Introduction to Sign Error Spectral Observer

The sign error observer algorithm introduced in the paper is based on the relationship between the least mean square (LMS) [1] and resonator based observer algorithms [2][3], but utilizes the sign error LMS algorithm [4] for estimating the state variables of the observed system. Since the algorithm uses the signum of the error of the estimation, significant reduction in the amount of data required for the algorithm and in the computational demand can be achieved. Hence the utilization of this algorithm reduces design restrictions in systems with limited resources (e.g. bandwidth of communication channels). Possible utilizations of the observer are the Fourier decomposition of signals and adaptive control. An application example is an active noise control (ANC) system [8] that uses wireless sensor network (WSN) for noise sensing [6]. This is a straightforward field for the deployment of this algorithm, since ANC systems require lots of sensors and relatively high sampling frequency taking into account the typical bandwidth of the WSN’s radio standards (e.g. ZigBee) and the real time data transmission, so data reduction plays important role.