Parameter Estimation in Dynamical Models
Parameter Estimation in Dynamical Models
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DOI：
10.1007/978-94-011-5096-5_16
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
G. Evensen;D. Dee;J. Schröter
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文献类型：
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作者：
G. Evensen;D. Dee;J. Schröter
本文对动态模型的参数估计问题作了一个一般性的介绍。在一个参数估计问题的基本配方和方法将进行讨论，并提出一些相当简单的例子。它将被证明，即使是线性动力学的参数估计问题变得非线性，并可能变得非常难以解决。此外，有一个适定的问题有一个唯一的解决方案，必须采取措施时，制定了参数估计问题。讨论得出的结论是，它是可能的，以估计在一个模型中，至少对于简单的动力学模型的参数，但必须注意有一个一致的解决方案。规则是，所有将被估计的参数都应该作为弱约束添加到惩罚函数中，以测量它们与某个范数中的第一猜测的距离。一些以前的作品中，数据同化方法已被用来提高估计的知之甚少的模式参数，甚至模式的偏差将简要回顾。[24]在参数的每次迭代中，将参数的第一次猜测值与当前估计值进行比较。这些当然应该保持不变。显然，[24]在每次迭代中解决了不同的反问题，并且根本没有任何真实的第一次猜测的惩罚。实际上，从他们的数字中并不清楚迭代是否收敛。
This paper gives a general introduction to the parameter estimation problem for dynamical models. The basic formulation and methodology in a parameter estimation problem will be discussed and some rather simple examples will be presented. It will be shown that even for linear dynamics the parameter estimation problem becomes nonlinear and may become extremely difficult to solve. Also, to have a well-posed problem with a unique solution, care must be taken when a parameter estimation problem is formulated. The discussion leads to the conclusion that it is possible to estimate poorly known parameters in a model, at least for simple dynamical models, but care must be taken to have a consistent solution. The rule is that all parameters which will be estimated should be added in a penalty function as weak constraints measuring their distance from a first guess in some norm. Some previous works in which data assimilation methods have been used to improve estimates of poorly known model parameters or even the model bias will be briefly reviewed. that [24]replacedthe first-guess values of the parameters with thecurrent estimatein each iteration of the parameters. These should of course be kept constant. Clearly, [24] solved a different inverse problem in each iteration and did not have any real penalty of the first guesses at all. Actually, it is not clear from their figures that the iterations did converge.