We consider the problem of building continuous occupancy representations in dynamic environments for robotics applications. The problem has hardly been discussed previously due to the complexity of patterns in urban environments, which have both spatial and temporal dependencies. We address the problem as learning a kernel classifier on an efficient feature space. The key novelty of our approach is the incorporation of variations in the time domain into the spatial domain. We propose a method to propagate motion uncertainty into the kernel using a hierarchical model. The main benefit of this approach is that it can directly predict the occupancy state of the map in the future from past observations, being a valuable tool for robot trajectory planning under uncertainty. Our approach preserves the main computational benefits of static Hilbert maps — using stochastic gradient descent for fast optimization of model parameters and incremental updates as new data are captured. Experiments conducted in road intersections of an urban environment demonstrated that spatio-temporal Hilbert maps can accurately model changes in the map while outperforming other techniques on various aspects.

Understanding and predicting how influenza propagates is vital to reduce its impact. In this paper we develop a nonparametric model based on Gaussian process (GP) regression to capture the complex spatial and temporal dependencies present in the data. A stochastic variational inference approach was adopted to address scalability. Rather than modeling the problem as a time-series as in many studies, we capture the space-time dependencies by combining different kernels. A kernel averaging technique which converts spatially-diffused point processes to an area process is proposed to model geographical distribution. Additionally, to accurately model the variable behavior of the time-series, the GP kernel is further modified to account for non-stationarity and seasonality. Experimental results on two datasets of state-wide US weekly flu-counts consisting of 19,698 and 89,474 data points, ranging over several years, illustrate the robustness of the model as a tool for further epidemiological investigations.