A Comparison Study of Single-Scale and Multiscale Approaches for Data-Driven and Model-Based Online Denoising

Signal denoising is a pervasive operation in most online applications, such as engineering process control and online optimization, strongly affecting the outcome of these higher‐level tasks and impacting the overall variability exhibited by processes and products. Therefore, it plays a fundamental role in improving process capability, which is, however, often overlooked. In this work, we compare the performance of different types of currently available online denoising filters using a variety of test signals that represent the diversity of situations likely to be found in practice, properly corrupted with additive noise of varying magnitudes. Both single‐scale/multiscale, data‐driven/model‐based and time domain/frequency domain, online filtering approaches were contemplated, in what is, to the best of the authors knowledge, the more extensive comparison study conducted on online denoising (or filtering) methodologies. A new class of multiscale denoising algorithms is also considered in this study, based on the online wavelet multiresolution decomposition. In this context, we propose and test a new formulation, called the online multiscale hybrid Kalman filter. After proper tuning, the methods are tested and their performances compared. As a result of the comparison study, clear guidelines are provided for practitioners on the use of online denoising methodologies, which allow for a better management of the impact of the propagation of unstructured components of variability in the final outcome of the processes.