Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-time System Identification

Block coordinate descent is an optimization technique that is used forestimating multi-input single-output (MISO) continuous-time models, as well assingle-input single output (SISO) models in additive form. Despite itswidespread use in various optimization contexts, the statistical properties ofblock coordinate descent in continuous-time system identification have not beencovered in the literature. The aim of this paper is to formally analyze thebias properties of the block coordinate descent approach for the identificationof MISO and additive SISO systems. We characterize the asymptotic bias at eachiteration, and provide sufficient conditions for the consistency of theestimator for each identification setting. The theoretical results aresupported by simulation examples.