Self-tuning asynchronous filter for linear Gaussian system and applications

In this paper, optimal filtering problem for a class of linear Gaussian systems is studied. The system states are updated at a fast uniform sampling rate and the measurements are sampled at a slow uniform sampling rate. The updating rate of system states is several times the sampling rate of measurements and the multiple is constant. To solve the problem, we will propose a self-tuning asynchronous filter whose contributions are twofold. First, the optimal filter at the sampling times when the measurements are available is derived in the linear minimum variance sense. Furthermore, considering the variation of noise statistics, a regulator is introduced to adjust the filtering coefficients adaptively. The case studies of wheeled robot navigation system and air quality evaluation system will show the effectiveness and practicability in engineering.