非线性参数估计的自适应松弛正则化算法

Adaptive Relaxation Regularization Algorithm for Nonlinear Parameter Estimation

非线性方程参数估计存在的弊端在于非线性观测方程存在不适定问题时,以线性化平差估计和高斯牛顿为代表的经典数值算法会产生较强的不稳定特征。因此,针对传统非线性最小二乘求解不稳定且可靠性低的特点,基于稳定泛函极小准则最优化思想,提出了一种自适应松弛正则化数值算法。该算法采用正则化参数几何递增计算方法和残差最小步长准则,实现了正则参数和迭代步长计算的完全自适应,提高了非线性迭代收敛效率。以病态仿真数据和水下实测数据为例,验证了该方法的数值收敛解优于线性平差估计解,收敛效率优于迭代Tikhonov正则化方法。

This paper discusses the ill-posed nonlinear least squares problem,and proposes an adaptive relaxation algorithm based on the regularization method for stabilizing the nonlinear parameter estimation.The improved algorithm achieves the adaptive selection on the regularization parameter and iterative step by using an incremental geometric regularization parameter and the minimal residual criterion.The numerical convergence experiments of the method are performed.The results show that the numerical precision of our proposed method is better than that of the linearized adjustment estimation,and the convergence property is more efficient than the iterative Tikhonov regularization method.