A survey on the applications of the Krein-space theory in signal estimation

In this paper, the applications of theory in the signal estimation problems are surveyed. The signal estimation under consideration includes filtering, prediction, smoothing and fault estimation. We first introduce the basic concepts about Krein spaces and the main principle of the linear estimation theory in Krein spaces. Then, the developments on various Krein-space-based filtering, prediction, smoothing technologies as well as their engineering applications are reviewed in great detail. Subsequently, the recent advances on the Krein-space-based fault estimation approaches are discussed. Finally, conclusions are drawn and several possible future research directions are pointed out.