Efficient Clustering for Continuous Occupancy Mapping Using a Mixture of Gaussian Processes

Abstract

This paper proposes a novel method for occupancy map building using a mixture of Gaussian processes. Gaussian processes have proven to be highly flexible and accurate for a robotic occupancy mapping problem, yet the high computational complexity has been a critical barrier for large-scale applications. We consider clustering the data into small, manageable subsets and applying a mixture of Gaussian processes. One of the problems in clustering is that the number of groups is not known a priori, thus requiring inputs from experts. We propose two efficient clustering methods utilizing (1) a Dirichlet process and (2) geometrical information in the context of occupancy mapping. We will show that the Dirichlet process-based clustering can significantly speed up the training step of the Gaussian process and if geometrical features, such as line features, are available, they can further improve the clustering accuracy. We will provide simulation results, analyze the performance and demonstrate the benefits of the proposed methods.

An Improved Mixture Model of Gaussian Processes and Its Classification Expectation–Maximization Algorithm

“…As seen in this figure, the MGP is a more effective non-stationary model than the GP. However, the parameter estimation of the MGP is a challenge due to the unknown indicator variable (regarded as the latent variable) and the highly correlated sample [17][18][19][20]. The Markov Chain Monte Carlo (MCMC) method employing Gibbs sampling and hybrid Monte Carlo approximates the intractable integration and summation by the simulated sample of the indicator variable and parameter [6,7,[21][22][23], and it is commonly used in a system of partial differential equations [24,25].…”