A-priori Fisher information of nonlinear state space models for experiment design

Abstract

This article presents advances in optimal experiment design, which are intended to improve the parameter identification of nonlinear state space models. Instead of using a sequence of samples from one or just a few coherent sequences, the idea of identifying nonlinear dynamic models at distinct points in the state space is considered. In this way, the placement of the experiment points is fully flexible with respect to the set of reachable points. Also, a method for model-based generation of prediction errors is proposed, which is used to compute an apriori estimate of the sample covariance of the prediction error. This covariance matrix may be used to approximate the Fisher information matrix a-priori. The availability of the Fisher matrix a-priori is a prerequisite for experiment optimization with respect to covariance in the parameter estimates. This work is driven by the problem of parameter identification of hydraulic models. There are methods for hydraulic systems regarding the estimation of parameters from experimental data, but the choice of experiments has not been treated adequately yet. A hydraulic servo system actuating a stewart platform serves as an illustrative example to which the methods above are applied.

Experimental design for estimating unknown hydraulic conductivity in an aquifer using a genetic algorithm and reduced order model

“…Unfortunately, this method can be too costly and time consuming to be feasible, particularly in the context of groundwater. We also could place an a-priori probability distribution on the parameters to derive an a-posteriori information matrix [33]. A third option would be to perform the optimization using the meta-Jacobian matrix as opposed to the standard Jacobian matrix [34].…”

Trajectory Synthesis for Fisher Information Maximization

“…Since the design of an experimental trajectory has a wide range of potential uses, there have been a number of contributions to the area from different fields. A large amount of literature on optimal experimental design exists in the fields of biology [5]- [7], chemistry [8], and systems [9]- [12]. Many of these results focus on particular applications to experiments specific to their respective fields; however, the underlying principles of information theory remain the same.…”

Local E-optimality conditions for trajectory design to estimate parameters in nonlinear systems

“…A large amount of literature on optimal experimental design exists in the fields of biology [4-6], chemistry [7], and systems [8-11]. …”