Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems

Table 3

MSE ratios for nonlinear parameters (small samples).

Prior	Low noise				High noise
	SIR	LV	GMA	FHN	SIR	LV	GMA	FHN
Low	23.0	1.7	1.1	1.1	6.6	1.1	1.0	1.0
Medium	8.7	1.2	1.0	1.0	2.6	0.9	1.0	1.0
High	1.0	1.0	0.9	1.0	0.4	0.9	0.9	1.0

The table displays the MSE ratios (computed through squared errors averaged over Monte-Carlo simulations) of NLS and SLS for estimating the nonlinear parameters. The experimental setup is as in Table 1. Values larger than 1 in the table correspond to the cases where SLS performs better than NLS. Since the prior information regarding nonlinear parameters stays invariant (see Section 3.1 for details), the table in particular shows the effects that the quality of initial guesses for linear parameters has on the estimation accuracy of NLS in the case of nonlinear ones. The results suggest that, in some settings, vague prior knowledge regarding linear parameters may have an adversary effect on the accuracy of NLS with respect to the nonlinear parameters.