  Tracking underwater autonomous platforms is often difficult because of noisy,
biased, and discretized input data. Classic filters and smoothers based on
standard assumptions of Gaussian white noise break down when presented with any
of these challenges. Robust models (such as the Huber loss) and constraints
(e.g. maximum velocity) are used to attenuate these issues. Here, we consider
robust smoothing with singular covariance, which covers bias and correlated
noise, as well as many specific model types, such as those used in navigation.
In particular, we show how to combine singular covariance models with robust
losses and state-space constraints in a unified framework that can handle very
low-fidelity data. A noisy, biased, and discretized navigation dataset from a
submerged, low-cost inertial measurement unit (IMU) package, with ultra short
baseline (USBL) data for ground truth, provides an opportunity to stress-test
the proposed framework with promising results. We show how robust modeling
elements improve our ability to analyze the data, and present batch processing
results for 10 minutes of data with three different frequencies of available
USBL position fixes (gaps of 30 seconds, 1 minute, and 2 minutes). The results
suggest that the framework can be extended to real-time tracking using robust
windowed estimation.
