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this direction; however, the path containing maximum pixels was often chosen
but incorrect.
Given the FHA specifications of lanes being 12ft wide [13] and assuming
that the vehicle is traveling in the middle of a straight road, the expected ideal
locations of left and right lane marker centers are shown in pink. The major
axis projection of an object is expected to be within the trapezoid at 0ft and
30ft to be considered as either a left or right lane marker candidate. The axis of
symmetry of the trapezoid is aligned with ideal lane marker locations with the
short base set to a length of 8ft, i.e. 4ft on either side of the ideal lane location
in the IPM image. The length of the long base is set to entirely accommodate
a circular arc within the 0-30ft range. This arc is assumed to represent lane
markers on a curve and is shown in purple in Fig. 6. The radius of curvature of
the arc is set to 65ft which is the American Association of State Highway and
Transportation Ocial's (AASHTO) recommendations for minimum radius of
curvature for a horizontal road curve with e=4.0% superelevation when traveling
at speed of 20mph [14]. An isosceles trapezoid is chosen as the shape of the green
window as opposed to a rectangle or triangle to allow detection of lane markers
on a curve that may be offset from the ideal lane locations while at the same
time reduce detection of artifacts or other markers far away from the vehicle. In
the case that a solid or broken line exists inside the trapezoid as shown by the
orange object, the pixel locations of the object are sampled at one foot intervals
shown by the vertical black lines in Fig. 6 within the 0-30ft range. The black
dots in each interval will serve as the measurements for the Kalman filter (see
next section).
5T king
The Kalman filter is used to estimate the lane marker movements from one frame
to next. Measurements are acquired by sampling the object at one foot intervals
inside the trapezoid as described earlier; consequently, separate Kalman filters
are evaluated at every interval for both left and right lane markers. The state
vector and corresponding equations are set as
x
(
n
)=
x
(
n
)
x
(
n
)
T
(3)
x
(
n
+1)=
11
01
x
(
n
)+
N
(0
,σ
w
1
)
N
(0
,σ
w
2
)
(4)
y
(
n
)=
10
x
(
n
)+
N
(0
,σ
v
) (5)
where
x
(
n
) is the position or y-value and
x
(
n
) is the velocity of the lane marker
in each interval. The noise in the state and measurement equations is assumed to
be white and each process is assumed to be uncorrelated with the others. After
initialization, if no measurement is made at a particular interval, the Kalman
filter relies on its prediction to produce the estimate. However, after 50 sequen-
tial predictions, it is deactivated at that particular interval to avoid producing
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