Memoryless nonlinear system identification with unknown model order

The problem of identifying a general memoryless input/output system from measurements of inputs and the corresponding outputs is considered. The measured output is sought to be represented as the linear combination of known functions of the input with some additive noise. The choice of model order to be used to fit the data is the main issue addressed, and a cost function involving the prediction error and the model order is derived. The cost function under certain approximations is shown to be similar to one obtained by H. Akaike (1969, 1970). If there is a real system generating the data, it is shown that the expected value of this cost function is always minimized at the true value of the order as long as the noise variance satisfies certain conditions. Asymptotic results for some cases are derived. An efficient algorithm is proposed for identifying the model order. Some simulation results using the proposed algorithm are also presented