Limits to resolution in nonlinear least squares model fitting

This note discusses properties of least squares estimates of the parameters of weighted sum models. These are weighted sums of functions of the same nonlinearly parametric family as, for example, multiexponentials. The unknown parameters are the weights and the non-linear parameters. It is shown that errors in the observations may preclude the resolving of distinct but close nonlinear parameters. The results presented generalize earlier work in which the weights were assumed known.