A seminar at the Department of Maths & Stats, University of Otago, in May 2016.
Title: Trajectory Estimation of Time Series GPS data with Adaptive Smoothing Spline
Abstract: GPS units record time series data of a moving object. Connecting position points consequently, will represent the trajectory of an individual or a vehicle. However, sparse points and data errors will give a trajectory with angels, which are unlike for a moving object. Smoothing spline methods can efficiently build up a more smooth trajectory. In conventional smoothing spline, the objective function tries to minimize errors of positions with a penalty term, who has a single parameter that controls the smoothness of reconstruction. Adaptive smoothing spline extends single parameter to a function varying in different domains and adapting the change of roughness. In this talk, I will introduce a tractor spline that incorporates both position and velocity information but penalizes excessive accelerations. The penalty term is dependent on mechanic boom status. A new parameter, which controls the errors of velocity, and adjusted penalty terms, which adapts to a more complicated curvature status, are introduced to the new objective function. We develop cross validation techniques to find the three smoothing parameters of interest. A short discussion of the relationship between spline method and Gaussian Process Regression will be given. A simulation study and real data example are presented to demonstrate the effectiveness of this new method.
