  Determining the noise parameters of a Kalman Filter (KF) has been researched
for decades. The research focuses on estimation of the noise under various
conditions, since noise estimation is considered equivalent to errors
minimization. However, we show that even a seemingly small violation of KF
assumptions can significantly modify the effective noise, breaking the
equivalence between the tasks and making noise estimation a highly sub-optimal
strategy. In particular, whoever tests a new learning-based algorithm in
comparison to a (variant of) KF with standard parameters tuning, essentially
conducts an unfair comparison between an optimized algorithm and a
non-optimized one. We suggest a method (based on Cholesky decomposition) to
apply gradient-based optimization efficiently to the symmetric and
positive-definite (SPD) parameters of KF, so that KF can be optimized similarly
to common neural networks. The benefits of this method are demonstrated for
both Radar tracking and video tracking. For Radar tracking we also show how a
non-linear neural-network-based model can seem to reduce the tracking errors
significantly compared to a KF - and how this reduction entirely vanishes once
the KF is optimized. Through a detailed case-study, we also demonstrate that KF
requires non-trivial design-decisions to be made, and that parameters
optimization makes KF more robust to these decisions.
