Parameter estimation: A new approach to weighting a priori information
Parameter estimation: A new approach to weighting a priori information
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参数估计：一种加权先验信息的新方法
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发表时间：
2007
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通讯作者：
J. Mead
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作者：
J. Mead
我们提出了一种在线性参数估计的最小二乘优化问题中对初始参数失配进行加权的新方法。参数失配权重是通过解决优化问题来找到的，该问题确保罚函数具有具有 n 个自由度的 � 2 随机变量的属性，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，所提出的算法找到的权重沿着对角矩阵变化而不是保持不变。另外，假设数据和参数是随机的，但不一定是正态分布的。该算法成功解决了三个基准问题，其中一个具有不连续解。更理想化的不连续问题的解决方案表明，即使双范数通常会平滑解决方案，该算法也可以成功地对初始参数失配进行加权。对于所有测试问题的样本解决方案表明，所提出的算法的结果比使用 L 曲线和广义交叉验证得到的结果更好。在参数估计不那么准确的情况下，它们相应的标准偏差或误差范围可以正确识别它们的不确定性。
We propose a new approach to weighting initial parameter misfits in a least squares opti- mization 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 � 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 con- stant. In addition, it is assumed that data and parameters ar e 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 suc- cessfully weight initial parameter misfits even though the t wo-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 param- eter estimates are not as accurate, their corresponding sta ndard deviations or error bounds correctly identify their uncertainty.