Estimating time-varying nonlinear autoregressive model parameters by minimizing hypersurface distance

A nonleast-squares (non-LS) based method is presented for modeling time-varying (TV) nonlinear systems. The proposed method combines basis function technique and minimization of hypersurface distance (MHD) to combat TV and nonlinear dynamics, respectively. The performance of TVMHD is compared to the LS and total LS methods using simulation examples as well as human heart rate data recorded during different body positions. With all data, TVMHD significantly outperforms the two other methods by a factor of one order of magnitude; the LS-based methods require double the number of parameters than TVMHD requires to obtain similar residual error values. The significance of TVMHD is that due to its accurate parameter estimates concomitant with a fewer number of parameters, we now have the possibility of pinpointing parameters that may be of physiological importance, where such application will be especially useful in discriminating diseased conditions. Furthermore, our algorithm allows discrimination of model terms, which are TV or time invariant, by examining those basis function coefficients that are designed to capture TV dynamics. However, it should be noted that the main disadvantage of TVMHD is that it requires significantly greater computational time than the LS-based methods.