Distance Estimation for BLE-based Contact Tracing A Measurement Study

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3 in db. In this work, we have chosen d = m as it reflects the COVID-19 distance of interest. The estimated distance is then given by D. UWB Distance Estimation ˆd ld = d PL PL,ld γ. () The UWB modules retrieve a distance estimate by timeof-flight (ToF) calculation, obtained from timestamps that are recorded upon packet transmission and reception. As the clocks of the receiver and the transmitter are not synchronized, the ToF can only be estimated. The most common estimation approach is double-sided two-way ranging (DS-TWR) [], which requires TX and RX time stamps of three packet echanges. We implement an etension to DS-TWR, known as cooperative synchronization and ranging [1]. The distance estimates are updated every ms. IV. MEASUREMENT STUDY In our measurement study, we aim at quantifying the accuracy of our proposed distance estimators (ear model, logarithmic model) based on BLE RSSI values. As BLE signal propagation is known to be effected by body shielding and multi-path propagation [1], we will in particular study these effects. A. Eperiment Setup Two test persons are each equipped with a smartphone (Samsung Cover, Samsung Galay S7) and connected UWB sensor that is mounted on the left upper arm of the person. The eperiments are recorded by the measurement app. The following properties are varied in our eperiments: Carrying position: The two test persons are always carrying the smartphone at the same position, which is either (i) head the smartphone is held at the left ear, (ii) trunk the smartphone is held in front of the trunk, or (iii) pelvis the smartphone is carried in the left front trouser s pocket. Distance d: The distance between the two persons is varied from 1 m to m in steps of 1 m. Environment: An anechoic chamber, a corridor, and a corner are selected, as depicted in Fig. -(c). Orientation: The relative orientation between the persons can be, 9, 18, or for head and pelvis carrying positions, and or 18 for trunk; see Fig. (d). Overall, the eperiment consists of 18 combinations, each setting is measured with a duration of min. The BLE pathloss of the whole eperiment is visualized in Fig. and ranges from db to db. In addition, the fitted ear model in (), here referred to as, and the fitted logarithmic model in (), referred to as, are depicted. The correlation coefficient of the ear approimation is r =.1, which is a weak correlation between distance and pathloss caused by the high variability of pathloss at each distance. The noise X g standard deviation is high with σ = 8.8 db (c) 9 18 Fig.. Schematics of environments: anechoic chamber, corridor, (c) corner. Locations of Person 1 and Person are depicted by blue and red circles, respectively, at si timesteps (at each location, each person is d/ away from, the start location), and (d) relative orientations. TABLE I ACCURACY OF EXPOSURE ESTIMATION Environ. Carrying Pos. Model r p r n F 1 MCC unknown unknown known unknown unknown known known known B. Distance and Eposure Estimation Accuracy The distance estimation accuracy is described by the rootmean-square error (RMSE) of the distance estimate and the ground truth distance. The eposure detector is configured with a threshold of. m, meaning that an eposure is detected when the estimated distance is below this threshold. The detector is evaluated by the true positive rate r p, the true negative rate r n, the F 1 score and the Matthews correlation coefficient (MCC). Four scenarios are studied to assess how awareness of the environment and/or the carrying position influences estimation accuracy. For evaluation, the dataset is first divided along the known contet settings (e.g., anechoic, corridor, corner), then each class is split equally into a training set and a test set. The training data is used to derive individual pathloss models for both model types (, ) considering censored pathloss measurements [1]. Comparing the case without contet awareness (unknown/unknown) with the case of full awareness (known/known) in Tab. I, the detection rates r p and r n increase; hereby the impact of knowing the carrying position is larger than the impact of knowing the environment. This effect is also described by the MCC. Note that the MCC is always above zero, which indicates that the estimate is always better than a random guess. The highest observed accuracy is MCC=.7 and F 1 =.7. The MCC is in the interval [ 1, 1], where values > indicate a performance better than a random guess. (d)

4 Pathloss / db.. Linear Model Log-Distance Model. d = 1 m d = m d = m d = m d = m d = m Fig.. Heat map of BLE pathloss at si distances, grouped by three environments (corner, corridor, anechoic chamber). The model parameters of the ear model are: PL, =.8 db, k =.7 db/m with a correlation coefficient of r =.1. The parameters of the log-distance model are: PL,ld = 7.1 db for reference distance d =. m, γ =., X g noise standard deviation σ = 8.8 db. anechoic Models: 9 18 corridor corner head trunk pelvis Fig.. BLE mean pathloss over actual distance (mean std. deviation is.9 db). The black dashed and dotted es depict the ear and, respectively, the log-distance fit, per environment and carrying position. head trunk pelvis anechoic corridor corner anechoic corridor corner C. Effect of Body Shielding To isolate the effect of body shielding, we now discuss the BLE attenuation in the anechoic chamber as visualized in Fig., left column. The phone s carrying position and orientation have a major influence on the pathloss. In LOS scenarios (head, 18 and ; trunk, ; pelvis, ) the mean pathloss is always lower than in the other non-los scenarios, at the respective same distance. The spread of pathloss is high in all carrying positions, i.e., up to 7.11 db (head, d = 1 m), 11.9 db (trunk, d = 1 m), and. db (pelvis, d = 1 m). The spread due to body shielding is often higher than the distance-dependent increase of attenuation. This is confirmed by the weak ear correlation coefficients between pathloss and distance ( model), which are r =. (head), r =. (c) Fig.. Distance estimation error for BLE with known carrying position and unknown environment, BLE with unknown carrying position and known environment, and (c) UWB. The boplots depict the median,. and.7 quantile and the corresponding whiskers. (trunk), and r =. (pelvis). (The model shows a similar behavior.) These results show that in particular in short ranges important for contact tracing (up to m), accurate distance estimation cannot be epected. The largest spread is found for head scenarios. For eample, at a distance of 1 m, the pathloss is db and db under LOS conditions (18 and ) and when fully blocked by the

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