We deal with problems connected with the identification of linear dynamic systems in situations when inputs and outputs may be contaminated by noise. The case of uncorrelated noise components and the bounded noise case is considered. If also the inputs may be contaminated by noise, a number of additional complications in identification arise, in particular the underlying system is not uniquely determined from the population second moments of the observations. A description of classes of observationally equivalent systems is given, continuity properties of mappings relating classes of observationally equivalent systems to the spectral densities of the observations are derived and the classes of spectral densities corresponding to a given maximum number of outputs are studied.
This study addressed the modeling of route travel times (including their associated uncertainty) in urban networks based on taxi floating car data. The model decomposes observed link travel speeds into the expected speed (modeled with daily and seasonal profiles) and deviations thereof. The latter were shown to be strongly heteroscedastic by providing an explicit model for the time variance. Temporal and spatial correlations were considered with a vector autoregression framework. Modeling was supported by automatic model selection methods for identifying the relevant effects and providing one-step-ahead predictions. The potential of the proposed model was investigated with taxi floating car data from a real-world test site near the city core of Vienna, Austria. Various specifications of the vector autoregression model were tested and compared. Taxi floating car measurements of local speeds were found to be strongly heteroscedastic, a factor that must be considered in estimation of models for expected travel speeds. The modeling of the mean suggested no remaining daily or weekly patterns, and it was superior to simple models explaining travel speeds as a linear function of the travel speeds in the last time period. The variance model successfully captured heteroscedasticity. More complex models for link travel speeds, including temporal and spatial correlation, do not increase prediction accuracy consistently; the lack indicates that a sampling frequency of 15 min for floating car data in urban settings is too low for use of temporal dependencies for prediction. An introduced method for computing route travel time uncertainty showed variability over the day for a highly frequented route.
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