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Requirements and Evaluation of a Smartphone Based Dead … 13
First of all, the behavior of the pedestrian has to be modeled. In general the 2D
position trajectory p pred ðtÞ of a pedestrian over a prediction interval t 2½0; t pred can
be expressed by
ZZ t
p pred ðÞ¼p t meas þ tv meas þ
0
a model ðÞdt t dt;
ð12Þ
where p meas and v meas are the position and velocity of the measurement, e.g. the
localization filter, and a model ðÞis t the predictive behavior model of the pedestrian.
[14, 15] show possibilities to choose the prediction model a model ðÞ. t If it is assumed
that p meas ; v meas and a model ðÞare t binomial normal distributed and time-invariant, the
predicted position p pred ðÞis t also binomial normal distributed with mean l pred ðÞ t
and covariance R pred ðÞ t
l pred ðÞ¼l t pred þ tl vmeas
þ t2 2 l a model
and ð13Þ
R pred ðÞ¼R t pred þ t 2 R vmeas þ t4 4 R a model
ð14Þ
Based on this information, the front collision probability P coll for a certain
prediction time t pred can be calculated as shown in [16]. It must be noted that the
uncertainty of position, velocity and orientation of the ego vehicle must be taken
into account for determining the collision probability P coll .
In the following, for simplicity, a diagonal covariance matrix R pred ðt TTC Þ ¼ r 2 I
is assumed. Figure 6 shows the front collision probability P coll of a pedestrian
Fig. 6 Front collision probability p coll respects to the standard deviation r of the position
measurement and the pedestrians crossing point p y of the vehicle front line. It is assumed that the
standard deviation r is not growing with the time. In the shaded area there is a front collision with
the vehicle. Only the half vehicle front line is represented with the middle of the vehicle at
p y ¼ 0m