Error bounds for Kalman filters on traffic networks

Abstract

This work analyzes the estimation performance of the Kalman filter (KF) on transportation networks with junctions. To facilitate the analysis, a hybrid linear model describing traffic dynamics on a network is derived. The model, referred to as the switching mode model for junctions, combines the discretized Lighthill-Whitham-Richards partial differential equation with a junction model. The system is shown to be unobservable under nearly all of the regimes of the model, motivating attention to the estimation error bounds in these modes. The evolution of the estimation error is investigated via exploring the interactions between the update scheme of the KF and the intrinsic physical properties embedded in the traffic model (e.g., conservation of vehicles and the flow-density relationship). It is shown that the state estimates of all the cells in the traffic network are ultimately bounded inside a physically meaningful interval, which cannot be achieved by an open-loop observer.

Flows of Substances in Networks and Network Channels: Selected Results and Applications

“…The mathematical aspects of network flow modeling are also of primary interest [ 122 , 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 ]. There has been special interest in research on the maximum flow problem [ 131 , 132 , 133 , 134 , 135 ] and finding the shortest path [ 136 , 137 , 138 ].…”

Autonomous vehicles: From vehicular control to traffic contro

“…Note that the theoretical performance analysis of traffic estimators at transportation networks with junctions described in Section 4.3.2 has fewer results. The set-valued estimation approach [77], and the work [131] deals with traffic dynamics at junctions, and all the results in [25,69,97,140] are restricted to one-dimensional road stretches without considering junction dynamics.…”