9 to 2.5 seconds to

react to a warning sign. To be on a safe side, we are

using the longest reaction time (2.5 s) for safe

distance calculations for our system.

Figure 5: Calculated safe distance vs. vehicle’s current speed for two different advisory speeds.

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

468













+



× (4)

Figure 5 shows the safe distance vs. vehicle’s

current speed for three different values of

deceleration rate (3.4, 6 and 8 m/s

) for each of the

two advisory speeds (55 and 70 mph). Although

system uses 3.4m/s

as deceleration rate, the higher

declaration rates (6 and 8 m/s

) have been

incorporated for reference only. It is to be noted that

the higher deceleration rates show the usage of

emergency brakes while reducing speed. When the

vehicle is driving at the same speed as the advisory

speed (V=V

), safe distance only accounts for

driver’s reaction time and will have some non-zero

value.

2.3 System Warning Generation

Based on safe distance analysis, our algorithm scans

a curve ahead at least half a mile in advance to ensure

that advanced curve warning can be issued in time.

Half a mile criterion gives 30 seconds buffer time at

the speed of 60 mph. Once the advisory speed is

determined and a safe distance is calculated, the

following two possible scenarios are evaluated prior

to issuing the warning.

 Vehicle’s current speed is higher than the

advisory speed.

 Vehicle’s current speed is less than or equal

to the advisory speed.

In both scenarios, our algorithm recommends the

same warning, however, the safe distance where the

warning will be issued will be different in both

scenarios. Once vehicle approaches at the safe

distance to the curve, the above warning will be

issued.

The warning message comprises of two important

pieces of information, first about the existence of

curve ahead and second about the advisory speed for

that curve. By giving the warning within the safe

distance, our algorithm ensures that the driver has

enough time to adjust vehicle’s speed comfortably.

Our prototype system displays a written warning on

the console for demonstration purposes.

3 FIELD TESTS AND RESULTS

The functional flow diagram for both lane departure

detection and advanced curve speed warning

Figure 6: Flow diagram showing the complete functionality of lane departure warning and advance curve speed warning

systems.

System

Initialization and

Data Processing

Calculate Lateral Deviation

Lane

Departure

Detection

Audible Warning

Curve

Detection

Calculate Safe Distance and

Advisory Speed

Issue Advance

Curve Warning

Yes

Curve Ahea

Advisor

eed: XX m

Advanced Curve Speed Warning System using Standard GPS Technology and Road-level Mapping Information

469

Figure 7: Database heading between consecutive shape points (black) and calculated reference heading (red dashed line)

versus road distance for a 4 km segment of Interstate I-35. The Google Earth view of the corresponding road segments with

shape points are also shown for reference.

algorithms are shown in Figure 6. We used a Savari

MobiWAVE unit to implement our algorithm and

evaluate its performance in the field. The Savari unit

has a built in GPS receiver and processing power to

implement our algorithm. The built-in GPS receiver

had a UBlox LEA-6 chipset which is a common

chipset in many GPS receivers. Please note that the

proposed algorithm can be implemented in any

navigational device having a standard GPS receiver

and necessary processing power.

The prototype system periodically (every 100 ms)

calculates instantaneous lateral distance and

accumulates it over time. If the accumulated lateral

distance crosses certain threshold, the system will

issue an audible warning to alert the driver of

unintentional lane drifting. Simultaneously, the

prototype system also checks if there is any curve

ahead. The system has the capability to differentiate

between curve and straight sections of the road in real

time. If a curve is detected, first its advisory speed is

determined and then a safe distance is calculated

based on vehicle’s current speed and the advisory

speed for the curve. The safe distance calculation

determines when to issue the advance curve speed

warning. In our prototype system, the warning is

issued as soon as the vehicle approaches within the

safe distance from the curve so the driver will have

enough time to reduce the vehicle’s speed. This whole

cycle of calculation is repeated every 100 msec and

appropriate warnings are given when warranted. In

this way, both lane departure and advanced curve

speed warning algorithms works simultaneously.

We tested our prototype system on two different

road segments, a 3 km long segment of Rice Lake

Road in Duluth, MN, and a 4 km long segment of

Interstate I-35 near Duluth, MN. Figure 7 shows the

reference heading for I-35 vs travelled distance as

extracted from the mapping database. The Google

Earth picture of the corresponding section of

Interstate I-35 is also shown on the top of the figure.

The I-35 test segment has three curves in 4 km

segment as can be seen in Figure 7.

The lane width for both road segments was 3.6 m

and the speed limit were 55 MPH for Rice Lake Road

and 70 MPH for Interstate I-35. The vehicle was

driven at about speed limit on both road segments and

many back-and-forth driving runs were made. During

these test runs, whenever, the vehicle was

approaching to a curve, the driver was warned about

the presence of the curve ahead along with its

advisory speed before the curve starts.

Figure 8: Snapshot from field demonstration showing

advanced curve speed warning while approaching a curve.

VEHITS 2020 - 6th International Conference on Vehicle Technology and Intelligent Transport Systems

470

Figure 8 shows a snapshot of the console during

one of our field tests while approaching one of the

three curve sections in the test segment. We evaluated

the accuracy of the algorithm by marking down the

distance where the warning was issued while driving

at different speeds. Each time, the curve was

successfully detected and the warning was shown at

the appropriate safe distance. We also evaluated the

system for lane departure warning by intentionally

making many back and forth lane changes on both

straight and curved sections of the test segment.

Those results have already been published elsewhere

(Muhammad Faizan et al. 2019).

4 CONCLUSIONS

Previously we proposed and demonstrated a novel

algorithm to detect an unintentional lane departure

and warn the driver in time. Now we have added

another feature in this algorithm which can detect an

upcoming curve and determines its advisory speed.

We designed the algorithm for this added feature and

demonstrated in the field by developing a prototype

system. Extensive field tests were performed to

evaluate the efficiency of the newly developed

algorithm on two different road segments. The

advance curve detection algorithm can detect the

upcoming curve and correctly determines its advisory

speed before issuing the appropriate warning at a safe

distance before the curve starts. We have performed

error analysis for the lane departure detection part of

this work but both the temporal and spatial scale

involved in an upcoming curve detection are large

enough to be ignored. An error in an upcoming curve

detection, can be up to  25 m in location which

translates to  1 second in time, is insignificant for

this feature.

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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