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S. Horvath, H.-B. Neuner:
"Comparison of Levenberg-Marquardt and Extended Kalman Filter based Parameter Estimation of Artificial Neural Networks in Modelling Deformation Processes";
Talk: Joint International Symposium on Deformation Monitoring 2016, Wien; 2016-03-30 - 2016-04-01; in: "Joint International Symposium on Deformation Monitoring 2016", (2016), 8 pages.

Abstract. In monitoring various deformation models are well-established. Considering deformations as a dynamic reaction of the object structure to influencing parameters describes the monitoring task in its entirety. However, if the structure and the response characteristics of the object are unknown or too complex to be modelled, a behavioural approach is formulated.
Estimating parameters of an unknown input-output dependency from observed data considering available a priori information is the aim of learning. In general, a learning algorithm consists of a set of approximating functions and an optimisation method. In this contribution the well-known Kalman filter is applied as an optimisation method in combination with artificial neural networks as a set of approximating functions. This approach will be compared with the prevailing optimisation method of Levenberg-Marquardt.
It is shown that the Levenberg-Marquardt is a particular case of the extended Kalman filter, which results under simplifying assumptions. Morover, the covariances included in the Kalman filter can be chosen reasonable and exhibit the same functionality as e.g. the step size in optimisation. The results obtained by the two optimisation methods are compared at a theoretical level as well as based on synthetic data.

Learning, Extended Kalman filter, Levenberg-Marquardt, ANN, System identification

http://publik.tuwien.ac.at/files/PubDat_250614.pdf