A priori weighting for parameter estimation
A priori weighting for parameter estimation
复制标题
参数估计的先验加权
DOI：
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发表时间：
2008
期刊：
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通讯作者：
J. Mead
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文献类型：
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作者：
J. Mead
摘要提出了一种新的加权初始参数失配的线性参数估计的最小二乘优化问题。通过求解一个优化问题来确定参数失配权重，该优化问题确保罚函数具有n个自由度的χ 2随机变量的性质，其中n是数据的数量。这种方法与其他方法的不同之处在于，所提出的算法发现的权重沿对角矩阵沿着变化，而不是保持恒定。此外，假设数据和参数是随机的，但不一定是正态分布的。所提出的算法成功地解决了三个基准问题，一个与不连续的解决方案。从一个更理想化的不连续问题的解决方案表明，该算法可以成功地加权初始参数失配，即使两个范数通常平滑的解决方案。对于所有测试问题的样本解决方案表明，从所提出的算法的结果可以更好地使用L曲线和广义交叉验证。在参数估计值不准确的情况下，其相应的标准差或误差范围可以正确识别其不确定性。
Abstract We propose a new approach to weighting initial parameter misfits in a least squares optimization problem for linear parameter estimation. Parameter misfit weights are found by solving an optimization problem which ensures the penalty function has the properties of a χ 2 random variable with n degrees of freedom, where n is the number of data. This approach differs from others in that weights found by the proposed algorithm vary along a diagonal matrix rather than remain constant. In addition, it is assumed that data and parameters are random, but not necessarily normally distributed. The proposed algorithm successfully solved three benchmark problems, one with discontinuous solutions. Solutions from a more idealized discontinuous problem show that the algorithm can successfully weight initial parameter misfits even though the two-norm typically smoothes solutions. For all test problems sample solutions show that results from the proposed algorithm can be better than those found using the L-curve and generalized cross-validation. In the cases where the parameter estimates are not as accurate, their corresponding standard deviations or error bounds correctly identify their uncertainty.