Resolvability of the Parameters of Multiexponentials and Other Sum Models
Resolvability of the Parameters of Multiexponentials and Other Sum Models
复制标题
多重指数和其他求和模型参数的可解性
DOI：
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发表时间：
1993
影响因子：
5.4
通讯作者：
J. Swarte
中科院分区：
文献类型：
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作者：
A. Bos;J. Swarte
它表明，模型拟合的解决方案，紧密定位的非线性参数的总和的功能相同的家庭，这样的多指数，只有不同的子空间的欧几里得空间的误差的观察。在互补空间中，两个或两个以上的非线性参数的解完全重合。互补空间的每个子空间对应于和模型的特定项的参数的解的重合。早期的研究集中在线性参数，如指数的振幅，是已知的，只有两个解决方案的非线性参数重合的情况下。本文的分析推广了这些结果，并将其推广到线性参数和多重重合的求解。此外，提出了一个程序的计算的错误，具有最小的能量之间的所有错误造成的重合。这个最小能量可以用作一个简单的标量标准，以找出在何种程度上的分辨率是预期的假设参数值和误差能量。对于最小二乘模型拟合，所提出的程序被证明是特别简单的。
It is shown that model-fitting solutions for closely located nonlinear parameters of sums of functions of the same family, such a multiexponentials, are only distinct in a sub- space of the Euclidean space of the errors in the observations. In the complementary space, the solutions for two or more of the nonlinear parameters exactly coincide. Subspaces of the complementary space each correspond with the coincidence of the solutions for the parameters of specific terms of the sum model. Earlier studies concentrated on the case that the linear parameters, such as the amplitudes of the exponentials, are known, and only two solutions for the nonlinear parameters coincide. The analysis presented generalizes these results and extends them to include the solving for the linear parameters and multiple coincidence. Also, a procedure is proposed for the computation of the errors that have minimum energy among all errors causing coincidence. This minimum energy may be used as a simple scalar criterion to find out to what extent res- olution is to be expected for assumed parameter values and er- ror energy. For least squares model fitting, the proposed pro- cedure is shown to be particularly simple.