Thanks, and I broadly agree with what you say. It's only under specific conditions (system dynamics, process covariance, measurement matrices, and measurement covariance are all static) that the Kalman filter converges to the Wiener filter, as Kálmán says in his paper.
I would contest that the reason a frequency filter doesn't work on a gyroscope is not because it's a MIMO system (which frequency domain techniques can generalize to; you just end up with n x m transfer functions) but because the system is not static, so it doesn't satisfy the conditions that would cause the Kalman filter to converge to a fixed-coefficient filter.
I would contest that the reason a frequency filter doesn't work on a gyroscope is not because it's a MIMO system (which frequency domain techniques can generalize to; you just end up with n x m transfer functions) but because the system is not static, so it doesn't satisfy the conditions that would cause the Kalman filter to converge to a fixed-coefficient filter.