Derivative abduction using a recurrent network architecture for parameter tracking algorithms

Abstract

To model the behaviour of complex natural and physical systems, the authors have recently developed a number of explicit static algorithms to estimate the parameters of recurrent second order models that approximate the behaviour of these complex higher order systems. These algorithms rely on the availability of the time derivatives of the trajectory. In this paper a cascaded recurrent network architecture is proposed to 'abduct' these derivatives in successive stages. The technique is tested successfully on a wide range of parameter tracking algorithms ranging from the constant parameter algorithm that only requires derivatives up to order 4 to an algorithm that tracks two variable parameters and requires up to the 8/sup th/ time derivatives.