Geometric Modeling of Vehicle Paths and Con dence Regions

In transportation systems today, there is a need to predict where a vehicle will be at a given time in order to ensure safety, expediency and eeciency of traf-c movement. There is generally a plan of travel, but outside forces (e.g., wind forecasting error, navigation system error) cause the actual path that is followed to be somewhat diierent from the planned path. The path of a vehicle is represented as a vector-valued curve in three-space. The construction of the conndence region about the curve takes advantage of an assumption that the deviation of the actual path from the predicted path will satisfy the conditions for a conditioned Brownian motion process. Using a cubic spline to estimate the predicted path, it is possible to obtain parameter values for the conditioned Brownian motion process, as well as error bounds for constructing the conndence region. An example is given to illustrate the forecasting technique, showing good results in predicting the path, constructing the conndence region, and detecting when the actual distribution of the deviation diiers from the estimated distribution.