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.
翻译:在系统识别方面,用有限的观测来估计一个模型的参数,结果不易辨别。为了应对这一问题,我们建议采用新方法,同时选择和估计敏感参数,作为关键模型参数参数,并将其余参数固定为一组典型值。我们的方法是作为非线性最低方正方数估计器,根据参数偏离一组典型值的情况,定出L1值。首先,我们提供拟议估算值的一致性和奥克莱特特性,作为理论基础。第二,我们根据Levenberg-Marquardt优化提供一种新颖方法,从数字上找到所拟订问题的解决方案。第三,为了显示有效性,我们提出一种应用,从有限数据中找出10个人类主体头部位置跟踪任务的生物机械性参数模型。在模拟研究中,估计参数的差异比没有L1常规值的估计参数减少96.1%,我们的方法改进了模型解释,在将参数数量上进行估计,同时从数字上找到所拟订问题的解决方案。此外,我们提出的一个应用是,根据有限数据对10个人类主体进行头方位跟踪任务的生物机械性准度定位模型模型模型模型模型模型模型模型,在8.2.5%以上,我们估计的精确度参数比正常度参数的比正常度的参数减少54倍。