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2018 | OriginalPaper | Chapter

7. State Estimation in Freeway Traffic Systems

Authors : Antonella Ferrara, Simona Sacone, Silvia Siri

Published in: Freeway Traffic Modelling and Control

Publisher: Springer International Publishing

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Abstract

Freeway networks are generally equipped with different types of sensors which are able to measure traffic conditions in real time. Such sensors are placed in fixed positions on the road network and, hence, measure traffic variables in specific positions, often far from each other, because their number is limited by technological and financial issues. In addition, the measurements provided by traffic sensors can be noisy and affected by failures. On the other hand, for designing efficient traffic control and monitoring systems, it is required to know the values of the traffic variables (flow, density, speed) on the different road segments, in real time. For these reasons, the problem of traffic estimation is quite relevant and has attracted the attention of researchers in the past decades. Such a problem will have to face new challenges in the near future, due to the fast development of intelligent and connected vehicles, which are able to measure traffic states and to transmit them in real time. These new technologies will enable much more traffic information than in the past, but providing mobile data that are, by nature, disaggregated and asynchronous.

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Footnotes
1
An autonomous switched linear system with switching function s(k) expressed as
$$\begin{aligned}&{\underline{\mathop {x}}}(k+1)=A^{s(k)}{\underline{\mathop {x}}}(k) + B_{\omega }^{s(k)}{\underline{\mathop {\omega }}}(k) \\&{\underline{\mathop {z}}}(k)=C_x^{s(k)}{\underline{\mathop {x}}}(k) + C_{\omega }^{s(k)}{\underline{\mathop {\omega }}}(k) \end{aligned}$$
is said to have \(\gamma \)-performance if the undisturbed system (i.e. with \({\underline{\mathop {\omega }}}(k)= 0\)) is asymptotically stable and, under zero initial conditions, the following relation is verified
$$\begin{aligned} \sum _{k=0}^{\infty } {{\underline{\mathop {z}}}^{\text {T}}(k){\underline{\mathop {z}}}(k)} < \gamma ^2 \sum _{k=0}^{\infty } {{\underline{\mathop {\omega }}}^{\text {T}}(k){\underline{\mathop {\omega }}}(k)} \quad \forall {\underline{\mathop {\omega }}}(k)\in \mathscr {L}_2 \end{aligned}$$
.
 
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Metadata
Title
State Estimation in Freeway Traffic Systems
Authors
Antonella Ferrara
Simona Sacone
Silvia Siri
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-75961-6_7