  The Kalman Filter (KF) parameters are traditionally determined by noise
estimation, since under the KF assumptions, the state prediction errors are
minimized when the parameters correspond to the noise covariance. However,
noise estimation remains the gold-standard regardless of the assumptions - even
when it is not equivalent to errors minimization. We demonstrate that even
seemingly simple problems may include multiple assumptions violations - which
are sometimes hard to even notice. We show theoretically and empirically that
even a minor violation may largely shift the optimal parameters. We propose a
gradient-based method along with the Cholesky parameterization to explicitly
optimize the state prediction errors. We show consistent improvement over noise
estimation in tens of experiments in 3 different domains. Finally, we
demonstrate that optimization makes the KF competitive with an LSTM model -
even in non linear problems.
