Nonlinear autoregressive and nonlinear autoregressive moving average model parameter estimation by minimizing hypersurface distance

The least squares (LS) can be used for nonlinear autoregressive (NAR) and nonlinear autoregressive moving average (NARMA) parameter estimation. However, for nonlinear cases, the LS results in biased parameter estimation due to its assumption that the independent variables are noise free. The total least squares (TLS) is another method that can used for nonlinear parameter estimation to increase the accuracy of the LS because it specifically accounts for the fact that the independent variables are noise corrupted. TLS has its own limitations, however, mainly because it is difficult for the method to isolate noise from the signal components. We present a new method that is based on minimization of hypersurface distance for accurate parameter estimation for NAR and NARMA models. Computer simulation examples show that the new method results in far more accurate NAR and NARMA model parameter estimates than do either the LS and TLS, with noise that is either white or colored, and retains its high accuracy even when the signal-to-noise ratio (SNR) is as low as 10 dB.