A Gap between Simulation and Practice for Recursive Filters: On the State Transition Noise

TL;DR

This paper highlights the discrepancy between simulation models and real-world practice in recursive filters, emphasizing the importance of matching simulation noise to filter speed for accurate evaluation.

Contribution

It clarifies the impact of mismatched simulation noise on filter performance evaluation and advocates for using appropriate noise levels aligned with filter sampling periods.

Findings

Mismatched simulation noise can lead to inaccurate filter performance assessment

Proper noise matching improves the validity of simulation-based evaluations

Highlights a common oversight in filter benchmarking practices

Abstract

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.