等式约束病态最小二乘的主成分Liu估计解法

Principal Component Liu Estimation Method of the Equation Constrained Ⅲ-Conditioned Least Squares

针对病态平差问题的参数估计,参数之间合理的等式先验信息有助于提高模型解的精度。本文在样本信息和等式先验信息下进行联合计算,基于病态最小二乘平差准则,通过主成分估计和Liu估计,构建一种新的有偏估计算法——主成分Liu估计;推导出等式约束最小二乘的主成分Liu估计参数解式,并利用均方误差最小化原理,导出修正因子的计算式;通过算例验证本文方法的有效性和可靠性,可适用于等式约束病态最小二乘参数求解问题。

For the parameter estimation of theⅢ-conditioned adjustment problem,reasonable equality prior information among parameters helps to improve the accuracy of the model solution.The joint calculation is carried out under the sample information and the prior information of the equation.Based on the morbid least squares adjustment criterion,a new biased estimation algorithm,principal component Liu estimation,is constructed through the principal component estimation and Liu estimation.The parameter solution of the principal component Liu estimation with equality constrained least squares is derived,and the formula of correction factor is derived by using the principle of mean square error minimization.The effectiveness and reliability of the proposed method are verified by an example,which can be applied to the problem of solvingⅢ-conditioned least squares parameters with equality constraints.