Systems and methods to measure the population of mobile devices in a predefined geographical region
Systems and method to measure a population size of mobile devices that have visited a region during a time period, by: converting location data of mobile devices into visitation data using a grid reference system, where for each mobile device and each of a plurality of time intervals in the time period, the visitation data identifies whether or not the mobile device has visited the region in the time interval; applying the visitation data as a capture history in an imaginary capture-recapture exercise, where whether or not a device has visited the region during a time interval represents whether the device is captured in the exercise in the respective capture occasion corresponding to the time interval; and estimating the population size based on an estimate of a population size of mobile devices that are not captured in the exercise from a capture-recapture statistical modeling of the capture history.
1. A non-transitory computer storage medium storing instructions which when executed by a computing apparatus, cause the computing apparatus to perform a method, the method comprising:
storing, in the computing apparatus, a plurality of location data points recorded for a time period, wherein each respective location data point of the plurality of location data points identifies:
a mobile device,
coordinates of a location of the mobile device, and
a time at which the mobile device is at the location identified by the coordinates;
determining, by the computing apparatus according to the respective location data point, whether the mobile device is within a predetermined region during any of a plurality of time intervals in the time period;
generating, by the computing apparatus, a set of visitation data points from the location data points, wherein each respective visitation data point in the set of visitation data points identifies:
a respective mobile device, and
for each respective time interval of the plurality of time intervals of the time period, whether or not the respective mobile device has at least one first location data point, in the plurality of location data points recorded for the time period, that identifies:
a time that is within the respective time interval, and
a location that is within the region;
providing, by the computing apparatus, at least a portion of the visitation data points as capture history data to a capture-recapture module, wherein:
the respective time interval corresponds to a respective capture occasion of a plurality of capture occasions,
whether or not the respective mobile device has at least one first location data point corresponds to whether or not the respective mobile device is captured in the respective capture occasion, and
the capture-recapture module is executed using the capture history data to obtain an estimate of a population size of mobile devices that are not captured; and
determining, by the computing apparatus, a population size of mobile devices that are within the region during the time period based at least in part on the estimate of the population size of mobile devices that are not captured.
2. The non-transitory computer storage medium of claim 1 , wherein the capture-recapture module fits the capture history data to a log-linear model.
3. The non-transitory computer storage medium of claim 2 , wherein the capture-recapture module fits the capture history data to the log-linear model using iterative re-weighted least square.
4. The non-transitory computer storage medium of claim 3 , wherein the capture-recapture module generates maximum likelihood estimates of parameters used to fit the capture history data to the log-linear model.
5. The non-transitory computer storage medium of claim 3 , wherein the capture-recapture module evaluates deviance and Akaike Information Criterion (AIC) to assist selection of a best fit.
6. The non-transitory computer storage medium of claim 1 , wherein the determining of whether the mobile device is within the predetermined region during any of the plurality of time intervals in the time period includes converting the coordinates of the location into a cell identifier in a grid reference system by:
generating two integers from longitude and latitude coordinates of the location according to a precision level; and
combining the two integers into the cell identifier without using a floating point number computation.
7. The non-transitory computer storage medium of claim 6 , wherein the converting further includes:
selecting digits from longitude and latitude coordinates of the location in accordance with the precision level to generate the two integers;
wherein the precision level corresponds to a cell resolution level in the grid reference system.
8. A computing apparatus, comprising:
at least one microprocessor;
memory storing instructions configured to instruct the at least one microprocessor to:
store, in the computing apparatus, a plurality of location data points recorded for a time period, wherein each respective location data point of the plurality of location data points identifies:
a mobile device,
coordinates of a location of the mobile device, and
a time at which the mobile device is at the location identified by the coordinates;
determine, by the computing apparatus according to the respective location data point, whether the mobile device is within a predetermined region during any of a plurality of time intervals in the time period;
generate, by the computing apparatus, a set of visitation data points from the location data points, wherein each respective visitation data point in the set of visitation data points identifies:
a respective mobile device, and
for each respective time interval of the plurality of time intervals of the time period, whether or not the respective mobile device has at least one first location data point, in the plurality of location data points recorded for the time period, that identifies:
a time that is within the respective time interval, and
a location that is within the region;
provide, by the computing apparatus, at least a portion of the visitation data points as capture history data to a capture-recapture module, wherein:
the respective time interval corresponds to a respective capture occasion of a plurality of capture occasions, and
whether or not the respective mobile device has at least one first location data point corresponds to whether or not the respective mobile device is captured in the respective capture occasion;
execute, by the computing apparatus, the capture-recapture module using the capture history data to obtain an estimate of a population size of mobile devices that are not captured; and
determine, by the computing apparatus, a population size of mobile devices that are within the region during the time period based at least in part on the estimate of the population size of mobile devices that are not captured.
9. The computing apparatus of claim 8 , wherein the instructions are further configured to instruct the at least one microprocessor to:
scale the set of visitation data points according to a ratio between:
a baseline rate of recording location data of mobile devices; and
a current rate of recording the plurality of location data points in the time period;
wherein the capture history data includes a scaled set of visitation data.
10. The computing apparatus of claim 9 , wherein the set of visitation data points are scaled to the scaled set of visitation data via:
randomly generating a visitation pattern for the plurality of time intervals; and
adding or removing a visitation data point identifying a mobile device having the visitation pattern.
11. The computing apparatus of claim 9 , wherein the set of visitation data points are scaled to the scaled set of visitation data via:
randomly adding visitation data points according to the ratio in response to a determination that the baseline rate is larger than the current rate of recording the plurality of location data points in the time period.
12. The computing apparatus of claim 9 , wherein the set of visitation data points are scaled to the scaled set of visitation data via:
randomly removing visitation data points according to the ratio in response to a determination that the baseline rate is smaller than the current rate of recording the plurality of location data points in the time period.
13. The computing apparatus of claim 9 , wherein the set of visitation data points before the scaling and the scaled set of visitation data have a same ratio of mobile devices in a plurality of groups, wherein respective mobile devices in each respective group in the plurality of groups have a same number of time intervals in which the respective mobile devices have visited the region according to the plurality of location data points.
14. The computing apparatus of claim 8 , wherein the capture-recapture module fits the capture history data to a log-linear model.
15. The computing apparatus of claim 14 , wherein the capture-recapture module fits the capture history data to the log-linear model using iterative re-weighted least square.
16. The computing apparatus of claim 15 , wherein the capture-recapture module generates maximum likelihood estimates of parameters used to fit the capture history data to the log-linear model.
17. The computing apparatus of claim 15 , wherein the capture-recapture module evaluates deviance and Akaike Information Criterion (AIC) to assist selection of a best fit.
18. The computing apparatus of claim 8 , wherein whether the mobile device is within the predetermined region during any of the plurality of time intervals in the time period is determined via converting the coordinates of the location into a cell identifier in a grid reference system by:
generating two integers from longitude and latitude coordinates of the location according to a precision level; and
combining the two integers into the cell identifier without using a floating point number computation.
19. The computing apparatus of claim 18 , wherein the converting further includes:
selecting digits from longitude and latitude coordinates of the location in accordance with the precision level to generate the two integers;
wherein the precision level corresponds to a cell resolution level in the grid reference system.
20. The computing apparatus of claim 19 , wherein a cell identified by the cell identifier is a rectangle area in a longitude latitude space of locations on the earth.
21. A method, comprising:
storing, in a computing apparatus, a plurality of location data points recorded for a time period, wherein each respective location data point of the plurality of location data points identifies:
a mobile device,
coordinates of a location of the mobile device, and
a time at which the mobile device is at the location identified by the coordinates;
determining, by the computing apparatus according to the respective location data point, whether the mobile device is within a predetermined region during any of a plurality of time intervals in the time period;
generating, by the computing apparatus, a set of visitation data points from the location data points, wherein each respective visitation data point in the set of visitation data points identifies:
a respective mobile device, and
for each respective time interval of the plurality of time intervals of the time period, whether or not the respective mobile device has at least one first location data point, in the plurality of location data points recorded for the time period, that identifies:
a time that is within the respective time interval, and
a location that is within the region;
providing, by the computing apparatus, at least a portion of the visitation data points as capture history data to a capture-recapture module, wherein:
the respective time interval corresponds to a respective capture occasion of a plurality of capture occasions,
whether or not the respective mobile device has at least one first location data point corresponds to whether or not the respective mobile device is captured in the respective capture occasion, and
the capture-recapture module is executed using the capture history data to obtain an estimate of a population size of mobile devices that are not captured; and
determining, by the computing apparatus, a population size of mobile devices that are within the region during the time period based at least in part on the estimate of the population size of mobile devices that are not captured.