This paper presents an adaptive Gaussian Mixture Model (aGMM) formulation for performing multiple-step probabilistic state predictions using a nonparametric Gaussian Process (GP) regression model. The presented prediction algorithm is applicable to any dynamic system that is challenging to model parametrically, but where data is available. Gaussian mixture elements are propagated through the GP by analytically evaluating expectation integrals for the moments of the output distribution. Two metrics are presented and compared for adaptively splitting the initial state distribution into a sum of Gaussians to reduce the effect of nonlinearities on prediction accuracy: (1) an analytical evaluation of the excess kurtosis which measures the non-Gaussianity of the output distribution, and (2) a weighted least-squares regression model which evaluates the local nonlinearity of the GP mapping with respect to the input distribution. In addition, an on-the-fly data selection method is presented to reduce the computational complexity associated with analytically evaluating the higher-order moments of the GP output distribution. The proposed adaptive GP-aGMM formulation is applied to the case of anticipating driver behavior at road intersections using a GP driver behavior model in combination with a parametric vehicle model. Prediction performance for this scenario is evaluated using driving data collected from three human subjects navigating a standard four-way intersection. Results demonstrate that the presented prediction algorithm is capable of accurately capturing multimodal behavior in the GP training data.
from robot theory http://ift.tt/1NrpOwp
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