Kalman Filter for Discrete Processes With Timing Jitter

Abstract

The sampling interval generated by a local clock (biological, physical, or digital) is known to have a certain amount of errors (deterministic or random) called timing jitter. The latter can vary in nature and magnitude depending on how accurately the time scale is formed and the dynamic process is sampled. In state estimation, timing jitter can cause extra errors that cannot always be ignored. In this paper, we modify the Kalman filter for discrete processes with random timing jitter and call it jitter Kalman filter (JKF). The JKF is developed both intuitively and in the first-order approximation. It is shown that to cope with timing jitter, the system noise covariance acquires an additional term, which is proportional to the fractional jitter standard deviation and the process rate. Based on extensive numerical simulations of polynomial and harmonic models, it is shown that unlimited increase in the process rate leads to the fact that the error caused by jitter also grow without limit. Thus, jitter is dangerous for fast processes, but can be neglected in slow processes. Experimental testing has confirmed the high efficiency of JKF.