Abstract
Filtering is a methodology used to combine a set of observations with a model to obtain the optimal state. This technique can be extended to estimate the state of the system as well as the unknown model parameters. Estimating the model parameters given a set of data is often referred to as the inverse problem. Filtering provides many benefits to the inverse problem by providing estimates in real time and allowing model errors to be taken into account. Assuming a linear model and Gaussian noises, the optimal filter is the Kalman filter. However, these assumptions rarely hold for many problems of interest, so a number of extensions have been proposed in the literature to deal with nonlinear dynamics. In this chapter, we illustrate the application of one approach to deal with nonlinear model dynamics, the so-called unscented Kalman filter. In addition, we will also show how some of the tools for model validation discussed in other chapters of this volume can be used to improve the estimation process.
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Acknowledgements
The author Hien Tran, gratefully acknowledges partial financial support from the National Institute of Allergy and Infectious Diseases (grant number R01AI071915-07) and from the National Science Foundation (grant number DMS-1022688).
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Attarian, A., Batzel, J.J., Matzuka, B., Tran, H. (2013). Application of the Unscented Kalman Filtering to Parameter Estimation. In: Batzel, J., Bachar, M., Kappel, F. (eds) Mathematical Modeling and Validation in Physiology. Lecture Notes in Mathematics(), vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32882-4_4
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DOI: https://doi.org/10.1007/978-3-642-32882-4_4
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