Kalman Filter Design for Intermittent Optical Wireless Communication Systems on Time Scales

Abstract

Time-scale theory, due to its ability to unify the continuous and discrete cases, allows handling intractable nonuniform measurements, such as intermittent received signals.In this work, we address the state estimation problem of a vibration-induced intermittent optical wireless communication (OWC) system by designing a Kalman filter on time scales. First, the algorithm of the time-scale Kalman filter is introduced and a numerical example is given for illustration. Then the studied intermittent OWC system is presented, and experimental data are collected to determine the time scale's form, which has bounded graininess (a.k.a, bounded time jumps). Finally, we design a Kalman filter on the previously defined time scale for the intermittent OWC system and critically analyzed its estimation performance. Moreover, the obtained conclusions are further validated on a reference system. The simulation results corroborate that the time-scale Kalman filtering technique is considerably promising to solve the state estimation problem with non-uniform measurements. This study reveals for the first time the feasibility of applying the time-scale Kalman filter theory to practical applications.

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“…where p and N , representing the process noise and observation noise, are independent, and follow normal distribution from 0 to Q and 0 to R, respectively In a real system, the process noise covariance matrix Q and the observation noise covariance matrix R change with each iteration [9]. The filtering process of the Kalman filter algorithm is shown in Fig.…”