The correlation memory matrix for parameter estimation

摘要

Dynamic systems described by nonlinear differential or difference equations are abound in the literature. Until recently, estimation of system parameters has been mainly carried out using iterative (search) techniques such as conjugate gradient, steepest descent and evolutionary algorithms. These methods vary in terms of their noise immunity and robustness but they all tend to require a considerable number of iterations in order for the solution to converge, especially in the presence of noise. This is a disadvantage for systems requiring real-time control. In continuation of a series of papers utilizing linear associative memories (LAM) for parameter estimation, this paper proposes a non-iterative single-pass technique for estimating these parameters using the well-known correlation memory matrix (CMM), previously used in pattern recognition. The CMM method is used to estimate the parameters of the Lotka–Volterra predator–prey model and the Van der Pol oscillator. It is shown that this class of linear associators is superior to other types of LAM in that it provides equally good parameter estimates while requiring neither matrix inversion nor extensive training. As nonlinear (quadratic) associations are incorporated into the CMM, the method becomes more robust than the linear version.