基于变分法的参数约束估计方法研究

Study on Parameter Constraints Estimation Based on Calculus of Variations

提出一种基于变分法的参数约束估计方法,以获得渐进无偏的估计参数。通过分析包含待估参数的系统输入输出方程,构造变分法中的性能范函和约束方程,将传统的参数估计问题化为带约束条件的最小二乘估计问题;利用拉格朗日乘子法,分析参数估计方程,得到参数的最优估计。计算机仿真的结果表明,该优于传统的最小二乘估计法,获得的估计参数是渐进无偏的,获得的估计参数的辨识精度更高,该参数约束估计法在系统辨识和参数估计领域具有极其重要的实际应用价值。

Parameter estimation method with constraints based on calculus of variations was introduced in order to get an asymptotic and unbiased estimation of parameters. The performance function and constraint equation in calculus of variations were constructed by analyzing input and output equations of the system containing parameters to be estimated. The traditional parameter estimation problem could be transformed to that of least squares estimation. Lagrange multiplication operator was used to analyze the parameter estimation equation for obtaining the optimized estimation of parameters. Computer simulation result showed that this method is better than traditional least squares estimation. The parameters obtained are asymptotic and unbiased, and parameter identification precision is higher. This method has very important actual application value in the areas of system identification and parameter estimation.