  In order to evaluate and compare different recursive filters, simulation is a
common tool and numerous simulation models are widely used as 'benchmark'. In
the simulation, the continuous time dynamic system is converted into a
discrete-time recursive system. As a result of this, the state indeed evolves
by Markov transitions in the simulation rather than in continuous time. One
significant issue involved with modeling of the system from practice to
simulation is that the simulation parameter, particularly e.g. the state Markov
transition noise, needs to match the iteration period of the filter. Otherwise,
the simulation performance may be far from the truth. Unfortunately, quite
commonly different-speed filters are evaluated and compared under the same
simulation model with the same state transition noise for simplicity regardless
of their real sampling periods. Here the note primarily aims at clarifying this
problem and point out that it is very necessary to use a proper simulation
noise that matches the filter's speed for evaluation and comparison under the
same simulation model.
