Inference of spatial distribution from multi-sensor measurements along trajectories with inaccurate location information

In this mini-project, we have defined the problem of inferring a spatially varying function given a finite set of noisy sensor observations. The challenge lies in the nonuniform noise in the input space of the observed data. The assumption is that samples generated along a particular trajectory tend to experience similar levels of noise in their location information. Therefore, we design an inference algorithm based on a Gaussian Process (GP) model with the flexibility to accommodate di↵erent noise variance associated with individual trajectories from which the samples are taken. Covariance Intersection (CI) has also been applied in our algorithm to fuse multiple sensor data of the same input location to the most informative form. An 1D experiment has been carried out with encouraging result that shows our algorithm works fairly well in this synthetic data with high accuracy estimate achieved when up to 48% of the samples are reported with wrong location labels.