sedentary living is increasingly common and contributes to approximately two million deaths per year  one of the top ten causes of preventable deaths worldwide . increased levels of physical inactivity have resulted from changes to the modern physical , economic , and social environment . moreover , the integration of advanced technologies has greatly reduced the amount of physical activity required for living and interacting socially . commercial solutions for physical activity tracking are increasingly available , leading to a strong academic interest in physical activity monitoring , particularly within the context of aging - in - place . however , the technology intended to promote independent living among older adults may present usability and acceptance concerns . older adults experience declines in physical , sensory , and cognitive capabilities as they age , which creates unique human - computer interaction design challenges that require careful consideration . older adults may experience apprehension from a lack of familiarity with advanced technology and obtrusiveness and privacy concerns . thus , research should be dedicated to developing physical activity tracking systems specific to the needs of aging adults . this work applies simulation and optimization techniques to demonstrate the possibility of collecting sufficient data to predict movement amounts of elderly adults , within their homes , using a small number of optimally placed sensors . our research found that it is possible to characterize the amount of error in these predictions , and attain globally optimal solutions for sensor placement in various senior living apartment layouts . this approach can therefore be valuable in obtaining low cost movement data which can support physical activity monitoring and promotion . current trends in physical activity monitoring take two forms : active ( typically , wearable ) sensor systems which require user actions to position and/or activate , and passive sensor systems ( typically , external systems with no sensors worn by the user ) which collect information without active initiation by the user . active sensing technologies typically collect physiological data from body - worn or clothing - embedded sensors . e.g. , unobtrusive wristbands or shirts  are typically low - cost , small , and powerful . such sensors are used to detect and record attributes including motion , location , temperature , steps taken / floors climbed , and activity duration / intensity . however , active sensors present challenges in terms of data collection and quality , particularly for older adults . first , research suggests that these technologies are not often developed with elderly consumers in mind , , . active sensing systems must be consciously affixed to the body , turned on , and checked to ensure they are functioning properly . often they require users have the technological sophistication connect and download data from the device . some depend on accelerometers for activity recognition and are therefore subject to error depending on placement on the body , , . additionally , some research has suggested that technologies worn on the wrist may be inappropriate for recognizing slow - speed ambulation activities . accidental arm movements can generate incorrect measurements and activity predictions , which may render these tools ineffective at adequately reflecting a user s energy expenditure . because older adults are often limited in the types of activity they can participate in , basic ambulation actions are sometimes their only observable activities . walking speed declines with advanced age ; therefore , technologies that are not precise enough to accurately reflect these movements are inadequate for use in this particular demographic . as an alternative to active sensors , passive systems have been proposed , where sensors are attached to objects in the user s environment , and inferences regarding the user s physical activity are made based on data captured by the sensors . unlike the active systems described above , users are not required to don , control , or download data from the sensors . tigerplace is an example of a residential community which extensively implemented sensors to support safe aging - in - place . a dense network of sensors allows researchers to integrate information from motion , bed , and stove sensors with a video sensor network and a behavioral reasoning system . however , as the number of sensors included in a system rises , the quantity and the complexity of the data collected increases , as does the cost to transmit the data , making it impractical for widespread implementation . in contrast , some other recent work has focused on more sparse passive monitoring systems . one such system   involves the use of ultrasonic range finders mounted in doorways to sense people as they walk between rooms . the system can differentiate among individuals based on height , infers their walking direction using signal processing , and identifies their room location based on the sequence of doorways through which they pass . while promising in terms of feasibility , using such low - density sensors raises questions regarding the degree to which the collected data can reliably measure an individual s physical activity level . our research considers whether or not a sparse network of doorway sensors could be useful for reliably capturing physical activity levels in a home . we conducted a simulation study is to determine the minimum number of doorway sensors required to produce useful information regarding the movement patterns of individuals within the home , as well as the optimal sensor placement . the following research questions are addressed : 
 1)whether a doorway - based system utilizing a small number of low - cost sensors is useful in predicting the amount of in - home movement.2)whether the amount of error in these predictions could be characterized as sensor number and placement changes to accommodate differences in senior living apartment layouts . whether a doorway - based system utilizing a small number of low - cost sensors is useful in predicting the amount of in - home movement . whether the amount of error in these predictions could be characterized as sensor number and placement changes to accommodate differences in senior living apartment layouts . these questions are explored using optimization and regression analyses involving five different apartment layouts taken from existing senior living communities , and simulated physical activities based on the american time use survey ( atus).http://www.infrahousing.com / verandah - project.html ( 1 - 3)http://www.sukhshanthi.com / index.php / specification / floorplanshttp://www.codechicdesigns.com / day - care - center - floor - plans/3/sample - daycare - floor - plan / http://www.swanbuild.com.au / kempton/ http://www.infrahousing.com/verandah-project.html ( 1 - 3 ) http://www.sukhshanthi.com/index.php/specification/floorplans http://www.codechicdesigns.com/day-care-center-floor-plans/3/sample-daycare-floor-plan/ http://www.swanbuild.com.au/kempton/ data were obtained from the atus micro - data files , made available by the us bureau of labor statistics . these surveys capture leisure and work - related activities of over 148,000 americans from 2003 to 2013 , providing activity - level information including activity code , location , duration , and activity start and stop times , on a per individual basis for one particular day . table 1 provides a snapshot of a data subset contained in the atus activity file . for each activity case i d , a combination of the three tier codes ( tutier ) indicates the activity performed . for instance , a combination of 01 ( tier1 ) , 02 ( tier2 ) and 01 ( tier3 ) corresponds to the activity of  washing , dressing and grooming oneself. a detailed list of what the activity codes correspond to are provided in the activity coding lexicons . the snapshot in table 1 indicates five different activities performed by a particular individual and provides information regarding the i d of the individual ( tucaseid ) , serial number of the activity performed ( act ) , the duration of the activity performed ( dur ) and what the actual activity was ( combination of tier1 , tier2 and tier3).http://www.bls.gov / tus/#datahttp://www.bls.gov / tus / lexicons.htmtable 1a sample subset of data found in atus activity filetucaseidactdurtier1tier2tier320060101020210121001010120060101020210240130131200601010202103400105012006010102021041011010120060101020210530180501 http://www.bls.gov/tus/#data http://www.bls.gov/tus/lexicons.htm a standard set of locations was identified by analyzing five senior citizen apartment layouts from communities across the united states . these locations included : kitchen , dining room , bedroom , washer / dryer , bathroom , and outside ( external to the apartment ) . the activity codes obtained from the atus were then mapped to a presumed activity location by manually creating a mapping from the activity type to the activity location . the average number of activities ( non - unique ) undertaken daily by each individual was 17.9 ( s.d . \documentclass[12pt]{minimal } 
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 \end{document}. fig . 1 shows the connectivity graph between rooms according to the floor plan for a particular apartment . each node corresponds to a room , and weights are assigned to the edges based on the sequence of rooms visited , representing the number of times a person travelled between the two nodes ( rooms ) at the end points of a particular edge . the complete dataset contains 2393 entries , one for each individual whose activity is being analyzed.table 3sample edge weight values for three individuals . the rooms are coded in numbers corresponding to fig . 1 ( 1 : bathroom , 2 : bedroom , 3 : kitchen , 4 : living room , 5 : laundry , 6 : outdoors)5434323136individual 127401individual 245709individual 325625 an integer programming model was constructed to study the percent of activity that could be detected by a limited number of placed sensors . let \documentclass[12pt]{minimal } 
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 \end{document } the objective function coefficients in ( 1 ) capture the total distance travelled by every individual through each edge of the connectivity graph . the constraint ( 1a ) ensures that the sensor placement is subject to the detection of at least \documentclass[12pt]{minimal } 
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 } { } $ w \times 100 $ 
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 \end{document } by the individual in the floor plan under consideration . the first 1500 data points in the atus dataset were used for training and the remaining 893 for testing . with the distance calculated in ( 2 ) as the dependent variable , and the number of crossings at a combination of the doorways ( from the  doorways crossings data ) taken \documentclass[12pt]{minimal } 
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 \end{document } corresponds to the number of sensors to be placed ) , a series of regression analyses ( using the method of least squares , owing to a linear model ) were performed to determine the doorway locations where sensor placement would produce the highest \documentclass[12pt]{minimal } 
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 \end{document}. table 5 displays the results of the optimal sensor assignment for different floor plans and numbers of sensors , providing the optimal sensor locations and the corresponding \documentclass[12pt]{minimal } 
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 \end{document}.table 5results for regression analysis to determine the optimal placement of sensors in order to obtain a model describing the best predictive analysis ( i.e. , highest r value)floor plan indexnumber of sensorslocation of sensorsr valuefloor plan 12bat - bed , bed - liv0.8663bat - bed , bed - liv , liv - out0.956floor plan 22liv - out , bed - liv0.8123bat - bed , bed - liv , kit - liv0.902floor plan 32liv - out , bed - liv0.83liv - out , bed - liv , liv - bat0.910floor plan 42bed - liv , kit - out0.9363kit - liv , bed - liv , kit - out0.964floor plan 52kit - liv , bed - liv,0.8513bat - liv , kit - liv , bed - liv0.881 table 5 displays a large \documentclass[12pt]{minimal } 
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 } { } $ r^{2}$ 
 \end{document } value ( approximately 0.92 on average ) for the placement of just three sensors , indicating that a predictive analysis is possible with a limited number of sensors . despite the overall large \documentclass[12pt]{minimal } 
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 } { } $ r^{2}$ 
 \end{document } values , it is possible for the model to prove unreliable ( i.e. , have large residual errors ) for specific cases . to assess the robustness of the predictions across the potential population , errors resulting from a predictive analysis of movement patterns , based on the atus data , were analyzed . in particular , information obtained from table 3 ( which was , in turn , generated from the atus data ) was used to determine the  actual distance ( ad ) travelled by an individual . in contrast , the  perceived distance ( pd ) was obtained by running the regression analysis of the distance travelled , based on data from placing a limited number of sensors . the optimal regression equation obtained was used to generate the  perceived distance ( pd ) and compared against the  actual distance ( ad ) to report the percentage error , \documentclass[12pt]{minimal } 
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 } { } \begin{equation * } error \% = 100\times \left ( { \frac { ad - pd}{ad } } \right ) \% . \tag{3}\end{equation * } 
 \end{document } equation ( 3 ) returns the value by which the  perceived distance ( pd ) differs from the actual distance . 2 shows the percentage error values over the testing population obtained from the regression analysis on floor plan 1 with three sensors . figure 2.histogram of error percentage in computing the perceived distance travelled ( via regression equation ) for each of the test data points ( each point corresponding to a unique individual ) . histogram of error percentage in computing the perceived distance travelled ( via regression equation ) for each of the test data points ( each point corresponding to a unique individual ) . errors were less than 25.8% for 85% of all individuals , indicating that it is feasible to perform a predictive analysis of movement patterns . the errors are skewed towards negative values signaling that the regression analysis tends to overestimate the distances travelled by the individuals . 3 demonstrates this phenomenon , by plotting percentage error for each of the 1007 individuals modeled , arranged in order of least- to most - distance travelled . as the ad travelled increases , the percentage error in the calculation of the pd travelled decreases . figure 3.plot describing the decrease in percent error in perceived distance ( pd ) with an increase in actual distance ( ad ) travelled by the members of the dataset . plot describing the decrease in percent error in perceived distance ( pd ) with an increase in actual distance ( ad ) travelled by the members of the dataset . one potential drawback of both the optimization study and the regression analysis is that they may be overly dependent on the way in which we assigned activity codes to location ( rooms ) . we , therefore , studied how the uncertainty / error in this assignment could have affected the above results . given a particular optimal sensor placement strategy based on possibly incorrect activity - to - location assignments , one can quantify the extent of the percentage error in pd due to the incorrect assignments . to this end , samples of  doorway crossings data for all individuals were drawn by randomly assigning activities to location codes in each sample ; the mean percentage error of the pd travelled by the individuals was computed from the regression study ( with respect to optimal sensor location assignment ) , and the variability in these mean percentage error values was assessed , across the samples . the random activity implies that a particular activity , e.g. , watching tv , is assigned a location at random from the set of all available rooms in the floor plan . given the optimal sensor placements for different floor plans ( table 5 ) , table 6 shows the possible error in placing the sensors in these locations if the activity codes had been assigned incorrectly in the first place.table 6results for mean and variance of mean percentage error values for the randomized sampling experimentfloor plan indexnumber of sensorsoptimal location of sensorsr valuemean percentage error*floor plan 12bat - bed , bed - liv0.86614.16  1.753bat - bed , bed - liv , liv - out0.95610.54  1.58floor plan 22liv - out , bed - liv0.81221.69  2.343bat - bed , bed - liv , kit - liv0.90214.86  2.09floor plan 32liv - out , bed - liv0.820.94  1.803liv - out , bed - liv , bed - bat0.91011.12  0.74floor plan 42bed - liv , kit - out0.93623.95  3.433kit - liv , bed - liv , kit - out0.9648.84  1.05floor plan 52kit - liv , bed - liv,0.85122.13  2.473bat - liv , kit - liv , bed - liv0.88113.29  1.80 table 6 indicates that the variance in mean percentage error values is reasonably small . this is encouraging , as even if some activity codes were to be assigned incorrectly , the sensor placements would still hold up for a robust regression analysis . this study shows that a small network of low - cost , minimally obtrusive sensors which tracks movement between rooms is a promising solution for monitoring the in - home physical activity of older adults . results indicated that placing three sensors could lead to an average regression coefficient of determination value of 0.922 for the five floor plans considered in this study , indicating the feasibility of a small , low - cost sensor system in a number of different environments . it is also possible to characterize movement patterns and errors for a large number and type of individuals by varying sensor number and placement . it is not unexpected that the \documentclass[12pt]{minimal } 
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 \end{document } values would turn out as high as they did , especially with two and three sensors , since the originally calculated distance travelled metric is , in itself , an approximation calculated relying on a linear equation [ eq . 1 ] , which assumes straight - line travel between the centers of two rooms . moreover , data regarding the number of passes between the various doorways is incorporated with a model involving specific floor plans , for analysis purposes . the actual movement patterns of the individuals would have been based on their own respective house plans . another potential source of error in this study is the method of data preprocessing : information regarding the rooms in which the activities occurred was not always available and could be subject to considerable variation between individuals . nonetheless , the data obtained from the simulation study is practically useful and results indicate that these limitations are unlikely to affect overall system performance . using the algorithm to outfit actual apartments in sensors would depend on specific floor plans and as such would need to be rerun for different apartment layouts . however , the model is fairly robust and resourceful enough that multiple reruns become a trivial matter . this is evident from the fact that a single instance of the algorithm would not involve more than 1020 variables and constraints . exploring methods of unobtrusive physical activity monitoring could have applications beyond supporting aging - in - place . for example , it could be used to monitor and provide feedback for individuals rehabilitating at home post - surgery , or generally provide feedback about activity levels to individuals concerned about wellness . future work should validate these models by comparing information that could be gained from optimal sensor placement with that gained from wearable activity trackers , in specific apartment settings . results from the study also suggest that certain floorplans are more conducive to collecting valuable activity data . it may be possible to design apartment layouts specifically to enable high reliability data collection with a sparse sensor network . an important next step in this line of research involves confirming the results with an actual series of experimental trials to gauge the overall impact of the methodology by incorporating a series of different floor plans .
an aging and more sedentary population requires interventions aimed at monitoring physical activity , particularly within the home . this research uses simulation , optimization , and regression analyses to assess the feasibility of using a small number of sensors to track movement and infer physical activity levels of older adults . based on activity data from the american time use survey and assisted living apartment layouts 
 , we determined that using three to four doorway sensors can be used to effectively capture a sufficient amount of movements in order to estimate activity . 
 the research also identified preferred approaches for assigning sensor locations , evaluated the error magnitude inherent in the approach , and developed a methodology to identify which apartment layouts would be best suited for these technologies .