  In system identification, estimating parameters of a model using limited
observations results in poor identifiability. To cope with this issue, we
propose a new method to simultaneously select and estimate sensitive parameters
as key model parameters and fix the remaining parameters to a set of typical
values. Our method is formulated as a nonlinear least squares estimator with
L1-regularization on the deviation of parameters from a set of typical values.
First, we provide consistency and oracle properties of the proposed estimator
as a theoretical foundation. Second, we provide a novel approach based on
Levenberg-Marquardt optimization to numerically find the solution to the
formulated problem. Third, to show the effectiveness, we present an application
identifying a biomechanical parametric model of a head position tracking task
for 10 human subjects from limited data. In a simulation study, the variances
of estimated parameters are decreased by 96.1% as compared to that of the
estimated parameters without L1-regularization. In an experimental study, our
method improves the model interpretation by reducing the number of parameters
to be estimated while maintaining variance accounted for (VAF) at above 82.5%.
Moreover, the variances of estimated parameters are reduced by 71.1% as
compared to that of the estimated parameters without L1-regularization. Our
method is 54 times faster than the standard simplex-based optimization to solve
the regularized nonlinear regression.
