Adaptive and robust experimental design for linear dynamical models using Kalman filter

TL;DR

This paper develops an adaptive and robust experimental design method for linear dynamical systems that accounts for both process and measurement noise by combining Bayesian and adaptive strategies with Kalman filtering.

Contribution

It introduces a novel methodology that integrates Bayesian averaging and adaptive updating to optimize experimental design under uncertainty in linear dynamical models.

Findings

Enhanced robustness in experimental design against model uncertainty

Improved information gain through adaptive updates during experiments

Effective handling of process and measurement noise in design optimization

Abstract

Current experimental design techniques for dynamical systems often only incorporate measurement noise, while dynamical systems also involve process noise. To construct experimental designs we need to quantify their information content. The Fisher information matrix is a popular tool to do so. Calculating the Fisher information matrix for linear dynamical systems with both process and measurement noise involves estimating the uncertain dynamical states using a Kalman filter. The Fisher information matrix, however, depends on the true but unknown model parameters. In this paper we combine two methods to solve this issue and develop a robust experimental design methodology. First, Bayesian experimental design averages the Fisher information matrix over a prior distribution of possible model parameter values. Second, adaptive experimental design allows for this information to be updated as measurements are being gathered. This updated information is then used to adapt the remainder of the design.