Exploring strengths and weaknesses of mobility inference from mobile phone data vs. travel surveys

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Taylor & Francis in Transportmetrica A: Transport Science, Volume 16, on January 2020, available at https://doi.org/10.1080/23249935.2020.1720857 © 2020 Hong Kong Society for Transportation Studies Limited. En idUS Licencia Creative Commons CC BY-NC Exploring strengths and weaknesses of mobility inference from mobile phone data vs. travel surveys Noelia Caceresa*, L.M. Romerob and Francisco G. Benitezb a Transportation Engineering Unit, AICIA, Seville, Spain; b Department of Transportation Engineering, School of Engineering, University of Seville, Seville, Spain Camino de los Descubrimientos s/n, 41092 Seville, Spain. Tel.: +34 95 448 8135. E-mail address: [email protected]s *corresponding author Exploring strengths and weaknesses of mobility inference from mobile phone data vs. travel surveys Origin–destination (OD) matrices serve as a basis for travel demand modelling. Traditionally, they are derived from travel surveys that collect detailed trip information but with several shortcomings. Mobile phones are regarded as a useful source of information on people’s daily mobility. This work explores the use of mobile data in the context of mobility studies by comparing matrices derived from both types of sources over the same region. The results reveal many common features in the trip information. Moreover, although the use of mobile technology may raise questions for short trips, the huge representativeness of this technology captures the mobility in OD connections extensively regardless the area. This is crucial for non-populated areas (e.g. industrial parks or educational campuses), which constitute important mobility hotspots. Based on these findings, an applicable data fusion approach to obtain the optimum accuracy from these heterogeneous sources is presented and applied. Keywords: mobile phone data; household travel surveys; OD matrices 1. Introduction Origin–destination (OD) or trip matrices are fundamental inputs for most problems regarding the planning and management of transportation systems. They reflect the mobility in an area of study during a particular period of time. Each cell in the matrix indicates the number of trips that depart from each origin zone to each destination zone. Hence travel demand is usually represented using an OD matrix. In the past few decades, OD matrices have been derived from travel surveys in which people are asked to describe their travel behaviour on an average day or to reconstruct their travel pattern on one or more previous days. Many types of surveys, such as home interviews, roadside interviews, or even a combination of them, are used to obtain OD matrices in practice; such surveys vary in complexity regarding the information which can feasibly be collected and in the level of interaction between the survey designer and the respondents (Richardson et al. 1995). Home or household interview surveys are the most widely used and are essentially intended to yield data on the travel behaviour of the residents of the household (e.g. number of trips made, their origin and destination, purpose of trip, mode(s) of travel, departure and arrival times, etc.) and the general characteristics of the household or respondent (e.g. family size, age, sex, income, vehicle ownership, etc.). Survey-based approaches involve costly and laborious processes for collecting, coding, and processing data (Stopher and Greaves 2007; Santos et al. 2011; Ortuzar and Willumsen 2011). As a result, surveys are not conducted frequently (about every five or even ten years) and various methods are used for estimating an OD matrix in practice (as reviewed in Abrahamsson 1998). Among them, the use of traffic counts as measurements of link flows in a network model in order to update an existing (probably outdated) matrix has been widely considered by many researchers (Van Zuylen and Willumsen 1980; Doblas and Benitez 2005; Cascetta et al. 2013). However inference approaches based on just link count data are known to be a challenging problem; normally there are a large number of matrices which reproduce the observed traffic counts (Abrahamsson 1998). Advances in data collection and computational techniques have incorporated other observed data sources in the estimation procedure, such as automated vehicle detection (Zhou and Mahmassani 2006; Castillo et al. 2013) or routing data (Herrera et al. 2010; Parry and Hazelton 2012). Obviously the accuracy of OD matrices obtained by these methods will be highly dependent on the quality of the information used. Road planners and practitioners demand more accurate and updated information for transport planning and decision making. Survey-based approaches strive to collect very detailed trip information, but they present several deficiencies (Brög and Erl 1999; Bonnel 2003; Ampt and Ortuzar 2004; Cools et al. 2010; Ortuzar et al. 2011), mainly related to sampling biases (e.g. falling response rates, vacant dwellings) and reporting errors (e.g. unreported trips, rounding of arrival and departure times). They no longer seem adequate to provide reliable OD matrices. In recent decades, mobile phone data have also become a promising data source. Mobile phones are pervasively embedded in people’s lives – more than one-third of consumers worldwide said they check their phone within five minutes of waking up in the morning, and 20 percent of them check their phone more than 50 times a day (Global Mobile Consumer Trends 2017). The deployment of mobile technology is producing a massive increase in the volume of data regarding where people have been and when they were there, which can not only lead to accurate and updated estimation of mobility matrices, but also to infer other valuable features for planning transport, exhaustive reviews can be found in Milne and Watling (2018) and Gadzinski (2018). The idea of using mobile phones to acquire transport information is becoming more and more widespread; reviews of current practices can be found in Steenbruggen et al. (2015); Chen et al. (2016); Diao et al., (2016); Rojas et al. (2016); Lee et al. (2016); Lu et al. (2017) Malleson et al. (2018); Wang et al. (2018) among others. In the field of OD matrices and travel behaviour, the use of mobile phone data has been explored by researchers working on simulated frameworks (Caceres et al. 2007; Sohn and Kim 2008; Zhang et al. 2010; Hofer et al. 2018) as well as in field tests (Mellegard et al. 2011; Calabrese et al. 2013; Widhalm et al, 2015, Demissie et al. 2015; Horn et al. 2017; Wang and Chen 2018; Ni et al. 2018). Their results reveal that mobile data can overcome typical limitations of traditional surveys, with higher sample size, wider coverage, and reduction of the time and cost of data collection and processing, while also providing valuable information on temporary mobility patterns. By contrast, these works also mention the problems associated with using mobile technology as a mobility data source, especially in terms of low spatial resolution and accuracy. To obtain more realistic matrices, recent approaches have combined mobile phone data with other types of data, such as traffic counts (Caceres et al. 2013; Iqbal et al. 2014; Wu et al. 2015; Meng et al. 2017), GPS traces (Gong et al. 2014; Ge and Fukuda 2016; Seo et al. 2017; Nigro et al. 2018), and even a fusion of crowdsourced geospatial information, smartcard transactions, census records, and/or surveys (Toole et al. 2015; Anda et al. 2017; de Regt et al. 2017; Bonnel et al., 2018). Despite the important efforts made in exploring the use of mobile phone data to characterise people’s mobility, there are still pending issues to be reviewed in the context of matrix estimation. This study is an attempt to extend the effort in the area to gain a clearer understanding of the potentialities and challenges of this technology compared to traditional survey sources, based on the outcomes derived from a real case study. This paper is organised as follows: Section 2 introduces an overall view of the case study, presenting the study area and the data sources. Section 3 exploits the transport data of the pilot case, derived from a household travel survey and a mobile phone telecommunication provider; a comparative analysis is carried out, highlighting the differences and similarities from the qualitative and quantitative points of view. Section 4 provides a discussion on the main advantages and drawbacks revealed by the analysis. Finally, the potentialities and challenges of mobile phone data in complementing traditional survey methods are illustrated in Section 5 along with some suggested directions for further practical applications. 2. Data and methods 2.1. Study area The study area corresponds to the urban agglomeration of Malaga, located in the south of Spain on the Mediterranean coast. It consists of the city of Malaga, which is the sixth most populated city in Spain, and 14 surrounding municipalities in both the coastal zone and the interior. The study area has a population of around one million inhabitants and covers approximately 1400 km2, divided into 178 transport zones (TZ) defined from census data (Fig. 1a). The zoning is also further aggregated into 46 macro-zones (MZ), more general areas based on adjacent (similar socioeconomic) transport zones (Fig. 1b). (a) (b) Fig. 1 Zoning of study area: (a) transport zones and (b) macro-zones. Cities are represented by different colours. 2.2. Trip matrices This study is based on available OD matrices derived from two sources: household travel surveys (HTS) and mobile phone data (MPD). The last household travel survey, led by the regional transport system planning administration, was conducted in October 2014 by the Malaga Area Metropolitan Transport Consortium (a Spanish public transport body) with the aim of characterising a detailed picture of workday mobility and travel choices made by residents of the study area. The survey reported all trips made by each resident of the sampled households. In particular, approximately 30,000 persons were interviewed (around 3% of the population in the region). The results were then statistically expanded and validated based on other socioeconomic datasets obtained by governmental agencies, deriving the corresponding OD matrices. Mobile phone data come from network operators which collect, store, and process massive datasets on subscribers so they can route calls and offer services. The data used for this study are based on aggregated and anonymised phone events collected and processed by a telecommunication operator with a large market share (around 40%) in the studied area. These events consist of active interactions related to phone calls and text messages, as well as passive interactions, which occur in the background (or idle status) without the user’s active participation. These passive interactions are associated with signalling, such as losing/regaining mobile signal or periodic records created when phones are on but have not created any other events for a sustained period of time (typically of the order of a few hours). Besides, there is also a relevant passive event associated with movement from one specific group of cells (called a location area, LA) to another. In mobile systems, the service coverage area is classified into cells and these are grouped into LAs. For mobile operating purposes, whenever a phone enters a new LA, it notifies the mobile network of its new position. This type of event substantially increases the number of the MPD events. Each one is characterised by an encrypted user ID (following strict anonymised protocols to guarantee privacy), a timestamp when the event occurs, and an event location estimated using algorithms based on triangulation of mobile phone mast signals. These events provide ‘footprints’ regarding where people have been and when they were there. In this study, a trip is regarded as a one-way movement from a zone of origin to a zone of destination at a particular starting time. Users are more likely to engage in an activity (by means of a trip) after a ‘stay’ at a particular location (that represents the origin or destination of a trip). The remaining footprints provided by the events occur during the displacement that takes place. Therefore, the first step is to identify which footprints are ‘stays’. For this purpose, several authors have developed different algorithms (Widhalm et al. 2015; Alexander et al. 2015; Toole et al. 2015; Jiang et al. 2017). In this work, the identification is based on a time threshold in the subsequence of events. This threshold for the time between consecutive events (tbce) has been taken as a simply rule-of-thumb for identifying if an event belongs to a possible new trip (tbce ≥30 min) or to the same trip after a brief stop (tbce <30 min). An event defines the end of a trip when the time difference to the next event is more than 30 minutes; this end defines the beginning of the ‘stay’ but also the origin of the next subsequence of events. By processing all existing events created by the sample of users, trips are inferred. These trips are derived by considering the proximity of events not only in terms of time but also regarding the space. For instance, it is necessary to analyse whether events reveal an actual movement or they are generated by static users due to the ping-pong records in the neighbouring towers. The characteristics of the transport network topology are also analysed. For instance, the associated distance between two consecutive events as well as the difference between their timestamps has to be checked to ensure that they are compatible with the travel distance and travel time, respectively, for the possible routes. Based on this, all events generated over the study area during two consecutive weeks in February 2015 (ten working days and four weekend days) were processed to infer trips made by the considered sample (approximately 200,000 persons, aged 18 years and above) based on subscribers of the particular operator. The results were expanded to represent the full population of the studied area based on census data taking into account the area where user’s home is located, similarly to expansion made in propose the use of the Mean Structural SIMilarity (MSSIM) index as an OD matrix comparator (Djukic et al. 2013; Pollard et al. 2013; Day-Pollard and Van Vuren 2015). The most important feature of this metric, developed for comparing images at pixel level (Wang et al., 2004), is the use of additional information in the evaluation process on the basis of the structural patterns in data. In general, images are highly structured, with pixels that are close to each other appearing to have strong dependencies. Based on this, the MSSIM computes statistics on groups of pixels (those within a window) and then takes the average (mean), rather than computing statistics based on all the pixels in the image together. If an image is equated to an OD matrix, the cells in the matrix (or OD pairs) can be seen as pixels that exhibit strong dependencies as well. If the two matrices describe similar transport patterns then, as with pixels, it is reasonable to expect similarities on windows of OD patterns (Pollard et al. 2013). The MSSIM index is designed to capture this property in a [–1, 1] scaled range. The largest positive value means the highest similarity (full match), while the smallest negative value entails the highest dissimilarity (significant differences). Although the MSSIM approach requires further refinement for use with OD matrices, the MSSIM index can identify structural differences better than traditional measures such as r-squared; conversely, MSSIM is successfully used as a measure of matrix similarity in the works referred to above. The MSSIM is calculated by summing and averaging Structural SIMilarity (SSIM) values across a whole matrix using an iterative procedure in which the SSIM is calculated over a part of the matrix (local window), generally a few cells wide by a few cells high. The expression used for calculating the MSSIM between two matrices, A and B, is: 1 1 ( , ) ( , ) M jj j MSSIM A B SSIM a b M= =  (1) where aj and bj are the OD matrix contents at the j-th local window and M is the number of local windows in the matrix. The local window, which may be a square box of N × N elements, moves cell-by-cell over the entire matrix. At each step, the local statistics and the SSIM index are calculated within the local window according to the following expression: 12 2 2 2 2 12 22 ( , ) a b a b a b a b CC SSIM a b CC          +  + = + + + + (2) where μa and μb are the mean values within this part of the matrices a and b, respectively; σa and σb are the variance of each dataset; σab is the covariance of the two matrices; and C1 and C2 are stabilisation coefficients. The SSIM is calculated according to the methodology described by Wang et al. (2004) and Pollard et al. (2013), with their values for C1 and C2. To define the window, it is assumed that the pixels of images that are closer to each other usually have a stronger relationship than the more distant ones. The contribution of the proximity in the SSIM calculation is then modulated by a Gaussian weighting function, w = {wi | i = 1, 2, …, N} for the local window of size N. The estimates of local statistics for the mean, variance, and covariance in (2) are then modified to incorporate such weights in the SSIM calculations. But in this sense, it is necessary to remark that, unlike in images, the proximity of cells in OD matrices does not guarantee that they are also close in space (e.g., zones 1 and 2 may be rather distant) and the window has to be established to consider this proximity. This issue was already considered in other works using this index for comparing OD matrices; Day-Pollard and Van Vuren (2015) proposed the Euclidean distance between two cells i and j defined in (3), using the xy-coordinates of the origin and destination centroid for OD pair i (xOi, yOi, xDi, yDi) and OD pair k (xOk, yOk, xDk, yDk), as a way of considering this fact in the SSIM calculations: ( ) ( ) ( ) ( ) 2 2 2 2 ( , ) i k Oi Ok Oi Ok Di Dk Di Dk d ODpair ODpair x x y y x x y y= − + − + − + − (3) This Euclidean distance d is then used in the Gaussian function () 2 d w exp  = to determine the contribution of OD pairs, with cells that are further apart contributing less. According to this, the MSSIM values between daily and hourly matrices from the two sources are calculated. At daily level, although slightly better results are obtained at macro-zone level than at transport zone level, the structural correlation reaches high values in both cases (MSSIMTZ = 0.78; MSSIMM Z = 0.83). Fig. 6 shows the structural correlation between matrices on an hourly basis, with similar values to the daily case in time periods in which workday traffic is usually concentrated (between 7:00 and 20:00 hours). This means that the structural patterns in the daily matrix derived from MPD are very close to those captured in the matrix derived from HTS, for example in terms of the distribution of trips over destinations. Fig. 7 a and b illustrate the flow distribution at the macro-zone level (only pairs with more than 1000 daily trips) for matrices derived from the HTS and MPD sources, respectively. A visual analysis reveals that both sources capture similar patterns, with the majority of flows directed to and from home and work areas in Malaga as well as a few flows to and from the second most populous city of the study area (Alhaurin de la Torre). In both cases, the highest flow occurs between the two cities located in the southwestern part of the area of study (Mijas and Fuengirola). Another interesting strand revealed by the analysis, focusing on the time periods between 7:00 and 20:00 hours, is that the MSSIM index remains around the same value (approx. 0.77) at both macro-zone and transport zone level. Unlike the linear correlation coefficient, which is more influenced by the sparsity of matrices, the MSSIM index does not appear to reflect significant changes working at different levels of zoning-system granularity. This is explained by the fact that the MSSIM index measures the structural aspects of how cells (OD pairs) relate to one another and not the individual cell values themselves. Therefore the MSSIM index, in addition to identifying structural differences better than traditional similarity/correlation indexes, makes it possible to simultaneously compare sparse and dense matrices under similar quantitative criteria. Fig. 6 MSSIM index at both transport zone and macro-zone level for the relationship in the OD-pair data derived from the two sources (MPD and HTS) by one-hour period. (a) (b) Fig. 7 Major OD flows between macro-zones: (a) daily matrix derived from the HTS and (b) daily matrix derived from the MPD. 3.1.3. Similarities in trip information: origins and destinations Additionally, the level of similarity by origin (aggregating columns in the matrix) and by destination (aggregating rows in the matrix) of trips has also been explored using the correlation coefficient. Table 1 presents the coefficients reached in these terms, with similar values to the values obtained at OD-pair level. The two sources are more correlated when the zoning system is rolled up to a lower granularity. Fig. 8 displays these coefficients for all onehour periods of a day. Table 1. Correlation between trip information from the two sources (MPD and HTS). Trip information Zoning system Rp By origins Transport zone level 0.38 Macro-zone level 0.80 By destination Transport zone level 0.38 Macro-zone level 0.79 (a) (b) Fig. 8 Pearson’s coefficient (Rp) by one-hour periods of the day, correlating MPD and HTS sources: (a) by origins and (b) by destinations of trips. (a) (b) (c) (d) Fig. 9 Number of trips during the morning-peak period (08:00–8:59): (a) trips originated in each macro-zone derived from HTS; (b) trips originated in each macro-zone derived from MPD; (c) trips terminated in each macro-zone derived from HTS; (d) trips terminated in each macro-zone derived from MPD. Fig. 9 represents the study area coloured by the number of trips originated or terminated in each macro-zone from the HTS and MPD, all of them referred to the morningpeak period. In general, the two sources generate similar results, except for major cities (with an important component of short-distance trips) and macro-zones including non-populated areas. Regarding this last point, an interesting observation can be made by analysing the macro-zones in which the major divergences are concentrated. For this purpose, Fig. 10 displays the proportional distribution of the numerical differences (errors) between the two data sources. A positive sign means that the number of HTS-based trips is larger than the number of MPD-based trips for each macro-zone, whereas a negative sign means the opposite. As can be seen, the major differences between sources occur in the macro-zones numbered 1, 14, 21, 26, and 27. In particular, for macro-zone number 1, containing the city centre, the analysis reveals that the number of trips originated using HTS is greater than the number from MPD. This macro-zone is characterised by an important component of shopping, services, and other leisure activities which imply mobility by walking and short trips, for which mobile technology may be less precise as a mobility probe (as discussed in the next sections). In contrast, the number of trips originated in macro-zones 14, 21, 26, and 27 derived from MPD is larger than the number derived from HTS. These macro-zones include university campuses and major industrial parks, indicating a significant divergence regarding the data-collection capability of HTS in these sectors. Fig. 10 Total error distribution in the number of daily trips originated in each macro-zone between the two data sources (HTS and MPD-based matrices). A closer look at the information by origins (MPD vs. HTS) now focusing on trips originated in each transport zone reveals an important finding when colour and size are added to include information on the population (Fig. 11). For trips generated during the whole day (Fig. 11a) and during the morning-peak period (Fig. 11b), the HTS source tends to underestimate those trips originated in non-populated zones (identified by big red dots). These transport zones are associated with mass transportation facilities (like the railway station, central bus terminal, and airport) as well as university campuses, industrial parks, and hospitals located in the study area. This suggests that these types of zones may not be properly represented in survey campaigns, despite being important centres where trips originate and terminate. In most cases, this is the fault of designing samples in survey-based campaigns based on population size and in terms of the number of households in the study area. Non-populated zones are excluded from the sampling frame (there are no households to be interviewed); other cases, such as non-resident populated zones, are also not identified by surveys based on census data (e.g. university residences). Hence, the sample might not be representative of all people travelling from/to these zones. There are other types of surveys (e.g. intercept surveys) that take place at non-residential sites while the respondent is in the course of carrying out an activity of some type (e.g. shopping). Although they can better synthesise the mobility over these zones, these types of surveys using uncontrolled quota sampling have controversial drawbacks regarding reliability. It is necessary to use a combination of survey methods to take advantage of their pros and cons, but even a combination of intercept and home interview surveys may fail to produce matrices where all cells have been sampled (Ortuzar and Willumsen 2011). However, the representativeness of the MPD sample, which is homogeneously distributed across the territory, captures trips with independence of the socioeconomic characteristics of the zone (origin or destination) of trips. Other concerns regarding sample size are addressed in the next section. (a) (b) Fig. 11 Number of trips originated in each transport zone (MPD vs. HTS) coloured according to the population: (a) during a day, and (b) during the morning peak period (08:00–8:59). 3.1.4. Trip distribution by distance From the mobile-data perspective, the detection of movements is strongly subject to the number of events generated by phones as they communicate with the network. The more events are generated, the more footprints are available from which to infer trips. In this regard, a longer trip duration increases the possibility of a call, message event, or even the abovementioned passive events. In a similar way, a longer trip distance also offers more opportunities to generate events (e.g. due to movement events created when a user changes from one group of cells to another). An example of this is depicted in Fig. 12a. In contrast, when trips are made in less time (because they imply shorter distances or are made at faster speeds), mobile phones leave fewer footprints of their ‘approximate’ locations during their movement (Fig. 12b). The consequences of these issues cannot be ignored when using MPD, since these types of short trips tend to be undercounted or completely overlooked when exploiting mobile data. (a) (b) Fig. 12 Examples of mobile-event generation during (a) a non-short trip and (b) a short trip. Therefore, focusing on distance travelled (based on the network shortest distance between the origin and destination centroids), Fig. 13a reveals that for medium and long distances, which are customarily made by motorised modes, travel rates are very similar for the two sources (MPD in blue and HTS in red). But for distances shorter than 2.5 km, a MEDIUM-DISTANCE TRIP: FROM HOME TO WORK Event 1 Turn on the phone on early morning Event 2 Change LA Event 3 Make a call SHORT-DISTANCE TRIP: DROP OFF CHILDREN AT SCHOOL Event 1 Turn on the phone on early morning Event 2 Periodic record significant reduction of the MPD rates is appreciated. This suggests that mobile data tend to under-report short-distance trips, as shown in Fig. 13b. In this respect, it is worth underlining that transport modes related to short-distance trips are usually non-motorised (Ryley 2008) and are primarily ‘walking’, although ‘cycling’ also occurs. Research in the literature shows that the average ‘walking’ speed is around 4 km per hour (km/h), while that of ‘cycling’ is around 10–12 km/h (Jensen et al. 2010), depending on factors such as the user's age, gender, or even surface condition. By cross-checking short-distance trips with low travel speeds, a dynamic mobility pattern on the scale of the neighbourhood in cities can be obtained; this pattern is difficult to detect with the spatial resolution offered by mobile technology (it is strongly dependent on the granularity of the mobile network), requiring additional methodologies like GPS (Ge and Fukuda 2016). Moreover, in terms of travel time, many of those short trips take less than 15–30 minutes, a quite reduced time window for generating mobile events. However, this comparison does not seem to be the most appropriate for contrast purposes, since survey-based approaches also present resolution problems in such time windows. For example, trips tend to be rounded to the nearest 10-minute or even 15- minute interval by survey respondents (Stopher and Greaves 2007) and daily travel times per person are considerably overestimated for the first 15-minute time interval (Gerike et al. 2015). Thus, to overcome these issues, Fig. 13a also displays travel rates derived from HTS considering only trips with durations (reported by respondents) greater than 15 minutes. These travel rates (bars in green) are certainly close to MPD rates (bars in blue), especially in the context of short distances. But the difference in magnitude of total trips between the two sources (Fig. 13b) reveals a concern that should be addressed when using MPD sources. events. Therefore, mobile events may be too sparse to determine these trips consistently. Of course, this does not mean that mobile technology is not able to capture short trips at all but merely indicates that short trips are more likely to be undetected than other trips according to the current state of this technology. • Separately, there is a facet that can also affect the under-reporting of short-trips. This issue is associated with the matching algorithms to convert the footprints (generated by mobile events during movement) into origins and destinations within the zoning system. In the context of this comparative study, both mobility sources (MPD and HTS) are referred to a traditional zoning system based on polygonal sectors corresponding to administrative divisions (or transport zones). However, mobile technology has no information about the exact positions of handsets in the study area (like GPS technology) but only has information about regions linked to the service coverage area of antennas (or cells). This coverage area varies from site to site, ranging from hundreds of metres in urban areas to tens of kilometres in low population areas. Since the location algorithm is based on the triangulation of cell tower signals, mobility data are constrained by the density of cell towers in the studied area. In this study, focusing on a dense urban area, cell tower triangulation works pretty well. In particular, the spatial resolution is claimed to be about a few hundreds of metres, ranging from 200 to 300 metres. But here, the location is referred to the zoning system of the studied area, adding a bit more spatial uncertainty. In mobile systems, the antennas are distributed following a Voronoi tessellation to provide adequate radio coverage for communication rather than transportation planning criteria (such as homogeneous socioeconomic characteristics) used for the zoning system. Then, usually a cell (black polygon in Fig. 14a) overlaps not exactly with a typical transport zone but partially with two or more transport zones (black polygon in Fig. 14b). Therefore, there are errors in the conversion of trips between cells and trips between transport zones. The larger the transport zone with which the cell has to be matched, the lower the matching error obtained (red polygon in Fig. 14). Moreover, mobile systems are designed to have an overlap between the cells to avoid coverage holes. Therefore, the complexity of matching ‘footprints’ provided by MPD with the zoning system is reduced by working at broader zones (i.e. lower granularity). (a) (b) Fig. 14 Area division (a) based on Voronoi tessellation in mobile networks; (b) by zoning system based on administrative divisions. Despite this last remark, matrices derived from MPD can be regarded as a complementary source of information that synthesises the overall picture of mobility over a region. In particular, when the zoning system is rolled up to a lower granularity, many common features in travel behaviour can be detected by cross-checking sources. Transportation studies have to be continuously adapted to the changing lifestyles in our society but also have to become much more economical to perform. In this sense, mobile data represent a valuable technology for transport modelling. The time and cost of data collection and processing are visibly reduced as data are automatically and passively generated by mobile users. Furthermore, despite the criticisms discussed in Sections 3.2.2 and 3.2.3 regarding sampling problems, this technology provides a means of sampling people’s mobility at large population scales. Therefore, this data collection method allows transportation studies to mitigate the effects of the major sources of errors in travel surveys: sampling, non-coverage, non-response, and measurement errors (Ortuzar and Willumsen 2011). This fact is also of paramount importance due to the growing difficulty of contacting and interviewing citizens regarding their travel behaviour. But nowadays, public administrations are demanding not only more updated information to analyse transportation strategies but also more detailed data. In this regard, surveys remain one of the most important ways of obtaining rich details about socioeconomic information, trip-making characteristics, or even stops. These pieces of information are extremely valuable for transport planning and decision making, and therefore it is envisaged that surveys will continue to be an integral part of transportation studies. 4.1. Data fusion approach Based on the previous discussion, the challenge is to develop data fusion methodologies able to obtain information with the optimum accuracy from a variety of heterogeneous sources. This involves taking advantage of the strengths of mobile data (e.g. extensiveness of OD relations and connections, representativeness), minimising their weaknesses (in particular inaccuracies for short trips) by means of other information sources like travel surveys. However, surveys do not have to come from exhaustive procedures intended to yield data on origin–destination flows, but on general characteristics of travel behaviour like total trips over the study region or trip distribution by distance, which are less costly. One possible way of addressing this issue can be seen as an OD matrix estimation problem, for which entropy maximisation and information minimisation principles have been commonly used (Wilson 1970; Willumsen 1978; Van Zuylen 1978; Van Zuylen and Willumsen 1980). These works demonstrated that by maximising the entropy, the most likely trip matrix could be estimated subject to a set of constraints. An attractive feature originally proposed by van Zuylen (1978) consisted of incorporating extra information (like a prior trip matrix) that might lead to a more realistic estimate of the trip matrix. With this choice, the relative entropy H of the estimated matrix G with respect to a prior matrix M is defined as follows: , ( , ) log 1 ij ij ij ij g H G M g m   =−        (4) where gij is the estimated number of trips from transport zone i to j, and mij is the number of trips between transport zones i and j from the prior matrix. In this case, the daily MPD-based matrix is selected as the prior matrix due to the strengths mentioned in the previous sections. The estimated matrix gij will have the same structure as the MPD-based matrix mij, conserving the extensiveness of OD relations and connections monitored by mobile technology. The entropy maximisation principle seeks to identify the most likely trip matrix consistent with the information available (Ortuzar and Willumsen 2011). However, additional information has to be included in the problem to correct inaccuracies detected in mobile data, specifically for short trips (which tend to be undercounted or completely overlooked in this source). This scheme is modelled by means of constrains based on information derived from the available travel survey. In the developed framework, the constraints are based on the total number of trips and the trip distribution by distance, provided by the HTS-based matrix. Therefore, the problem can be reformulated based on this information and the objective function, in a simplistic way as follows:     , () min log 1 .. 1,..., ( ) , 1,..., ( ) ij ij ij gij ij ij b ij Bin b ij ij i I j J i I j J g gm st g P T b B a g m I J MZ b        −       =    =       (5) Problem (5) resembles the classical double constrained distribution problem. In the expressions, the notation adopted uses the uppercase indices to denote macro-level zones, whereas transport zone levels are represented by means of lowercase indices. The optimisation problem aims to find the OD matrix gij with the closest similar structure to the mobile phone matrix, mij, using the criterion of minimising its relative entropy, which can be considered as a distance function between matrices G and M. Restrictions in (5) impose that the resulting matrix must fulfil a set of state constraints. The constraints defined by (a) will be referred to hereafter as ‘histogram restrictions’, and they are aimed at maintaining the trip distribution by distance provided by the HTS-based matrix. For its definition, it is necessary to distribute OD pairs according to the distance travelled (based on the network shortest distance between origin and destination centroids). Therefore each OD-pair is classified in a discrete number of intervals or bins, |B|, where Pb is the proportion of trips in the distance range identified by bin b, and T is the total number of trips, both magnitudes provided by the HTS-based matrix. With the product of the proportion of trips Pb and the total number of trips T, the number of trips for each bin is obtained directly. During the estimation procedure, the cells in the estimated matrix gij are modified to fulfil the imposed ‘histogram restrictions’. However, the prior matrix (MPD-based matrix) contains valuable information regarding the ‘true’ matrix, thus the estimation method pays careful attention to the distortion of the information contained in it. To control the distortion at each cell, of the estimated matrix (number of trips from transport zone i to j) with respect to the prior one, an additional set of constraints (b) is imposed. In this case, the constrains are built to maintain the number of trips at macro-zone level. As mentioned in section 3.1.2, the number of trips between macro-zones is more accurate when the zoning system is rolled up to a lower granularity. In fact, the two sources (HTS and MPD) reflect a strong linear relationship between the numerical values (trips) at macro-zone level, not only for OD trips but also for trips either by origins or by destinations. Hence, trips at macro-zone level have to be maintained during the estimation procedure. Thus, the number of trips between macro-zones I and J in the estimated matrix are forced to be equal to those trips between the same macro-zones in the prior matrix, where I, J belong to the set MZ of 46 macro-zones defined in the study area. The analytical solution to the optimisation problem (5) is well-known, and it is expressed as: ( ) ( )ij b ij IJ ij ij gm  =   (6) where the lengths of vectors of coefficients α and β are respectively |B| and |MZ|. The solution obtained corresponds to a multiplicative model, which implies that original zeros in the prior matrix mij are kept as zeros in the final matrix gij, preserving the original structure of mij. According to this, the total number of trips T is now distributed among the number of OD connections captured by mobile technology, which is clearly higher than those captured by surveys. As mentioned in Section 3.1.1, HTS-based matrices have to distribute this total number of trips among a substantially fewer number of elements; consequently, the number of HTS-based trips tends to be overestimated. The problem (5) can be solved by means of an iterative proportional fitting procedure, largely used in transportation studies (Furness 1965; Lamond and Stewart 1981; Erlander and Stewart 1990), whose proof of the convergence is reported in Bregman (1967). The estimated matrix G obtained preserves the strong linear relationship with the prior matrix regarding the numerical values (trips) contained in OD pairs at traffic zone level (Rp = 0.91); due to the imposed constraints (b), the Pearson’s coefficient at macro-zone level is 1. At this point the inaccuracies related to short trips have been overcome in the estimated matrix with regard to the prior one. Fig. 15a presents the trip distribution versus distance, the estimated matrix (in cyan) gets similar travel rates to those from HTS source (in red), correcting the under-reporting of short trips from MPD (in blue). This correction is more easily appreciated in Fig. 15b. (a) (b) Fig. 15 Trip distribution from the estimated matrix (G) and the two sources (MPD and HTS- based matrix): (a) percentage of daily trips by ranges (bins) of the distance travelled; (b) total daily trips. 5. Conclusions In today's world, new technologies offer effective options for complementing or even replacing traditional transport data collection methods. In particular, the pervasive use of mobile phones has made this technology emerge as a promising alternative for generating OD matrices, traditionally extracted from survey-based approaches. Through passive and active events, footprints are generated that reveal the ‘approximate’ locations where people have been and the times at which they were there. A number of techniques have already been developed in the literature for converting these data into trips. But, in order to provide a clearer understanding of the potentialities and challenges of mobile phone data regarding traditional survey methods, this work has conducted a comparison among matrices derived from both types of sources over the same area of study: the urban agglomeration of Malaga, in the south of Spain. The conclusions have been derived by using statistical techniques and other methodologies like MSSIM. As a result of the comparative analysis presented in this work and other experiences with mobile data that have been investigated and reviewed, one can conclude that mobile data can be used to draw a complete and representative picture of mobility flows over a region, especially when the zoning system is rolled up to a lower granularity. In particular, this comparative study has not only demonstrated the existence of many common features in the travel characteristics reflected in traditional survey sources but also shown that the huge representativeness of this technology allows inherent problems in survey sampling frames to be overcome, capturing mobility in OD connections extensively with independence of the socioeconomic characteristics of the studied area. This fact is of paramount importance for monitoring mobility in non-populated areas such as mass transportation facilities, industrial parks, educational campuses, or hospitals, which are regularly excluded from the sampling frame (when no households are available to be interviewed). Hence, mobile technology can be used as a complementary information source for generating trip matrices using larger zones. However, as finer zoning systems are used, the use of mobile technology may raise questions about the accuracy of estimated trips, especially for short trips (which imply shorter distances or displacements made at faster speeds), which tend to be undercounted or completely overlooked in mobile data. Obviously, the importance that this fact may have in estimating the origin and destination flows depends on the nature of the studied problem itself. The severity is not the same in mobility studies at a national/regional level as in an urban context where the occurrence of this segment of mobility cannot be neglected. In this sense, the magnitude of the total number of trips is a concern when using mobile phone data, which should be addressed in conjunction with location-based services data generated by smartphone applications (with larger spatial precision) or other available data (e.g. outdated matrices or traffic sensor data) in order to extend and validate the collected data. The findings of this work form the basis for further research on developing data fusion methodologies to obtain the optimum accuracy from these heterogeneous sources. In such a framework, there are modelling tools and optimisation techniques that can also be implemented to minimise inaccuracies for short trips. The use of mobile data augmented with less costly travel surveys with the main aim of, for example, capturing the magnitude of short trips or even total trips over the study region (instead of exhaustive origin–destination flows) also deserves further research. In any case, traditional surveys still constitute an extremely valuable source of information to be used in transportation studies because of the rich data they provide, especially in terms of socioeconomic characteristics. Only a full consideration of all available sources can lead to high-quality data collection results. Acknowledgments. This work was supported by the ERDF of the European Union for financial support via the project DIURMOVIL under ‘Programa Operativo FEDER de Andalucia 2011-2015’, and by the Public Works Agency and Regional Ministry of Public Works and Housing of the Regional Government of Andalusia. One of the authors also acknowledges funding provided by the Spanish Ministry of Economy and Competitiveness through the Torres Quevedo Programme (PTQ-13-06428). The authors would like to thank two anonymous referees who provided valuable constructive criticism on an earlier version of this paper. Disclosure statement. No potential conflict of interest was reported by the authors. References Abrahamsson, T. (1998). Estimation of origin–destination matrices using traffic counts—a literature survey. Report IR-98021, International Institute for Applied Systems Analysis (IIASA). Alexander, L.P., Jiang, S., Murga, M., and Gonzalez, M.C. (2015). 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