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 method implemented in a computing apparatus, 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, by:
converting the coordinates of the location into a cell identifier in a grid reference system;
determining whether or not the location identified by the coordinates is in the predetermined region based on whether or not the cell identifier is one of identifiers of cells predetermined to be within the region; and
determining whether the time at which the mobile device is at the location identified by the coordinates is in any of the plurality of time intervals;
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, 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;
executing, 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
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 method of claim 1 , further comprising:
determining a baseline rate of recording location data of mobile devices; and
scaling the set of visitation data points according to a ratio between the baseline rate 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.
3. The method of claim 2 , wherein the scaling comprises:
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.
4. The method of claim 2 , wherein the scaling comprises 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.
5. The method of claim 2 , wherein the scaling comprises 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.
6. The method of claim 2 , 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.
7. The method of claim 1 , wherein the capture-recapture module fits the capture history data to a log-linear model.
8. The method of claim 7 , wherein the capture-recapture module fits the capture history data to the log-linear model using iterative re-weighted least square.
9. The method of claim 8 , wherein the capture-recapture module generates maximum likelihood estimates of parameters used to fit the capture history data to the log-linear model.
10. The method of claim 8 , wherein the capture-recapture module evaluates deviance and Akaike Information Criterion (AIC) to assist selection of a best fit.
11. The method of claim 1 , wherein the converting of the coordinates of the location into the cell identifier in the grid reference system comprises:
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.
12. The method of claim 11 , wherein a cell identified by the cell identifier is a rectangle area in a longitude latitude space of locations on the earth.
13. The method of claim 12 , 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.
14. 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, by:
converting the coordinates of the location into a cell identifier in a grid reference system;
determining whether or not the location identified by the coordinates is in the predetermined region based on whether or not the cell identifier is one of identifiers of cells predetermined to be within the region; and
determining whether the time at which the mobile device is at the location identified by the coordinates is in any of the plurality of time intervals;
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, 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;
executing, 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
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.
15. The non-transitory computer storage medium of claim 14 , wherein the method further comprises: determining a baseline rate of recording location data of mobile devices; and scaling the set of visitation data points according to a ratio between the baseline rate 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.
16. The non-transitory computer storage medium of claim 15 , wherein the scaling comprises:
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.
17. The non-transitory computer storage medium of claim 15 , wherein the scaling comprises 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.
18. The non-transitory computer storage medium of claim 15 , wherein the scaling comprises 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.
19. The non-transitory computer storage medium of claim 15 , 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.
20. The non-transitory computer storage medium of claim 14 , wherein the capture-recapture module fits the capture history data to a log-linear model.