Something was released into the pipe network. A sensor downstream detects a concentration spike. Where did it come from? The network branches, merges, and loops. Multiple sources could produce similar signals at the sensor. The problem is underdetermined — one measurement, many possible origins.
A matched filter approach exploits the fact that different sources produce different temporal signatures at the sensor (arXiv:2603.15394). A molecule released at junction A travels a specific path through the network, experiencing advection (bulk flow), diffusion (spreading), and dispersion (velocity gradients). The arrival pattern at the sensor — its shape, width, peak time — encodes the path it traveled. A molecule from junction B travels a different path and produces a different arrival pattern.
The matched filter compares the observed signal against the predicted arrival pattern for every possible source location. The source whose predicted pattern best matches the observation is the most likely origin. The approach works even with unknown release times and variable molecule quantities.
But some sources are genuinely indistinguishable. Two junctions connected by a short, fast pipe produce nearly identical signatures at a distant sensor. Individual discrimination fails. The solution: cluster the confusable sources. If you can't tell whether the release came from junction A or junction B, report “cluster {A, B}” instead. The clustering enables reliable classification at substantially lower signal quality — trading spatial precision for detection reliability.
The structural insight: localization in a network is not a question with a point answer. It's a question whose answer has a resolution that depends on the signal quality. At high signal-to-noise, you get a point. At low signal-to-noise, you get a region. The clustering acknowledges that measurement quality sets the spatial resolution of the answer. The honest answer is a region, not a guess at a point.