Denoising Rather Than Gap Filling: Missing-Data Handling in Sparse Outdoor BLE Positioning

Abstract

Received signal strength indicator (RSSI) positioning outdoors has one to two orders of magnitude fewer anchors than the indoor systems its methods come from. In the ten-day cattle-tracking deployment reported here, four gateways cover $4,302{\mathrm{m}}^2$, or $0.93$ anchors per $1000{\mathrm{m}}^2$. An animal is heard by $0.99$ gateways per second on average, so the observation vector for a given second is almost never complete. How the gaps are filled is therefore a first-order design choice, not a preprocessing detail. Filling at all is worth $8.1\mathrm{m}$, $96\%$ of the improvement the hold-length setting can deliver and a $29\%$ error reduction. How long a value is then held is worth the remaining $4\%$, from four seconds to unbounded. Once a value is available, the gain comes from removing noise rather than rebuilding the lost sample: a filtered channel estimate improves on a held raw sample, whereas filling backwards from future samples makes it worse. As that mechanism predicts, smoothing strength has a real interior optimum that is costly to miss in either direction. A smoother allowed to read the future gains only $0.55\mathrm{m}$, one fifteenth of what filling is worth, which bounds what any offline method can add. Three method families do not apply here for structural reasons rather than poor performance: two or more of the four channels are live in only $25\%$ of seconds, so the cross-channel structure generative imputation must learn is largely unobserved.

6 pages