基于Rayleigh商的不等精度二次曲线拟合的WTLS迭代解法

针对独立不等精度离散点的二次曲线拟合问题，以系数矩阵元素的一阶误差传播得到的方差为权倒数，采用加权总体最小二乘估计方法求解拟合参数，将加权总体最小二乘问题转化为Rayleigh商问题，从而只需求一正定矩阵的特征值和特征向量，便可通过迭代计算得到待估参数的解。该方法性能稳定且计算量较小，是针对WTLS问题的一种相对简捷高效的计算方法。

A Rayleigh Quotient Based Iterative Weighted Total Least Squares Methods for Heteroscedastic Conic Fitting

A weighted total least squares (WTLS) cost function is obtained by considering the first-order error propagation of the design matrix elements in conic fitting problems with heteroscedastic measurements. The cost function is justified as the Rayleigh quotient form, which means the parameters to be estimated are the eigenvector associated with the smallest eigenvalue of a given positive-defined matrix. Our algorithm is an iterative singular value decomposition, and a simulated data experiment is also presented to verify the algorithm. The results show that this method is more stable, demands less calculation, and is relatively simple and efficient．