An Approximate Bayesian Approach to Optimal Input Signal Design for System Identification

Abstract

The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and nonlinearity. This paper develops a Bayesian approach that uses the mutual information (MI) between observations and parameters as the utility function. To address the computational intractability of the MI, we maximize a tractable MI lower bound. The method is then applied to the design of an input signals for the identification of quasi-linear stochastic dynamical systems. Evaluating the MI lower bound requires inversion of large covariance matrices whose dimensions scale with the number of data points $N$. To overcome this problem, an algorithm that reduces the dimension of the matrices to be inverted by a factor of $N$ is developed, making the approach feasible for long experiments. The proposed Bayesian method is compared with the average D-optimal design method, a semi-Bayesian approach, and its advantages are demonstrated. The effectiveness of the proposed method is further illustrated through four examples, including atomic sensor models, where the input signals that generates large MI are especially important for reducing the estimation error.

34 pages, 10 figures, GitHub code avaliable

References in corpus (10)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Quantum control theory and applications: A survey
• Real-time optimal quantum control of mechanical motion at room temperature
• Modeling and Control of Quantum Systems: An Introduction
• Optimal experimental design and some related control problems
• How to build a magnetometer with thermal atomic vapor: A tutorial
• Estimating Mixture Entropy with Pairwise Distances
• Optimal experimental design: Formulations and computations
• Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering
• Noisy atomic magnetometry with Kalman filtering and measurement-based feedback