  Many state estimation algorithms must be tuned given the state space process
and observation models, the process and observation noise parameters must be
chosen. Conventional tuning approaches rely on heuristic hand-tuning or
gradient-based optimization techniques to minimize a performance cost function.
However, the relationship between tuned noise values and estimator performance
is highly nonlinear and stochastic. Therefore, the tuning solutions can easily
get trapped in local minima, which can lead to poor choices of noise parameters
and suboptimal estimator performance. This paper describes how Bayesian
Optimization (BO) can overcome these issues. BO poses optimization as a
Bayesian search problem for a stochastic ``black box'' cost function, where the
goal is to search the solution space to maximize the probability of improving
the current best solution. As such, BO offers a principled approach to
optimization-based estimator tuning in the presence of local minima and
performance stochasticity. While extended Kalman filters (EKFs) are the main
focus of this work, BO can be similarly used to tune other related state space
filters. The method presented here uses performance metrics derived from
normalized innovation squared (NIS) filter residuals obtained via sensor data,
which renders knowledge of ground-truth states unnecessary. The robustness,
accuracy, and reliability of BO-based tuning is illustrated on practical
nonlinear state estimation problems,losed-loop aero-robotic control.
