Nested Sampling for Non-Gaussian Inference in SLAM Factor Graphs

Qiangqiang Huang, Alan Papalia, John J. Leonard

Abstract: We present nested sampling for factor graphs (NSFG), a novel nested sampling approach to approximate inference for posterior distributions expressed over factor-graphs. Performing such inference is a key step in simultaneous localization and mapping (SLAM). Although the Gaussian approximation often works well, in other more challenging SLAM situations, the posterior distribution is non-Gaussian and cannot be explicitly represented with standard distributions. Our technique applies to settings where the posterior distribution is substantially non-Gaussian (e.g., multi-modal) and thus needs a more expressive representation. NSFG exploits nested sampling methods to directly sample the posterior to represent the distribution without parametric density models. While nested sampling methods are known for their powerful capability in sampling multi-modal distributions, the application of the methods to SLAM factor graphs is not straightforward. NSFG leverages the structure of factor graphs to construct informative prior distributions which are efficiently sampled and provide notable computational benefits for nested sampling methods. We compare NSFG to state-of-the-art sampling approaches and Gaussian/non-Gaussian SLAM techniques in experiments. NSFG performs most robustly in describing non-Gaussian posteriors and computes solutions over an order of magnitude faster than other sampling approaches.s We believe the primary value of NSFG is as a reference solution of posterior distributions, aiding offline accuracy evaluation of approximate distributions found by other SLAM algorithms.