论文标题
基于前向内核的状态和任意顺序线性系统的参数估计
Forward-backward kernel-based state and parameter estimation for linear systems of arbitrary order
论文作者
论文摘要
以前与代数状态和线性系统的参数估计有关的结果基于线性差异不变的前向内内核表示的特殊构建，以处理输出测量中的大噪声。首先说明并证明了任意顺序的单输入，单输出（SISO）线性时间流（LTI）系统的内核函数的显式表达式。接下来提出了估计问题的两个阶段解决方案。参数估计子问题是第一阶段的任务，通过随机回归解决。使用多重回归增强了早期出版物中介绍的参数估计方法。回归模型不能满足高斯 - 马尔科夫定理的假设，因为随机回归器是异性弹性的。这不会阻碍达到高度估计的准确性。可行的具有协方差加权的可行的概括最小二乘的递归版本用于减弱由于异方差性而导致的不良反应。系统的输出及其时间衍生物通过投影的第二阶段在第二阶段进行重建，同时最大程度地减少均方根标准。
Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in output measurement. Explicit expressions for the kernel functions for single-input, single-output (SISO) linear time-invariant (LTI) systems of arbitrary order are first stated and proved. A two-stage solution of the estimation problem is proposed next. The parameter estimation sub-problem, which is the task of the first stage, is solved by way of stochastic regression. The parameter estimation method presented in earlier publications is enhanced using multiple regression. The regression model does not satisfy the assumptions of the Gauss-Markov theorem in that the random regressor is heteroskedastic. This does not impede achieving high accuracy of estimation. A recursive version of a feasible generalized least squares with covariance weighting is employed to attenuate adverse effects due to heteroskedasticity. The output of the system and its time derivatives are reconstructed smoothly in the second stage of the approach by way of projection, while minimizing a mean square criterion.
