Fault-tolerant discrete-time linear time-invariant filters

Modular redundancy, the traditional approach to fault tolerance, is prohibitively expensive because of the overhead in replicating the hardware. In this paper we discuss alternative methods for obtaining fault-tolerant architectures for discrete-time (DT) linear time-invariant (LTI) filters. We view such filters as dynamic systems and provide fault tolerance to them by embedding their state into redundant state-spaces of higher dimensions. The embedding for a given filter is achieved systematically in a way that preserves the functionality of the filter, perhaps in some encoded form. The resulting redundant filtering architecture allows us to detect, identify and correct hardware failures by performing simple (linear) checks. As we show through examples, our approach generalizes previous schemes and leads to new fault-tolerant architectures for DT LTI filtering.