  This work introduces a scalable filtering algorithm for multi-agent traffic
estimation. Large-scale networks are spatially partitioned into overlapping
road sections. The traffic dynamics of each section is given by the switching
mode model (SMM) using a conservation principle, and the traffic state in each
section is estimated by a local agent. In the proposed filter, a consensus term
is applied to promote inter-agent agreement on overlapping sections. The new
filter, termed a (spatially) distributed local Kalman consensus filter (DLKCF),
is shown to maintain globally asymptotically stable (GAS) mean error dynamics
when all sections switch among observable modes. When a section is
unobservable, we show that the mean estimate of each state variable in the
section is ultimately bounded, which is achieved by exploring the interaction
between the properties of the traffic model and the measurement feedback of the
filter. Based on the above results, the boundedness of the mean estimation
error of the DLKCF under switching sequences with observable and unobservable
modes is established to address the overall performance of the filter.
Numerical experiments show the ability of the DLKCF to promote consensus,
increase estimation accuracy compared to a local filter, and reduce the
computational load compared to a centralized approach.

Systems and Control