For various applications in traffic engineering, it is fundamental to know about the traffic conditions on a road stretch with high certainty and sufficient spatio-temporal accuracy. A complete representation of traffic conditions is especially crucial for understanding traffic flow, for the effectivity analysis of control measures and for training data-driven prediction models. In contrast to real-time or predictive state estimation, these applications are usually applied retrospectively.

The retrospective analysis often focuses on average vehicle speeds per time and space interval on a road since this provides benefits such as enabling the deduction of travel times for road users, providing jam tail warnings (Rempe et al., 2017b) aiming at the reduction of rear-end collisions at jam tails, etc. However, using current sensor technology, average vehicle speeds are not measured for all times and places on a road stretch. Rather, various types of sensors are available that provide traffic-related data at different times for different places. Raw sensor data must therefore be processed in order to determine an accurate reconstruction of traffic conditions.

Nowadays, several sensor technologies are in place that gather data, each coming with advantages and limitations when applied. Induction loops, that are buried in the road surface, provide very exact and reliable speed information but are mainly limited to few road stretches since the installation and maintenance costs are high. Floating-Car Data (FCD), also called probe data, are gathered from vehicles or smartphones that determine their position via Global Navigation Satellite Systems (GNSS) and report this position on a regular basis to a central server. Time and space differences allow for reconstructing the probe’s speed profile on a road. FCD are available wherever traffic is flowing, but represent only a sub-sample of the whole fleet. With WiFi/Bluetooth (BT) sensor technology, the unique hardware address of a device that passes two neighboring stations is registered, allowing the derivation of the travel time and therefore the average speed of devices that pass two neighboring stations (Haghani et al., 2010; Barcelo et al., 2010; Martchouk et al., 2011; Lesani et al., 2016; Margreiter, 2018). BT installation is not expensive but – like FCD – the receivers do not collect information from all vehicles and additionally, since they are conceivably placed several kilometers apart from each other, the average speed can be less granular.

Measuring traffic conditions with various sensors offers a great opportunity to increase the accuracy of traffic state estimates. However, the mentioned differences and characteristics of each technology challenge the fusion of the sources. The aim of an advanced fusion method is to make use of all information hidden in the data and compute a combined result that outperforms estimates based on a single source. Additionally, a combination of satisfactorily precise sensor combinations, which are available at lower costs, might be a reasonable compromise for decision makers, so knowing these combinations would be beneficial to them.

Given various sensor technologies, and various algorithms to process collected data, it is difficult to decide, which technology one should adopt and which algorithm one should deploy. This paper seeks to support decision makers, practitioners and researchers in selecting the combination of sensor data and a reconstruction approach that provides the greatest benefit for their specific problem. Since a real-world application requires algorithms to cope with sparse and missing data, this paper studies approaches with high robustness that can be applied directly. Based on real data collected on a German freeway, various algorithms and combinations of sensor technologies are evaluated. Results comprise the accuracy of reconstructed space-time speeds as well as the accuracy of deduced travel times.

The paper is structured as follows. Section 2 gives a literature review on the comparison of different traffic data detection systems and on information fusion approaches. Section 3 describes the study site and data that are used to evaluate subsequent approaches. In section 4, existing applicable fusion methods are briefly summarized. Sub section 4.3 describes the adaption of the Phase-Based Smoothing Method (PSM) to consider BT data in a dynamic way. Section 5 presents the applied quality metrics and the obtained results applying the methods to varying sensor setups. The conclusion in section 6 wraps up the results and provides potential further research directions.

Comparisons of different traffic detection technologies have been widely performed in the past. In Klein (2020), a comprehensive summary of available sensors and fusion techniques is given. The authors of Bachmann et al. (2013b) compared Bluetooth measurements and loop detector data in the Greater Toronto Area on a stretch of several kilometers. In Kessler et al. (2018a), the authors describe an offline comparison between loop detectors and floating cars, determining which is able to detect a traffic incident earlier. In Cohen and Christoforou (2015), the authors statistically analyze the differences between loop detectors and floating car data in the area of Lille, France.

Additionally, different fusion techniques have been investigated. Faouzi and Klein (2016) give a survey of current data fusion techniques for intelligent transportation systems. In Klein (2019), they present three widely applied data fusion techniques and describe their relevance to Intelligent Transportation Systems (ITS): Bayesian inference, Dempster–Shafer evidential reasoning, and Kalman filtering. In Zeng et al. (2008), an evidence-theory-based data fusion approach for traffic incident detection is described. Data from inductive detectors, camera observation and floating car data are fused on a rather short stretch of a few hundred meters on an urban highway. Corsi and Capitanelli (2011) applied data fusion techniques for traffic planning and control in a setting with satellite images, acoustic and GPS data. In Zhou and Mirchandani (2015), the authors describe a real-time capable framework for the fusion of loop detector and GPS data. This framework is able to distinguish lane-based traffic states. The authors of Faouzi et al. (2009) study the fusion of loop data and toll collection data using a Dempster-Shafer approach in order to get an improved travel time estimate. In Yuan et al. (2014), an approach to network-wide traffic state estimation combining loop detector and floating car data is presented. Rempe et al. (2017b) developed a model to fuse FCD and loop detector data to forecast congestion fronts on a freeway.

A comparison of two model-based approaches on filtering methods is conducted in Trinh et al. (2019). The results are confirmed using synthetic data from a simulation. Liu et al. (2018) describe an extended Kalman filter method for freeway traffic state estimation fusing two data sources: wireless communication records and microwave sensor detections. Another Kalman filter based approach is given in Fulari et al. (2015). In He et al. (2016), the authors discuss a data fusion approach for cellphone probes and fixed sensors, and give a sensitivity analysis on impact factors. The article (Chang et al., 2016) describes a data fusion for travel time estimation from toll collection stations and stationary vehicle detectors in Taiwan. Rostami-Shahrbabaki et al. (2018) propose a fusion of loop data and FCD at intersections to estimate queue lengths and outflows. In Ambühl and Menendez (2016) and Dakic and Menendez (2018), also a fusion of loop data and FCD is described with the goal to approximate the Macroscopic Fundamental Diagram of urban networks. Bachmann (2011) and Bachmann et al. (2013a) compared seven fusion methods for traffic speeds and travel time estimations. One key finding is that a simple convex combination of loop detectors and BT measurements is one of the best fusion strategies. However, data stems from micro-simulations which tend to idealize real data. The authors of Hegyi et al. (2013) fuse various sensors, loops, FCD and camera data using the Adaptive Smoothing Method (ASM) to improve the speed of jam detection and respective control measures. An evaluation is performed using simulated data.

The mentioned studies are mostly limited to the usage of two different data sources, which limits the applicability in many scenarios. Furthermore, they mostly consider only one quality metric that is investigated, e.g., the spatio-temporal speed distribution or travel time. Some of the mentioned studies focus on the estimation of traffic conditions in dense networks, which is a different challenge than the one emphasized in this paper. Furthermore, data are often derived from micro-simulations, which allow for extensive studies but result in data that are usually more homogeneous and less noisy than real data. If studies utilize empirical data, they often focus on a rather short road stretch which gives an insight into only that specific freeway section.

The approach described in this paper is based on empirical data collected via three common sensor technologies: loop detectors, FCD and low-frequency travel time data from BT devices on a long stretch of a German freeway. The number of data points is large, which allows a detailed study of all combinations of data as well as several algorithms processing the data. Furthermore, this work applies two metrics which provides insights into the accuracy of both reconstructed traffic speeds and reconstructed travel times. The algorithms compared in this study are state-of-the-art methods such as the ASM, the PSM, simple averaging methods and an extension of the PSM. This extension is a minor, but effective change to the PSM, which allows for the integration of low-frequency travel time data in order to achieve higher reconstruction accuracies.

Speed measurements for all sensors are considered on a road stretch with length X and a time period T. The data of all detection technologies are represented as spatio-temporally discrete speed values in a uniform grid with step size ΔX = 100m and ΔT = 60s. Thus, the domain can be represented as a matrix with n _X rows and n _T columns, where an entry (also called cell in the following) is referred to as (i, j), where i = 1, …, n _X and j = 1, …, n _T . In each cell, the speed value is constant per data source and is denoted as v _i,j . Given a set S of sensor technologies on the considered road stretch, V _s , s ∈ S with S = {LOOP, FCD, BT} denote the speed matrices of loop detectors, FCD and BT sensors, respectively.

Speeds measured by loop detectors are given at discrete positions along the road stretch, and with a temporal resolution of one minute. For each loop detector, the measured speeds are assigned to corresponding cells in the grid. The given name is V L O O P ∈ R n X × n T .

FCD comprise trajectories of vehicles. A trajectory of one vehicle contains all information that a vehicle, equipped with a GNSS, collects about its space-time speed. An equipped vehicle samples its current position x at time t with a certain frequency, and thus generates tuples of (t, x), t ∈ [0, T], x ∈ [0, X] along the road stretch. Since no further speed information is given, for simplicity, the vehicle’s speed between two sampled positions is assumed to be constant. With sampling frequencies, that are in the same order of magnitude as the time discretization of the domain, this basic assumption is sufficient. In order to turn the piece-wise linearly interpolated vehicle position into grid speeds, for each grid cell, which is passed by the vehicle, i.e., the vehicle traveled Δx _i,j : Δx _i,j ≥ 0 m and Δt _i,j > 0 s in that cell, a cell-wise speed is computed as v _i,j = Δx _i,j /Δt _i,j . All cell-wise speeds of all traces are computed, and subsequently, the speeds of all traces are aggregated. If there are multiple speeds for the same cell, the harmonic mean of all assigned speed values is considered. The respective output matrix comprising all speed data from all equipped vehicles is denominated as V F C D ∈ R n X × n T .

Travel times collected via vehicle re-identification and provided by BT sensors are interpolated based on the Low-Resolution Travel Time Smoothing Method (LTSM) (Kessler et al., 2019). This method considers travel times through predefined cells and weights all crossing paths through any cell according to the share of the path inside the cell in order to obtain an averaged speed distribution V B T ∈ R n X × n T .

The studies presented in the subsequent sections are applied to data collected on May 29, 2019 on the German autobahn A9 (Figure 1) in the northbound direction during severe traffic congestion. The markers depict the positions of the loop detectors and Bluetooth receivers, respectively. FCD are collected from a fleet of cars, which are equipped with a GNSS device. With sampling times between 5 and 20 s, depending on the software version, the vehicle collects positions and timestamps. Packets of positions and timestamps are reported to a central server. In order to ensure privacy, the transmission ID is shuffled from time to time, and some packets are retained such that tracing a vehicle over its entire journey is not possible.

All in all, time-discrete data of 27 loop detectors, 1,578 FCD traces and 11,722 BT samples are available. Figure 2 displays the raw data.

The present study examines two major aspects of a multi-sensor data fusion: the reconstruction accuracy using different combinations of sensor data, and the accuracy applying different state-of-the-art algorithms (as well as a novel approach) to different sensor combinations. Additionally, the reconstruction accuracy is measured using two metrics.

A welcome result of such a study would be a clear recommendation on which algorithm or data to use in general in order to obtain the most accurate estimates. However, as the comparison showed, the choice of metric has an influence on the most accurate approach and sensor combination. For example, adding BT data barely improved, and sometimes even worsened, the quality of the space-time speed reconstruction. The data quality of BT has a great impact here and possible outliers should be eliminated rigorously beforehand. On the other hand, the travel time accuracy of virtual trajectories improved by adding BT. The same is true for the choice of algorithm. If only loop data are given, the ASM performs best in IMAE and MAPE. Given other data, specially BT data, the weighted PSM-W performs best. Compared to the original PSM, its accuracy is the same or better, thus, it successfully extends this approach without compromises. Thus, as a result, depending on the desired speed and travel time accuracy, this study helps to pick the optimal sensor setup or algorithm, depending on the given situation.

Some factors which may have an impact on the results are set as fixed in this study, though they may vary in other applications. First, the penetration rate and sampling interval of FCD and the spacing of stationary detectors may vary. Secondly, the situation used for assessment in this paper is a mixture of two traffic patterns using the classification of the Three-Phase theory: mega-jam and General Pattern (Kerner, 1999). These patterns cause large travel time losses, and thus, are especially important to reconstruct accurately. For further work, the study may be extended to further congestion patterns occurring on different days and roads.

This paper studies a multi-sensor data fusion for accurate traffic speed and travel time reconstruction. Two aspects are analyzed: 1) Which is the most accurate algorithm depending on different combinations of data sources, and 2) which is the best performance one can achieve with a flexible sensor setup. To this end, three state-of-the-art methods such as the ASM, the PSM and a simple averaging method, as well as a novel approach, are used to jointly reconstruct the traffic speed and travel times given sparse data.

The novel approach extends the PSM. It introduces a variable weighting of BT measurements, depending on detector spacing and measured travel time, which expresses the trustworthiness of a single measurement. The weighting allows for a dynamic integration of BT data with other data sources.

The mentioned questions are studied using empirical loop data, FCD and BT data collected during severe congestion on a German freeway. Data are divided into a reconstruction and a test set. Various combinations of algorithms and data are used to reconstruct the space-time traffic speed and the travel times. The error metrics IMAE and MAPE are used to assess the resulting reconstruction accuracies.

Key findings are that the novel approach outperforms the other algorithms in most of the cases. Furthermore, a combination of FCD and loop detector data provides the best overall results. The integration of Bluetooth data does not necessarily improve the reconstruction quality, depending on the error measure chosen. However, if no FCD are available, a combination of loop data and BT data is a better choice than only one source of data.

Next steps comprise a comprehensive pre-processing of travel time derived data to ensure consistency and to reduce outliers. Also, future research may include a mathematical optimization of the applied parameters and further studies on sensor spacings. Furthermore, the study could be extended to other locations and congestion patterns.