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In the end, we can obtain the identification results:
v
f
=
e
θ
1
e
ρ
cr
=
(15)
1
√
−αα
5 Numerical Example
The simulation is validated using synthetic trac data from a section of sim-
ulated highway and the inputs signals are the speed measurements and flow
measurements from loop detectors. We assume
ξ
i
(
k
)and
ξ
i
(
k
) are zero-mean
Gaussian white measurement noises respectively to reflect the measuring inac-
curacies. That means the noisy speed and trac flow measurements are [20]:
v
mi
(
k
)=
v
i
(
k
)+
ξ
i
(
k
),
q
mi
(
k
)=
q
i
(
k
)+
ξ
i
(
k
), and
ξ
i
(
k
)
N
(0
,
0
.
01),
ξ
i
(
k
)
∼
N
(0
,
0
.
01). The identification result following the proposed procedure in noisy
conditions is shown in figure 3. The initial parameter estimated are selected:
v
f
(0) = 100 km/h,
ρ
cr
(0) = 20 veh/km/lane,
α
=1
.
5.
∼
Fig. 3.
Identification results
It can be seen that after a very short “warm up” period, with the evolution
of the highway trac dynamic, the key parameters of trac model can be iden-
tified rapidly and the identification results are consistent with the pre-setting
values. Therefore, we can apply the on-line identification result to subsequent
trac control scheme, such as ramp metering, and design the control algorithm,
including model-free control, adaptive control, PI control and so on. Ultimately,
this allows people to maneuver the trac in desired fashion.
6Con lu on
In this study, we have presented an on-line algebraic parameters identification
scheme by means of differential algebra and operational calculus. The free speed
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