Spatio-Temporal Hilbert Maps for Continuous Occupancy Representation in Dynamic Environments
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.
The paper presents an approach to maintain and update a spatio-temporal occupancy map. Given a spatial position and time, the map gives a probability that location is occupied. Their first approach uses pre-processing of laser scans to get observations of motion for objects and fit a GP per object to predict its future motion. These GPs are then used to define features for a logistic regression classifier that predicts the probability a location is occupied. They also propose an approach that uses random Fourier features. They provide experiments to verify the utility of both of these approaches with respect to prior art. 
Overall, the paper was well-written and proposes an improvement on an important problem.   As a general point, I'm not sure about the utility of including the Fourier features approach. Right now, that part of the paper seems under motivated and insufficiently evaluated. The best motivation is at the end of section 4, I think it would be better to move this further forward in the paper. If you decide to include this part of the paper, the experiments should be expanded. 5.2.1 currently shows that RFF features perform better in the temporal domain, but does not give a case for why RFF features are good for learning general motion dynamics or priors.  I think the explanation of the approach is section 3 is fairly approachable but it isn't until the end of the section that the reader gets a sense of what is being conveyed. I would include a simple example or step through of the process at the beginning of the section to give a broad strokes overview of the approach. It could also be useful to move Figure 1 higher up in the paper and refer to it earlier. I think it is also important to give some intuition for why the approach uses a feature embedding (rather than directly putting a GP on the occupancy map). It is done for efficiency reasons, but this is not made explicit for the reader.   Finally, the experiments section could use some work to make them more accessible. There are 6 experiments to evaluate the HF-STHM, please make it easier for readers to determine which figures and tables correspond to which experiments. Figure 2 shows the results of experiment 5.1.4, Figure 3 shows an illustration of the environment, Figure 4 shows the results of experiment 5.1.1, Figure 5 is not mentioned in the text (but I guess that it is the results of experiment 5.1.5). Please try to place figures in the order the appear in the text and include informative captions that explain the significance of the image. Please also make sure that each experiment clearly states: 1) the methods compared; 2) the dependent variables measured; and 3) the results of the experiment.    Figure 1 (b) also has some errors in it and should be revised.