  We present a new method to obtain spatio-temporal information from aggregated
data of stationary traffic detectors, the ``adaptive smoothing method''. In
essential, a nonlinear spatio-temporal lowpass filter is applied to the input
detector data. This filter exploits the fact that, in congested traffic,
perturbations travel upstream at a constant speed, while in free traffic,
information propagates downstream. As a result, one obtains velocity, flow, or
other traffic variables as smooth functions of space and time. Applications
include traffic-state visualization, reconstruction of traffic situations from
incomplete information, fast identification of traffic breakdowns (e.g., in
incident detection), and experimental verification of traffic models.
  We apply the adaptive smoothing method to observed congestion patterns on
several German freeways. It manages to make sense out of data where
conventional visualization techniques fail. By ignoring up to 65% of the
detectors and applying the method to the reduced data set, we show that the
results are robust. The method works well if the distances between neighbouring
detector cross sections do not exceed 3 km.
