Estimation of the parameters of a second order nonlinear system

We have presented an approach to estimate the parameters of a memoryless quadratic transformation based on the third order cumulant sequence sample of noisy measurement. The derivations are valid for zero mean measurement noise which is symmetrically distributed and is independent of the nonlinear process. We exploit the property of third order cumulants that they are identically zero for symmetric distributions. What we have here are just preliminary results. Comparisons have to be made — both in terms of theory and experiments — with techniques such as the least squares and maximum likelihood estimators with different contaminating noise characteristics. Extensions to dynamic second order nonlinear systems need to be made. Work related to these problems is in progress.

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