Developing a Relationship between Time, Distance, and Alert Thresholds James Han jhan31903@gmail.com Abstract— This paper explores a novel way to measure the II. HYPOTHESIS/HYPOTHESES distance between two bluetooth devices for a certain amount of My hypothesis is the following: time by converting RSSI values into power, then accumulating the power through time by summing each value. I can use the idea of accumulated power to measure thresholds I. INTRODUCTION for the “too close for too long” protocol, and use these thresholds to determine what sets off the protocol at different My project develops a relationship between time, distances for different times. This will allow me to develop an distance, and alert thresholds to try to quantify and determine accurate quantifiable model, not just an estimation, for what what is considered “too close for too long” at certain constitutes “too close for too long” at distances other than 6 distances. The conventional threshold is 6 feet for 10 minutes. feet. To quantify this, I converted all the RSSI values received for 6ft and 10 minutes, and converted them to power in mW, • piPACT can use my model to determine the precise using the following equation: relationship between time together and distance, and if to set off the protocols. • I need to investigate the accumulated powers for distances of 6ft and closer, ideally one foot apart, for 10 minutes. • I need to gather a lot of trials so as to retrieve the most Converting from dBm to power allowed me to add up all the accurate results. To do this I will average out the power accumulated throughout the 10 minutes for each RSSI accumulated powers for each trial at each distance. value, since RSSI values were typically negative for all trials. By accumulating the power for 6 feet and 10 minutes, I was • In a piPACT seminar, the Instructor said that there has not able to develop an “accumulated power threshold” for each of been such model to determine what constitutes too close for the 6 feet trials and average them out. For each distance too long at distances other than 6 feet. I tried to develop a shorter than 6 feet, then, I can see at what point in time when model using quantifiable data rather than estimations. receiving RSSI signals that the accumulated power for that distance surpasses the threshold made at 6 feet for 10 minutes. III. EXPERIMENTS AND DATA COLLECTIONS This will allow piPACT to use my model to determine what is I did three sets of experiments. The first set served to considered too close for too long, depending on the distance determine the accumulated power thresholds for 6 feet apart at between the two people/bluetooth devices. My project can 10 minutes, the conventional time and distance to set off the lead to a deeper understanding of the relationship between “too close for too long” protocol. I The second set was more virus transmission, distance, and time between the two people data collection. I collected data at 5 feet apart, all the way to 1 involved. For example, PACT can use my model, or a more feet apart, at intervals of 1 foot. The third set of data collection developer version of it, to determine when two people are 3 was to examine why the three feet and 5 feet sets of data were feet apart, if they are together for longer than, say 30 seconds, producing unexpected results. They were mainly for error is “too close for too long" and execute the following necessary analysis. protocols for alerting them. This project involved the use of 2 raspberry pi 4s. There were I. EXAMPLE EXPERIMENT OVERVIEW many assumptions made when doing this project, since I was not able to create an ideal testing environment due to Exp. # Hypothesis Reason Repetitions restrictions on WiFi connection and power supply. This experiment was entirely done indoors. I assumed that both of Effect of distance and Determining the bluetooth transmitting raspberry pis worked identically, thresholds for 6 1 time on protocol 10 feet apart for 10 and ideally in each trial. I also assumed that signals would not execution minutes be affected or minimally affected by the environment. I did not address the effect of these variables on my test results, rather I assumed ideal conditions. 1 Exp. # Hypothesis Reason Repetitions Gathering experimental data Effect of distance and 5 times for for different 2 time on protocol each distances ( 5 feet, 4 execution distance feet, 3 feet, 2 feet, 1 foot ) 5 more Effect of distance and Error Analysis, times for 3 3 time on protocol getting unexpected feet and 5 execution results feet A. Plan and Execution I set up the two raspberry pis on my bed, one on a bedpost and one on a stack of sheets and pillows, with the pi being on top of a book to level the pi out with the other pi. The scanner pi was on the wooden Figure 1 : The xaxis is the scan number, with bed frame, and the advertiser pi was on the book. I approximately ~450 scans happening for each 10 minute used a measuring tape to determine the distance interval that was measured for each of the distances. The y between the pis, and I moved the stack with the axis is the accumulated power in mW. advertiser pi around to set the varying distances IV. ANALYSIS AND ALGORITHMS between the pis. I tried making the distance as exact as possible to the After converting each received RSSI value and converting distance I was experimenting with at the time. To it to power, I averaged the power at each scan interval for all produce reliable results, I repeated each trial multiple trials for a given distance. Then, with the calculated power at times and then averaged out the accumulated powers each scan interval, I measured the accumulated power at each for each trial in order to get the best possible scan interval. For 6 feet and 10 minutes, the averaged measurements. I was not able to overcome to effect of accumulated power threshold turned out to be other variables on my results, such as signal ~0.003315839266 mW. This value represents how the sum of reflections. I had to do my experiment indoors due to the RSSI converted into power at each scan interval over the period of 10 minutes. Now, all I need to do is do the same restrictions on WiFi connection to my raspberry pis. process for each distance, and see where the accumulated B. Data Relevance power would surpass the calculated threshold of ~0.003 mW. As you can see in Figure 1, the point at which the maximum 6 The data I collected supports my hypothesis because these exact distances and times that I measured can be used to feet value is very low on the graphs of the other distances. To develop the model of my hypothesis. For example, I would need RSSI measurements of my pis at 3 feet apart for 10 minutes in order to determine when the accumulated power at this distance would surpass the threshold made at 6 feet apart. From the point at which the accumulated power surpasses the threshold, I would be able to pinpoint the exact time at which the accumulated power passes the threshold and therefore what is considered “too close for too long” at that specific distance. C. Examples Here is a graph of accumulated power for 1 feet, 2 feet, 3 feet, 4 feet, 5 feet and 6 feet apart over 10 minutes. We will be tinkering with this graph to figure out when exactly at each distance breaks the accumulated power threshold at 6 feet apart for 10 minutes (see Figure 1). scale the data better in order to see exactly where the intersections happened between the maximum accumulated power for 6 feet and the other distances, I scaled the data into a logarithmic graph in order to see the differences better. This graph can be seen in figure 2. 2 Figure 2: this graph is figure 1, with each y value turning execution. My experiment serves to show a novel way to into 10 * log(y). determine how close two devices were together for how long: through measuring accumulated power. Since RSSI values are typically negative, by converting the RSSI values to a positive number that increases if the received signal is stronger and summing them. If the accumulated power increases greatly at a As you can see, we can see where the maximum y value for quick rate, that is indication that two bluetooth devices are in 6 feet would intersect for the other distances much better. close proximity to each other, and have been for a long time. Some errors I would like to address would be the graphs for Through this experiment I was able to learn how to use 5 feet and 3 feet. As you can see, the 5 feet line is lower than raspberry pis and their bluetooth functions, as well as many the 6 feet graph, when theoretically this would not be the case, different aspects of signal strengths variations and factors that since RSSI values would be higher at the 5 feet in comparison affect RSSI. I learned that there are huge variances in RSSI to RSSI values for 6 feet. Also, the 3 feet RSSI values are very values depending on the distance between two devices. For small and fluctuate greatly. This might have happened due to example, at 3 feet, the RSSI values were very low, even if experimental errors that I could not control. The graph seems theoretically they should be higher at 3 feet compared to 4 feet. to resemble noise. However, this was not the case. I discovered that due to these After realizing these errors, I did 5 more trials for both 5 high varying RSSI values, I could not quantify accurately at feet and 3 feet, however I got the about the same results for which point the accumulated power would surpass the both distances. threshold made at 6 feet for 10 minutes. These results would have made no sense, since typically at a closer distance, the V. CONCLUSIONS time at which the protocol would execute would be shorter. With the data that I collected, I was able to find the VI. NEXT STEPS hypothesis true to a certain extent. Due to the errors that I received at 3 feet and 5 feet, I was unable to make exact In order to refine my hypothesis and experiments, I would predictions at those distances. Here is what I was able to make need to create a more ideal testing environment. Some for the other distances. These values are the times at which the examples would be to create an indoor space with minimal accumulated power for each distances would surpass signal reflections, identical raspberry pis, and ideal accumulated power at 6 feet for 10 minutes. environmental conditions. I would also do hundreds of more trials in order to get more accurate and precise results, since my • At 4 feet, it takes 1 minute and 28 seconds for the experiment is one where more data means a better chance of accumulated power to surpass ~0.0033. having a more generalized model that fits better to what is expected. • At 2 feet, it takes 14 seconds for the accumulated power to surpass ~0.0033. To utilize this research for the benefit of the PACT protocol, I would need to delve deeper into how power relates • At 1 feet, it takes 6 seconds for the accumulated power to to distance and time, as well as if this is a good way to develop surpass ~0.0033. a relationship between the time and distance to predict what I expected for the relationship to be more linear. For constitutes “too close for too long.” This model can be used in example, at 4 feet, I expected the accumulated power to situations where if two people are standing next to each other surpass the 6 feet threshold after a much lengthier time, at distances closer than 6 feet, we would not fire the protocol however from the accumulated power values, I found out the unless they were in that proximity for longer than what the opposite. I found that at varying distances, the accumulated model predicts surpasses the accumulated power threshold for power reaches the 6 feet and 10 minutes threshold at a much 6 feet at 10 minutes. quicker rate than expected. I am also depending on the huge assumption that virus transmission occurs in proportion to the REFERENCES accumulated power, since accumulated power would increase 1. https://en.wikipedia.org/wiki/DBm if the distance between to people, or pis in my experiment, 2. https://www.cnbc.com/2020/05/22/dranthonyfaucisaysstaying would decrease. closedfortoolongcouldcauseirreparabledamage.html 3. https://nj1015.com/keepyourdistancehowcloseistooclosefor Before, I said that my hypothesis was true to a certain coronavirus/ extent because I was able to develop a model at which the “too 4. https://www.fs.fed.us/emc/nepa/ecr2008/sessions/materials/18/ close for too long” protocol would be executed at distances Modeling%20&%20System%20Handout.pdf other than 6 feet. However, I am not sure whether this supports 5. https://www.itl.nist.gov/div898/handbook/pmd/section4/pmd41.htm that accumulated power is a good way to measure the relationship between time, distance, and the protocol 3
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