M. Fliess and M. Mboup
New estimation techniques have recently emerged in control theory allowing considerable advances for linear and nonlinear systems, particularly in the areas of closed-loop identification of unknown parameters, efficient state reconstructors, and real-time fault diagnosis and fault tolerant control. The extension to signal processing has given surprisingly straightforward solutions to many longstanding problems such as the analysis of chirp signals, the detection of piecewise polynomial signals and their discontinuities, and the compression of fast transient signals, among other applications. Our standpoint, which derives from differential algebra, noncommutative ring theory, and operational calculus, offers the following features: (i) no precise statistical knowledge of the noise is required; (ii) the “true” physical nature of the signal is retained (often otherwise discarded from sampling operations); (iii) no distinction between stationary and nonstationary signals is necessary; and (iv) all estimation steps lend themselves to on-line computations. The aim of this tutorial is to explain this departure from today’s most customary approaches via several examples. We will also focus on potential new connections between automatic control and signal processing, two fields of engineering that have drifted apart over the past two decades.
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