  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 present simulated experiments which demonstrate that NSFG
is more robust and computes solutions over an order of magnitude faster than
state-of-the-art sampling techniques. Similarly, we compare NSFG to
state-of-the-art Gaussian and non-Gaussian SLAM approaches and demonstrate that
NSFG is notably more robust in describing non-Gaussian posteriors.
