SmoothedLinearModel

public class SmoothedLinearModel : Aggregate

Distance model based on cable car experiment data collected on test rig 2

• Interference stems from a combination of reflections in the environment (random) and mixture of the three BLE advertising channels (more predictable). For reference, channel 37 = 2.402 GHz, channel 38 = 2.426 GHz, and channel 39 = 2.480 GHz.
• Simulations have shown mixture of BLE channels play a significant part in RSSI variance over minute distances, e.g. a change of 1cm can result in large RSSI change due to subtle change in phases between the three channels. The impact of this is particularly dominant at short range (0 - 2 metres).
• A range of modelling and smoothing algorithms were investigated to counter the impact of reflections and channel mixing. Test results have shown the most widely applicable method that is effective irrespective of environment is running a sliding window of fixed duration (last 60 seconds) over the raw RSSI samples to calculate the median RSSI value. Assuming the phones are not perfectly static (i.e. resting on a desk), the small movements between two phones when carried on a person should be sufficient to produce a wide range of interference patterns that on average offer a reasonably stable estimate of the actual measurement.
• Experiments were conducted using different pairs of iOS and Android phones using test rig 2, to capture raw RSSI measurements from 0 - 3.4 metres at 1cm resolution. On average at least 60 RSSI measurements were taken at every 1cm. The data from all the test runs were combined using dynamic time warping to align the RSSI data at each distance. The result was then smoothed using median of a sliding window, then linear regression was applied to estimate the intercept and coefficient for translating RSSI to distance. Linear regression offered the following equation: DistanceInMetres = Intercept + Coefficient x MedianOfRssi
• Physical models for electromagnetic wave signal propagation are typically based on log or squared distance, i.e. signal strength degrades logarithmically over distance. The test rig 2 results confirm this, but also shows logarithmic degradation is only obvious within the initial 0 - 20cm, then becomes linear. Given the intended purpose of the distance metric (contact tracing) where risk score remains constant below 1m and also the significant impact of interference within a short range, a linear model avoids being skewed by the 0 - 20cm range, and offer simplicity for fitting the data range of interest (1 - 8m).