Precise Vehicle Position and Heading Estimation Using a Binary Road Marking Map · 2019. 7. 30. · 1-bit information instead of probability, map matching is possible by the simple

Research ArticlePrecise Vehicle Position and Heading Estimation Using a BinaryRoad Marking Map

Kyu-Won Kim ,1 Jun-Hyuck Im,1 Moon-Beom Heo,2 and Gyu-In Jee 1

1Department of Electronic Engineering, Konkuk University, Seoul 05029, Republic of Korea2Satellite Navigation Team, Korea Aerospace Research Institute (KARI), Daejeon 34133, Republic of Korea

Correspondence should be addressed to Kyu-Won Kim; [email protected]

Received 9 September 2018; Revised 6 November 2018; Accepted 12 November 2018; Published 20 January 2019

Academic Editor: Vincenzo Marletta

Copyright © 2019 Kyu-Won Kim et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Road markings are always present on roads to guide and control traffic. Therefore, they can be used at any time for vehiclelocalization. Moreover, they can be easily extracted by using light detection and ranging (LIDAR) intensity because they arebrightly colored. We propose a vehicle localization method using a 2D road marking grid map. The grid map inserts the mapinformation into the grid directly. Thus, an additional process (such as line detection) is not required and there is no problemdue to false detection. We obtained road marking using a 3D LIDAR (Velodyne HDL-32E) and binarized this information tostore in the map. Thus, we could reduce the map size significantly. In the previous research, the road marking grid map wasused only for position estimation. However, we propose a position-and-heading estimation algorithm using the binary roadmarking grid map. Accordingly, we derive more precise position estimation results. Moreover, position reliability is animportant factor for vehicle localization. Autonomous vehicles may cause accidents if they cannot maintain their lanemomentarily. Therefore, we propose an algorithm for evaluating map matching results. Consequently, we can use onlyreliable matching results and increase position reliability. The experiment was conducted in Gangnam, Seoul, where GPSerror occurs largely. In the experimental results, the lateral root mean square (RMS) error was 0.05m and longitudinalRMS error was 0.08m. Further, we obtained a position error of less than 50 cm in both lateral and longitudinal directionswith a 99% confidence level.

1. Introduction

Precise vehicle localization is essential for driving safety inautonomous vehicles. Generally, a submeter level of localiza-tion performance is required for the autonomous vehicle tomaintain its own lane, and it should be estimated with a highreliability of 95% [1] or more. Usually, Global PositioningSystem (GPS) is used for vehicle localization. However, GPSdoes not provide the position accuracy required for autono-mous vehicles. Especially in urban areas, even if an expensiveGPS (RTK)/INS is used, a position error of more than 1m canoccur. To solve this problem, many studies that improve posi-tion accuracy by combining various sensors (such as GPS,inertial measurement unit (IMU), vision, and light detectionand ranging (LIDAR)) have been researched continuously.

Recently, many studies have been conducted to correctGPS error by generating maps based on LIDAR [2] because

LIDAR-based maps can be generated precisely and accu-rately. Li et al. [3] expressed the 3D environment on bothsides of the road as a type of a depth map called roadDNA. In addition, Im et al. [4] detected corners of verticalstructures such as buildings and generated a corner-basedlandmark map. However, the above methods have disad-vantages in that they cannot be used when there are no ver-tical structures, such as a highway.

Therefore, we focused on the map using road markings.Road markings are always available because they exist every-where the vehicle goes. Moreover, because of the use of brightcolors, it is easy to detect them using the intensity of LIDAR,and there is a potential for robust localization performancebecause of the use of letters and symbols as well as lines suchas lanes or stop lines. Therefore, road marking map-basedvehicle localization has been studied in this work. Levinsonet al. [5, 6] and Wolcott and Eustice [7] performed vehicle

HindawiJournal of SensorsVolume 2019, Article ID 1296175, 18 pageshttps://doi.org/10.1155/2019/1296175

http://orcid.org/0000-0002-5775-6402http://orcid.org/0000-0002-4736-5993https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2019/1296175

localization on LIDAR and camera based on the intensityroad marking grid map, respectively. Intensity road markinggrid map-based localization provides high accuracy. How-ever, the intensity of LIDAR varies depending on the roadsurface, so the performance may deteriorate depending onthe road surface condition of a given day. Further, theintensity grid map has the disadvantage of large map size.Schreiber et al. [8] used LIDAR to create a line map usingroad marking (such as lane, stop line, and curb). A stereocamera was used to estimate the vehicle position. A linemap has the advantage of small map size. However, the esti-mation performance is relatively low and the road marking ofletters and symbols is difficult to detect. Therefore, it cannotbe used with such robust information.

In this paper, we proposed a method for the estimation ofvehicle position and heading based on a binary grid mapusing road markings. The road marking grid map is atwo-dimensional (2D) map that stores the road markinginformation scanned by the LIDAR directly on the grid.Therefore, since the detection process is not necessary,complex letters and symbols can be stored and used for local-ization. However, the grid map has disadvantages that thesize increases exponentially according to the grid size andmap scale. Therefore, we generated the binary road markinginformation by binarizing the intensity of the LIDAR scandata and stored this information in the grid map. The binaryroad marking information has only 1-bit information. Thus,we can reduce the map size significantly compared to theintensity road marking grid map. In addition, the problemof varying the intensity level according to the road surfacecondition is solved through intensity binarization. Most ofthe grid maps using road marking information are in theform of an occupancy grid map [9]. Therefore, each gridhas a probability. However, the binary road marking gridmap has only 1-bit information. Thus, 0 indicates no roadmarking and 1 indicates road marking. Therefore, the mapsize becomes more compact. Moreover, since it contains only1-bit information instead of probability, map matching ispossible by the simple correlation method.

Because road markings are on the road, the map match-ing performance deterioration in a situation such as trafficcongestion is a disadvantage. Therefore, we used the accumu-lated scan data [10, 11] to generate a precise local map andmatch with the global map. Consequently, the problem ofpoor performance under traffic congestion was solved. Inaddition, the position and attitude for the precise local mapwere derived by accumulating incremental values of positionand attitude derived from the iterative closest point (ICP)algorithm based on the geometric relationship betweenLIDAR scan data.

Vehicle localization using existing 2D grid-based roadmarking maps [12] only estimated the vehicle position.However, it is necessary to estimate not only the positionbut also the heading to ensure driving safety in autonomousvehicles. Therefore, we proposed a position-and-headingestimation algorithm based on the binary road markingmap. In the case of position estimation, fast and robust posi-tion estimation performance is derived using fast Fouriertransform- (FFT-) based phase correlation [13, 14]. Further,

the heading is derived by converting the grid map to thepoints and matching between the map points and the binaryroad marking points. The highly reliable position and head-ing matching results are derived using the algorithm for theevaluation of map matching result, and we used only theseresults for precise vehicle localization.

The contributions of this paper are as follows:

(i) Proposed a method of the binary road marking gridmap generation and vehicle position and headingestimation method using this map

(ii) Derived reliable and accurate estimation results usingthe binary road marking grid map

We propose a new type of the road marking grid mapusing the binary information that is not a traditional roadmarking-based occupancy grid map. In addition, we proposethe vehicle position and heading estimation algorithm usingthis map. Vehicle localization using the existing 2D grid-based road marking map only estimates the position. How-ever, we propose an algorithm to estimate the heading inaddition to the position. The RMS position error is approxi-mately 0.10m in both lateral and longitudinal directions inurban areas, and the estimation results are derived with aposition error within 50 cmwith 99% reliability. Accordingly,it is confirmed that very accurate and precise position andheading estimation results can be derived by using a binaryroad marking grid map.

The composition of this paper is as follows. In Section 2,we introduce a method for binarizing LIDAR intensity. Sec-tion 3 describes how to generate the binary road marking gridmap, and Section 4 describes how to generate a precise localmap by accumulating scan data. In Section 5, the mapmatch-ing and vehicle localization algorithm are described. Theexperimental result is described in Section 6. Finally, the con-clusion is given in Section 7.

2. Method of Road Marking Extraction UsingIntensity Binarization

Road markings are the devices on paved roadways that pro-vide guidance and information to drivers. They are madewith bright paint so that the driver can distinguish themeasily. Therefore, they can be easily extracted by using theintensity of LIDAR. Specifically, the three-dimensional(3D) LIDAR [15] used in this paper provides 8-bit intensityinformation. Thus, various values of intensity informationcan be obtained.

As shown in Figure 1, the 3D LIDAR produces 3D scandata by scanning. Figure 2 shows the intensity of the roadscan data among the 3D scan data. A road marking on theroad is distinguished from the asphalt.

In this paper, we binarized 8 bits of intensity to 1 bit. Inthe case of intensity, it is possible to express an image in grayscale, as shown in Figure 2, because it provides informationwith 8 bits. Thus, the intensity can be regarded as the bright-ness of the image, and binarization is possible by applying thethreshold. For binarization, it is necessary to set the threshold

2 Journal of Sensors

value of the intensity. To solve this, Otsu’s thresholdingmethod [16] is used. Otsu thresholding is a method to findthe optimal threshold using the brightness distribution ofall pixel values in the image. Using this method, we can findthe threshold even if the intensity is changed in every scene.

However, even when scanning the same road marking,there is a difference in intensity among the vertical layers ofthe 3D LIDAR [17]. Figure 3 shows the intensity of the sameroad marking scanned by a 3D LIDAR for each vertical layer.The vertical layer means the number of vertically scanned 3DLIDAR channels. In this research, we used 32-channel 3DLIDAR and 12 channels are used for scanning the road mark-ing. As shown in this figure, intensity values are differentdepending on the vertical layer. Thus, if we binarize to thethreshold of the entire layer, the road marking cannot be

extracted properly. Therefore, we applied thresholding andbinarization to each layer.

Figure 4 shows the result of binarizing intensity data ofFigure 2. Low-intensity values, such as those for asphalt, areeliminated, and only the road marking is extracted. Thus,the road marking can be extracted from 3D LIDAR scan data.

3. Binary Road Marking Map Generation

3.1. Graph Optimization and Map Generation. A global mapis essential for localization. In addition, a precise vehicle

800 605

1015

100 4020

500

−200−40

−60-50−80

−100

Figure 1: Scan data from the 3D LIDAR.

Figure 2: Road scan data represented by intensity. 0

10

20

30

40

50

60

70

80

90

Inte

nsity

Intensity of each layer

0 2 4 6 8 10 12Vertical layer

Figure 3: Road marking intensity of each vertical layer.

3Journal of Sensors

trajectory is required to generate a precise global map. Ingeneral, when using simultaneous localization and mapping(SLAM) [18], errors accumulate as the vehicle progresses.Therefore, when a global map is generated, the road markingdoes not match.

Figure 5 shows the binary road marking grid map gen-erated by using the GPS (RTK)/INS (NovAtel RTK/SPANsystem) trajectory. As shown in this figure, it can be con-firmed that the road marking is not consistent. Therefore,we performed graph optimization using graph SLAM [19,20]. Graph optimization is a method of setting constraintsfor each node and optimizing the trajectory using edgerelationships between nodes. The incremental pose infor-mation outputted from the ICP scan matching algorithmwas used as the edge measurement of the graph.

Figure 6 shows the result of graph optimization. Asshown in this figure, the edge relation connected by blacklines is set for all nodes and the optimization is performedusing them. Nodes connected by black lines are the trajecto-ries of different laps, and loop closure is performed by deriv-ing edge relationships between these nodes. After that, thetrajectory is optimized like a red dot. Figure 7 shows thebinary road marking grid map generated by using the GraphSLAM-optimized trajectory. The binary road marking grid

Figure 4: Intensity binarization result.

Figure 5: Result of binary grid map generation (trajectory: GPS(RTK)/INS).

Graph SLAM result

Graph SLAM result

160

155

150

145

(Met

ers)

(Meters)

140

135

130

−345 −340 −335 −330 −325 −325 −315 −310

GPS (RTK)/INS

−305

Figure 6: Result of graph optimization.

Figure 7: Result of binary grid map generation (trajectory: GraphSLAM-optimized result).

Table 1: Comparison of map size.

Grid resolution Probability map Binary mapBinary map

(sparse matrix)

15 cm 62MB 986 kB 245 kB

10 cm 106MB 2.01MB 450 kB

5 cm 384MB 7.83MB 1.21MB

Table 2: An example of saving a binary road marking grid map.

Index X (grid) Y (grid)

Matrix size 14000 14000

1 1214 2451

2 1312 4285

⋮ ⋮ ⋮n 8413 11231


map was generated by accumulating the road markingsextracted by the binarization process. Unlike the case inFigure 5, the road markings are consistent. In addition, theoptimized trajectory is assumed to be the ground truth.

3.2. Advantage of Using a Binary Road Marking Map. Themap used for vehicle localization using the difference inintensity is the intensity road marking grid map, and it isstored by using 8-bit intensity values. Generally, the intensityroad marking grid map is used in the form of a probabilitymap [5, 6] that stores the mean and variance of the intensity.Further, due to the characteristic of the 2D grid map, whenthe grid size is smaller and the map scale is larger, the mapsize becomes larger. However, if the intensity is binarizedand stored in a map, the size becomes very small as the infor-mation is compressed.

Table 1 gives a comparison of map size. The proba-bility map stores the intensity mean and variance, andthe binary map stores the binarized road marking infor-mation. As shown in Table 1, the map size of the binarymap is approximately under 2% of the probability map.Unlike the probability map, in which the map size growsexponentially as the grid size becomes smaller, the mapsize of the binary map is very small and the amount ofincrease in size is not large as the resolution increases.In addition, the binary map consists of 0 s and 1 s. Thecharacteristic of a road marking grid map is that thereare many more 0 s in the map. Therefore, if we remove0 and save it as a sparse matrix, the map size is furtherreduced and can be reduced to 0.4% of the probabilitymap as shown in Table 1.

Table 2 shows an example of saving a binary road mark-ing grid map. Only the grid position where the road markingis stored can be saved because the map format is 1 bit. There-fore, it is not necessary to save the map as a 2D full matrixformat and it is possible to store a 2D road marking gridmap efficiently.

When intensity is binarized, loss of information occurs.Therefore, we might think that in using the binary map for

map matching, localization performance is poor comparedwith the intensity map. On the contrary, matching perfor-mance may deteriorate because intensity has more informa-tion. For example, the value of intensity changes accordingto the road surface condition [21]. Thus, when the roadsurface gets wet, the intensity value is larger than that fora dry road surface.

Figure 8 shows the intensity map of dry and wet roadsurfaces. Further, Figure 9 compares the intensity countand threshold of Figure 8. Because the total intensityamount of the two cases is different, the count is normal-ized. As shown in Figure 9, the intensity threshold islarger on the wet road surface. Therefore, this differencein intensity causes poor localization performance. On the

(a) (b)

Figure 8: Intensity maps for different road surface conditions. (a) Dry road. (b) Wet road.

0 20 40 60 80 100Intensity

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45N

orm

aliz

ed co

unt

Intensity count

Threshold = 12

Threshold = 16

Dry roadWet road

Figure 9: Intensity count and threshold.

5Journal of Sensors

other hand, if the intensity is binarized, the road markingcan be extracted regardless of the road surface condition.Consequently, more robust localization performance canbe obtained.

Figure 10 shows the binary map of dry and wet roads.It can be seen in this figure that there is almost no differ-ence in the extraction results between the two maps. Thus,using a binary road marking grid map, we can use roadmarking information regardless of road surface condition.In addition, when using the binary road marking grid map, itis obvious whether it is road marking or not. Therefore, moreclear matching results can be obtained in map matching.

4. Precise Local Map Generation

In this section, we describe how to generate a precise localmap [22]. It is generated by using the result obtained bybinarizing the road marking in Section 2. Generally, theinterval between the vertical layers of 3D LIDAR is largerthan horizontal scan interval. Therefore, the local mapgenerated by only one scan data has insufficient longitudi-nal direction information. In addition, the road marking islocated under the vehicle. Thus, the problem is that onlylittle road marking information can be extracted in traffic

congestion situations. To solve this problem, we generateda local map by accumulating extracted road marking datafor a certain period and defined it as a precise local map.

Figure 11 shows the flow chart of precise local mapgeneration. First, data is accumulated by combining theprevious data with the current position, pose increment,and LIDAR scan data. Next, a precise local map updateis conducted using the accumulated data. The accumulateddata are used to generate the precise local map at the nexttime. In addition, the sliding window method [10] wasapplied to the data accumulated.

In the case of local map generation using data accumu-lation, position and pose errors are also accumulated. Inparticular, in the case of commercial GPS/DR (dead reck-oning), considerable errors may accumulate even in a shorttime. Therefore, we used the position and pose incrementderived from the ICP scan matching. The ICP scan match-ing is matched using a precise 3D LIDAR point cloud.Thus, we can obtain more precise position and headingincrement values.

Figure 12 shows an example of position and pose incre-ment derived using ICP. The precise local map is generatedby accumulating the scan data at the position and pose incre-ment obtained from each node. In this case, the scan data isthe road marking information extracted from the binariza-tion process of Section 2.

As shown in Figure 13, it can be seen that as the dataaccumulates, the road marking information generated inthe local map becomes sufficient, especially longitudinaldirection. Consequently, sufficient road marking informa-tion can be obtained for matching even in traffic conges-tion situations.

5. Map Matching and VehicleLocalization Algorithm

In this section, we describe the estimation of position andheading using the map matching algorithm. The map match-ing result is used as the final measurement value of the navi-gation filter only for good results by executing the evaluation

(a) (b)

Figure 10: Binary maps of different road surface conditions. (a) Dry road. (b) Wet road.

LIDARscan data

Position& pose increment

Dataaccumulation

Preciselocal map

update

Previous data

Figure 11: Flow chart of precise local map generation.


of the matching result algorithm. The navigation filter usesthe Kalman filter (KF). The specific vehicle localization algo-rithm is shown in Figure 14.

5.1. Map Matching Algorithm. In this part, we describe themap matching algorithm. δx δy δθ

T is the map matchingresult between the global map and the local map. Theglobal map is taken from predicted vehicle position usingthe time update, and the local map is generated at the cur-rent vehicle position. Therefore, we can obtain error cor-rection values between the predicted vehicle position andcurrent vehicle position from map matching. Further, the

predicted vehicle position was derived by using the incre-ment value of position and heading from ICP scan match-ing algorithm.

5.1.1. Position. FFT-based phase correlation [13, 14] is usedto estimate the vehicle position. Correlation is a methodmainly used for matching two data sets. In particular,phase correlation is a technique used mainly for imageregistration. Because phase information is separated andcorrelated in the frequency domain, phase correlation hasrobustness to noise. Further, unlike the serial-search-based correlation, which sets the search area and performsindividual correlation in the area, the FFT-based correlation

Figure 13: Process of precise local map generation.

Δx1

Δy1

Δ𝜃1

Δx2

Δy2

Δ𝜃2

Δx3

Δy3

Δ𝜃3

Δx4

Δy4

Δ𝜃4

Figure 12: Example of derived position and pose increment using ICP.

7Journal of Sensors

can match the large image at high speed because of corre-lated images simultaneously. The frequency domain trans-formation of the global and local maps for phasecorrelation is as follows:

M u, v = F m x, y ,

Z u, v = F z x, y ,1

where m x, y and z x, y are the global map and local map,respectively. M u, v and Z u, v are transformations in the

frequency domain using FFT. The global map is taken fromthe predicted vehicle position, and the local map is generatedat the current vehicle position. Therefore, matching result isrepresented as the error correction value from the predictedvehicle position. Thus, if δx and δy are the error correctionvalues, Z u, v can be expressed as follows:

Z u, v =M u, v e−2πj uδx+vδy 2

For phase correlation, we need to know the phasedifference between two images. Thus, the normalizedcross power spectrum is calculated, and the equation isas follows:

C u, v = M u, v Z∗ u, v

M u, v Z∗ u, v= M u, v M

∗ u, v e2πj uδx+vδyM u, v M∗ u, v

= e2πj uδx+vδy

3

Inverse Fourier transform (IFT) can be used toobtain the final phase correlation from equation (3).

PC m x, y , z x, y = F−1 e2πj uδx+vδy 4

GPS/DR LIDAR

InitializationICP

scan matching

Time update

Map matching

Evaluatemap matching result

Measurementupdate

Global map

Precise local mapgeneration

Accumulatedpose & scan data

[

[ ]T

]T

]TxDR yDR 𝜃DR

[ΔxICP ΔyICP Δ𝜃ICP

𝛿x δy δ𝜃

x̂t

Figure 14: Flow chart of the vehicle localization algorithm.

Phase correlation result

0.06

0.05

0.04

0.03

0.02

0.01

01000

500

0 0200

400600

800

East

1000

Figure 15: Result of phase correlation.


The matching result through phase correlation isshown in Figure 15.

As shown in Figure 15, sharp peaks are extracted usingphase correlation. However, if the road marking informa-tion of the local map is insufficient, the peaks do notappear or multiple peaks may occur. To solve this prob-lem, we applied a Gaussian filter. By setting the regionof interest (ROI) using a Gaussian filter, noise and multi-ple peaks can be removed. The ROI is set by consideringthe vehicle speed based on the current estimated positionusing σ. The Gaussian filter equation is as follows:

PGauss = expx2 + y2

−2σ2,

Pw = PC m x, y , z x, y × PGauss5

Figure 16 shows the result of applying a Gaussian fil-ter. Noise and multiple peaks are removed through theGaussian filter, and a sharp peak is extracted. The resultof the map matching is as follows:

δx =∑Pw x, y ⋅ x∑Pw x, y

,

δy =∑Pw x, y ⋅ y∑Pw x, y

6

Since the map used for map matching is a grid map,the estimated value oscillates if the maximum value ofPw x, y is taken as the matching result because it is asuncertain as the grid size. Therefore, by using the peakand value around the peak as in equation (6), the uncer-tainty is reduced and the oscillation is prevented.

0.025

0.02

0.015

0.01

0.005

0600400

2000 0 100

200300400

500

0.025

0.02

0.015

0.01

0.005

0600400

2000 0 100

200300400500

×10−38

6

4

2

0600

400200

0 0 100200300

400500

Figure 16: Result of applying a Gaussian filter.

Figure 17: Transformed grid to point.

9Journal of Sensors

5.1.2. Heading. The ICP algorithm [23] was used to estimatethe vehicle heading. The binary road marking grid map is thestored road marking information in the grid. Therefore, forpoint matching, the global map and local map are convertedto points based on the grid center.

The road marking in the grid is converted to a point, asshown in Figure 17. The local map used in position estima-tion is a precise local map using accumulated data. However,in the case of heading, accurate error estimation cannot beperformed because the error is mixed by accumulating data.Therefore, when the heading is estimated, the local map isgenerated using the current scan data and matched with theglobal map.

The ICP algorithm is executed in two stages:

(1) Find the corresponding point between the twodata sets

(2) Compute a transformation matrix that minimizes thedistance between corresponding points

Repeat the above two steps until it is below the thresholdto derive the final transformation matrix. In addition, dmax isset to prevent fault matching by outliers. Algorithm 1 showsthe ICP algorithm.

As shown in Figure 18, the points of the local map arecorrected through the ICP algorithm.

T = R t ,

R =cos δθ −sin δθsin δθ cos δθ

,

δθ = arcsin sin δθ

7

Input: Two point cloud dat →Map = m , Local map = ziOutput: The correct transformation T, which aligns Map and Local mapT = ToWhile ε > Threshold

for i = 1 Nmi = f ind closest point in map T , ziif mi − T∙zi < dmax

wi = 1elseif

wi = 0end

endT = arg min

T∑iwi mi − T ⋅ zi

2

ε =max m − T∙zend

Algorithm 1: ICP algorithm.

−3 −2 −1 0 1 2 3 4 5 6(m)

−7.5−7

−6.5−6

−5.5−5

−4.5−4

−3.5−3

−2.5

(m)

ICP matching result (corrected heading angle: −0.73 deg)

Map pointLocal map pointCorrected point

Figure 18: Result of ICP matching between the map and local map.

2 4 6 8 10 12 14Epoch (0.1 sec)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Er

ror (

deg)

Heading error

GPS/DREstimated result

Figure 19: Heading error.


Equation (7) is used to obtain the heading correctionvalue using the transformation matrix. Since the global mapis based on the predicted position of the vehicle and the localmap is based on the current vehicle position, δθ is the correc-tion value of the heading.

There are two reasons why heading estimation isrequired for vehicle localization. First, if the position esti-mation is accurate but the heading error is large, thedirection of the autonomous vehicle will be deviated fromthe lane continuously. Next, the precise local map gener-ated accumulated increment of position and heading. Weobtain the increment of position and heading throughICP scan matching. However, to match with the globalmap, we need to add the heading value from GPS/DR.Therefore, if the GPS/DR heading error is large, the roadmarking information of the generated precise local mapdoes not match the global map.

Figure 19 shows the heading error of GPS/DR andestimated heading result. Figure 20 shows the result ofoverlapping of the global and local maps at the true refer-ence position. The local map is represented by black, andthe global map is represented by gray. In Figure 20, thelocal map is generated by using GPS/DR heading angleand estimated heading result, respectively. If the headingangle is same with true reference, global and local mapsmust be matched each other. As shown in this figure, (a)is not consistent with each other, while (b) is almost con-sistent. Consequently, if the heading estimation is not con-ducted, map matching error increases. Therefore, headingestimation is required for vehicle localization.

5.2. Evaluation of Map Matching Result. Vehicle localizationthrough map matching can lead to large errors if the match-ing results are wrong. In particular, in the case of autono-mous vehicles, a wrong localization result may cause a bigaccident. Therefore, when the map matching result is wrong,

it should be detected and the wrong matching result must notbe used. In this paper, we conducted an evaluation of positionand heading matching results. Accordingly, only good resultswere used for localization.

5.2.1. Evaluation of Position Matching Result. In this paper,we used two parameters to evaluate of the position matchingresult. One is the protection level (PL) of the matching result,and the other is the peak-to-side lobe ratio (PSR).

PL is a parameter [24] used to determine the reliability ofaircraft GPS. When the PL exceeds a certain threshold, a falsealarm indicates that the localization result is wrong. Weapplied that to the vehicle [25, 26]. The equation for the PLof a vehicle is as follows:

K = Rayleigh−1 1 − Pmd ,

PL = K × σpos,8

where K is the probability of missed detection and it is calcu-lated as the Rayleigh inverse cumulative distribution func-tion. The term σpos can be estimated as the maximumeigenvalue of the covariance matrix.

PSR [27] is a parameter that determines the sharpness ofthe correlation peak. A sharp peak means that the matchingresult is reliable. Therefore, PSR can be a basis for evaluatingof the matching result.

Figure 21 shows an example of the peak and side lobe.The peak means the peak of correlation, and side lobe meansnoise around the peak.

PSR =peak −mean side lobe

std side lobe9

As shown in equation (9), the PSR can be obtained byusing the peak and side lobe and the sharpness of the peakcan be determined by the ratio of the peak to the side lobe.

Inconsistent

(a)

Consistent

(b)

Figure 20: Result of the overlapping global and local maps at true reference position. (a) GPS/DR. (b) Estimated heading result.

11Journal of Sensors

The above two parameters are used to evaluate the posi-tion matching result. We set the threshold of the two param-eters to evaluate the position matching result.

Figure 22 shows an example of the threshold settingfor PL and PSR, where the blue points denote the match-ing result. In the case of PL, the lower the value and thehigher the PSR, the higher the reliability of the matchingresult will be. Thus, out of the four ranges shown inFigure 22, (a) gives highly reliable results. Therefore, weused map matching results in the range (a) as a measure-ment in the navigation filter and did not use the results ofthe remaining range.

5.2.2. Evaluation of Heading Matching Result. The headingmatching result is also evaluated by two parameters. One isthe number of points, and the other is the distance ratio ofthe corresponding points. In the case of heading matching,since the ICP algorithm is used, the number of points plays

an important role in convergence and derivation of the trans-formationmatrix. In addition, the distance of the correspond-ing points can also be a determining factor for the matchingperformance because the ICP algorithm is used to find thetransformation matrix with the closest distance of corre-sponding points. The distance between the correspondingpoints was derived using the nearest neighbor search (NNS)algorithm. Next, we extracted corresponding points whosedistances are within a certain threshold. Finally, the ratiobetween the extracted points and the total number of pointswas used as a parameter for evaluating the heading matchingresult. We set the threshold of the two parameters and usedthe result in the range as a measurement value in the naviga-tion filter.

5.3. Navigation Filter Configuration. In this paper, the KF[28] is used as a navigation filter for vehicle localization.The KF is the most common filter used for localization. Touse this filter, it is necessary to define the state vector andinput vector.

x̂ = x y θ T ,

u = ΔxICP ΔyICP ΔθICPT

10

In equation (10), x̂ is the state vector that represents theposition and heading of the vehicle in the global frame andu is the input vector that refers to the increment of the posi-tion and heading derived from the ICP scan matching algo-rithm. The state variables are predicted by the time update.The time update is as follows:

x̂0 = xDR + δx yDR + δy θDR + δθT ,

F =

1 0 0

0 1 0

0 0 1

,

Gt =

cos θt −sin θt 0

sin θt cos θt 0

0 0 1

,

x̂t+1 = F x̂t +Gtut ,

Pt+1 = FPtFT +Q

11

In equation (11), we need to initialize the state vec-tor and covariance matrix before the time update. Theinitial state vector is obtained from the GPS/DR positionand heading angle. However, since the GPS/DR positionand heading error are large, map matching is performedonce to correct position and heading. Because the posi-tion and heading error are large, they cause a largeresidual in the measurement update. After the initializa-tion, the time update is conducted by the input vector.The increments from ICP scan matching are based onthe vehicle frame. Therefore, we need to transform tothe world frame through the transformation matrix Gt .

0 0.2 0.4 0.6 0.8 1PL

0

10

20

30

40

50

60

PSR

PL & PSR

(a) (b)

(d)(c)

Figure 22: Example of PL and PSR threshold.

Peak

Side lobe

Figure 21: Example of peak and side lobe.


After the time update, we derive x̂t+1 and Pt+1. x̂t+1 isthe predicted state vector, and Pt+1 is the predictedcovariance matrix.

H =

1 0 0

0 1 0

0 0 1

,

yt = z −Hx̂t = δx δy δθT

12

In equation (12), we defined observation matrix andmeasurement residual. The measurement residual isderived from map matching.

K = P−t HT HP−t H

T + R −1,

x̂+t = x̂−t + Kyt ,

P+t = I − KH P−t

13

Equation (13) is the measurement update. After themeasurement update, we derive x̂+t and P

+t . Further, x̂

+t

and P+t are used for the next state estimation.

6. Experimental Result

In this section, we analyze the performance of precisevehicle localization using a binary road marking gridmap through experiments.

Figure 23 shows the experimental area. The experimentwas carried out in Gangnam, Seoul, which is surrounded bybuildings, and was carried out in a traffic congestion situa-tion. In addition, data collected from two laps were com-pleted in the experimental area and the length of theexperimental area was approximately 5 km. Figure 24 is typesof road markings in the experimental area. As shown in thisfigure, there are many kinds of road markings on the road.Therefore, it is possible to obtain robust localization perfor-mance by using them. We used a commercial GPS/DR(Micro-Infinite CruzCore DS6200) and 32-channel 3DLIDAR (Velodyne HDL-32E). Generally, the localizationmethod using 3D LIDAR-based road marking grid mapshas intensity information in the grid [6, 7]. Therefore, wecompared vehicle localization results using the binary roadmarking map and the intensity road marking map. Throughthis, we can demonstrate the advantages of using the binaryroad marking map mentioned in Section 3, as well as thecomparison of localization performance using intensity roadmarking map and binary road marking map.

Table 3 shows the ratio of the matching result reliabil-ity of the intensity map and binary map. It is calculated asthe ratio between the entire map matching result and thereliable matching result derived from the evaluation ofthe position matching result in Section 5. As shown in thistable, map matching using a binary map is more reliablethan using an intensity map and better matching perfor-mance can be expected.

In Figures 25 and 26, the blue line represents the posi-tion error of the GPS/DR, the red line represents the

127.054 127.056 127.058 127.06 127.062 127.064

37.507

37.508

37.509

37.51

37.511

37.512

37.513

37.514

Figure 23: Experimental area.


position error of the localization result using the intensitymap, and the black line represents the position error ofthe localization result using the binary map. As shown inTable 4, the lateral and longitudinal RMS position errorsusing the intensity map are greater than those using thebinary map because the map matching using the intensitymap has an ambiguity greater than the map matching usingthe binary map. Intensity data provides 8 bits of informa-tion. Therefore, the difference in the intensity level betweenthe global map and local map affects the localization per-formance. In particular, when we use 3D LIDAR, the inten-sity level depends on the vertical layers, even though thesame road marking is scanned. On the other hand, thebinary map is made of binarized intensity. Therefore, ithas information only in the form of 0 s and 1 s. Therefore,the above ambiguity problem does not occur.

In Figures 27 and 28, the blue line represents the CDFof the position error result using the intensity map andthe red line represents the CDF of the position error resultusing the binary map. Table 5 gives the position errorwith a 99% confidence level. It also shows that the errorwith the intensity map is larger than that with the binarymap. As shown in Table 5, the lateral error is under 0.5m

with a 99% confidence level using the binary map. Itmeans that the lane-keeping condition is satisfied forautonomous driving. On the other hand, when using theintensity map, the lateral error is more than 0.5m with a99% confidence level. In addition, the maximum error is0.70m for the intensity map and 0.26m for the binarymap. Therefore, it is possible to maintain the lane whenwe use a binary map for vehicle localization, while lanedeparture may occur when we use an intensity map. Also,the longitudinal error is under 0.5m with a 99% confi-dence level using the binary map. That is a very goodresult considering that the longitudinal error conditionfor safe autonomous driving is generally 1m. On the otherhand, the longitudinal error with a 99% confidence levelexceeds 1m when using the intensity map. In particular,the maximum error is 2.08m for the intensity map and0.55m for the binary map. Vehicle localization usingintensity map can create a dangerous situation due to alarge instantaneous error. On the other hand, when weuse a binary map for vehicle localization, the vehicle canbe driven more safely because of the small error.

Figure 29 shows the heading error. The intensity mapcontains intensity information of all objects on the road.Thus, heading estimation cannot be done using the mapmatching algorithm described in Section 5 because we cannotextract only road marking information. Therefore, we com-pared the heading results between GPS/DR with thoseobtained by using the binary map. Table 6 shows the RMSheading error. As shown in Table 6, when we use the binary

Table 3: Ratio of the matching result reliability.

Intensity map Binary map

92.6% 97.1%

Lane Letter Arrow

Crosswalk Symbol

Figure 24: Types of road markings in the experimental area.


map, the heading performance can be improved. Moreover,the maximum heading error was 2.12° for GPS/DR and1.45° for heading estimation using the binary map.

Thus far, we analyzed the localization result in the sameroad condition. However, common vehicle localization may

have different road surface conditions. Therefore, we com-pared the matching performance for different road surfaceconditions, as shown in Figure 29. However, there is a prob-lem that the ground truth cannot be set because the data aredifferent from each other. Therefore, we analyzed the match-ing performance using the PSR. Because the PSR is a param-eter that determines the sharpness of the correlation peak asdescribed in Section 5, the higher the PSR, the higher thematching performance will be.

Figure 30 shows a comparison of PSR between differentdata, and Table 7 shows the average of PSR. The globalmap is a wet road surface, and the local map is a dry road

0 5000 10000 15000Epoch (0.1 sec) Epoch (0.1 sec)

−20

−15

−10

−5

0

5

10

15Er

ror (

m)

Erro

r (m

)

Lateral position error Lateral position error

GPS/DRIntensity mapBinary map

0 2000 4000 6000 8000 10000 12000 14000−1

−0.5

0

0.5

1

1.5


Figure 25: Lateral position error.

0 5000 10000 15000Epoch (0.1 sec)

−20

−15

−10

−5

0

5

10

15

Erro

r (m

)

Longitudinal position error

Epoch (0.1 sec)

Erro

r (m

)

Longitudinal position error


0 2000 4000 6000 8000 10000 12000 14000−1

−0.5

0

0.5

1

1.5

2

2.5


Figure 26: Longitudinal position error.

Table 4: RMS position error.

RMS error (m) GPS/DR Intensity map Binary map

Lateral 8.78 0.19 0.05

Longitudinal 9.66 0.32 0.08


surface. As shown in this figure, the PSR of the binary map ishigher overall. Therefore, we can confirm that the matchingperformance of the binary map is better than the intensitymap even in different road surface conditions.

Thus far, we analyzed the experimental result of thebinary road marking grid map-based precise vehicle position

and heading estimation. The results show that the binaryroad marking map matching method can provide good posi-tion and heading estimation accuracy.

0 0.2 0.4 0.6 0.8 1Error (m)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Prob

abili

ty

CDF of lateral position error

Intensity mapBinary map

Figure 27: Cumulated distribution function (CDF) of the lateralposition error.

0 0.5 1 1.5 2 2.5Error (m)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Prob

abili

ty

CDF of longitudinal position error


Figure 28: CDF of the longitudinal position error.

Table 5: Position error with a 99% confidence level.

99% confidence level (m) Intensity map Binary map

Lateral 0.68 0.21

Longitudinal 1.44 0.36

0 5000 10000 15000Epoch (0.1 sec)

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Erro

r (de

g)

Heading error

GPS/DRBinary map

Figure 29: Heading error.

Table 6: RMS heading error.

GPS/DR Binary map

RMS error (degree) 0.46 0.26

0 500 1000 1500Epoch (0.1 sec)

0

10

20

30

40

50

60

70

PSR

valu

e

Comparison of PSR between different data


Figure 30: Comparison of PSR between different data.

Table 7: Average of PSR.

Intensity map Binary map

PSR 20.55 23.28


7. Conclusions

In this paper, we proposed the binary road marking gridmap-based precise vehicle localization method using 3DLIDAR. First, the intensity scan data obtained from 3DLIDAR was binarized using Otsu’s thresholding. After binar-izing the intensity, we generated the binary road markinggrid map and precise local map for map matching. The posi-tion and heading are estimated through the map matchingand navigation filter. In the experimental result, the 2D lat-eral RMS error was approximately 0.05m and longitudinalRMS error was approximately 0.08m. In addition, a CDFanalysis of the error showed that the lateral error was0.21m and longitudinal error was 0.36m with a 99% confi-dence level. Thus, we confirmed that vehicle localizationusing the binary road marking grid map provides very pre-cise and reliable estimation results.

The advantage of using the binary road marking gridmap is as follows. First, a very small size map can be gener-ated. A typical grid map increases the size exponentiallywhen the grid size is smaller and map scale is bigger. How-ever, the binary road marking grid map has only 1-bit infor-mation. Therefore, map size can be reduced efficiently.Second, unlike the intensity road marking information wherethe level changes according to the road surface condition,binary road marking information provides reliable and accu-rate estimation results that can be used even if the intensitychanges. Therefore, map matching using road marking ispossible under any situation.

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that there is no conflict of interestregarding the publication of this paper.

Acknowledgments

This research was supported by a grant (18TLRP-C113269-03) from the Transportation Logistics Research Programfunded by theMinistry of Land, Infrastructure and Transportof Korean government.

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Precise Vehicle Position and Heading Estimation Using a Binary Road Marking Map · 2019. 7. 30. · 1-bit information instead of probability, map matching is possible by the simple