Gaussian Markov Random Fields for fusion in information form

2.5D maps are preferable for representing the environment owing to their compactness. When noisy observations from multiple diverse sensors at different resolutions are available, the problem of 2.5D mapping turns to how to compound the information in an effective and efficient manner. This paper proposes a generic probabilistic framework for fusing efficiently multiple sources of sensor data to generate amendable, high-resolution 2.5D maps. The key idea is to exploit the sparse structure of the information matrix. Gaussian Markov Random Fields are employed to learn a prior map, which uses the conditional independence property between spatial location to obtain a representation of the state with a sparse information matrix. This prior map encoded in information form can then be updated with other sources of sensor data in constant time. Later, mean state vector and variances can be also efficiently recovered using sparse matrices techniques. The proposed approach allows accurate estimation of 2.5D maps at arbitrary resolution, while incorporating sensor noise and spatial dependency in a statistically sound way. We apply the proposed framework to pipe wall thickness mapping and fuse data from two diverse sensors that have different resolutions. Experimental results are compared with three other methods, showing that, while greatly reducing computation time, the proposed framework is able to capture in large extend the spatial correlation to generate equivalent results to the computationally expensive optimal fusion method in covariance form with a Gaussian Process prior.