全最小二乘法及其在参数估计中的应用
Total Least Square Method and its Applicaion to Parameter Estiation
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摘要: 本文介绍了全最小二乘法的基本原理及其在参数估计中的应用.文中采用矩阵逼近和线 性空间分解的理论推导了全最小二乘法的解及其性质,并且证明了全最小二乘解对数据拟合 的残差平方和小于一般最小二乘解的残差平方和.仿真结果验证了理论,显示了全最小二乘 法的优越性.Abstract: The Total least squares (TLS) method and its application to parameter estimation are introduced. The theory of matrix approximation and linear space decomposition are used to derive the solution and properties of TLS. It is proved that the sum of squared residual of data fitting using TLS is less than that using least squares (LS) method. Simulation results verified the theoratical derivation and the superiority of TLS over LS method.
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Key words:
- Total least squares method /
- Parameter estimation /
- Data fitting
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