Data-Driven Filtering and Control

Abstract

The bottleneck in solving real-life data processing problems, such as dynamic measurement in metrology, noise cancellation in acoustics, and ranking papers in scientometrics is obtaining an adequate model for the data generating process. Classical modeling methods ignore the subsequent usage of the model for design of a predictor, controller, or classifier. This issue is often addressed by trial-and-error human interaction. The approach presented in this chapter is to merge the data modeling and model-based design subproblems into one joint problem, called data-driven design. Its benefits are optimality of the overall design and automation of the design process, which reduce the cost and increase the overall design reliability. The chapter is organized as follows. Section 6.1 gives motivation and introduction to data-driven signal processing and control. The main idea—posing data-driven problems as missing data estimation—is informally presented in Sect. 6.2. Specific examples that illustrate the idea are shown in Sect. 6.3. Section 6.4 describes the solution approach. First, we establish the equivalence of the data-driven problem and a weighted structured low-rank matrix approximation and completion problem. For the solution of the latter problem, we use the variable projection method of Sect. 4.4. A simulation example of data-driven impulse response simulation illustrate the theoretical properties and compares the method based on the variable projection with a subspace method as well as a classical model-based method.

If the model of a system is exact, it is optimal for all applications. However, if the model is only an approximation of the “true system”, then the quality of the model should be dependent on the intended application.

Gevers (2004)