Call detail records (CDR)-Based road travel speed estimation: a location area code (LAC) sequence matching method

Although Call Detail Records (CDRs) provide a promising low-cost data source for large-scale traffic-state monitoring, their coarse spatial resolution and irregular temporal sampling make road-level speed estimation challenging. To address this problem, this study proposes a two-stage Location Area Code (LAC) sequence matching framework, which first identifies candidate road segments using LAC sequences and then refines route matching with cell-level information. The method is validated using mobile network data and GPS-based Floating Car Data (FCD) on the South Third Ring Road and the Jingcheng Expressway in Beijing. The results show that the optimal LAC sequence length is environment-dependent: longer sequences improve road-matching specificity in dense urban networks, whereas shorter sequences are sufficient on suburban expressways with lower base-station density. The analysis also reveals a precision-coverage trade-off, as stricter sequence matching improves accuracy but reduces the effective sample size. In addition, CDR-based estimates tend to be lower than FCD speeds on urban roads, which may be related to the difference between person-based CDR sampling and vehicle-based FCD sampling. These findings demonstrate the feasibility of LAC-sequence-based speed estimation and provide practical guidance for adaptive parameter selection in heterogeneous road environments.

Traffic congestion imposes substantial economic and environmental costs worldwide. Effective congestion mitigation depends on accurate, real-time road travel speed monitoring at network scale. Beyond operational efficiency, traffic-state information has also been used to support safety-oriented analyses, including real-time crash risk prediction and lane-changing risk assessment (Chen et al., 2024; Luo et al., 2026a), as well as hazardous-location identification, conflict prediction, and hotspot migration in complex traffic environments (Ghoul et al., 2023; Luo et al., 2026b). More broadly, data-driven methods have also been increasingly applied in intelligent infrastructure management, including pavement crack detection using super-resolution and diffusion models (Yao et al., 2025) and spatio-temporal dynamic evaluation of operation-and-maintenance performance for large facilities (Liu et al., 2024).

Conventional monitoring technologies—inductive loop detectors, roadside cameras, and dedicated short-range communication (DSRC) systems—offer high accuracy but suffer from limited spatial coverage and prohibitive deployment costs, leaving the majority of urban and suburban road segments unmonitored. Floating Car Data (FCD) from GPS-equipped probe vehicles extends coverage significantly and has been widely used for real-time traffic estimation and speed monitoring (De Fabritiis et al., 2008; Pu et al., 2009; Wang et al., 2015; Song et al., 2015), yet probe penetration rates in many cities remain below 5%, producing sparse and temporally biased samples (Kong et al., 2016). Against this backdrop, mobile phone Call Detail Records (CDR) have emerged as a promising complementary data source, offering near-universal user coverage at marginal incremental cost.

CDRs are passively generated by telecommunication networks whenever a mobile device triggers a network event. These events include active communication (call initiation, SMS transmission), periodic and normal location area updates during standby-state mobility, cell handovers during active calls, and device power cycling (He et al., 2013; Nalin et al., 2024). Each record carries a timestamp, a base station Cell-ID, and a Location Area Code (LAC) that identifies the serving cell’s administrative grouping. These records are generated as a byproduct of routine network operations. Therefore, they can provide large-scale, all-day mobility observations without requiring additional sensing infrastructure. However, CDR data also present two fundamental challenges for traffic state estimation. First, positioning accuracy is constrained by base station spacing (typically 200–2000 m in urban areas and larger in suburban regions), resulting in spatial resolution that is much coarser than GPS. Second, event generation follows user behavior rather than a fixed sampling schedule, which produces highly irregular temporal intervals ranging from seconds during active calls to hours during standby periods. These characteristics render conventional GPS-oriented map-matching algorithms inapplicable and demand specialized trajectory reconstruction methods tailored to CDR data.

Compared with infrastructure-based and FCD-based monitoring, CDR-based approaches offer three decisive advantages: (i) near-universal user penetration—mobile subscription rates exceed 120% in most urban areas worldwide; (ii) continuous all-day operation, capturing both peak and off-peak travel patterns without sampling bias toward specific vehicle types; and (iii) marginal data acquisition costs limited to interface modification at the operator side, avoiding the capital expenditure of roadside sensor deployment. These properties make CDRs useful for areas with limited monitoring infrastructure. They are particularly relevant for emerging economies and secondary road networks. Therefore, the core research challenge is not data availability. Instead, the key challenge is to develop robust algorithms that can extract reliable speed estimates from spatially coarse and temporally irregular CDR trajectories.

Research on mobile phone positioning data for traffic monitoring has converged on two principal methodological paradigms: handover-based location monitoring and cell-sequence-based matching. We review each in turn, highlighting their respective strengths and the limitations that motivate the present work.

The handover-based approach leverages cell handover events—generated when an active call is transferred between base stations as the user moves along a road segment. By pre-surveying handover locations along target roads and comparing real-time handover sequences against these reference patterns, travel speed can be inferred (Yuan and Guan, 2012; Caceres et al., 2012; Chen et al., 2016). Laboratory and field tests have demonstrated that under controlled conditions with frequent handover events, this method achieves positioning accuracy comparable to GPS-based FCD. However, two critical limitations constrain its practical deployability. First, handover events occur only during active calls; in typical urban environments, the proportion of users engaged in calls at any given time is below 5%, resulting in extremely sparse samples during off-peak hours and on low-traffic roads. Second, the reliance on pre-calibrated handover location databases introduces a maintenance burden: changes in base station configuration or radio propagation conditions require periodic re-surveying, limiting scalability to city-wide and regional networks (Yuan and Guan, 2011; Lv et al., 2024). Extending this line of research, Janecek et al. (2015) demonstrated the feasibility of using the cellular network itself as a real-time traffic sensor by processing anonymized signaling data at the network operator level, achieving city-scale coverage without additional hardware deployment. More recently, Derrmann et al. (2017) proposed a method for estimating urban road traffic states directly from mobile network signaling data, showing that even coarse-grained cell-level information can provide useful traffic state estimates when aggregated over sufficient user populations. These advances confirm the viability of network-side data for traffic monitoring, yet they remain constrained by the fundamental limitation that handover-based approaches require active-call states.

The cell-sequence-based method circumvents the active-call requirement by exploiting the sequence of base station Cells that a mobile device associates with during standby-state mobility (Yuan et al., 2010; Fiadino et al., 2012; Janecek et al., 2012; Huang et al., 2021; Wang et al., 2024; Maiwada et al., 2025). A reference cell sequence is constructed for each road segment by aggregating the Cells whose coverage footprints intersect the road. User-generated cell sequences are then compared against these references using sequence-similarity metrics, enabling trajectory reconstruction for all mobile devices regardless of call activity. This dramatically expands the effective sample size—potentially to the entire subscriber base—and has been demonstrated in city-wide deployments (Huang et al., 2021; Zhao et al., 2023). Nevertheless, the approach inherits a fundamental accuracy limitation: cell coverage radii range from several hundred meters to several kilometers, meaning that a single road segment may intersect only one or two Cells, producing sequences that are too short to uniquely identify the road. In suburban and rural areas where base station density is low, this ambiguity becomes acute, and the method’s accuracy degrades substantially (Janecek et al., 2012; Gregg et al., 2024). To improve matching accuracy with short cell sequences, Dong et al. (2018) employed a Longest Common Subsequence (LCS) algorithm to compare mobile phone location sequences against road-side cell sequences, achieving improved map-matching performance for low-frequency trajectories. Zhu et al. (2016) developed a freeway traffic speed estimation model that processes massive cellular signaling data, demonstrating that travel speed can be inferred from network-side records at scale. More recently, Wu et al. (2023) proposed a feature denoising method for mobile phone signaling data specifically designed for expressway traffic state estimation, showing that data quality enhancement is a critical prerequisite for reliable speed inference from cellular records.

Beyond the two traditional paradigms reviewed above, several recent methodological developments merit attention. First, data-driven and deep learning approaches have been applied to mobile trajectory data: Yu (2019) proposed a transfer learning framework for online traffic speed estimation in urban road networks with sparse data coverage, while Liu et al. (2018) developed real-time speed estimation techniques for sparsely sampled crowdsourced trajectory data. These methods offer the potential to relax the sample density requirements that constrain conventional approaches. Second, multi-source data fusion has emerged as a key strategy: Bonnel et al. (2018) demonstrated the use of mobile network probe data for origin-destination estimation, and Andersson et al. (2024) integrated mobile phone network data with traditional travel surveys for mode choice modeling on a national scale. Third, Chung and Nam (2024) exploited mobile phone signaling data to decompose travel time expenditure from individual mobility trajectories, illustrating the richness of information that can be extracted beyond simple speed estimation. Finally, a recent comprehensive review by Urbano et al. (2026) surveyed the use of aggregated mobile phone data in transportation research, concluding that while data availability has grown exponentially, the development of robust algorithms that can handle the inherent sparsity and positioning imprecision of cellular data remains an open challenge. Despite these advances, no existing method systematically exploits Location Area Codes (LACs) as an intermediate matching layer that bridges the gap between broad coverage and spatial precision.

Recent studies on non-traditional traffic sensing also indicate that travel speed estimation is increasingly shifting from single-source monitoring to multi-source and probe-based frameworks. FCD-based methods can provide high-resolution vehicle trajectories but are often constrained by probe penetration rate and vehicle-composition bias (Kong et al., 2016; Kessler et al., 2021). Bluetooth-based monitoring derives travel times and average speeds from device detections between readers, offering a low-cost alternative but requiring careful filtering of stationary or non-corridor devices (Kessler et al., 2021; Ipekyuz et al., 2025). Multi-source fusion studies further show that combining FCD, Bluetooth, loop detectors, or other sensor data can improve robustness and spatial coverage, although fusion performance depends strongly on data quality, temporal aggregation, and sensor layout. These findings provide a broader benchmark for evaluating CDR-based speed estimation, which seeks to exploit the wide user coverage of mobile networks while addressing their coarse positioning and irregular sampling limitations.

The foregoing review reveals a persistent tension in CDR-based speed estimation: handover-based methods offer spatial precision but require sustained active calls, limiting sample coverage; cell-sequence methods achieve broad coverage by exploiting standby-state data but suffer from insufficient spatial resolution when cell spacing is coarse. No existing method exploits Location Area Codes (LACs) — a coarser but more stable spatial identifier that aggregates multiple Cells—as an intermediate matching layer. LACs offer a critical advantage: because normal location updates are triggered whenever a user crosses an LAC boundary in standby state, LAC transitions are recorded for every mobile device, providing universal sampling while offering sequence lengths sufficient for robust road matching. As confirmed by Urbano et al. (2026), this tension between coverage and precision persists across the recent literature on mobile phone data applications in transportation. This study addresses the gap by proposing a hierarchical, two-stage LAC-sequence matching framework that integrates the respective strengths of handover-based and cell-sequence approaches.

Compared with conventional cell-sequence matching, the proposed LAC sequence method uses a coarser but more stable spatial identifier as the primary matching layer. Cell sequences provide finer spatial granularity but may be too short or unstable when a road segment intersects only a small number of cells. Handover-based methods can achieve higher spatial precision under active-call conditions but suffer from limited sample coverage. In contrast, LAC transitions are generated during normal location updates and can be observed for a much larger user population, allowing the method to balance sample coverage and road-matching uniqueness. Therefore, the LAC sequence layer functions as an intermediate matching scale between cell-level precision and network-wide user coverage.

Specifically, this paper makes the following contributions. (1) We propose a LAC-sequence matching method that uses Location Area Code (LAC) sequences—a coarser but more stable spatial identifier that aggregates multiple Cells—as the matching key for road identification. By leveraging the longer effective sequence length of LAC-based matching compared to cell-only approaches, the method improves the uniqueness of road matching while maintaining the broad coverage advantage of standby-state cellular data. (2) We provide an empirical characterization of the relationship between LAC sequence length and estimation accuracy across heterogeneous road environments, using ground-truth Floating Car Data (FCD) from GPS-equipped probe vehicles and Mobile Data (MD) from cellular network CDRs collected on urban (South Third Ring Road) and suburban (Jingcheng Expressway) road sections in Beijing. (3) We quantify the precision–coverage trade-off inherent in the method, demonstrating that the optimal sequence length is environment-dependent and identifying conditions under which CDR-based speed estimation achieves accuracy comparable to GPS-based alternatives.

The remainder of this paper is organized as follows. Section 2 describes the CDR and FCD datasets and presents the LAC sequence matching methodology, including LAC sequence construction, pre-matching sequence generation, similarity index computation, and travel speed estimation. Section 3 reports validation results on urban and suburban road sections, analyzing the effects of LAC sequence length and effective sample size on estimation accuracy. Section 4 discusses the implications of the findings, identifies model limitations, and outlines directions for future research.

Data

In this study, two types of reference data are utilized: Floating Car Data (FCD) from GPS-equipped probe vehicles and Mobile Data (MD) from cellular network Call Detail Records.

The CDR dataset has broad population coverage, but it should not be interpreted as a direct observation of all vehicles on the road. CDR records are generated by user-triggered communication events and network location updates, so their temporal density varies with user activity, time of day, and communication behavior. Consequently, CDR-based speed estimates are best understood as traffic-state indicators inferred from a large-scale mobile-user sample.

The FCD dataset used in this study was collected from more than 60,000 GPS-equipped taxis in Beijing and provides road-link travel speeds at 5-min intervals. This dataset has a penetration rate of approximately 2.5% among all vehicles in Beijing and has been widely used as a practical source of travel-speed observations for road traffic monitoring. Therefore, the FCD dataset provides an appropriate reference benchmark for validating CDR-based speed estimates in this study.

Data size

Each time a user triggers an event, a corresponding location point is recorded. In general, the greater the number of recorded location points, the easier it is to reconstruct and track an individual’s travel trajectory, and vice versa. When analyzing user travel speed, trajectory points must be matched to the road network. Therefore, examining the trajectory characteristics captured by Call Detail Records in advance is essential for selecting appropriate modeling and analysis methods. This study conducts empirical tests using mobile phone data provided by China Mobile in Beijing. In the Beijing area, the periodic location update interval is 2 h. Statistics on the number of user communication events are presented in Figure 1. On average, each user generates 53.8 valid records per day. The corresponding value is approximately 55.2 on weekdays, which is higher than the weekend average of 49.7. This difference can be attributed to more frequent phone calls and text messages on weekdays, resulting in a larger number of triggered events.

An analysis of user-triggered events across different time periods of the day (Figure 2A) shows that, on average, each user generates approximately 2.1 events per hour. However, substantial temporal heterogeneity is observed over the 24 h. From midnight to 06:00, the average number of events per hour is fewer than one. This pattern arises because users are typically inactive during nighttime hours, and the recorded data mainly originates from periodic location update events rather than active communications. In contrast, between 08:00 and 18:00, the number of communication events increases to approximately three per hour, corresponding to an average reporting interval of about 20 min.

Different types of events exhibit pronounced heterogeneity in both their proportions and density characteristics over the course of a day. On weekdays (Figure 2B), the density of communication events differs substantially between daytime and nighttime. During daytime hours, the average event density reaches approximately 6 events per person per hour, whereas after midnight it drops to fewer than 1 event per person per hour. This contrast is particularly evident for normal location update events and call-related events. During the daytime, increased inter-area mobility leads to a normal location update density of about 1 event per person per hour and a call-related event density of approximately 4 events per person per hour. At night, when most users remain at home, the density of normal location updates decreases to around 0.1 events per person per hour, while call-related events decline to about 0.2 events per person per hour. In terms of event composition, the proportions of periodic location updates and call-related events vary markedly throughout the day. During daytime hours, more than 60% of communication events are associated with phone calls, whereas at night, approximately 40% of events correspond to periodic location updates. Power-on and power-off events consistently account for only a small fraction of total events during both daytime and nighttime periods.

On weekends (Figures 2C,D), the overall density of communication events is slightly lower than that on weekdays, whereas differences in event composition are relatively small.

Consequently, individual CDR trajectories have irregular and often long temporal gaps. They also lack a fixed reporting cycle and show clear differences between daytime and nighttime periods.

Time interval

Based on the preceding analysis, Call Detail Record data are not collected at fixed intervals. By ordering records chronologically, the time differences between consecutive records are computed for different periods of the day. As shown in Figure 3, during daytime hours (07:00–19:00), the average inter-record interval is approximately 1,800 s, with a standard deviation of around 3,000 s. During nighttime hours, the mean inter-record interval increases to approximately 4,000 s, with a standard deviation of about 4,500 s. These results indicate that the average sampling interval of Call Detail Records is shorter during the daytime than at night. Moreover, substantial variability is observed in consecutive time intervals, with greater fluctuations occurring during nighttime periods.

Base station connection characteristics in the moving state

When users are traveling along roadways, mobile terminals maintain real-time connections with the communication network through surrounding base stations. In theory, a terminal may connect to any base station whose signal covers the road segment; however, base station density and signal strength substantially influence the actual connection behavior. To investigate these effects, field experiments were conducted on three representative road types. The experimental setup and testing platform are described as follows.

Test software: A custom Android application was independently developed based on the Android platform and can collect the Cell-ID, Location Area Code (LAC), strength of base station signals, and other information about connections between cellphones and base stations and neighboring base stations, with the interfaces and working states of the software shown below.

Test periods: morning peak, evening peak, and off-peak periods.

Tested roads: South Third Ring, Beijing (urban road); Sixth Ring Road, Beijing (suburban road); Jingcheng Expressway, Beijing (suburban road).

Test times: three times for two directions of the road.

Test environment: sampling period 1 s; model of terminal: Motorola ME865; terminal operating system: Android 4.04.

For each test dataset, the duration of mobile phone connections to base stations and the corresponding distances between base stations and road segments were analyzed. The results are presented in Figure 4. For users traveling along the South Third Ring Road, approximately 95% of the connection time is associated with base stations located within 300 m of the roadway. This finding indicates a 95% confidence level for successful connections to base stations within this distance. Beyond 300 m, the cumulative proportion increases only marginally with increasing distance. On the Sixth Ring Road, about 90% of the connection time falls within a coverage distance of 1,000 m, and 95% within 1,600 m. Once the distance exceeds 1,000 m, further increases in distance contribute only minor gains in the cumulative proportion. For the Jingcheng Expressway, approximately 90% of the connection time occurs within 900 m, and 95% within 1,200 m. Similarly, when the distance exceeds 1,000 m, the cumulative proportion increases only slightly with additional distance.

The coverage features of LAC around roads

When a user moves from one location area to another, the mobile terminal must register in the new location area, and the corresponding location information is recorded. This process does not depend on the occurrence of other communication events and is referred to as a normal location update. Each location area is identified by a LAC. When defining location areas, telecommunication operators carefully consider their spatial extent. If a location area is configured too small, the frequency of location updates increases, leading to higher signaling traffic. Conversely, if the area is too large, paging channel loads become excessive, which also increases overall system traffic. Therefore, the fundamental principle of location area design is to minimize the frequency of location updates while ensuring that paging loads remain within acceptable limits. A schematic illustration of location area coverage for base stations along roadways is shown in Figure 5, where different colors denote different location areas.

Statistical results of LAC coverage across different road types (see Table 1) indicate that on urban roads, such as the Third Ring Road, a single LAC covers an average roadway length of only 1.86 km. As roads extend farther from the urban core, the roadway length covered by a single LAC increases progressively, reflecting a decreasing density of base stations. For example, on sections of the Beijing–Harbin Expressway outside the Fifth Ring Road, the average roadway length covered by one LAC is approximately 8.6 km, while on the Beijing–Chengde Expressway, it reaches 10.83 km.

Modeling

Based on the preceding analysis, communication events triggered as users travel along roadways form natural sequences of LACs. By comparing these observed LAC sequences with predefined LAC sequences associated with specific road segments, mobile communication data can be matched to roadways. Combined with event timestamps and the spatial distribution of base stations, this matching enables the estimation of travel speed. This approach is referred to as the LAC sequence method. The implementation procedure, illustrated in Figure 6, consists of three main steps. To begin with, the set of base station sectors that a user is likely to connect to while traveling along a given road segment is identified, and a predefined LAC sequence is constructed along the road direction. Furthermore, the raw communication records are organized into preliminary matching sequences. Finally, the preliminary sequences are compared with the predefined LAC sequences to perform matching and identification, from which travel speed is estimated.

Building the LAC sequence of the road

Based on the database of base station sectors surrounding roadways, the sectors located in the vicinity of the target road are first selected. Using the LACs associated with the filtered base station sectors (identified via their Cell IDs), two ordered sets of location area codes covering the target road are constructed: a forward distribution sequence. L 1, n x 1, x 2... x n and a reverse distribution sequence L n, 1 x n, x n − 1... x 1. The forward sequence consists of all location area codes covering the target road, ordered from the road origin to the destination along the direction of travel. The reverse sequence contains the same set of location area codes but ordered from the road destination back to the origin, as illustrated in Figure 7.

Building pre-matching sequence

The records of user communication events of all base stations covering target roads are extracted. And the record of the i th user is R i = U s e r I D i, l a c i, C e l l I D i, T i. And U s e r I D represents the serial number of the user, l a c represents the serial number of the location area, C e l l I D represents the serial number of the base station, and T represents time.

Each user record extracted is sorted by time. Replacement records are utilized to substitute all consecutive records with the same location area number. The replacement process involves identifying the maximum and minimum time within consecutively identical location area number records, calculating the intermediate time between these extremes, and selecting the record closest to this intermediate time as the replacement. Subsequently, for the sorted records, each record is considered as the starting point, denoted as L, and any record can be chosen as the replacement. The replacement record is selected based on its proximity to the middle time of all records sharing the same location area number. In cases where multiple records are equidistant from the middle time, any one of them can be chosen as the replacement. Then, the records are selected from the sequenced records according to time sequence, with each record as the starting point and m as the length to form n sequences, and n sequences constitute a set of pre-matching sequences l a c Y.

The matching identification of the LAC sequence and the road

C n m sequences are selected from L 1, n x 1, x 2... x n and L n, 1 x n, x n − 1... x 1 under the precondition of keeping the context of lac position unchanged to form route lac sequence set C = c 1, ⋯, c 2 c n m, and the similarity index λ between all elements in l a c Y and all elements in the route lac sequence set is calculated; the similarity index λ Y j C i between the j th element Y j in pre-matching sequence set l a c Y and the i th element C i in route, the lac sequence set is calculated as follows:

When the time difference between any two records in Y j is less than 60 min, otherwise,

In the equation:

M: the number of elements whose context of lac in Y j is in line with its context of lac in C i;

M: the number of records in Y j;

For all calculated similarity indexes, when λ = 1, road matching is successful, C i corresponding to the λ is considered as the route of successful matching, and the road sections covered by C i is denoted by Link, representing the road sections matching Y j;

The estimation of the travel speed of the road

For the successfully matched Y j in Section 2.2.3, the user movement speeds V Y j, Lin k la c l, la c l + 1 at the road section Link covered by LAC in Y j are respectively calculated,

In the equation.

V Y j, Lin k la c l, la c l + 1: the movement speed of cellphone users on the roads covered by l a c l, l a c l + 1,

D C e l l i d l, C e l l i d l + 1: the distance between the projection coordinates of the base station l and the road section Link,

l: the ordinal positions recorded in Y j and for l < m, the meaning of m is the same as above,

T l: the time corresponding to the lth record in Y j;

After the prematching sequence, set l a c Y all finish the matching identification between the LAC sequence and roads, and the average speed V ¯ L i n k l a c l, l a c l + 1 of cellphone users at all road sections is calculated:

In the equation:

V Y j, L i n k l a c l, l a c l + 1: its meaning is the same as above,

n: the number of successfully matched pre-matching sequences on the road sections covered by l a c l, l a c l + 1.

Parameter calibration challenges

The previously proposed analytical model effectively addresses issues such as large gaps in Call Detail Records and the absence of periodicity. However, in practical applications, the values of several key parameters are critical, as they significantly influence the accuracy of the results. These parameters include the selection of base stations covering the road, the length of the LAC sequence, and the road length covered by a single LAC.

The results in Section 2.3 indicate that the density of base station deployment is strongly influenced by the location of the road. For urban roads, moving users can receive signals from base stations up to approximately 500 m away, whereas for suburban roads, this distance increases to around 1,600 m. This metric is used for preliminary filtering of valid user data: the closer a user’s connected base station is to the road under study, the higher the probability that the user is moving along that road. As shown in Figure 8, this probability decreases with distance. At greater distances, signals are more likely to be influenced by nearby roads, causing users who are actually on other roads to be misidentified as being on the study road. Therefore, selecting base stations closer to the road improves the accuracy of individual user measurements, while those farther away reduce accuracy. However, if the base stations are too close, valid users may be lost, also reducing accuracy. Consequently, for different roads under study, there exists an optimal distance that balances these effects.

The length of the LAC sequence, denoted as n, is crucial for aligning the user’s movement trajectory with the road network. As the LAC sequence length m increases, the likelihood of successfully matching the user to the road also rises; conversely, a shorter length reduces this probability. Users located at the boundaries of LACs may transition between adjacent LACs, resulting in a practical value of m that exceeds 2, as illustrated in Figure 8.

In practical applications, the value of n should be selected according to local road-network complexity, LAC coverage density, base-station density, and the minimum sample size required for stable speed estimation. A larger n generally improves the uniqueness of road matching because longer LAC sequences reduce the probability of confusing adjacent roads or parallel corridors. However, increasing n also excludes users whose CDR trajectories do not contain enough consecutive LAC transitions, thereby reducing the effective sample size. The recommended parameter is therefore not fixed, but should be determined by the trade-off between matching specificity and sample coverage. For dense urban networks with many candidate routes, a moderately longer sequence may be needed, whereas in suburban expressway environments with sparse road alternatives and larger LAC coverage, a shorter sequence may be sufficient.

The South Third Ring Road and Jingcheng Expressway in Beijing were again selected for accuracy analysis of the results.

The analysis indicates that the length of the LAC sequence significantly influences the precision of the method’s calculation results. Theoretically, in the absence of other influencing factors, an increase in n correlates with higher road matching accuracy and precision, while also increasing the likelihood of matching misjudgments. However, in practice, as n increases, the number of available samples decreases, potentially leading to a reduction in precision. Consequently, this study examines the effects of sample size and model results across different values of n. The range of n is detailed in Table 2. When set to 1, the presence of a substantial amount of non-road user data can significantly affect the results. Therefore, the analysis focuses on n values ranging from 2 to 5, with the urban roads covering a length of 9.3 km and the suburban roads extending 43 km.

Three sections were selected along the South Third Ring Road (as shown in Table 3; Figure 9A). Section 1 and Section 3 are located at road bends, while Section 2 is on a straight road. The base station sector density of Section 1 is 5.09 sectors/km 2, while Section 2 and Section 3 have higher densities, reaching 7 sectors/km 2. Sections 4 and 5 are located on the Jingcheng Expressway (Figure 9B), with a base station sector density of 0.84 sectors/km 2 in both sections.

The relation between length and precision of the LAC sequence

Different values of n were used to estimate the traffic flow speed on each section using the LAC sequence method. The test results were compared with the GPS data analysis (as shown in Figures 10–12). The data trends for the three test sections of the Third Ring Road in the urban area closely matched the GPS data. For example, the GPS data showed speed dips at 11:00 a.m. and 1:00 p.m. on Section 1, between 3:00 p.m. and 5:00 p.m. on Section 2, and around 10:00 a.m. on Section 3, and the speeds calculated using the LAC sequence method accurately reflected these dips.

The observed relationship between LAC sequence length n and estimation precision can be interpreted through a bias-variance decomposition framework. The total estimation error comprises two competing components: matching bias (which decreases with n) and sampling variance (which increases with n as sample size shrinks). The superposition of these two opposing trends produces a U-shaped error curve, with the optimal n occurring at the point where the marginal reduction in matching bias is offset by the marginal increase in sampling variance. A detailed quantitative analysis of this trade-off is presented below and in Section 4.2.

Different values of n yield varying relative error values. Across the three test sections, negative errors occur more frequently than positive errors, suggesting that speed estimates derived from the LAC sequence method are generally lower than those obtained from GPS data. When n is set to 2 or 5, the relative errors are larger and exhibit greater volatility compared to when n is 3 or 4, indicating the existence of an optimal value for n in the LAC sequence method. At this optimal value, errors are minimized, while excessively large or small values tend to introduce additional errors. The distribution of relative errors also reveals that, for all three sections, there are instances of sharp increases in relative error, such as at 11:00 a.m. and 1:00 p.m. in Section 1, and around 3:00 p.m. and 7:00 p.m. in Section 2. In comparison to GPS data, during these time periods, the estimated speed experiences a significant decline, indicating that the LAC sequence method is less responsive to samples at lower operational speeds than GPS data.

Quantitatively, the error reduction achieved by increasing n from 2 to the optimal value is substantial and varies markedly across road sections. On Section 1, MAE decreases from 0.204 (n = 2) to 0.185 (n = 4), a reduction of 9.3%; on Section 2, from 0.235 to 0.115, a reduction of 51.1%; and on Section 3, from 0.307 to 0.246, a reduction of 19.9% (Table 4). The dramatic improvement on Section 2 — a straight road segment with the highest base station sector density (7.07 sectors/km 2, Table 3) — suggests that n is especially consequential on road segments where dense base station deployment increases the matching ambiguity of short LAC sequences. On such high-density segments, a short sequence (n = 2, spanning only 3.72 km on urban roads per Table 2) may fail to distinguish among multiple candidate routes within the same LAC coverage zone. Conversely, when n is increased beyond the optimal value to 5, the MAE on Section 2 rises to 0.179, representing a 55.7% increase from the optimal MAE of 0.115. This asymmetry—where over-filtering degrades accuracy more sharply than under-filtering on high-density segments—has practical implications for parameter selection: in operational deployments where ground-truth validation data are scarce, erring toward a slightly smaller n may be preferable to overly aggressive filtering that risks losing statistical power.

The speed analysis results for the two sections of the Jingcheng Expressway are shown in Figures 13, 14. The model’s calculated data closely align with the GPS data. For instance, at 1:00 p.m. and 9:00 p.m. on Section 4, and from 3:00 p.m. to 9:00 p.m. on Section 5, a speed “dip” was observed, with the speeds calculated using the LAC sequence method similarly reflecting these dips. However, during the early morning hours, the LAC sequence method lacks a significant amount of speed data due to lower traveler activity and reduced traffic flow on the expressway, leading to a lack of valid samples. Additionally, the speed volatility during these hours is relatively high, which is also a result of the limited sample size. During the speed dip periods, the LAC sequence method calculated speeds for the South Third Ring Road were consistently lower than the GPS data speeds, whereas for the same dip periods on the Jingcheng Expressway, the speeds were almost identical. The fundamental cause of this difference lies in the fact that expressway users generally drive a more uniform type of vehicle with stable speeds, while the South Third Ring Road accommodates a wider variety of vehicles, such as buses, which have larger passenger capacities and lower operational speeds compared to smaller cars. This compositional bias results in an overall average speed that is lower than the GPS data’s calculated speed.

The systematic underestimation of travel speeds on urban roads relative to GPS data can be further analyzed through the lens of vehicle composition effects. GPS floating car data predominantly samples passenger vehicles (taxis and ride-hailing fleets), whereas CDR-based estimation captures all cellphone users traveling along the roadway regardless of vehicle type. On urban arterials such as the South Third Ring Road, buses, trucks, and other heavy vehicles constitute a non-negligible fraction of traffic flow and operate at lower speeds than passenger cars, thereby pulling the CDR-estimated mean speed below the GPS-derived mean. On controlled-access expressways, where vehicle composition is more homogeneous and speed variance among vehicle types is smaller, this sampling bias is minimal. Furthermore, the temporal autocorrelation of estimation errors—where negative errors persist across consecutive hours during speed-dip periods—indicates that the LAC sequence method exhibits a systematic low-speed bias rather than purely random measurement noise. This temporal structure suggests that a post hoc calibration, stratified by time-of-day or real-time traffic state, could further reduce systematic error without requiring additional data collection.

Compared to the three test sections on the South Third Ring Road, the relative error for the two test sections on the Jingcheng Expressway shows greater overall volatility throughout the day. However, the difference in the value of n has a smaller effect on the relative error. This insensitivity is related to the suburban characteristics of the Jingcheng Expressway. The LAC sequence method covers longer road distances in this environment and can still achieve higher accuracy when n is small. This environmental dependency is related to the larger LAC coverage length on suburban roads. On the Jingcheng Expressway, each LAC covers an average of 10.83 km of roadway (Table 1), which exceeds the typical distance between consecutive LAC boundary crossings. Consequently, even the shortest LAC sequence (n = 2) spans a sufficient road length of approximately 17–26 km. This is enough to identify the target expressway segment, so additional sequence length provides limited matching benefits. In contrast, on the urban South Third Ring Road where LAC coverage averages only 1.86 km, longer sequences are required to disambiguate among closely spaced parallel and intersecting roads.

The statistical results for the mean absolute error and variance in each validation section are presented in Table 4. For the South Third Ring Road, when n equals 4, the mean absolute error for Section 1 is minimized to 0.185, while for Section 2, it is minimized to 0.115, and for Section 3, it is minimized to 0.246. These findings further corroborate the earlier conclusions.

The statistical robustness of these findings warrants closer examination. On the South Third Ring Road, the difference in MAE between the optimal n = 4 and the worst-performing n is 0.019, 0.120, and 0.061 for Sections 1, 2, and 3, respectively. The particularly large gap on Section 2 (0.120, representing a >50% relative improvement) suggests that the effect of n on accuracy reflects a genuine structural property of the matching algorithm rather than sampling noise. Road geometry also modulates this relationship: Sections 1, 3, located at road curves where base station sector density is lower (5.09 and 6.93 sectors/km 2 vs. 7.07 sectors/km 2 for the straight Section 2), exhibit higher absolute MAE values across all n. This result is consistent with the expectation that curved road segments present greater matching challenges—the non-linear relationship between road geometry and LAC boundary shapes introduces additional spatial ambiguity that even longer LAC sequences can only partially resolve. The interaction between n, road curvature, and base station density suggests that a spatially adaptive n—where the LAC sequence length is dynamically tuned according to local road network characteristics—could outperform a globally fixed parameter in large-scale deployment.

Table 5 summarizes the estimation performance and recommended LAC sequence length under different road environments. As shown in Table 5, urban arterial sections exhibit a clearer dependence on LAC sequence length. For the three urban sections, n = 4 generally provides the best balance between matching accuracy and sample retention. In contrast, the suburban expressway sections show only minor differences in MAE across different n values, indicating that shorter sequences may be sufficient when the road environment is less spatially ambiguous and sample coverage is limited.

On the Jingcheng Expressway, the mean absolute error exhibits minimal variation as the value of n increases. In Section 4, the minimum value is 0.177, while the maximum is 0.178; in Section 5, the minimum is 0.200, and the maximum is 0.210. This observation further supports the conclusion that, owing to the extensive road coverage provided by the LAC sequence method, the value of n has a negligible effect on the mean absolute error. The standard deviation of the absolute error exhibited a similarly stable pattern, remaining within ±0.04 of the MAE across all m values for both expressway sections, confirming the robustness of the estimation on low-density suburban road networks.

The near-constant MAE across n values on the Jingcheng Expressway reveals a fundamental property of the LAC sequence method on low-density road networks: matching accuracy reaches an error floor at very short sequence lengths, beyond which additional LAC transitions provide negligible discriminative power. This error floor—approximately 0.178 for Section 4 and 0.202 for Section 5 — is determined not by the quality of sequence matching, but primarily by the inherent temporal sparsity of CDR data and the residual uncertainty in individual speed point estimates. Once the LAC sequence is sufficiently long to uniquely identify the target expressway (which, as argued above, occurs at n = 2 given the 10.83 km average LAC coverage), further increases in n only reduce sample size without improving matching precision. This finding carries important operational implications: for suburban and rural road monitoring applications, a minimal LAC sequence length of n = 2 is sufficient to achieve near-optimal accuracy while maximizing sample coverage. The computational savings from avoiding higher-n matching on low-density networks can be substantial in large-scale deployments spanning thousands of kilometers of roadway, where each additional unit of n multiplies the combinatorial complexity of the sequence matching procedure.

The relation between size and precision of effective samples

As the length of the LAC sequence, denoted as n, increases, the data filtering becomes more stringent, resulting in the exclusion of a considerable number of questionable users. This stricter filtering; however, also leads to a significant decrease in the number of valid users, thereby reducing the overall sample size. The effective sample size for each of the three test sections was calculated independently. For the South Third Ring Road, illustrated in Figure 15A, the effective sample size for each section reaches its peak when n = 2. Specifically, Section 1 averages 1,000 samples per hour, Section 2 approximately 400 samples per hour, and Section 3 fewer than 100 samples per hour. Conversely, when n = 5, the effective sample size for each section plummets to fewer than 100 samples per hour. In comparison, the effective sample size on the Jingcheng Expressway is significantly lower than that on the South Third Ring Road, with both sections recording fewer than 100 samples per hour, as depicted in Figure 15B.

Quantitatively, the decay in effective sample size as n increases follows a steep, non-linear trajectory. On the South Third Ring Road, moving from n = 2 to n = 3 reduces the sample by an estimated 40%–60% across sections; from n = 3 to n = 4, a further 30%–50% reduction occurs; and from n = 4 to n = 5, the remaining samples diminish to fewer than 100 per hour across all three sections. This pattern—a steep initial decline followed by a long, thin tail—is characteristic of a heavy-tailed distribution of user LAC sequence lengths within a fixed observation window. The majority of mobile users generate only 1–2 LAC transitions during a typical trip through the study corridor, a minority generate 3–4, and very few generate 5 or more. This distributional property imposes a hard constraint on the maximum usable n. The marked disparity in baseline sample size across the three test sections at n = 2 (Section 1: ∼1,000; Section 2: ∼400; Section 3: <100 samples per hour) warrants closer examination. Section 1, despite being a curved road segment with moderate sector density (5.09 sectors/km 2, Table 3), serves the highest traffic volume among the three sections, contributing to its larger sample pool. Section 3, also a curved segment but with higher sector density (6.93 sectors/km 2), exhibits the lowest sample count, suggesting that road curvature may introduce additional LAC boundary complexity that reduces the effective capture rate of valid user trajectories—users traversing curved road segments are more likely to briefly connect to base stations outside the predefined road corridor, causing their LAC sequences to be rejected even at low n. Section 2, as a straight segment with the highest sector density (7.07 sectors/km 2), achieves intermediate sample counts and benefits most from increasing n, as its simpler geometry and dense sector coverage together produce LAC sequences that are both abundant and discriminating. This three-way interaction—among traffic volume, base station density, and road geometry—determines the baseline sample pool from which progressively longer LAC sequences can be drawn, and therefore governs the feasibility of parameter choices for any given road segment.

The precision–coverage trade-off is a fundamental characteristic of sequence-matching methods: longer sequences improve matching specificity but reduce the eligible user population, as fewer users generate sufficiently long LAC sequences within the target time window. The sharp decline in effective sample size from n = 2 to n = 5 reflects the underlying distribution of user mobility patterns—most mobile users cross 1–2 LAC boundaries during a typical trip, while only a small fraction traverse 4 or more. This distributional constraint defines the practical upper bound of m for any given road environment and user population.

The intersection of the sample-size decay curve and the precision curve defines the operating envelope of the LAC sequence method. On the South Third Ring Road, the optimal operating point occurs at n = 4, where the effective sample size has contracted to approximately 50–100 samples per hour on Section 1, yet the matching precision reaches its peak (MAE = 0.185). This counterintuitive result—that fewer samples yield higher accuracy—demonstrates that matching quality dominates sample quantity in high-density urban road networks: the elimination of incorrectly matched users more than compensates for the loss of valid but ambiguous trajectories. The implication is that, in urban environments, investing computational effort in stricter sequence matching (higher n) yields greater accuracy returns than maximizing raw sample count. For operational deployment, a minimum hourly sample size of approximately 30–50 valid users per road section appears necessary to maintain estimate stability; below this threshold, the variance of the mean speed estimate becomes unacceptably large due to the central limit theorem’s finite-sample limitations. This threshold is consistently met on the South Third Ring Road at n ≤ 4 but is violated at n = 5 for Sections 2 and 3, directly explaining the observed accuracy degradation at the highest filtering level. On the Jingcheng Expressway, the effective sample size remains below 100 per hour across all n values, indicating that the estimation operates near the sample-size floor throughout. This scarcity is primarily driven by lower traffic demand on suburban expressways rather than by limitations of the LAC sequence method itself—a distinction with important implications for method transferability to rural monitoring contexts. The temporal dimension adds further nuance: during off-peak hours (e.g., early morning, 0:00–6:00), even the most permissive filtering (n = 2) may fail to accumulate sufficient samples for a reliable speed estimate. This temporal sample drought—visible in Figures 13, 14 as missing or highly volatile data points during early morning hours—represents a fundamental limitation of passive CDR-based monitoring on low-traffic road segments. A practical mitigation strategy involves temporal aggregation: pooling samples across a wider time window (e.g., from 1-h to 2-h bins) during low-demand periods to maintain statistical reliability, at the acceptable cost of reduced temporal resolution during hours when traffic conditions are inherently stable.

The results presented in Section 4 demonstrate that the proposed LAC sequence matching method can effectively estimate road travel speeds from CDR data, achieving a mean absolute error of 0.115–0.246 on urban roads and 0.177–0.210 on suburban expressways. These error magnitudes are comparable to those reported for cell-sequence-based methods: Huang et al. (2021) reported city-wide traffic state estimation errors of approximately 15%–25% using mobile signaling data in a Chinese metropolitan area, while Derrmann et al. (2017) achieved errors of 10%–20% on urban road segments using network-side signaling data. The LAC-based approach offers a distinct advantage over these methods in that it does not require active-call states (unlike handover-based methods) and achieves longer effective sequence lengths than cell-only approaches, thereby improving the uniqueness of road matching. The key empirical finding—that the optimal LAC sequence length n is environment-dependent—has important practical implications. On the urban South Third Ring Road, where base station density is high (5–7 sectors/km 2), n = 4 provides the best accuracy–coverage balance because shorter sequences insufficiently resolve complex road geometries while longer sequences excessively reduce sample size. Conversely, on the suburban Jingcheng Expressway with lower base station density (0.84 sectors/km 2), even n = 2 can uniquely identify the target road because each LAC covers an average of 10.8 km of expressway—a distance exceeding the typical spacing between consecutive LAC boundaries, thereby rendering longer sequences redundant. This environment-dependent behavior aligns with the findings of Janecek et al. (2015), who observed that the information content of cellular handover events is inversely related to base station density, and extends this insight to the LAC domain.

The proposed framework also differs from recent mobile-phone-based traffic monitoring approaches. Handover-based approaches depend heavily on active-call states and pre-calibrated handover locations, while cell-sequence approaches improve coverage but may suffer from short and ambiguous cell sequences in complex networks. The LAC sequence method uses a higher-level location area as the matching unit, which reduces dependence on active calls and improves the availability of trajectory sequences. However, this advantage is accompanied by a loss of spatial precision, meaning that the method is most suitable for corridor-level or link-level speed estimation rather than lane-level traffic monitoring.

Several limitations of the current study warrant discussion. First, the method suffers from Vehicle Composition Heterogeneity. The observed systematic underestimation of travel speeds relative to GPS floating car data (FCD) is fundamentally rooted in the distinct nature of the two data sources: FCD (primarily derived from taxis) represents a Vehicle-Averaged Speed, whereas CDR data captures a Person-Averaged Speed.

Because CDR sampling depends on active mobile devices, vehicles with high passenger capacities (e.g., public transit buses) contribute disproportionately more data points to the estimation pool than single-occupancy private cars. This passenger-density weighting effect can be conceptually expressed as: where N is the total number of vehicles on the road segment, P i is the number of active mobile devices (passengers) in vehicle i, and V i is the operational speed of vehicle i. On urban arterials like the South Third Ring Road, buses carry a high density of passengers but operate at lower speeds due to frequent stop-and-go patterns. Consequently, the high P i and low V i of public transit significantly pull down the overall speed estimate. Therefore, CDR-derived speeds in complex urban networks should be rigorously interpreted as a lower-bound estimator of general traffic speed.

This hypothesis is powerfully corroborated by our findings on the Jingcheng Expressway. On suburban expressways, the traffic flow exhibits high homogeneity, consisting predominantly of private cars and trucks with similar, low passenger densities. The absence of bus stops also eliminates stop-and-go delays. In this homogeneous environment, the Person-Averaged Speed converges with the Vehicle-Averaged Speed, which explains why the LAC sequence method aligns almost perfectly with GPS FCD during the speed dip periods on the expressway.

However, this study does not have direct information on public-transit passenger shares, passenger occupancy, individual travel modes, or detailed vehicle-type composition. Therefore, the vehicle-composition mechanism cannot be directly verified with additional statistical evidence in the present study. Future research should integrate CDR data with bus GPS data, vehicle classification data, transit smart-card records, or more detailed probe-vehicle datasets to examine this mechanism more rigorously.

Second, the validation is currently limited to two road corridors in a single metropolitan area (Beijing). While these corridors represent contrasting environments (high-density urban vs. low-density suburban), generalization to other road types—including signalized urban arterials, rural highways, and multi-level interchanges—remains to be demonstrated. Third, the temporal granularity of the LAC-based estimate is constrained by the mean inter-record interval of CDR data (approximately 1,800 s during daytime), which limits its applicability to real-time traffic management applications requiring sub-5-min update cycles. Finally, the method assumes static base station coverage footprints; in operational networks, coverage areas may shift due to dynamic load balancing, cell breathing, and periodic reconfiguration, potentially degrading matching accuracy over time.

In addition, model performance may vary across mobile network operators because LAC configuration rules, base-station density, and location-update strategies are not identical across networks. Regional differences in communication infrastructure and user behavior may also affect the probability of obtaining sufficiently long and reliable LAC sequences. For example, dense urban cores may require longer sequences to resolve spatial ambiguity, whereas rural or suburban corridors may be identifiable with shorter sequences but may suffer from insufficient sample size. These factors should be explicitly calibrated when transferring the method to other cities or communication-network environments.

Validation on urban (South Third Ring Road, Beijing) and suburban (Jingcheng Expressway) road sections demonstrated that the proposed LAC sequence method achieves competitive accuracy compared with GPS-based floating car data. On the South Third Ring Road, the optimal LAC sequence length of n = 4 yielded a minimum mean absolute error of 0.115–0.185 across three test sections with heterogeneous geometries (curves and straight segments). On the Jingcheng Expressway, the MAE remained stable (0.177–0.210) regardless of n due to low base station density, confirming that the optimal LAC sequence length is conditional on road environment characteristics. The effective sample size declined sharply as m increased, from approximately 1,000 records per hour (n = 2) to fewer than 100 (n = 5) on the South Third Ring Road, empirically quantifying the precision–coverage trade-off. These findings show that CDR-based speed estimation is practically feasible under favorable conditions. At the same time, estimation accuracy is governed by the interplay among LAC sequence length, base-station density, and road geometry.

Future work should proceed along three directions. (1) An adaptive n-selection framework should be developed that dynamically tunes the LAC sequence length based on real-time estimates of local base station density, road network complexity, and sample availability, thereby optimizing the precision–coverage trade-off without manual calibration. (2) Multi-modal inference and Data Fusion: To address the systematic speed underestimation caused by modal bias, future research should explore machine learning algorithms to disaggregate trajectories by transportation mode prior to speed estimation. For instance, analyzing stationary dwell times (e.g., stopping at known bus station coordinates) could help separate the “public transit cohort” from the “private vehicle cohort.” Furthermore, fusing CDR-based estimates with sparse but highly accurate FCD could recalibrate the passenger-density weighting effect, yielding a more precise representation of comprehensive urban network speeds and improving temporal resolution. (3) The method should be validated on additional road types (e.g., signalized urban arterials, rural highways, and expressways in other metropolitan regions) and evaluated against evolving 5G network architectures, where ultra-dense small-cell deployments and increased handover frequency may both challenge and potentially enhance the LAC-based matching paradigm. Future research should also compare different mobile network operators and examine whether adaptive aggregation windows can improve estimation stability during low-demand periods.