Hyperbolic particle swarm optimization with application in rational identification

The rational function systems proved to be useful in several areas including system and control theories and signal processing. In this paper, we present an extension of the well-known particle swarm optimization (PSO) method based on the hyperbolic geometry. We applied this method on digital signals to determine the optimal parameters of the rational function systems. Our goal is to minimize the error between the approximation and the original signal while the poles of the system remain stable. Namely, we show that the presented algorithm is suitable to localize the same poles by using different initial conditions.