Inferring Mobility Measures from GPS Traces with Missing Data

TL;DR

This paper presents a statistical method to accurately impute missing GPS mobility data from smartphones, enabling large-scale mobility studies by overcoming data gaps caused by battery-saving measures.

Contribution

A novel weighted resampling imputation technique for GPS data missingness, outperforming linear interpolation in preserving human mobility patterns.

Findings

Imputation reduces error in mobility measures by 10-fold compared to linear interpolation.

Method effectively captures human mobility patterns in GPS data with substantial missingness.

Approach validated on 182 individuals' GPS traces from the Geolife dataset.

Abstract

With increasing availability of smartphones with GPS capabilities, large-scale studies relating individual-level mobility patterns to a wide variety of patient-centered outcomes, from mood disorders to surgical recovery, are becoming a reality. Similar past studies have been small in scale and have provided wearable GPS devices to subjects. These devices typically collect mobility traces continuously without significant gaps in the data, and consequently the problem of data missingness has been safely ignored. Leveraging subjects' own smartphones makes it possible to scale up and extend the duration of these types of studies, but at the same time introduces a substantial challenge: to preserve a smartphone's battery, GPS can be active only for a small portion of the time, frequently less than $10\%$, leading to a tremendous missing data problem. We introduce a principled statistical approach, based on weighted resampling of the observed data, to impute the missing mobility traces, which we then summarize using different mobility measures. We compare the strengths of our approach to linear interpolation, a popular approach for dealing with missing data, both analytically and through simulation of missingness for empirical data. We conclude that our imputation approach better mirrors human mobility both theoretically and over a sample of GPS mobility traces from 182 individuals in the Geolife data set, where, relative to linear interpolation, imputation resulted in a 10-fold reduction in the error averaged across all mobility features.