The RDT approach originates from two different applications: radar processing and physiological signal monitoring (anomaly detection) in intensive care units (ICUs). These two applications, and more particularly the detection of anomalies in physiological signals, strongly motivated my research and the development of the RDT theory.

1) In radar processing, I had the opportunity to work on the detection of radar targets in presence of sea clutter. The interested reader can refer to Laurent Dejean's PhD dissertation or my HDR (Habilitation à Diriger des Recherches/Accreditation to supervise research) dissertation, both downlable from the 'Shared files' page. In short, the problem is that, in presence of sea clutter, you always an interference (the sea clutter) even in absence of any radar target. In other words, the model summarized by Eq. (1) above does not apply because, under the null hypothesis, you don't have noise alone but noise and clutter. And under the alternative hypothesis, you don't have signal + noise only but signal + noise + ... clutter! One way to cope with this situation is to introduce a statistical model for the clutter (that's the approach followed in Dejean's PhD) and to resort to likelihood ratio tests. When I was with Signaal in the Netherlands, I already worked on the same topic. One of my conclusions was that it was rather intricate to come up with a statistical model whose parameters are sufficiently well known to adjust a dedicated detector of the target in sea clutter: “even if the model is reasonably good, our knowledge of the parameters in it, [...] may not be enough to justify a direct numerical evaluation of formulas derived from the model.” [Kailath, 1999]. The RDT approach is thus an alternative to likelihood ratio tests because it does not require prior knowledge on the clutter distribution. Instead, it will assume that the clutter amplitude is upper-bounded via the tolerance. This application of RDT is treated in [RDT, Section VI].

2) In mechanical ventilation, you actively insufflate air into the patient's lungs. The monitoring system then lets the lungs empty in a passive way and during an expiratory time specified by the clinician. At the end of this expiratory time, the expiratory flow is expected to return to zero and a new cycle of mechanical ventilation starts. Unfortunately, if the time given to the expiratory is insufficient, the system will prematurely re-insufflate air into the not yet empty patient's lungs, which may induce dynamic hyperinflation.

This real expiratory flow is far from 0 at the end of the expiratory time and this may entail dynamic hyperinflation. Excerpt from 'Contributions to statistical signal processing with applications in biomedical engineering', Q.T. Nguyen, PhD dissertation, 2012

The early detection of a non-zero expiratory air flow at the end of the expiratory phase and before the beginning of new cycle is thus helpful to avoid dynamic hyperinflation and thus, to optimize care. But the problem does not boil down to deciding whether the expiratory flow is zero or not. The problem is more difficult than that. Indeed, the measure of the expiratory flow is performed in presence of noise (electronic noise, noise in the pipework). In addition, and that's crucial, can we really expect a null expiratory flow? No! The expiratory flow will often be non-null in practice at the end of the cycle, even when the expiratory time is well-tuned. Therefore, a way to proceed is to introduce an interval [\tau,0], within which the expiratory flow should remain in absence of hyperinflation. An alarm should therefore be triggered if the expiratory flow is outside this interval at the end of the cycle. It behooves to the clinician to fix the tolerance \tau on the basis of his/her experience. The detection of dynamic hyperinflation is an RDT problem (see Eq. (2)). Indeed, this practical problem motivated strongly all the development of the RDT approach. In this respect, the interested reader can refer to the following papers dedicated to the monitoring of physiological signals.