Speed estimation and length based vehicle classification from freeway single-loop detectors

Abstract

Roadway usage, particularly by large vehicles, is one of the fundamental factors determining the lifespan of highway infrastructure. Operating agencies typically employ expensive classification stations to monitor large vehicle usage. Meanwhile, single-loop detectors are the most common vehicle detector and many new, out-of-pavement detectors seek to replace loop detectors by emulating the operation of single-loop detectors. In either case, collecting reliable length data from these detectors has been considered impossible due to the noisy speed estimates provided by conventional data aggregation at single-loop detectors. This research refines non-conventional techniques for estimating speed at single-loop detectors, yielding estimates that approach the accuracy of a dual-loop detector’s measurements. Employing these speed estimation advances, this research brings length based vehicle classification to single-loop detectors (and by extension, many of the emerging out-of-pavement detectors). The classification methodology is evaluated against concurrent measurements from video and dual-loop detectors. To capture higher truck volumes than empirically observed, a process of generating synthetic detector actuations is developed. By extending vehicle classification to single-loop detectors, this work leverages the existing investment deployed in single-loop detector count stations and real-time traffic management stations. The work also offers a viable treatment in the event that one of the loops in a dual-loop detector classification station fails and thus, also promises to improve the reliability of existing classification stations.

Introduction

Roadway usage, particularly by large vehicles, is one of the fundamental factors determining the lifespan of highway infrastructure. The importance of road usage is evidenced by the federally mandated highway performance monitoring system (HPMS) and the significance of large vehicles is reflected in the weigh in motion (WIM) data collected for the long term pavement performance (LTPP) program in the United States. Interest in the movement of these large vehicles has also increased from the transportation planning perspective, as freight shipments are becoming more common in the planning process.

Each state in the US typically has several dozen WIM stations to monitor large vehicle usage. These stations are expensive to install and maintain, so they are usually supplemented with many more vehicle classification stations. Some of the classification stations employ axle counters, but the simplest of these stations use dual-loop detectors to measure vehicle length from the product of measured speed and detector on-time, and classify vehicles based on this measurement.

Meanwhile, single-loop detectors are the most common vehicle detector in use to monitor traffic, both for real-time operations and for collecting census data such as annual average daily travel (AADT). New, out-of-pavement detectors seek to replace loop detectors using wayside mounted sensors, e.g., the remote traffic microwave sensor (RTMS), but most of these detectors emulate the operation of single-loop detectors. Collecting reliable length data from single-loop detectors (and emulators) has heretofore been considered impossible due to the noisy speed estimates provided by conventional data aggregation at single-loop detectors.

In an effort to extend vehicle classification to single-loop detectors this research refines non-conventional techniques for estimating speed at these detectors, yielding estimates that approach the accuracy of a dual-loop detector’s measurements. Combining these single-loop detector speed estimation advances with a commonly used length based classification scheme for dual-loop detectors, this research brings length based vehicle classification to single-loop detectors, (and by extension, many of the emerging out-of-pavement detectors). By extending vehicle classification to single-loop detectors, this work leverages the existing investment deployed in single-loop detector count stations and real-time traffic management stations. The work also offers a viable treatment in the event that one of the loops in a dual-loop detector classification station fails and thus, also promises to improve the reliability of existing classification stations.

After reviewing the related literature, this work presents the new speed estimation techniques. Vehicle length is then estimated from the product of speed and on-time. To capture higher truck volumes than empirically observed, a process of generating synthetic on-times is developed. Following the Ohio Department of Transportation (ODOT) length based classification scheme for dual-loop detectors, the lengths are used to classify vehicles into three bins with divisions at effective vehicle lengths of 28 feet and 46 feet. This classification is evaluated against concurrent measurements from video and dual-loop detectors.

This research seeks to mainstream advances in speed and length estimation from single-loop detectors and develop a vehicle classification methodology for these detectors. Benekohal and Girianna (2003) note that it is, “necessary to encourage state DOTs to include classification counts in their annual traffic monitoring program.” As noted in a draft research statement from the Transportation Research Board’s Committee on Highway Traffic Monitoring, “Classification based solely on vehicle length is an alternative to axle-based classification but there has been no systematic study of how well it works – or how it should work.” The present research had to address many of these issues in the course of verifying the performance of single-loop detector based classification. This section reviews the literature on loop detector based speed estimation, vehicle length estimation, and vehicle classification.

For length based classification from loop detectors, there are three interrelated parameters that can be measured or estimated for each passing vehicle, namely vehicle length¹ (l), speed (v) and the amount of time the detector is “on”, i.e., the on-time (on). These parameters are related by the following equation:

$$l=v·\mathit{on}$$

The distinction between different detection technologies is important. At a single-loop detector, only the on-time can be measured directly, while a dual-loop detector can measure the speed from the quotient of the detector spacing and the difference in actuation times at the two loops. Given two of the three parameters, obviously the third is defined by Eq. (1). As such, dual-loop detectors are often employed to classify individual vehicles via Eq. (1). Conventional single-loop detectors, however, do not provide accurate estimates of v or l. As a result, these single-loop detectors have not been used to classify vehicles or estimate individual vehicle length in standard practice.

Many researchers have sought better estimates of average speed over a sample from single-loop detectors. The preceding research has emphasized techniques that use many samples of aggregate flow (q) and occupancy (occ) to reduce the estimation error one sees in a single sample, e.g., Mikhalkin et al., 1972, Pushkar et al., 1994, Dailey, 1999, Wang and Nihan, 2000, Coifman, 2001. Although rarely noted, these techniques effectively seek to reduce the bias due to long vehicles in measured occupancy. Rather than manipulating aggregate data, we developed new aggregation methods to reduce the estimation errors.

Provided that vehicle lengths and vehicle speeds are uncorrelated, (see, e.g., Coifman, 2001), following conventional practice, speed (space mean v, i.e., the harmonic mean) and assumed mean vehicle length (L^A) for a given sample are related by:

$$\mathit{space}\_\mathit{mean}v\approx \frac{q·L^A}{\mathit{occ}}$$

This equation is an extension of Eq. (1), since,

$$\frac{q·L^A}{\mathit{occ}}=\frac{L^A}{\mathit{mean}(\mathit{on})}$$

and as with Eq. (1), average length and average speed cannot be measured independently at a single-loop detector. Typically, an operating agency will set L^A to a constant value and use Eq. (2) to estimate speed from single-loop detector measurements. But this approach fails to account for the fact that the percentage of long vehicles may change during the day or the simple fact that a sample may not include “typical” vehicle lengths. Particularly during low flow, when the number of vehicles in a sample is small, a long vehicle can skew occupancy simply because it takes more time for that vehicle to pass the detector. For example, at one detector station Coifman (2001) found that approximately 85% of the individual vehicle lengths observed were between 15 and 22 feet, but some vehicles were as long as 85 feet, or roughly four times the median length. This large range of average vehicle lengths arises due to the small number of vehicles with lengths far from the center of the skewed distribution. The median of a sample is much less sensitive to these outliers, and

$$\mathit{medianv}\approx \frac{L^A}{\mathit{median}(\mathit{on})}$$

provides an alternative estimate of the center sample speed. As shown in Coifman et al. (2003), Eq. (4) performs significantly better than Eq. (2), and in fact it approaches the accuracy of dual-loop detector measurements for that study’s data.

There have also been several efforts based on time-series trends in flow and occupancy to estimate the percentage of vehicles that are long passing a single-loop detector. Kwon et al. (2003) developed a method employing aggregate flow and occupancy from single-loop detectors to estimate the percentage of long vehicles that passed. The work depends on two fundamental assumptions: the presence of a truck-free lane, and that the detector station exhibits high lane-to-lane speed correlation. They employed conventional detectors, used many days, using several stations from three facilities. The work only validated the results against aggregate dual-loop detector measurements and WIM data. The former yielded good results, while the latter had 20% overestimation. The fact that the overestimation results were only evident in the WIM data highlights the importance of employing a truly independent measure of ground truth. The research studied facilities with low to moderate truck volumes (under 10% of the fleet) and did not explicitly single out performance in congested conditions. In fact the authors note that, “the estimate of truck volume is biased and unstable at the start of the congestion period.”

Wang and Nihan, 2003, Wang and Nihan, 2004 also developed a method employing aggregate flow and occupancy from single-loop detectors to estimate the percentage of long vehicles that passed. Like Kwon et al., their work also depends on two fundamental assumptions, though slightly different, “constant average speed for each [3 min long] time period and at least two intervals containing only [short vehicles] in each period.” They employed conventional detectors, used many days, and studied four detector stations. The work only validated the results against aggregate dual-loop detector measurements. The research studied facilities with low to moderate truck volumes (under 10% of the fleet) and did not explicitly single out performance in congested conditions. These authors note, “the algorithm should work better under less congested conditions.” The authors also explicitly note the limitation of the small number of test sites, stating that, “future research is needed to handle the conditions when one or both of the assumptions are violated in order to reduce estimation errors…. The proposed algorithm will be more robust and accurate when the violation circumstances are properly addressed.” More recently, the group has revised their methodology (Zhang et al., 2006). This recent study is subject to many of the same limitations as their earlier work, it employs aggregate flow and occupancy, was tested at only two detector stations (with approximately 10% truck flow), and only compared the results against aggregate dual-loop detector measurements. The final conclusion of Zhang et al. states that although the method produced favorable bin volumes, further improvements to its performance are possible through optimizing its design and training, especially under heavily congested conditions.

Both of these efforts, Kwon et al., 2003, Wang and Nihan, 2003, Wang and Nihan, 2004, only estimate the percent of vehicles that are long within a sample, they do not estimate length or classify vehicles individually. More importantly, the fundamental assumptions of common speed (either across lanes or over time) and of one or more samples without any long vehicles may be unrealistic at times and thus, could limit the accuracy of their algorithms.

There have also been efforts to use new loop detector sensors to measure the inductive vehicle signature for vehicle classification, e.g., Reijmers, 1979, Gajda et al., 2001. While these inductive signature based efforts are promising, the published studies typically employ validation sets on the order of 100 vehicles. Conventional binary loop detector output remains by far the dominant configuration for single-loop detectors.

As noted earlier, most of the non-invasive vehicle detectors that have entered conventional practice mimic the operation of single-loop detectors, the two most prevalent examples of these detectors being the SmartSensor by Wavetronix and RTMS by EIS. Both sensors can provide length based classification data, though the specific algorithms are proprietary. While the sensors often provide reasonable counts and speed estimates in aggregate data, per-vehicle analysis has shown that the aggregate data allow over-counting errors to cancel under-counting errors and that individual vehicle on-times can be subject to large errors (see, e.g., Zwahlen et al., 2005, Coifman, 2006a). The literature is surprisingly lacking in evaluations of the classification performance from these sensors. Among the few available studies, Zwahlen et al., 2005 evaluated the SmartSensor in uncongested, low volume traffic, with low truck flows. While these conditions should lead to favorable performance by the sensor, after comparing the classification results against manually generated ground truth data the authors concluded that, “vehicle classification is unreliable; the fraction of trucks in a lane can be severely overestimated or underestimated.” Trucks were undercounted by as much as 80% in the worst case and “at this time, the system does not reliably estimate the number of trucks in the traffic stream.” French and French (2006) examined the performance of RTMS and SmartSensor, including vehicle classification, at four temporary locations and three fixed locations. Even though manufacturer representatives calibrated the detectors, the reported truck counts from the non-invasive detectors were typically off by a factor of two and sometimes as much as a factor of ten. Almost all of the test locations were characterized by low truck flows, below 5% of the traffic. So while the manufacturers offer vehicle classification from these non-invasive sensors, the specific algorithms are undocumented and to the extent that they have been evaluated in the literature, the performance is poor.

Returning the focus to conventional single-loop detectors, the present research seeks to estimate vehicle lengths and classify vehicles. Assuming the loop detector is functioning properly, Eq. (1) shows that a given on-time measurement is simply a function of the vehicle’s length and speed. During free flow conditions the vehicle speeds typically fall in a small range and during congested conditions the difference between two successive vehicles’ speeds is usually small. If one assumes that all of the vehicles in a sample are traveling near the median speed, one can use Eq. (4) in conjunction with measured on-times to estimate individual vehicle lengths. Of course the number of vehicles per sample must be small enough for the speed assumption to hold and one must control for low speed conditions, when acceleration becomes non-negligible within the sample.² Using samples of ten consecutive vehicles and restricting the analysis to samples with v > 20 mph (from Eq. (4)), Coifman et al. (2003) found the average absolute error in estimated length (via Eq. (1)) is less than 6% compared to measured length from dual-loop detectors for 210,000 vehicles in the sample data set. Like so many of the other studies, the results come from a location with approximately 10% truck flow.

In the presence of heavy truck traffic, e.g., 40–60% of the flow, the improvements from Eq. (4) degrade because of the high variability in the true but unobserved sample median vehicle length. Using data from a detector with heavy truck traffic, Neelisetty and Coifman (2004) developed a methodology to address this problem. As demonstrated in Neelisetty and Coifman, two consecutive vehicles usually have similar speed, even during congestion, and thus, from Eq. (1), the ratio of the on-times is a good approximation of the ratio of their lengths. The extension explicitly recalibrates speed estimates by looking for two consecutive vehicle measurements possessing the longest feasible vehicle length and the shortest feasible length, roughly 80 feet and 18 feet, respectively or a ratio of 4:1 in successive on-times. When this ratio is observed in the on-times, one can deduce the vehicle lengths and use Eq. (1) to estimate speed from the measured on-times. Further checks are then made to eliminate transient detection errors that would otherwise disrupt this speed estimation. The paper reported an average absolute percent error in speed estimation under 6% for a detector with heavy truck traffic, but the site also had little congestion. Neelisetty and Coifman did not explicitly examine length estimation.

All of the previous studies using single-loop detectors for individual vehicle length estimation, vehicle classification, or estimating the number of trucks in a sample suffer from the following limitations. Most of the studies only compared the results against concurrent measurements from dual-loop detectors, without any manual validation and thus, any errors present in the dual-loop detectors would go unaccounted for. In the few cases that employed manual validation, the study data set is very small, under 1000 vehicles and often under 100 vehicles. Presumably the problems of a small data set are obvious, but trusting that the dual-loop detector results are accurate can be equally problematic, e.g., as shown herein, we found a case where the loop detectors were “dropping-out” in the middle of semi-trailer trucks, a problem that impacted both dual- and single-loop detector classifications alike. The prior studies have also been limited by the vehicle fleet; except for Neelisetty and Coifman, they have all used facilities where trucks comprise at most 10% of the traffic flow. As trucks become a larger portion of the flow, the assumptions underlying Eqs. (2), (4) break down. In most cases, the studies have also explicitly avoided congested traffic conditions, where slow-and-go or stop-and-go traffic degrade the speed estimation for similar reasons. As such, the present research explicitly seeks out the challenging conditions: congestion, and high percentages of long vehicles.