Ultra Low-Power, Lightweight, Probabilistic RSS-Based Path Reconstruction: A System for Landscape-Scale Bee Tracking

Christopher J. Noroozi; Joseph L. Woodgate; Michael Mangan; Michael T. Smith

cs.LGAug 27, 2026

Ultra Low-Power, Lightweight, Probabilistic RSS-Based Path Reconstruction: A System for Landscape-Scale Bee Tracking

Authors: Christopher J. Noroozi, Joseph L. Woodgate, Michael Mangan, Michael T. Smith

Organizations: School of Computer Science, University of Sheffield, Sheffield, UK

Abstract

Applications in fields such as movement ecology, Internet of Things or robotics share the need for systems that localize devices that are too small and power constrained to implement GNSS (Global Navigation Satellite Systems). Alternative low-power localization methods often rely on only measurements of RSS (Received Signal Strength) to infer the AoA (Angle of Arrival) of a transmitted radio frequency signal, but are limited by range and the power demand of the large number of RSS measurements required to infer an accurate AoA. In this paper we address these issues with a novel RSS-based method for tracking ultra lightweight and low-power moving receivers across a complex landscape, achieved by using a minimal number of RSS measurements from simple rotating high-gain transmitters with a range of 300m, and applying probabilistic modelling to infer their AoA. The receiver's movement path is then modelled using a Gaussian process and reconstructed using doubly stochastic variational inference, resulting in approximately 15m accuracy tracking of receivers weighing 38mg (including power source) over a scalable landscape range while consuming less than 180uW, increased to approximately 10m accuracy at less than 600uW by taking more RSS measurements. We anticipate that this method will support fields such as the behavioural study of flying insect species, which we demonstrate by applying the system to track Bombus terrestris nest return flights.

Figures & tables

Fig. 1: The 38mg supercapacitor powered receiver that the system will track. (a) The receiver, affixed to a green queen bee marking tag. Ruler provided for scale. (b) One side of the receiver showing the supercapacitor and a pad for charging, the white outline bounds the receiver on the PCB, the tracks and pads outside this region are used for programming the DA14531 and then removed. (c) Other side of the receiver, showing the DA14531, crystal oscillator, multi-layer ceramic capacitors, ground pad for charging and a pad to trigger an interrupt for reading data off the receiver.

Fig. 2: Our simple 30rpm rotating high-gain transmitter with a 14dBi Yagi Uda antenna mounted on a 1.5 meter tall tripod in the field, transmitting packets used to track the receiver.

Fig. 3: The problem of inferring receiver angle from packets received. (a) Definitions of angles. We seek $\theta$ , the angle the receiver lies upon from the transmitter relative to North. $\gamma$ is the angle relative to North that the transmitter and therefore its ARP is oriented towards, this is always known as it is encoded in the packets received. (b) Polar plot of the ARP of our transmitter’s 14 dBi Yagi Uda antenna oriented 45 ∘ from North, to show how the antenna’s gain varies by angle. The ARP was measured empirically as described in Section VI-A , and averaged at each angle to remove noise as suggested by Kim et al. [ 59 ] .

Panel of Figure 4 — Fig. 4: The simple graphical model relating the angle $\theta$ the receiver lies upon relative to North and the observed RSS measurements $\bm{y}$ - a set of $k$ RSS observations taken at angles $\bm{\gamma}$ of transmitter rotation relative to North. We assume that the ‘true’ unattenuated signal strength, $t_{i}$ , depends on just the angle $\theta-\gamma_{i}$ . We assume in this model that all the RSS measurements were taken close enough together in time that they all were generated by angles close to $\theta$ and experienced the same attenuation $a$ to result in signal strengths $\bm{f}$ . Finally the RSS measurements actually observed by the receiver, $\bm{y}$ , are modelled by assuming some Gaussian noise corrupts this attenuated signal.

Fig. 5: Example of AoA prediction returned by full probability distribution approach. (a) An example of a burst of RSS measurements (red), taken at a true angle of 4.6 radians (green), of packets received from a single rotating high gain transmitter. This burst was 2000ms in duration, and receiving duty cycles were performed at an interval of 120ms, resulting in a total of $k=15$ samples taken. (b) The calculated probability distribution of the predicted angle $p(\theta|\bm{y},\bm{\gamma})$ from the full probability distribution method given the RSS measurements taken (blue). Note that the probability density is highest around the true angle, showing that our $p(\theta|\bm{y},\bm{\gamma})$ closely represents the true angle $\theta$ that generated the RSS observations $\bm{y}$ at angles of transmitter rotation $\bm{\gamma}$ .

Fig. 6: Example of AoA predictions returned by rejection sampling approach. (b) A plot of RSS measurements made when the receiver was positioned $\pi$ radians relative to North from the transmitter and captured packets (red) every 50ms for 10 seconds. (a) The data in (b) is subsampled, such that, at each time point just 5 packets spaced evenly 1 second to either side are used with the rejection sampling approach: The angles associated in the training set with similar relative signal strengths are plotted in black (approximating $p(\theta|\bm{y},\bm{\gamma})$ ). One can see that, from RSS measurements taken around the main lobe of the transmitter’s antenna (where the RSS peaks), the samples from $p(\theta|\bm{y},\bm{\gamma})$ are confidently centred around the true angle $\theta=\pi$ (blue line). Samples taken away from the main lobe are instead highly uncertain and distributed across many values of $\theta$ .

Fig. 7: Image of Bombus terrestris tagged with a receiver described in Section III (glued to a green queen marking tag) sitting on the plunger of a queen marking pot following release during the experiment described in Section VI-E .

Fig. 8: Plots showing the MAE in degrees of each AoA inference method across a range of $k$ number of RSS measurements used in the burst scan from which the angles were inferred. One standard deviation above and below the mean result is represented by the shaded areas. (a) MAE of rejection sampling method. (b) MAE of peak RSS method. (c) MAE of full probability distribution method.

Fig. 9: Plot of mean NLPD against mean entropy for our predicted angle distribution $p(\theta|\bm{y},\bm{\gamma})$ calculated for 1000 $\bm{y}$ subsampled from the test data across several values of $k$ , showing that, as the predictive ability of $p(\theta|\bm{y},\bm{\gamma})$ decays with reducing values of $k$ , its entropy increases therefore capturing the uncertainty of our reduced accuracy predictions.

Fig. 10: Example of one of the six paths used for assessing path reconstruction accuracy. The four transmitters are labelled, the blue path is the GNSS ground truth (3m accuracy), the orange path is the mean of the reconstructed path and the ellipses are 2 standard deviations of the covariance matrix at time points every 10 seconds along the inferred path. $k=10$ samples were used per burst in these examples, and a path reconstructed from AoAs inferred via the (a) full probability distribution method and (b) peak finding method are presented. (c) A satellite view of Norfolk Heritage Park, Sheffield, UK at which the paths took place is also presented, retrieved from Google Maps [ 71 ] . Note that the inferred paths’ uncertainty grows at the beginning and end of the tracked paths, as before/after these points in time respectively there are no observations.

Fig. 11: Plot of the MAE (m) of paths reconstructed using variational inference, from $k$ AoA observations inferred via two angle inference methods using parameter choices as presented in Section VI-C . The coloured shaded areas represent one standard deviation above and below the MAE. The gray shaded indicates the estimated lower bound on the MAE achievable using this evaluation method. This bound arises from the positional uncertainty of the GNSS ( $\approx$ 3m) used to collect the ground truthed path and the positions of the four transmitters. Assuming these errors are independent, their root-sum-of-squares yields a minimum error of $\sim$ 4m.

Fig. 12: Empirical cumulative distribution plot of point-wise error in meters between all six reconstructed paths and their corresponding GNSS ground truth, from AoA observations inferred using (a) the peak finding method and (b) the full probability distribution method, at four selected values of $k$ . The horizontal axis is truncated at 50m due to the poor performance of the peak finding method at $k=3$ , approaching a random estimate of the ground truth path, and therefore having a large number of predictions exceed 50m of error.

Fig. 13: Plot of the MAE of AoA inference (blue) and resulting path reconstruction (green) from varying an allowance of 100 RSS measurements across values of $k$ (number of burst scans is 100/ $k$ ) using synthetic data. The green shaded area is one standard deviation above and below the MAE of the path reconstruction.

Fig. 14: Plot of the MAE of AoA inference (blue) and resulting path reconstruction (green) from varying an allowance of 100 RSS measurements across values of $k$ , for several burst scan lengths: (a) 2000ms, (b) 1500ms, (c) 1000ms, (d) 500ms. The green shaded area is one standard deviation above and below the MAE of the path reconstruction.

Fig. 15: Reconstructed path (using full distribution AoA method and variational inference as described in Sections IV-A and V ) of a tagged Bombus terrestris worker, caught at the Nest Box and displaced & released at the Release Site. The bee after release was re-observed at the Nest Box and the path reconstructed from its retrieved tag successfully shows the bee flying from the Release Site to the Nest Box. The mean of the reconstructed path is represented by the blue line and the shaded blue region is the uncertainty encoded by the reconstructed path’s covariance matrix ( ${}^{+}_{-}$ 2 standard deviations). The three transmitters b,e and f are also shown, overlain onto a satellite image of Common Lane Open Space, Sheffield, UK retrieved from Google Maps [ 71 ] .

Fig. S1: An illustration of the distance $d$ between the random variable $\bm{y}$ and the line defined by $\hat{\bm{x}}$ .

Fig. S2: An illustration of the the point $\alpha\hat{\bm{x}}$ on the line defined by $\hat{\bm{x}}$ that is closest to $\bm{y}$ .

Fig. S3: Plot of path one’s GNSS ground truth (blue) and a reconstructed path’s mean (orange) and standard deviation of its covariance matrix at 20 evenly spaced time points across the path (black ellipses). The transmitters a,b,c,e are plotted and labelled. Path reconstructions using $k=3,5,10\text{ }\&\text{ }25$ packets per burst were used alongside the peak finding (left) and full probability distribution (right) AoA inference methods.

Fig. S4: Plot of path two’s GNSS ground truth (blue) and a reconstructed path’s mean (orange) and standard deviation of its covariance matrix at 20 evenly spaced time points across the path (black ellipses). The transmitters a,b,c,e are plotted and labelled. Path reconstructions using $k=3,5,10\text{ }\&\text{ }25$ packets per burst were used alongside the peak finding (left) and full probability distribution (right) AoA inference methods.

Fig. S5: Plot of path three’s GNSS ground truth (blue) and a reconstructed path’s mean (orange) and standard deviation of its covariance matrix at 20 evenly spaced time points across the path (black ellipses). The transmitters a,b,c,e are plotted and labelled. Path reconstructions using $k=3,5,10\text{ }\&\text{ }25$ packets per burst were used alongside the peak finding (left) and full probability distribution (right) AoA inference methods.

Fig. S6: Plot of path four’s GNSS ground truth (blue) and a reconstructed path’s mean (orange) and standard deviation of its covariance matrix at 20 evenly spaced time points across the path (black ellipses). The transmitters a,b,c,e are plotted and labelled. Path reconstructions using $k=3,5,10\text{ }\&\text{ }25$ packets per burst were used alongside the peak finding (left) and full probability distribution (right) AoA inference methods.

Fig. S7: Plot of path five’s GNSS ground truth (blue) and a reconstructed path’s mean (orange) and standard deviation of its covariance matrix at 20 evenly spaced time points across the path (black ellipses). The transmitters a,b,c,e are plotted and labelled. Path reconstructions using $k=3,5,10\text{ }\&\text{ }25$ packets per burst were used alongside the peak finding (left) and full probability distribution (right) AoA inference methods.

Fig. S8: Plot of path six’s GNSS ground truth (blue) and a reconstructed path’s mean (orange) and standard deviation of its covariance matrix at 20 evenly spaced time points across the path (black ellipses). The transmitters a,b,c,e are plotted and labelled. Path reconstructions using $k=3,5,10\text{ }\&\text{ }25$ packets per burst were used alongside the peak finding (left) and full probability distribution (right) AoA inference methods.

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