  Implicit neural representations and neural rendering have gained increasing
attention for bathymetry estimation from sidescan sonar (SSS). These methods
incorporate multiple observations of the same place from SSS data to constrain
the elevation estimate, converging to a globally-consistent bathymetric model.
However, the quality and precision of the bathymetric estimate are limited by
the positioning accuracy of the autonomous underwater vehicle (AUV) equipped
with the sonar. The global positioning estimate of the AUV relying on dead
reckoning (DR) has an unbounded error due to the absence of a geo-reference
system like GPS underwater. To address this challenge, we propose in this
letter a modern and scalable framework, NeuRSS, for SSS SLAM based on DR and
loop closures (LCs) over large timescales, with an elevation prior provided by
the bathymetric estimate using neural rendering from SSS. This framework is an
iterative procedure that improves localization and bathymetric mapping.
Initially, the bathymetry estimated from SSS using the DR estimate, though
crude, can provide an important elevation prior in the nonlinear least-squares
(NLS) optimization that estimates the relative pose between two loop-closure
vertices in a pose graph. Subsequently, the global pose estimate from the SLAM
component improves the positioning estimate of the vehicle, thus improving the
bathymetry estimation. We validate our localization and mapping approach on two
large surveys collected with a surface vessel and an AUV, respectively. We
evaluate their localization results against the ground truth and compare the
bathymetry estimation against data collected with multibeam echo sounders
(MBES).
