  Kalman filters are routinely used for many data fusion applications including
navigation, tracking, and simultaneous localization and mapping problems.
However, significant time and effort is frequently required to tune various
Kalman filter model parameters, e.g. process noise covariance, pre-whitening
filter models for non-white noise, etc. Conventional optimization techniques
for tuning can get stuck in poor local minima and can be expensive to implement
with real sensor data. To address these issues, a new "black box" Bayesian
optimization strategy is developed for automatically tuning Kalman filters. In
this approach, performance is characterized by one of two stochastic objective
functions: normalized estimation error squared (NEES) when ground truth state
models are available, or the normalized innovation error squared (NIS) when
only sensor data is available. By intelligently sampling the parameter space to
both learn and exploit a nonparametric Gaussian process surrogate function for
the NEES/NIS costs, Bayesian optimization can efficiently identify multiple
local minima and provide uncertainty quantification on its results.
