Direct and indirect least squares methods in continuous-time parameter estimation

The discrete-time least squares approach is extended to the estimation of parameters in continuous nonlinear models. The resulting direct integral least squares (DILS) method is both simple and numerically efficient and it usually improves the mean-squared error of the estimates compared with the conventional indirect least squares (ILS) method. The biasedness of the DILS estimates may become serious if the sample points are widely spaced in time and/or the signal-to-noise ratio is low and so a continuous-time symmetric bootstrap (SB) estimator which removes this problem is described. The DILS, SB and ILS methods form a three-stage procedure combining the robustness and numerical efficiency of direct methods with the asymptotic unbiasedness of ILS procedures.