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A Lane Change Detection Approach using Feature Ranking with
Maximized Predictive Power
Julian Schlechtriemen1, Andreas Wedel2, Joerg Hillenbrand3, Gabi Breuel4, Klaus-Dieter Kuhnert5
Published in: 2016 IEEE Intelligent Vehicles Symposium (IV), DOI: 10.1109/IVS.2014.6856491.
© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media,
including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers
or lists, or reuse of any copyrighted component of this work in other works.
Abstract— Risk estimation for the current traffic situation
is crucial for safe autonomous driving systems. One part
of the uncertainty in risk estimation is the behavior of the
surrounding traffic participants. In this paper we focus on
highway scenarios, where possible behaviors consist of a change
in acceleration and lane change maneuvers. We present a novel
approach for the recognition of lane change intentions of traffic
participants.
Our novel approach is an extension of the Na¨
ıve Bayesian
approach and results in a generative model. It builds on the
relations to the directly surrounding vehicles and to the static
traffic environment. We obtain the conditional probabilities of
all relevant features using Gaussian mixtures with a flexible
number of components. We systematically reduce the number
of features by selecting the most powerful ones. Furthermore
we investigate the predictive power of each feature with respect
to the time before a lane change event.
In a large scale experiment on real world data with over
160.781 samples collected on a test drive of 1100km we trained
and validated our intention prediction model and achieved a
significant improvement in the recognition performance of lane
change intentions compared to current state of the art methods.
I. INTRODUCTION
Scene understanding and scene interpretation are crucial
for the progress from assisted to semi-autonomous or even
fully autonomous driving. Especially the task of risk assess-
ment has to be thoroughly performed by an autonomous car
as the driver is not in the loop. The intention recognition,
whether an observed vehicle will change its lane in the near
future is a special case of this challenge. In this paper we
focus on estimating the probability for such a lane change
event. Such probabilistic information is not only needed to
determine the risk of the current situation, it might also be
important for an adaptive cruise control system. It creates the
1Julian Schlechtriemen is with Daimler AG, 71034 B¨
oblingen, Germany
julian.schlechtriemen@daimler.com
2Andreas Wedel is with Daimler AG, 71034 B¨
oblingen, Germany
andreas.wedel@daimler.com
3J¨
org Hillenbrand is with Daimler AG, 70163 Sindelfingen, Germany
joerg.hillenbrand@daimler.com
4Gabi Breuel is with Daimler AG, 71034 B¨
oblingen Germany
gabi.breuel@daimler.com
5Klaus-Dieter Kuhnert is with the Institute for Real-
Time Learning Systems, University of Siegen, Germany
kuhnert@fb12.uni-siegen.de
© 2014 IEEE. Personal use of this material is permitted. Permission from
IEEE must be obtained for all other uses, in any current or future media,
including reprinting/republishing this material for advertising or promotional
purposes, creating new collective works, for resale or redistribution to
servers or lists, or reuse of any copyrighted component of this work in
other works.
Fig. 1. Typical traffic scene on highways. Can a lane change be detected
before lateral speed and offset to the lane center become significant?
possibility for an early reaction to cut-in maneuvers. This is
not only desirable under comfort aspects but also helps to
reduce fuel consumption by avoiding unnecessary accelera-
tion. Lane change recognition or prediction has already been
investigated in various publications, see Sec. II. However, a
large part of the described methods is only able to detect
lane changes for the ego (system) vehicle. An often used
feature in this context for example is the yaw rate, which is
not directly measurable and can only be used as derived and
noise affected feature for other traffic participants. On the
other hand, more global information like the relation to the
vehicle in front, the traffic flow on the neighboring lanes,
the topology of the road, the distance to the next freeway
exit ramp and other factors influence the behavior of human
drivers and are not investigated in theses approaches. Another
problem which has to be taken into account, is the uncer-
tainty of the measured values which is significantly higher
for the measurements of observed vehicles in comparison
to the values relating to the ego vehicle. These aspects are
implicitly handled with our proposed approach. We also
investigate two important questions regarding lane change
recognition:
•How early can a lane change be detected based on all
the information available in a typical traffic scene?
•Which subset of all conceivable features shows the
best trade-off between classification performance and
a desirable small number of features?
In this paper, we propose a general bottom-up approach.
In the first step, we define relational features for a defined set
of surrounding vehicles. These include relative speeds, time
gaps, time-to-collision and the required acceleration to avoid
a collision with all related vehicles. On top, features like the
absolute speed, the distances to the relative left and right
lane marking, the curvature of the street, and the number of
available lanes to the left and right are collected. After the
collection step, we analyse the contribution of each feature
to the classification results in different time-intervals before
the lane change event.
To estimate the conditional probabilities of the different
features, we analyze the respective distributions. In [1], the
authors show that a single Gaussian distribution is often
not precise enough. In order to meet the real-time and
low memory-usage requirements of embedded systems, we
chose to use the Gaussian mixture approach. We use the
Schwarz Criterion [2] to ensure maximum entropy for our
model selection.
The paper is structured as follows. In Section II related
work is described. The perception model and the situation
description parameters are derived in Section III. Finally, we
give an overview on our experimental results in Section IV
and conclude with Section V.
II. REL ATE D WORK
The term ”recognition of driving maneuvers” is strongly
linked to terms like prediction, intention recognition and
situation assessment. In this section, we review approaches
addressing the ”recognition of lane change maneuvers” be-
fore giving a short overview of our environment model and
used features in the following section.
In [3], a Support Vector Machine(SVM) is used with a
feature vector consisting of the lateral relative position of
a car in the lane, the steering angle relative to the road
curvature and the first derivatives of these two features. By
using a Bradley Terry Model [4], a probabilistic output is
generated from the result of the SVM. This probabilistic
output is then processed by a Bayesian filter for the fi-
nal lane change intention prediction. By using this filter
the precision of the classification algorithm is significantly
improved, mainly due to noise in the input data. In [5],
Feed Forward Neural Networks (FFFN), Recurrent Neural
Networks (RNN) and SVMs were compared using different
combination of features consisting of lateral relations to the
corresponding lane, steering angle, the Time To Collision
(TTC) to the preceding car and the curvature of the road. It
was shown, that the SVM achieved the best results followed
by the RNN. Furthermore, the usage of the TTC to the Car
in Front reduced the false positive and false negative rate
and increased the prediction time. In [6], an object oriented
Bayesian network is used for the recognition of lane changes.
The feature set consists of the movement in relation to the
assigned lane and a free-space representation. The approach
predicts a lane change 0.6s earlier than a standard adaptive
cruise control system. The authors point out that there is
always a trade-off between an earlier detection and the false
positive rate. In [7], a Case-based reasoning approach was
used to detect cut-in maneuvers of vehicles into the lane
of a system vehicle with a feature set based on the relative
distance and velocity to the vehicle in front and the system
vehfo
vehfr
vehl
vehbl
vehbo
vehbr vehr
vehfl
Fig. 2. Relation vectors Rrare generated to the cars which directly
surround the observed vehicle o, for which we want to determine PLcL
PLcR and PF lw. In this example we show the vector Rf l, which is the
relation between oand the vehicle positioned relative in (f)ront on the (l)eft
lane.
vehicle. The final features were chosen using temporal ab-
straction and consisted of trend and level information of the
distance and relative velocity. It was shown that the approach
has the ability to detect lane change maneuvers until 2.3s
before a car is in the target lane with a percentage of correct
classifications of 79%.
The contributions of our paper are twofold. We consider
our main contribution to be the investigation of the most
relevant features for lane change recognition in highway
scenarios. This is quite unlike previous strategies [3] [6]
[7] where the feature set was chosen by experience. We
investigate the relevance of the features against the time
until a vehicle changes its lane assignment. The secondary
contribution concerns the use of the Na¨
ıve Bayes Classifier
using Gaussian mixtures for probability density estimation.
We show, that this simple strategy is able to achieve the
best results without the additional need of more sophisticated
methods like Gaussian Filtering and the Hidden Markov
Models. Because the term prediction time is not used con-
sistently in the different approaches, we need to determine
a time reference. All our time statements refer to the time-
point when the center of a vehicle crosses the lane marking.
This time-point is relatively earlier than the time reference
used in [6] [7] but consistent with the research done in [3].
III. PROP OSE D APPRO ACH
In the following section, we compare three classification
algorithms in III-D, which need distribution estimates de-
scribed in III-B. In III-C we explain the strategy used for
the selection of the features, which were used as input for
our classification algorithm, where the environment model
consisting of all possible features is specified in III-A. The
performance of the classifiers will be compared in Sec. IV.
A. Environment Model
All data used in the environment model is measured
by an ego vehicle, which is equipped with a front facing
TABLE I
DES CRIP TION O F THE EVAL UATE D FEATU RE S fFOR A N OB SE RVE D VE HI CL E o
R f description constraint
Rrdrel
x,r longitudinal distance between ovs. related vehicle r
vrel
x,r longitudinal relative speed between ovs. related vehicle r
areq
x,r longitudinal decleration required for oto avoid a collision with the related vehicle rconstant acceleration
ttcx,r time to a longitudinal collision between ovs related vehicle rconstant acceleration
τx,r timegap between oand related vehicle r
vy,r lateral velocity of a related vehicle r
Rlane dml
ylateral distance between the center of oand left marking
dmr
ydistance between the center of oand right marking
dcl distance between center of oand centerline of assigned lane
ttcrmr
ytime to cross the right marking of assigned lane for oconstant velocity
ttcrml
ytime to cross the left marking of assigned lane for oconstant velocity
areq
yrequired acceleration which is needed to stay in the current lane constant acceleration
ψangle of the observed vehicle relative to the direction of the lane
vylateral speed of the observed vehicle relative to the lane
nlanernumber of lanes on the right side of observed the vehicle
nlanelnumber of lanes on the left of observed the vehicle
tm
ltype of marking left (0 = dashed, 1 = solid)
tm
rtype of marking right (0 = dashed, 1 = solid)
Rinfr a c0curvature of the road clothoid model
da
xdistance to the next approach to the highway
de
xdistance to the next exit of the highway
va
xspeedlimit of the current highway section
stereo camera and several radar sensors to obtain a 360◦
field of view. It is obvious that the performance of the
proposed algorithm strongly depends on the quality of the
sensor measurements. Furthermore, the environment model is
simplified by using a curvilinear coordinate system along the
curvature of the road, in which all of the following measures
are computed. To reduce the overall number of the possible
features, which depend on relations to surrounding vehicles,
we only take the direct neighbor vehicles into account, see
Fig. 2.
Using the features from Tab. I, the feature vector Fsit is
therefore defined as
Fsit =RvRlane Rinf ra >(1)
where Rvis the concatenation of the relations to the neigh-
bouring vehicles,
Rv=Rfl Rf o Rf r RlRrRbl Rbo Rbr >.
The feature vector Fsit is computed every 100ms for every
measured vehicle with sufficient measurement confidence of
our system-vehicle and row-wise written into a database.
Even if it is obvious that some of those features are highly
dependent, we are interested in a subset of the information
which performs best in the proposed classification algorithm.
As above we denote the time where a lane marking is crossed
by the center of a vehicle as the time point of a lane change.
By an offline evaluation of the data, the time until the next
lane change to the left lane tLcL and a lane change to the
right lane tLcR were computed for every vehicle and later
on used for labeling.
B. Distribution model
Although most implementations of the Na¨
ıve Bayes Clas-
sification algorithm (see III-D) assume a normal distribution
of the variables, this is obviously not a valid assumption in
our case. For example, ttcrml
yfor lane changing vehicles
in the time interval 1s to 2s before the lane change event
strongly depends on different driver profiles. Because the
assumption of an univariate normal distribution is inappropri-
ate for a single feature (see Fig. 5 for example), we propose
to use a Gaussian mixture. This gives us the possibility to
precisely estimate the probability density [8] without using
a large amount of kernels, which would lead to a higher
consumption of memory and processing time.
The use of Gaussian mixtures results in the question which
number of kernels is optimal. This again depends on the
distribution of the features for which the probability density
function should be estimated. One option is to select the
number of kernels after visual data inspection. The second
way is the scoring of different models for the distribution
estimate. In case of Gaussian mixture models this is a trade-
off between the maximization of the likelihood function
(which leads to a larger amount of kernels and therefore
to the risk of overfitting) and the number of kernels. For
the scoring of the models, we use the Bayesian Information
Criterion (or Schwarz Criterion) [2]
BI C =−2∗ˆ
li(D) + ki∗ln(n)(2)
where ˆ
lis the log-likelihood of the data Daccording to the
current model iwith nsamples in Dand kifree parameters
in i. The value of kiis, in case of a Gaussian mixture the sum
of c−1probabilities, cmeans and cvariance estimates, where
cis the number of Gauss kernels. The model with the smaller
BIC should be preferred. To increase the robustness of our
approach against outliers, we use the DB-Scan algorithm [9]
to estimate one single Gaussian mixture distribution for every
(a) EM-Algorithm executed for
all values
(b) EM-Algorithm executed for
DB-SCAN clusters
Fig. 3. Difference between the models with the lowest BIC for EM
Algorithm used for all data or for the DB-SCAN clusters
value range where a continuous distribution exists (Alg. 1).
This is required because the expectation maximization (EM)
[10] algorithm is designed to work with missing values
and cannot distinguish between wrongly assigned numerical
values and the surrounding values of missing data, see Fig.
3.
Algorithm 1 Estimation of the Gaussian Mixture Distribu-
tion
1: procedure EST IMATE GMDISTRIBUTION(D,u)
2: [K,Pk] = dbscan(D)
3: for i←1, k do
4: [Ci,Σi, Pi] = EMB IC (DK)
5: result.push(Ce,Σe, Pe∗Pk(i))
6: end for
7: return(result)
8: end procedure
9: procedure EMBI C (D)
10: BI C =∞
11: for j←1, kmax do
12: [Cj,Σj, Pj]←EM(D,j)
13: [BI Ci]←computeBIC(Cj,Σj, Pj, D)
14: if BI Ci< BIC then
15: BI C ←BICi
16: [C, Σ, P ]←[Cj,Σj, Pj]
17: end if
18: end for
19: end procedure
C. Feature Selection
It is useful to find a small subset of features which
maximize the predictive power, in order to implement a
classification algorithm which can be executed in real-time
and optimizes the results of the Na¨
ıve Bayes Classifier. To
select this subset of features, which are useful to build a
good predictor, different techniques can be applied [11].
Another problem which has to be solved is, how early
a lane change manoeuver of an opponent vehicle can be
detected before it crosses the lane markings based on all the
potential features in Fsit. We propose the use of Area under
the Curve AUC of the Receiver Operating Characteristic
(ROC), which is useful for skewed distributions, because it
is insensitive to changes in class distributions [12]. We define
the classification task to the recognition of three maneuver
classes: lane-following F lw, lane change to the left lane
LcL and lane change to the right lane LcR. To handle
the problem, that ROC graphs can only handle two-class
problems, a ROC graph is generated for every class against
the remaining two classes. The area under the curve for
multiclass problems can be calculated according to [12] by
AUCtotal =X
c∈M
AUCc∗p(c)(3)
where Mis the aggregate of the maneuvers LcL,LcR and
F lw. To get a statement over the time, we take data at
different time intervals before a lane marking is crossed. We
can now denote a function for a feature vector Fwhich
describes the predictive power of the classifier Cat a time
instance tmbefore a lane change maneuver
AUCC
t(tm) = AUCC
total(Ft=tm)(4)
D. Classification Algorithm
The Na¨
ıve Bayes algorithm is a generative learning al-
gorithm. Its naivety is reasoned in the assumed conditional
independence between the different features. While it has
a higher asymptotic error than discriminative models, when
the number of training samples increases, it approaches its
asymptotic error much faster than a discriminative classi-
fication model [13]. Besides the classification performance
on real world applications is often surprisingly good [14].
In the following two subsections we give an overview over
the compared algorithms for probability estimation, where
decision making can be realized for example by the winner
takes all.
1) Na¨
ıve Bayes Algorithm: The probability of a sample
Z=f1, f2...fnwith the features fbelonging to a maneuver
mwith M={m|m∈ {F lw, LcL, LcR}} at a timepoint t
is
p(m|Zt)∝p(Zt|m)p(m)(5)
and
p(Zt|m) =
n
Y
i
p(fi|m)(6)
2) Hidden Markov Model and Gaussian Filtering: Be-
sides this, the probability p(m|Z0:t)is also of interest. It
can be computed using a Hidden Markov Model (HMM)
[15] by setting the outputs of the Na¨
ıve Bayes algorithm as
emissions of the HMM, see Fig. 4.
Em=p(m|Zt)(7)
The prediction step is then defined as:
¯p(Sk
t) = X
M
p(St=Sk|St−1=Sm)p(Sm
t−1)(8)
and the update step:
p(Sk
t) = ηp(EΣ
t|St=Sk)¯p(Sk
t)(9)
SLcL SFlw SLcR
ELcL ELcR
EFlw
Fig. 4. Hidden Markov Model for the three maneuver classes
with:
p(EΣ
t|St=Sk) = X
M
p(St=Sk|Em
t)p(Em
t)(10)
The conditional state transition probabilities of Eqn. 8 are
stored in the matrix Tand the conditional emission probabil-
ities of Eqn. 10 in the matrix E. For the proposed approach
of Bayesian filtering in [3], Eis set to the identity matrix
I.
IV. RES U LTS
We base our investigations on a database consisting of
feature vectors Fsit collected from 13 hours on German
highways. Our experimental vehicle was equipped with a
sensor fusion using automotive sensors consisting of a front-
facing stereo camera, front- and back-facing long range radar
sensors, and two sensors at the left and right side of the
vehicle. With a cycle-time of 100ms, a feature vector for
every observed and tracked vehicle using a single track
model [16] was written to the database. The database consists
of a total of 160781 samples. Labeling vehicles 2sbefore
a lane change event as positives samples results in a-priori
class probabilities of PLcL = 0.0051,PLcR = 0.0037 and
PF LW = 0.9911.
Due to the problem that positive examples are very rare,
evaluation metrics like accuracy,precision and the F1
measure are not well-conditioned to evaluate the performance
of the classifier [17], because even a classification algorithm
predicting every measured sample of a vehicle as Flw
would lead to an accuracy of 99,1% (corresponding to the
probability of PF lw). Some authors have therefore evaluated
the performance of their classification algorithm on nearly
equally distributed classes [3], [7]. In order to make use of
the non-equal distribution of our data set, we propose the
use of a balanced precision measure defined according to
the definition of balanced accuracy in [18] as
precisionbal =TPR
TPR+FPR (11)
and the balanced F1measure defined as
Fbal
1= 2 ∗precisionbal ∗recall
precisionbal +recall (12)
where TPRdenotes the true positive rate and FPR the false
positive rate. Both measures are independent from class skew
and are directly comparable to the results of precision and
F1of test data with equal distributed classes.
We divide our evaluation into the two parts: feature
evaluation and classification performance.
A. Feature Evaluation
In the first experiment, we approximated the probability
density functions for every feature and analyzed its pre-
dictive power. For this, we used single variable classifiers
and computed AUCCf
t(tm)values for every single variable
classifier Cffor the time interval [0s, 15s], see also III-C. By
selecting only values bigger than AUCC
t(tmax)> AU Cmin,
we were able to compute a timepoint tmax for which a
specific feature loses its predictive power for our lane change
recognition algorithm. For the result in Tab. II, we set
AUCmin = 0.7and sorted the features according to their
classification contribution.
One can clearly see from the results, that the relative
velocity to the front vehicle, vrel
x,fo, contributes significantly
already 2.2 seconds before the lane change event and the
lateral velocity of the vehicle with respect to its lane,
vy, contributes 2.0 seconds prior to the lane change. The
following features ttcrml
yand areq
yare clearly correlated to
the lateral velocity and therefore it is not surprising, that they
contribute similarly. The lateral displacement dcl
ycontributes
significantly up to 1.0 second before the lane change event.
All remaining features show less predictive power.
Therefore, we focus in the following on the three most
valuable features vrel
x,o,vy, and dcl
yas input for our clas-
sification algorithm. Fig. 5 depicts the probability density
functions for the three classes LcL,F lw, and LcR for these
chosen features.
B. Classification Performance
In the second experiment, we evaluated the classification
performance when combining the three features vrel
x,o,vy, and
dc
yl. Tab. III shows the result using the Na¨
ıve Bayes algorithm
using cross-validation with a winner takes all strategy. One
can clearly see, that a balanced performance score should be
used in order to compare the results with results from other
papers. As explained above, the precision does increase using
the balanced score which can be explained with the a-priori
class probabilities from the samples. The accuracy shows
a small decrease as expected, because of the class skew
with PF lw = 0.991 and therefore a dominating behaviour of
F lw in the evaluation. We then compared the Na¨
ıve Bayes
algorithm with Gaussian Filtering and the HMM approach,
TABLE II
PREDICTIVE POWE R OF F EATU RE S fAN D TH EI R SPE AR MA N’S R AN K
CORRELATION COEFFICIENT ρTO THE CHOSEN FEATURES
f
tmax
ρvrel
x,fo
ρ(vy)
ρdcl
y
vrel
x,fo 2.2 1 -0.05 -0.07
vy2.0 -0.05 1 0.15
ttcrml
y1.8 0.03 -0.65 -0.19
areq
y1.8 0.05 -0.96 -0.17
dcl
y1.0 -0.07 0.15 1
dmr
y1.0 -0.09 0.14 0.88
dml
y1.0 0.06 -0.12 -0.88
ttcrmr
y0.8 -0.06 0.69 0.2
areq
x,fo 0.8 0.62 -0.06 -0.06
TABLE III
EVALUATI ON O F TH E NA¨
IVE BAYES ALGORITHM USING 2-FO LD
CROSS-VALIDATI ON
fold
precisionLcL
bal
recallLcL
F1LcL
bal
precisionLcR
bal
recallLcR
F1LcR
bal
accuracybal
10.99 0.77 0.87 0.99 0.95 0.97 0.89
20.99 0.73 0.84 0.99 0.85 0.92 0.85
precisionLcL
recallLcL
F1LcL
precisionLcR
recallLcR
F1LcR
accuracy
10.43 0.77 0.55 0.17 0.95 0.29 0.99
20.37 0.73 0.49 0.39 0.85 0.53 0.99
see also III-D. For this, we reduced the output of the Na¨
ıve
Bayes algorithm via the winner takes all strategy to a binary
output. This output for each class has then been used to train
the Emission Matrix Eof our HMM:
E=
EF lw ELcl ELcr
SF lw 0.97 0.01 0.02
SLcl 0.35 0.60 0.05
SLcr 0.20 0.03 0.77
(13)
and accordingly, we determined the state transition matrix:
T=
SF lw
tSLcl
tSLcr
t
SF lw
t−10.99 0.0003 0.0003
SLcl
t−10.14 0.86 0
SLcr
t−10.15 0 0.85
.(14)
Fig. 6 shows the result from the Na¨
ıve Bayes Classificator
with the results of the Gaussian Filtering using recall and
precisionbal at different timepoints before a lane change
using the winner takes all strategy. As can be seen in
the figure, the Na¨
ıve Bayes Algorithm shows better results
without the use of Gaussian Filtering and even the use of
a HMM in Fig. 6 doesn’t improve the classification perfor-
mance. Reasons for the missing benefit of the HMM and the
Gaussian Filtering can be expected by the already Kalman-
Filtered lane and vehicle data, such that a filter in the domain
does not extract additional information. The predictive power
of the proposed Na¨
ıve Bayes Algorithm is depicted in Fig. 7
using the Receiver Operating Characteristic.
V. CONCLUSIONS
This paper presented a novel approach for the recognition
of lane change events utilizing a feature set which maximizes
the predictive power. In a large scale experiment, we showed
that our proposed approach is able to precisely detect lane
changes of other traffic participants up to 2.2s before the lane
assignment changes. We showed significant improvement
in the precision of the classification problem compared to
approaches, which focus only on the lateral behavior of
vehicles [11]. By investigating the most significant features,
we also showed, that the lateral velocity relative to the lane,
the relative velocity of the preceding car and the lateral offset
to the lane center are the most discrimant features for lane
change recognition. Future work involves the calibration of
the probabilities of the Na¨
ıve Bayes classifier [19] to obtain
more interpretable and better weighted values between the
manoveurs LcL and LcR.
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(a) dc
yl(b) vy(c) vrel
x,o
Fig. 5. Probability density functions of the different features, LcL (green), Fl w (blue) and LcR (red). One can see, that a good seperation between the
the three classes is possible for each of the chosen features
(a) LcL(Gaussianfiltering)(b) LcR(Gaussianfiltering)
(c) LcL(HM M )(d) LcR(HM M)
Fig. 6. Comparison between the Gaussian filtering (red) and the Na¨
ıve Bayes Algorithm (blue) in (a) and (b) for the recognition of the maneuver classes
LcL and LcR plotted against the time before a lane change occurs. Same in (c) and (d) for the comparison between the HMM (red) and the Na¨
ıve Bayes
Algorithm (blue). As can be seen in the graphs, the Na¨
ıve Bayes Algorithm is superior to the Gaussian Filtering and the results of the HMM in recall
and precisionbal
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Receiver Operating Characteristic of: Naive Bayes GM
AUC−left = 0.99124
AUC−right = 0.99519
False−Positive Rate
True−Positive Rate
ROC of left
ROC of right
(a) ROC-0-1s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Receiver Operating Characteristic of: Naive Bayes GM
AUC−left = 0.96961
AUC−right = 0.99116
False−Positive Rate
True−Positive Rate
ROC of left
ROC of right
(b) ROC-0-2s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Receiver Operating Characteristic of: Naive Bayes GM
AUC−left = 0.91695
AUC−right = 0.96985
False−Positive Rate
True−Positive Rate
ROC of left
ROC of right
(c) ROC-0-3s
Fig. 7. Receiver Operating Characteristic showing the predictive power of our proposed Na¨
ıve Bayes Algorithm for samples in different time intervals
before a lane-change
