Nonlinear filtering methodologies for parameter estimation

Filtering is a methodology used to combine a set of observations with a model to get the optimal state. This technique can be extended to not just estimate the state of the system, but also 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 state space 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. To determine the best method for a given problem, we do a comprehensive comparison study of five filtering methods in the estimation of the state of the system and its unknown model parameters. The performance of the methods are tested across several test problems which cover a wide range of potential issues that can be encountered including numerical stiffness, the size of system and parameters, chaotic dynamics, the nature of nonlinearities, the type of error model, the data sampling frequency, and other issues. These examples are used to give recommendations as to which filter is best under the various conditions.

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