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Development of City-Wide Road Grade Profiles Utilising Advanced Bus Transportation Systems
15th IFAC Symposium on Control in Transportation Systems 15th IFAC Symposium on Control in Transportation Systems June 6-8, 2018. Savona,on Italy 15th IFAC Symposium Control in Transportation Systems June 6-8, 2018. Savona, Italy Available online at www.sciencedirect.com 15th Symposium Control in Transportation Systems JuneIFAC 6-8, 2018. Savona,on Italy June 6-8, 2018. Savona, Italy
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Development of City-Wide Road Grade Development of City-Wide Road Grade Development of City-Wide Road Grade Profiles Utilising Advanced Bus Development of City-Wide RoadBus Grade Profiles Utilising Advanced Profiles Utilising Advanced Bus Transportation Systems Bus Profiles Utilising Advanced Transportation Transportation Systems Systems Transportation Systems Tushti Singla, Mike Brady, Jared Magrath
Tushti Singla, Mike Brady, Jared Magrath Tushti Singla, Mike Brady, Jared Magrath Singla, Mike Brady, Jared Magrath School ofTushti Computer Science and Statistics, University of Dublin, School Science and Statistics, University of School of of Computer Computer Science and Statistics, University of Dublin, Dublin, Trinity College Dublin, Ireland Trinity College Dublin, Ireland School of Computer Science and Dublin, Statistics, University of Dublin, Trinity College Ireland e-mail: [email protected] e-mail: [email protected] Trinity College Dublin, Ireland e-mail: [email protected] e-mail: [email protected] Abstract: Road grade is of vital importance in determining a vehicle’s fuel consumption and Abstract: Road grade is importance in aa vehicle’s fuel consumption and Abstract: gradeeco-routing is of of vital vital solutions. importanceConsequently, in determining determiningthere vehicle’s fuel and therefore in Road designing is a need to consumption develop accurate therefore in designing eco-routing solutions. Consequently, there is a need to develop accurate Abstract: Road grade is of scale vital solutions. importance in determining a vehicle’s fuel and therefore designing there is a need to consumption develop accurate road gradeinprofiles on aeco-routing large with a high Consequently, degree of accuracy. Advanced Bus Transportation road grade on large scale with degree of Bus Transportation therefore inprofiles designing solutions. Consequently, thereAdvanced isofa data need about to develop accurate road grade profiles on a aeco-routing large scale with aa high high degreelarge of accuracy. accuracy. Advanced Bus Transportation Systems (ABTS) provide an opportunity to collect amounts bus routes in Systems (ABTS) provide an scale opportunity to collect collect large amounts of data data about about bus routes routes in in road grade on a large with a high degree ofdevelopment accuracy. Advanced Bus Transportation Systems (ABTS) provide an opportunity to large amounts of bus the form of profiles GPS traces, which in turn could enable the road grade profiles within of road grade profiles within the form of GPS traces, which in turn could enable the development Systems (ABTS) provide an paper opportunity collect large amounts of datalarge about busroad routes in the formcatchment of GPS traces, in turn couldtoon enable the development grade profiles within a large area. which This reports an approach to developing scale grade of road a large area. This reports on an to developing large scale road grade the formcatchment traces, which inThe turn couldinvestigates enable the development of road grade profiles aprofiles large catchment area.process. This paper paper reports on an approach approach large scale roadwithin grade inof aGPS multistep work the to usedeveloping of GPS trace information from profiles in multistep process. The work investigates the use of trace information from a large catchment area.with Thiselevation paper on an approach to developing large scale road grade profiles in a a combined multistep process. Thereports work investigates the use of GPS GPS trace information from Dublin Bus, information from the Shuttle Radar Topography Mission Dublin Bus, combined with elevation information from the Shuttle Radar Topography Mission profiles in a multistep process. The work investigates the use of GPS trace information from Dublin combined with elevation from the Shuttle Radar Topography Mission (SRTM)Bus, to develop road grade profilesinformation for all bus routes in the company’s system, covering the (SRTM) to develop road grade profiles for all bus routes in the company’s system, covering the Dublin Bus, combined with elevation information from the Shuttle Radar Topography Mission (SRTM) to develop road grade profiles for all bus routes in the company’s system, covering the major areas of the city of Dublin, Ireland. The results are compared with road grades derived major areas of the of Dublin, Ireland. The results with road derived (SRTM) to develop road profiles for all bus routesare in compared the company’s covering the major areas of the city city ofgrade Dublin, Ireland. The results are compared with system, road grades grades derived from Google elevation data. from Google elevation data. major areas of the citydata. of Dublin, Ireland. The results are compared with road grades derived from Google elevation © 2018, IFAC elevation (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. from Google Keywords: Road Grade,data. Elevation, Transportation, Global positioning systems, Filtering Keywords: Road Grade, Elevation, Transportation, Global positioning systems, Filtering techniques,Road Interpolation algorithms, Smoothing filters, Signal processing, Advanced Bus Keywords: Grade, Elevation, Transportation, Global positioning systems, Filtering techniques, Interpolation algorithms, Smoothing filters, Signal processing, Advanced Bus Keywords: Road Grade, Elevation, Transportation, Global positioning systems, Filtering filters, Signal processing, Advanced Bus Transportation Systems, OpenStreetMap. techniques, Interpolation algorithms, Smoothing Transportation Systems, OpenStreetMap. techniques, Interpolation algorithms, Smoothing filters, Signal processing, Advanced Bus Transportation Systems, OpenStreetMap. Transportation Systems, OpenStreetMap. 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION Road grade is an important factor in the fuel consumption Road grade is an important factor in the fuel consumption of Frey al. Zhang and Road grade (e.g. is an see important in the fuel consumption of vehicles vehicles (e.g. see Frey et etfactor al. (2008); (2008); Zhang and Frey Frey Road grade is et anal. important in fuel consumption (2006); Wood (2014b); Levin et the al. (2014)). However, of vehicles (e.g. see Frey etfactor al. (2008); Zhang and Frey (2006); Wood et al. (2014b); Levin et al. (2014)). However, of vehicles (e.g. see(2014b); Frey etLevin al.used, (2008); Zhang and (2006); Wood et al. et al. However, many fuel-consumption models for(2014)). instance, in Frey ecomany fuel-consumption models used, for instance, in eco(2006); Wood et al.account (2014b); Levin et grade al. However, routing, do not for road (Zhou et ecoal., many fuel-consumption models used, for(2014)). instance, in routing, do not account for road grade (Zhou et ecoal., many used, forconsumption instance, 2016). fuel-consumption Neglecting road models grade in fuel routing, do not account for road grade (Zhou in et and al., 2016). Neglecting road grade in fuel consumption and routing, domodelling not account for road grade (Zhou et and al., emissions cangrade result erroneous estimates 2016). Neglecting road in infuel consumption emissions modelling can result in erroneous estimates 2016). Neglecting road grade in fuel consumption and emissions modelling can result in erroneous estimates (Zhang and Frey, 2006; Levin et al., 2014). The availability (Zhang andmodelling Frey, 2006;can Levin et al.,in2014). The availability emissions result erroneous estimates of road and grade information on eta al., large scaleThe is therefore of (Zhang Frey, 2006; Levin 2014). availability of road and grade information on eta al., large scaleThe is therefore of (Zhang Frey, 2006; Levin 2014). availability increasing importance due to in fuel of road grade information onongoing a large developments scale is therefore of increasing importance due to ongoing in of road grade information oneco-routing. a large developments scale is therefore of increasing importance due ongoing developments in fuel fuel consumption modelling andto consumption modelling and eco-routing. increasing importance ongoing developments in fuel consumption modellingdue andtoeco-routing. While commercial implementations of large scale road consumption modelling and eco-routing. While commercial implementations of large scale road While commercial implementations largewould scale most road grade profiles are already under way,ofthese grade profiles are already under way, these would most While commercial implementations large scale most road grade profiles already under way,ofthese probably not beare freely available (Sahlholm andwould Johansson, probably not beare freely available (Sahlholm and Johansson, grade profiles already under way,into these most 2010). facilitate continued research and probably not be freely available (Sahlholm andwould Johansson, 2010). To To not facilitate continued research into eco-routing eco-routing and probably be freely available (Sahlholm and fuel consumption there is a into need to Johansson, develop 2010). To facilitate models, continued research eco-routing anda fuel consumption models, there is a need to develop 2010). Totofacilitate continued research eco-routing andaa fuel consumption models, is a into need to develop method determine road there grade profiles on a large scale method to determine road grade profiles on a large scale fuel models, a need develop a method to determine road there grade is profiles on to a large scale from consumption public information. from public information. method to determine road grade profiles on a large scale Fig. 1. The city of Dublin overlaid with the approximately from public information. Development of these large-scale maps has been investi- Fig. 1. The city of Dublin overlaid with the approximately from public information. Development of these large-scale maps has been investi- Fig. 1. 150,000 GPS the data, The city of points Dublinpresent overlaidin with the approximately gated by a number researchersmaps (Wood al., investi2014a, Fig. 1. Development of theseoflarge-scale has et been 150,000 GPS points present inwith the test test data, compriscomprisThe city of Dublin overlaid the approximately gated by a number of researchers (Wood et al., 2014a, ing 120 different routes in both directions of travel. 150,000 GPS points present in the test data, comprisDevelopment of these maps has been 2015; John al., 2017; Sahlholm, 2008). However, these gated by a et number oflarge-scale researchers (Wood et al., investi2014a, ing 120 120 GPS different routes in both both directions of travel. 150,000 points present in the test data, compris2015; John et al., 2017; Sahlholm, 2008). However, these ing different routes in directions of travel. The map is approximately 36 km on a side. gated by a number of researchers (Wood et al., 2014a, approaches which may hinder their use on 2015; John have et al.,limitations 2017; Sahlholm, 2008). However, these The map is approximately 36 km on a side. ing routes in 36 both The 120 mapdifferent is approximately kmdirections on a side. of travel. approaches have which hinder their on 2015; et al.,limitations 2017; Sahlholm, 2008). However, these approaches have limitations which may may hinder their use use on a largeJohn scale. The map is approximately 36 km on a side. a large scale. approaches have limitations which may hinder their use on ated against commercially-available TomTom datasets a large scale. ated against commercially-available TomTom datasets in in Wood et al. (2015), at the U.S. National Renewable Energy aWood largeetscale. localised and aggregate test areas of the United States. ated against commercially-available TomTom datasets in al. (2015), at the U.S. National Renewable Energy Wood et al. (2015), at the U.S. National Renewable Energy ated localised and commercially-available aggregate test areas of TomTom the Uniteddatasets States. in Laboratory (NREL), developed a method of appending against localised and aggregate test areas of the United States. Laboratory (NREL), developed a method of appending Wood et al.from (2015), at the U.S. National Renewable Energy elevations a high-resolution to ofhigh sample localised John developed aa methodology for utilising Laboratory (NREL), developed a DEM method appending and(2017) aggregate test areas of the United John et et al. al. (2017) developed methodology forStates. utilising elevations from a high-resolution DEM to high sample Laboratory (NREL), method ofhigh appending rate GPS traces a developed large-scalea manner. was evalu- John voluntarily-collected GPS traces to determine city-wide elevations from ainhigh-resolution DEM toIt sample et al. (2017) developed a methodology for utilising voluntarily-collected GPS traces to determine city-wide rate GPS traces inhigh-resolution a large-scale manner. Ithigh was sample evalu- John elevations from a DEM to et al. (2017) developed a methodology for utilising rate GPS traces in a large-scale manner. It was evalu- voluntarily-collected GPS traces to determine city-wide rate GPS© 2018, traces in (International a large-scaleFederation manner.of Automatic It was evaluvoluntarily-collected GPS to determine city-wide 2405-8963 IFAC Control) Hosting by Elsevier Ltd. All rightstraces reserved.
Copyright © 2018 IFAC 428 Copyright 2018 responsibility IFAC 428Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 428 10.1016/j.ifacol.2018.07.070 Copyright © 2018 IFAC 428
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road grades with a view to updating the OpenStreetMaps (OSM) database. The researchers concluded that the use of voluntarilycollected traces, collected in a non-homogeneous manner, resulted in low absolute accuracy. Further, these traces were “not available for a significant share of street segments”. In his doctoral thesis, Sahlholm (2008) investigated the use of Heavy Duty Vehicles (HDVs) to repeatedly update a database of road grade estimates of routes taken by the vehicles. The work highlighted the importance of averaging repeated traversals of routes for improving results. However, the study was limited to the use of HDVs, thus tending to favour long-haul routes with less coverage of cities.
Fig. 2. Elevation profiles generated from ASTER (drawn in black) and SRTM-1 (in red) DEMs.
The present paper investigates the development of road grade profiles on a large scale, using GPS traces taken from Advanced Bus Transportation Systems (ABTS), combined with elevation estimates extracted from the Shuttle Radar Topography Mission (SRTM). The approach has been tested on data from the urban area of Dublin, Ireland and the results are compared against Google API estimates. Comparing this work with the work cited above, the DEM used is of lower resolution and the GPS sampling intervals are longer than those used by Wood et al. (2015). Compared to the work of John et al. (2017), the GPS traces gathered are from a relatively homogeneous fleet of vehicles operating over most of the city. Similarly, by comparison with Sahlholm (2008), a greater coverage of city routes is obtained. Data is processed in a multistep work flow, as depicted in Fig. 3. A range of methods is explored for each step, consisting of newly developed algorithms as well as replicated studies. The best solutions for each step are presented, and an investigation is carried out to determine the merits of the resulting pipeline of methods. 2. EXPERIMENTAL SET-UP Route data was obtained from Dublin Bus’s information site (National Transport Authority, 2013). The bus network consists of approximately 120 routes and covers all major areas of the city – see Fig. 1. Each route has two directions of travel – outbound and inbound – which may be slightly different. The data for each route consists of GPS traces of multiple trips in both directions. In all, the data comprised over 150,000 GPS points. Results were generated for every route and direction. For brevity, the results and illustrations in the rest of this paper refer to one particular route – Route 27B (Outbound). The route data contains no information about elevation and therefore elevations were extracted from a DEM. Two DEMs available for the city of Dublin, SRTM-1 (USGS, 2009) and ASTER (Yamaguchi et al., 1998; Jet Propulsion Laboratory, 1999), were compared for use in this study. Elevation profiles drawn from each source (see Fig. 2) show that profiles developed from ASTER data have significantly more variability than those generated from SRTM1. ASTER elevations have sudden jumps with peaks and troughs, whereas SRTM-1 elevations are smoother and 429
Fig. 3. Workflow for generating road grade profiles. have more gradual changes. Therefore, SRTM-1 was used in this study, as it more faithfully represents the terrain. To automate the generation of road grade profiles, a multistep procedure was applied to the entire dataset, as illustrated in Fig. 3. (1) The GPS data and SRTM elevations were loaded onto a Postgres + PostGIS database developed for this study. (2) The database was queried for one route at a time. (3) The route queried was split into two data frames depending upon direction of travel. Each data frame was proceeded with separately. (4) The data was processed through four stages (detailed below) – Data Cleansing, Route Averaging, Elevation Interpolation and Smoothing. (5) The resulting elevations were used to calculate road grade angles at 100 metre intervals and the database was updated with the calculated road grade estimates for each point. (6) Elevation profiles and road grade profiles were generated for the route. (7) Steps 3 – 6 were repeated for each route. Google elevations were used to evaluate the results. The original intention was to use LiDAR elevations for this purpose, but the data was not freely available. What was
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available was a small set of LiDAR elevations scattered around the city centre and not part of any bus route. Nevertheless, these elevations were compared with equivalent Google elevations. A Pearson correlation coefficient of 0.8118 between the LiDAR elevations and the Google elevations suggests that Google elevations are accurate enough to be used in place of LiDAR data and have the merit of being freely available. 3. DATA CLEANSING The route data had anomalies due to variations in time and distance travelled during different trips along the route. These may have been caused by weather conditions, traffic congestion, diversions, partially recorded trips or other factors. These anomalies cause errors in the calculation of route length and hence in elevation profile estimates. A number of techniques were therefore developed and evaluated to cleanse the data. OSM data was used to aid the cleansing process as follows: For each GPS point in the data, the closest OSM node was selected as its reference point. This gave an OSM node ID to each GPS point in the dataset. Having assigned the reference points, three algorithms were evaluated to filter out anomalous data points depending upon their frequency of occurrence across different trips in a route. (1) Algorithm 1 filtered out those OSM nodes (and corresponding GPS points) that were not present in all trips of a route. This resulted in an incomplete route profile because some trips only had partial traces of the route. Although the method developed did not suit the test data in this project, it would be suitable where the data for all trips is complete. (2) Algorithm 2 removed those OSM nodes (and corresponding GPS points) which had a frequency of occurrence in trips less than a threshold, chosen to be 33%. This generated a complete and clean GPS profile but the data still contained some irregularities that resulted in incorrect calculations of cumulative distance in elevation profiles. This method would be worth considering if it was known that no trips had any diversions from the route. (3) Algorithm 3 removed those entire trips that contained any OSM nodes that had a frequency of occurrence below the threshold of 33%. This method worked effectively to cleanse data for all routes in the diverse dataset. Algorithm 3 was chosen to cleanse the data for all routes in the study. The possibility of using Google API route data was explored. However, the method was not considered suitable because the query limits of Google API make it infeasible to retrieve data for such a large dataset. Further, the study aimed to develop a generic process that does not rely on commercial services. 4. ROUTE AVERAGING Averaging GPS points from different traversals of a route is known to help to produce better route estimates, which are less susceptible to outlier GPS points and horizontal errors 430
(i.e. errors in distance rather than elevation). Studies by Sahlholm and Johansson (2010), Boroujeni et al. (2013), and Boroujeni and Frey (2014) made use of GPS data from multiple passes over the same road. Sahlholm and Johansson (2010) used Kalman filtering to average the GPS data and stated that “GPS position estimates are generally bias free when averaged over long time periods and the error is approximately normally distributed.” Hence, averaging data from multiple runs can lead to more accurate GPS position estimates and thereby road grade profiles. Thus, after cleaning the route data, the multiple trips of a route were averaged as now described. To perform the averaging, data from all trips of a route was combined, sorted by distance and passed to a low-pass filter. A number of low-pass filters were evaluated in the study: (1) A 4-point moving average filter, (2) Exponential filters with smoothing factor of 0.8, 0.9 and 0.95, (3) A 5-point binomial filter with weights [1, 4, 6, 4, 1], (4) A 5-point Savitzky-Golay Filter with weights [-3, 12, 17, 12, -3], (5) A 5-point combined Binomial and Savitzky-Golay Filter with the same weights as the individual filters above. The quality of the averaging process was assessed by comparing the output of different filters with the route as depicted on the map. In analysing the effects of the different filters, it was observed that the Moving Average Filter produced the most accurate representation of the route by uniformly filling the gaps along the route between the GPS points. The Binomial Filter proved to be the second-best choice, followed by the combined Binomial and Savitzky-Golay Filter. The Savitzky-Golay Filter and the Exponential Filter performed poorly, scattering points beyond the boundaries of the roads. The averaged route profile so obtained was then used for elevation extraction and smoothing as described in the following sections. 5. ELEVATION INTERPOLATION Having obtained estimates of the route, the next step was to calculate elevations of points along the route from the SRTM data. Studies by Wood et al. (2014a) and Henriques and Bento (2013) validate the possibility of extracting elevations from DEMs to calculate road grade. Additionally, DEMs offer reasonable accuracy at no cost, making them a good choice for experiments of this type. However, DEMs do not provide good elevation estimates by themselves. Due to abrupt elevation changes between tiles on a DEM grid, and due to the size of the tiles – SRTM-1 tiles are approximately 30m on a side – elevation profiles derived from DEMs have a ragged, stair-like contour. To obtain smooth elevation profiles, therefore, there is a need to interpolate elevation at points other than the centres of the tiles. A number of interpolation techniques were evaluated: (1) Bilinear Interpolation: Elevation was interpolated using a 2x2 grid of neighbouring cells. Linear interpola-
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tion was done along the longitude axis first and the interpolated values were used to linearly interpolate along the latitude axis. Although each step is linear, the overall interpolation is quadratic. (2) Advanced Bilinear Interpolation: This was an extension of bilinear interpolation employed in the study by Henriques and Bento (2013). In this study, an extended bilinear interpolation was used, where elevations of the neighbouring grid cells were weighted according to their distance from the reference cell to estimate the new elevation. (3) Bicubic Interpolation: Elevation was interpolated using a 4x4 grid of neighbouring cells. This was implemented similarly to bilinear interpolation such that four cubic interpolations were performed along the longitude axis first and the results obtained were then used to perform a cubic interpolation on the latitude axis. To validate the accuracy of these techniques, as previously noted, interpolated elevations were compared with Google elevations. The results are presented in Fig. 4.
Fig. 4. Mean Absolute Error (MAE) in raw and interpolated SRTM elevations. Each bar gives the MAE of the particular series as compared to Google elevations.
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6. SMOOTHING The final step in the workflow involved smoothing elevation and road grade profiles. The SRTM is a Digital Terrain Model, which means that it records the lowest elevation at any given point. This works for straight roads, but it poses a problem at intersections between rivers and bridges, or highways and overpasses, where the SRTM records the lower of the two elevations. This leads to irregularly low elevation areas and produces discrepancies in elevation profile. To resolve this issue, Wood et al. (2014a) developed a multistage smoothing technique to filter out erroneously low lying elevations. The same technique was implemented in this work, with parameters such as the down-sampling interval and the window size of the filter begin chosen to suit both the data and the purpose of the work. It consisted of the following steps: (1) The data was down-sampled using a uniform distance of 100 metres. A sampling interval of 100 metres was chosen as it proved to suit the lengths of the routes. (2) It was passed through a nine-point combined Binomial and Savitzky-Golay Filter to remove high fluctuations in elevation. Since the study by Wood et al. (2014a) did not indicate the window size of the filter used, a choice was made to use a nine-point filter in this experiment. (3) Outliers, i.e. elevation values that differed by more than 10 metres, were removed and then backfilled via linear interpolation. (4) The data was filtered a second time through the aforementioned filter. (5) This data was then linearly interpolated using original distances before down-sampling to restore data length. (6) The smoothed elevations so obtained were used to estimate road grade angles at 100 metre intervals suitable for calculating road grade profile over the entire route. 7. RESULTS AND DISCUSSION
As expected, DEM elevations have the highest MAE amongst all the series compared. The interpolated elevations are observed to have lower MAE than raw DEM elevations, showing an improvement caused by interpolating DEM data. The difference in the correlation values between the (standard) Bilinear and the Advanced Bilinear methods is quite small. The Advanced Bilinear method had the closest correspondence to Google data. Hence, it was chosen in this work.
Fig. 5 shows a sharp contrast between the rugged and irregular raw DEM elevations before processing and the smoothed elevation profile obtained as an end-result of the multistage approach employed in this study. Similarly, the road slope angles calculated using the raw DEM data (Fig. 6) have a high fluctuation rate, which is unrealistic. The smoothed elevations give rise to continuous and gradually changing road grade profiles, which is how roads are built in real life (Sheng, 1990).
An interesting result was that although bicubic methods might be generally expected to outperform bilinear methods, this was not the case here. This can be attributed to the fact that bicubic methods require partial derivatives and cross-derivatives for accurate calculations in interpolation, and are based on the condition that slopes match on the boundaries. However, since no information about derivatives was available for this data, estimates for slope were used and it was hypothesised that slope does not change across points, which is likely to have led to a reduction in the accuracy of elevations.
Better estimates were obtained by interpolating elevations followed by smoothing than by interpolating alone or by smoothing alone, as done in previous studies. To validate this, elevation estimates from the different stages of the pipeline were each compared statistically to Google elevations. The Pearson correlation coefficient and the Mean Absolute Error were calculated for (i) raw DEM elevations, (ii) the intermediate interpolated elevations and (iii) the final elevations produced by the pipeline against Google elevations and are shown in Figures 8 and 9. The high correlation of 0.9971 between the Google elevations and
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Fig. 5. Elevation profiles obtained from raw DEM elevations (in black) compared to final smoothed elevations (in red).
Fig. 8. Correlation between Google elevations and elevations from (i) raw SRTM data, (ii) SRTM data after interpolation and (iii) SRTM data after interpolation and smoothing. Each bar represents the correlation of the particular series with Google elevations.
Fig. 6. Road Grade profiles derived from raw DEM elevations (in black) and from final smoothed elevations (in red). Fig. 9. Mean Absolute Error (MAE) between elevations derived from Google data and those derived from (i) raw SRTM data, (ii) SRTM data after interpolation and (iii) SRTM data after interpolation and smoothing. Each bar represents the MAE of the particular series as compared to Google elevations.
Fig. 7. Google API elevation profiles (in black) compared to the final smoothed elevations (in red). elevations resulting from the pipeline supports the usefulness of the methodology implemented in the current study. Fig. 7 shows the smoothed elevation profile in close correspondence with Google elevations. Discrepancies between the profiles may be due to the presence of bridges, overpasses or similar structures (Magrath and Brady, 2017). 8. CONCLUSION The work presented demonstrates that road grade profiles and elevation profiles can be derived on a large scale from GPS trace data combined with DEM information. 432
A pipeline of methods for data cleansing, route averaging, elevation interpolation and smoothing was implemented and evaluated. The pipeline worked successfully and individual elevation profiles and road grade profiles were generated for all 120 routes of Dublin Bus network for which data was available. An overview of combined citywide road grade maps is presented in Fig. 10. The staged, modular nature of the pipeline enabled the separate stages of processing to be developed and validated independently. The pipeline does not rely on commercial services. A number of data cleansing schemes were developed and evaluated. A relatively strict scheme for removing anomalous trip data – Algorithm 3 – gave the best results. A number of methods for averaging GPS position estimates from different trips of a route were evaluated. A 4-point moving average filter performed best in smoothing route profiles. An analysis of interpolation methods for DEM elevations showed that an Advanced Bilinear Interpolation method
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Fig. 10. Bus routes in the Dublin area with road grades. Grades from zero to one degree are shown in black. Grades between one and two degrees are shown in blue, and grades greater than two degrees are depicted in red. (Henriques and Bento, 2013) was most effective, producing best agreement with Google elevation data. A combination of interpolation and smoothing techniques yielded results in better agreement with Google data than either one individually. A Pearson correlation of 0.9971 between the final elevations and Google elevations indicates a high degree of accuracy and underscores the viability of the pipeline approach. Since the pipeline and associated techniques worked well for the Dublin Bus route data, it would be interesting indeed to use it on data from other locations. REFERENCES Boroujeni, B.Y. and Frey, H.C. (2014). Road grade quantification based on global positioning system data obtained from real-world vehicle fuel use and emissions measurements. Atmospheric Environment, 85, 179–186. Boroujeni, B.Y., Frey, H.C., and Sandhu, G.S. (2013). Road grade measurement using in-vehicle, stand-alone GPS with barometric altimeter. Journal of Transportation Engineering, 139(6), 605–611. Frey, H.C., Zhang, K., and Rouphail, N.M. (2008). Fuel use and emissions comparisons for alternative routes, time of day, road grade, and vehicles based on in-use measurements. Environmental Science & Technology, 42(7), 2483–2489. Henriques, N. and Bento, C. (2013). Integration of GPS Traces and Digital Elevation Maps for Improving Bicycle Traffic Simulation Behavior. In Transportation Research Board 92nd Annual Meeting, Transportation Research Board. Jet Propulsion Laboratory (1999). Aster: Advanced spaceborne thermal emission and reflection radiometer. URL https://asterweb.jpl.nasa.gov/. Accessed on October 2017. John, S., Hahmann, S., Rousell, A., L¨ owner, M.O., and Zipf, A. (2017). Deriving incline values for street networks from voluntarily collected gps traces. Cartography and Geographic Information Science, 44(2), 152–169. Levin, M.W., Duell, M., and Waller, S.T. (2014). The effect of road elevation on network wide vehicle energy consumption and eco-routing. Transportation Research Record: Journal of the Transportation Research Board. Magrath, J. and Brady, M. (2017). Evaluating different methods for determining road grade best suited to 433
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ITS. In IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI 2017). National Transport Authority (2013). Public Transport Route Networks. URL https://data.dublinked.ie/ dataset/public-transport-route-networks/. Accessed July 2017. Sahlholm, P. (2008). Iterative road grade estimation for heavy duty vehicle control. Ph.D. thesis, KTH. Sahlholm, P. and Johansson, K.H. (2010). Road grade estimation for look-ahead vehicle control using multiple measurement runs. Control Engineering Practice, 18(11), 1328–1341. Sheng, T. (1990). Watershed management field manual. FAO conservation guide, 13(6). USGS (2009). Shuttle radar tomography mission (SRTM). URL https://pubs.usgs.gov/fs/2009/3087/. Accessed on October 2017. Wood, E., Burton, E., Duran, A., Gonder, J., et al. (2014a). Appending high resolution elevation data to GPS speed traces for vehicle energy modeling and simulation. National Renewable Energy Laboratory. Wood, E., Burton, E., Duran, A., and Gonder, J. (2014b). Contribution of road grade to the energy use of modern automobiles across large datasets of real-world drive cycles. Technical report, SAE Technical Paper. Wood, E., Duran, A., Burton, E., Gonder, J., and Kelly, K. (2015). EPA GHG Certification of Medium-and Heavy-Duty Vehicles: Development of Road Grade Profiles Representative of US Controlled Access Highways. Technical report, National Renewable Energy Laboratory (NREL), Golden, CO (United States). Yamaguchi, Y., Kahle, A.B., Tsu, H., Kawakami, T., and Pniel, M. (1998). Overview of advanced spaceborne thermal emission and reflection radiometer (ASTER). IEEE Transactions on geoscience and remote sensing, 36(4), 1062–1071. Zhang, K. and Frey, H.C. (2006). Road grade estimation for on-road vehicle emissions modeling using light detection and ranging data. Journal of the Air & Waste Management Association, 56(6), 777–788. Zhou, M., Jin, H., and Wang, W. (2016). A review of vehicle fuel consumption models to evaluate ecodriving and eco-routing. Transportation Research Part D: Transport and Environment, 49, 203–218.
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Development of City-Wide Road Grade Development of City-Wide Road Grade Development of City-Wide Road Grade Profiles Utilising Advanced Bus Development of City-Wide RoadBus Grade Profiles Utilising Advanced Profiles Utilising Advanced Bus Transportation Systems Bus Profiles Utilising Advanced Transportation Transportation Systems Systems Transportation Systems Tushti Singla, Mike Brady, Jared Magrath
Tushti Singla, Mike Brady, Jared Magrath Tushti Singla, Mike Brady, Jared Magrath Singla, Mike Brady, Jared Magrath School ofTushti Computer Science and Statistics, University of Dublin, School Science and Statistics, University of School of of Computer Computer Science and Statistics, University of Dublin, Dublin, Trinity College Dublin, Ireland Trinity College Dublin, Ireland School of Computer Science and Dublin, Statistics, University of Dublin, Trinity College Ireland e-mail: [email protected] e-mail: [email protected] Trinity College Dublin, Ireland e-mail: [email protected] e-mail: [email protected] Abstract: Road grade is of vital importance in determining a vehicle’s fuel consumption and Abstract: Road grade is importance in aa vehicle’s fuel consumption and Abstract: gradeeco-routing is of of vital vital solutions. importanceConsequently, in determining determiningthere vehicle’s fuel and therefore in Road designing is a need to consumption develop accurate therefore in designing eco-routing solutions. Consequently, there is a need to develop accurate Abstract: Road grade is of scale vital solutions. importance in determining a vehicle’s fuel and therefore designing there is a need to consumption develop accurate road gradeinprofiles on aeco-routing large with a high Consequently, degree of accuracy. Advanced Bus Transportation road grade on large scale with degree of Bus Transportation therefore inprofiles designing solutions. Consequently, thereAdvanced isofa data need about to develop accurate road grade profiles on a aeco-routing large scale with aa high high degreelarge of accuracy. accuracy. Advanced Bus Transportation Systems (ABTS) provide an opportunity to collect amounts bus routes in Systems (ABTS) provide an scale opportunity to collect collect large amounts of data data about about bus routes routes in in road grade on a large with a high degree ofdevelopment accuracy. Advanced Bus Transportation Systems (ABTS) provide an opportunity to large amounts of bus the form of profiles GPS traces, which in turn could enable the road grade profiles within of road grade profiles within the form of GPS traces, which in turn could enable the development Systems (ABTS) provide an paper opportunity collect large amounts of datalarge about busroad routes in the formcatchment of GPS traces, in turn couldtoon enable the development grade profiles within a large area. which This reports an approach to developing scale grade of road a large area. This reports on an to developing large scale road grade the formcatchment traces, which inThe turn couldinvestigates enable the development of road grade profiles aprofiles large catchment area.process. This paper paper reports on an approach approach large scale roadwithin grade inof aGPS multistep work the to usedeveloping of GPS trace information from profiles in multistep process. The work investigates the use of trace information from a large catchment area.with Thiselevation paper on an approach to developing large scale road grade profiles in a a combined multistep process. Thereports work investigates the use of GPS GPS trace information from Dublin Bus, information from the Shuttle Radar Topography Mission Dublin Bus, combined with elevation information from the Shuttle Radar Topography Mission profiles in a multistep process. The work investigates the use of GPS trace information from Dublin combined with elevation from the Shuttle Radar Topography Mission (SRTM)Bus, to develop road grade profilesinformation for all bus routes in the company’s system, covering the (SRTM) to develop road grade profiles for all bus routes in the company’s system, covering the Dublin Bus, combined with elevation information from the Shuttle Radar Topography Mission (SRTM) to develop road grade profiles for all bus routes in the company’s system, covering the major areas of the city of Dublin, Ireland. The results are compared with road grades derived major areas of the of Dublin, Ireland. The results with road derived (SRTM) to develop road profiles for all bus routesare in compared the company’s covering the major areas of the city city ofgrade Dublin, Ireland. The results are compared with system, road grades grades derived from Google elevation data. from Google elevation data. major areas of the citydata. of Dublin, Ireland. The results are compared with road grades derived from Google elevation © 2018, IFAC elevation (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. from Google Keywords: Road Grade,data. Elevation, Transportation, Global positioning systems, Filtering Keywords: Road Grade, Elevation, Transportation, Global positioning systems, Filtering techniques,Road Interpolation algorithms, Smoothing filters, Signal processing, Advanced Bus Keywords: Grade, Elevation, Transportation, Global positioning systems, Filtering techniques, Interpolation algorithms, Smoothing filters, Signal processing, Advanced Bus Keywords: Road Grade, Elevation, Transportation, Global positioning systems, Filtering filters, Signal processing, Advanced Bus Transportation Systems, OpenStreetMap. techniques, Interpolation algorithms, Smoothing Transportation Systems, OpenStreetMap. techniques, Interpolation algorithms, Smoothing filters, Signal processing, Advanced Bus Transportation Systems, OpenStreetMap. Transportation Systems, OpenStreetMap. 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION Road grade is an important factor in the fuel consumption Road grade is an important factor in the fuel consumption of Frey al. Zhang and Road grade (e.g. is an see important in the fuel consumption of vehicles vehicles (e.g. see Frey et etfactor al. (2008); (2008); Zhang and Frey Frey Road grade is et anal. important in fuel consumption (2006); Wood (2014b); Levin et the al. (2014)). However, of vehicles (e.g. see Frey etfactor al. (2008); Zhang and Frey (2006); Wood et al. (2014b); Levin et al. (2014)). However, of vehicles (e.g. see(2014b); Frey etLevin al.used, (2008); Zhang and (2006); Wood et al. et al. However, many fuel-consumption models for(2014)). instance, in Frey ecomany fuel-consumption models used, for instance, in eco(2006); Wood et al.account (2014b); Levin et grade al. However, routing, do not for road (Zhou et ecoal., many fuel-consumption models used, for(2014)). instance, in routing, do not account for road grade (Zhou et ecoal., many used, forconsumption instance, 2016). fuel-consumption Neglecting road models grade in fuel routing, do not account for road grade (Zhou in et and al., 2016). Neglecting road grade in fuel consumption and routing, domodelling not account for road grade (Zhou et and al., emissions cangrade result erroneous estimates 2016). Neglecting road in infuel consumption emissions modelling can result in erroneous estimates 2016). Neglecting road grade in fuel consumption and emissions modelling can result in erroneous estimates (Zhang and Frey, 2006; Levin et al., 2014). The availability (Zhang andmodelling Frey, 2006;can Levin et al.,in2014). The availability emissions result erroneous estimates of road and grade information on eta al., large scaleThe is therefore of (Zhang Frey, 2006; Levin 2014). availability of road and grade information on eta al., large scaleThe is therefore of (Zhang Frey, 2006; Levin 2014). availability increasing importance due to in fuel of road grade information onongoing a large developments scale is therefore of increasing importance due to ongoing in of road grade information oneco-routing. a large developments scale is therefore of increasing importance due ongoing developments in fuel fuel consumption modelling andto consumption modelling and eco-routing. increasing importance ongoing developments in fuel consumption modellingdue andtoeco-routing. While commercial implementations of large scale road consumption modelling and eco-routing. While commercial implementations of large scale road While commercial implementations largewould scale most road grade profiles are already under way,ofthese grade profiles are already under way, these would most While commercial implementations large scale most road grade profiles already under way,ofthese probably not beare freely available (Sahlholm andwould Johansson, probably not beare freely available (Sahlholm and Johansson, grade profiles already under way,into these most 2010). facilitate continued research and probably not be freely available (Sahlholm andwould Johansson, 2010). To To not facilitate continued research into eco-routing eco-routing and probably be freely available (Sahlholm and fuel consumption there is a into need to Johansson, develop 2010). To facilitate models, continued research eco-routing anda fuel consumption models, there is a need to develop 2010). Totofacilitate continued research eco-routing andaa fuel consumption models, is a into need to develop method determine road there grade profiles on a large scale method to determine road grade profiles on a large scale fuel models, a need develop a method to determine road there grade is profiles on to a large scale from consumption public information. from public information. method to determine road grade profiles on a large scale Fig. 1. The city of Dublin overlaid with the approximately from public information. Development of these large-scale maps has been investi- Fig. 1. The city of Dublin overlaid with the approximately from public information. Development of these large-scale maps has been investi- Fig. 1. 150,000 GPS the data, The city of points Dublinpresent overlaidin with the approximately gated by a number researchersmaps (Wood al., investi2014a, Fig. 1. Development of theseoflarge-scale has et been 150,000 GPS points present inwith the test test data, compriscomprisThe city of Dublin overlaid the approximately gated by a number of researchers (Wood et al., 2014a, ing 120 different routes in both directions of travel. 150,000 GPS points present in the test data, comprisDevelopment of these maps has been 2015; John al., 2017; Sahlholm, 2008). However, these gated by a et number oflarge-scale researchers (Wood et al., investi2014a, ing 120 120 GPS different routes in both both directions of travel. 150,000 points present in the test data, compris2015; John et al., 2017; Sahlholm, 2008). However, these ing different routes in directions of travel. The map is approximately 36 km on a side. gated by a number of researchers (Wood et al., 2014a, approaches which may hinder their use on 2015; John have et al.,limitations 2017; Sahlholm, 2008). However, these The map is approximately 36 km on a side. ing routes in 36 both The 120 mapdifferent is approximately kmdirections on a side. of travel. approaches have which hinder their on 2015; et al.,limitations 2017; Sahlholm, 2008). However, these approaches have limitations which may may hinder their use use on a largeJohn scale. The map is approximately 36 km on a side. a large scale. approaches have limitations which may hinder their use on ated against commercially-available TomTom datasets a large scale. ated against commercially-available TomTom datasets in in Wood et al. (2015), at the U.S. National Renewable Energy aWood largeetscale. localised and aggregate test areas of the United States. ated against commercially-available TomTom datasets in al. (2015), at the U.S. National Renewable Energy Wood et al. (2015), at the U.S. National Renewable Energy ated localised and commercially-available aggregate test areas of TomTom the Uniteddatasets States. in Laboratory (NREL), developed a method of appending against localised and aggregate test areas of the United States. Laboratory (NREL), developed a method of appending Wood et al.from (2015), at the U.S. National Renewable Energy elevations a high-resolution to ofhigh sample localised John developed aa methodology for utilising Laboratory (NREL), developed a DEM method appending and(2017) aggregate test areas of the United John et et al. al. (2017) developed methodology forStates. utilising elevations from a high-resolution DEM to high sample Laboratory (NREL), method ofhigh appending rate GPS traces a developed large-scalea manner. was evalu- John voluntarily-collected GPS traces to determine city-wide elevations from ainhigh-resolution DEM toIt sample et al. (2017) developed a methodology for utilising voluntarily-collected GPS traces to determine city-wide rate GPS traces inhigh-resolution a large-scale manner. Ithigh was sample evalu- John elevations from a DEM to et al. (2017) developed a methodology for utilising rate GPS traces in a large-scale manner. It was evalu- voluntarily-collected GPS traces to determine city-wide rate GPS© 2018, traces in (International a large-scaleFederation manner.of Automatic It was evaluvoluntarily-collected GPS to determine city-wide 2405-8963 IFAC Control) Hosting by Elsevier Ltd. All rightstraces reserved.
Copyright © 2018 IFAC 428 Copyright 2018 responsibility IFAC 428Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 428 10.1016/j.ifacol.2018.07.070 Copyright © 2018 IFAC 428
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road grades with a view to updating the OpenStreetMaps (OSM) database. The researchers concluded that the use of voluntarilycollected traces, collected in a non-homogeneous manner, resulted in low absolute accuracy. Further, these traces were “not available for a significant share of street segments”. In his doctoral thesis, Sahlholm (2008) investigated the use of Heavy Duty Vehicles (HDVs) to repeatedly update a database of road grade estimates of routes taken by the vehicles. The work highlighted the importance of averaging repeated traversals of routes for improving results. However, the study was limited to the use of HDVs, thus tending to favour long-haul routes with less coverage of cities.
Fig. 2. Elevation profiles generated from ASTER (drawn in black) and SRTM-1 (in red) DEMs.
The present paper investigates the development of road grade profiles on a large scale, using GPS traces taken from Advanced Bus Transportation Systems (ABTS), combined with elevation estimates extracted from the Shuttle Radar Topography Mission (SRTM). The approach has been tested on data from the urban area of Dublin, Ireland and the results are compared against Google API estimates. Comparing this work with the work cited above, the DEM used is of lower resolution and the GPS sampling intervals are longer than those used by Wood et al. (2015). Compared to the work of John et al. (2017), the GPS traces gathered are from a relatively homogeneous fleet of vehicles operating over most of the city. Similarly, by comparison with Sahlholm (2008), a greater coverage of city routes is obtained. Data is processed in a multistep work flow, as depicted in Fig. 3. A range of methods is explored for each step, consisting of newly developed algorithms as well as replicated studies. The best solutions for each step are presented, and an investigation is carried out to determine the merits of the resulting pipeline of methods. 2. EXPERIMENTAL SET-UP Route data was obtained from Dublin Bus’s information site (National Transport Authority, 2013). The bus network consists of approximately 120 routes and covers all major areas of the city – see Fig. 1. Each route has two directions of travel – outbound and inbound – which may be slightly different. The data for each route consists of GPS traces of multiple trips in both directions. In all, the data comprised over 150,000 GPS points. Results were generated for every route and direction. For brevity, the results and illustrations in the rest of this paper refer to one particular route – Route 27B (Outbound). The route data contains no information about elevation and therefore elevations were extracted from a DEM. Two DEMs available for the city of Dublin, SRTM-1 (USGS, 2009) and ASTER (Yamaguchi et al., 1998; Jet Propulsion Laboratory, 1999), were compared for use in this study. Elevation profiles drawn from each source (see Fig. 2) show that profiles developed from ASTER data have significantly more variability than those generated from SRTM1. ASTER elevations have sudden jumps with peaks and troughs, whereas SRTM-1 elevations are smoother and 429
Fig. 3. Workflow for generating road grade profiles. have more gradual changes. Therefore, SRTM-1 was used in this study, as it more faithfully represents the terrain. To automate the generation of road grade profiles, a multistep procedure was applied to the entire dataset, as illustrated in Fig. 3. (1) The GPS data and SRTM elevations were loaded onto a Postgres + PostGIS database developed for this study. (2) The database was queried for one route at a time. (3) The route queried was split into two data frames depending upon direction of travel. Each data frame was proceeded with separately. (4) The data was processed through four stages (detailed below) – Data Cleansing, Route Averaging, Elevation Interpolation and Smoothing. (5) The resulting elevations were used to calculate road grade angles at 100 metre intervals and the database was updated with the calculated road grade estimates for each point. (6) Elevation profiles and road grade profiles were generated for the route. (7) Steps 3 – 6 were repeated for each route. Google elevations were used to evaluate the results. The original intention was to use LiDAR elevations for this purpose, but the data was not freely available. What was
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available was a small set of LiDAR elevations scattered around the city centre and not part of any bus route. Nevertheless, these elevations were compared with equivalent Google elevations. A Pearson correlation coefficient of 0.8118 between the LiDAR elevations and the Google elevations suggests that Google elevations are accurate enough to be used in place of LiDAR data and have the merit of being freely available. 3. DATA CLEANSING The route data had anomalies due to variations in time and distance travelled during different trips along the route. These may have been caused by weather conditions, traffic congestion, diversions, partially recorded trips or other factors. These anomalies cause errors in the calculation of route length and hence in elevation profile estimates. A number of techniques were therefore developed and evaluated to cleanse the data. OSM data was used to aid the cleansing process as follows: For each GPS point in the data, the closest OSM node was selected as its reference point. This gave an OSM node ID to each GPS point in the dataset. Having assigned the reference points, three algorithms were evaluated to filter out anomalous data points depending upon their frequency of occurrence across different trips in a route. (1) Algorithm 1 filtered out those OSM nodes (and corresponding GPS points) that were not present in all trips of a route. This resulted in an incomplete route profile because some trips only had partial traces of the route. Although the method developed did not suit the test data in this project, it would be suitable where the data for all trips is complete. (2) Algorithm 2 removed those OSM nodes (and corresponding GPS points) which had a frequency of occurrence in trips less than a threshold, chosen to be 33%. This generated a complete and clean GPS profile but the data still contained some irregularities that resulted in incorrect calculations of cumulative distance in elevation profiles. This method would be worth considering if it was known that no trips had any diversions from the route. (3) Algorithm 3 removed those entire trips that contained any OSM nodes that had a frequency of occurrence below the threshold of 33%. This method worked effectively to cleanse data for all routes in the diverse dataset. Algorithm 3 was chosen to cleanse the data for all routes in the study. The possibility of using Google API route data was explored. However, the method was not considered suitable because the query limits of Google API make it infeasible to retrieve data for such a large dataset. Further, the study aimed to develop a generic process that does not rely on commercial services. 4. ROUTE AVERAGING Averaging GPS points from different traversals of a route is known to help to produce better route estimates, which are less susceptible to outlier GPS points and horizontal errors 430
(i.e. errors in distance rather than elevation). Studies by Sahlholm and Johansson (2010), Boroujeni et al. (2013), and Boroujeni and Frey (2014) made use of GPS data from multiple passes over the same road. Sahlholm and Johansson (2010) used Kalman filtering to average the GPS data and stated that “GPS position estimates are generally bias free when averaged over long time periods and the error is approximately normally distributed.” Hence, averaging data from multiple runs can lead to more accurate GPS position estimates and thereby road grade profiles. Thus, after cleaning the route data, the multiple trips of a route were averaged as now described. To perform the averaging, data from all trips of a route was combined, sorted by distance and passed to a low-pass filter. A number of low-pass filters were evaluated in the study: (1) A 4-point moving average filter, (2) Exponential filters with smoothing factor of 0.8, 0.9 and 0.95, (3) A 5-point binomial filter with weights [1, 4, 6, 4, 1], (4) A 5-point Savitzky-Golay Filter with weights [-3, 12, 17, 12, -3], (5) A 5-point combined Binomial and Savitzky-Golay Filter with the same weights as the individual filters above. The quality of the averaging process was assessed by comparing the output of different filters with the route as depicted on the map. In analysing the effects of the different filters, it was observed that the Moving Average Filter produced the most accurate representation of the route by uniformly filling the gaps along the route between the GPS points. The Binomial Filter proved to be the second-best choice, followed by the combined Binomial and Savitzky-Golay Filter. The Savitzky-Golay Filter and the Exponential Filter performed poorly, scattering points beyond the boundaries of the roads. The averaged route profile so obtained was then used for elevation extraction and smoothing as described in the following sections. 5. ELEVATION INTERPOLATION Having obtained estimates of the route, the next step was to calculate elevations of points along the route from the SRTM data. Studies by Wood et al. (2014a) and Henriques and Bento (2013) validate the possibility of extracting elevations from DEMs to calculate road grade. Additionally, DEMs offer reasonable accuracy at no cost, making them a good choice for experiments of this type. However, DEMs do not provide good elevation estimates by themselves. Due to abrupt elevation changes between tiles on a DEM grid, and due to the size of the tiles – SRTM-1 tiles are approximately 30m on a side – elevation profiles derived from DEMs have a ragged, stair-like contour. To obtain smooth elevation profiles, therefore, there is a need to interpolate elevation at points other than the centres of the tiles. A number of interpolation techniques were evaluated: (1) Bilinear Interpolation: Elevation was interpolated using a 2x2 grid of neighbouring cells. Linear interpola-
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tion was done along the longitude axis first and the interpolated values were used to linearly interpolate along the latitude axis. Although each step is linear, the overall interpolation is quadratic. (2) Advanced Bilinear Interpolation: This was an extension of bilinear interpolation employed in the study by Henriques and Bento (2013). In this study, an extended bilinear interpolation was used, where elevations of the neighbouring grid cells were weighted according to their distance from the reference cell to estimate the new elevation. (3) Bicubic Interpolation: Elevation was interpolated using a 4x4 grid of neighbouring cells. This was implemented similarly to bilinear interpolation such that four cubic interpolations were performed along the longitude axis first and the results obtained were then used to perform a cubic interpolation on the latitude axis. To validate the accuracy of these techniques, as previously noted, interpolated elevations were compared with Google elevations. The results are presented in Fig. 4.
Fig. 4. Mean Absolute Error (MAE) in raw and interpolated SRTM elevations. Each bar gives the MAE of the particular series as compared to Google elevations.
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6. SMOOTHING The final step in the workflow involved smoothing elevation and road grade profiles. The SRTM is a Digital Terrain Model, which means that it records the lowest elevation at any given point. This works for straight roads, but it poses a problem at intersections between rivers and bridges, or highways and overpasses, where the SRTM records the lower of the two elevations. This leads to irregularly low elevation areas and produces discrepancies in elevation profile. To resolve this issue, Wood et al. (2014a) developed a multistage smoothing technique to filter out erroneously low lying elevations. The same technique was implemented in this work, with parameters such as the down-sampling interval and the window size of the filter begin chosen to suit both the data and the purpose of the work. It consisted of the following steps: (1) The data was down-sampled using a uniform distance of 100 metres. A sampling interval of 100 metres was chosen as it proved to suit the lengths of the routes. (2) It was passed through a nine-point combined Binomial and Savitzky-Golay Filter to remove high fluctuations in elevation. Since the study by Wood et al. (2014a) did not indicate the window size of the filter used, a choice was made to use a nine-point filter in this experiment. (3) Outliers, i.e. elevation values that differed by more than 10 metres, were removed and then backfilled via linear interpolation. (4) The data was filtered a second time through the aforementioned filter. (5) This data was then linearly interpolated using original distances before down-sampling to restore data length. (6) The smoothed elevations so obtained were used to estimate road grade angles at 100 metre intervals suitable for calculating road grade profile over the entire route. 7. RESULTS AND DISCUSSION
As expected, DEM elevations have the highest MAE amongst all the series compared. The interpolated elevations are observed to have lower MAE than raw DEM elevations, showing an improvement caused by interpolating DEM data. The difference in the correlation values between the (standard) Bilinear and the Advanced Bilinear methods is quite small. The Advanced Bilinear method had the closest correspondence to Google data. Hence, it was chosen in this work.
Fig. 5 shows a sharp contrast between the rugged and irregular raw DEM elevations before processing and the smoothed elevation profile obtained as an end-result of the multistage approach employed in this study. Similarly, the road slope angles calculated using the raw DEM data (Fig. 6) have a high fluctuation rate, which is unrealistic. The smoothed elevations give rise to continuous and gradually changing road grade profiles, which is how roads are built in real life (Sheng, 1990).
An interesting result was that although bicubic methods might be generally expected to outperform bilinear methods, this was not the case here. This can be attributed to the fact that bicubic methods require partial derivatives and cross-derivatives for accurate calculations in interpolation, and are based on the condition that slopes match on the boundaries. However, since no information about derivatives was available for this data, estimates for slope were used and it was hypothesised that slope does not change across points, which is likely to have led to a reduction in the accuracy of elevations.
Better estimates were obtained by interpolating elevations followed by smoothing than by interpolating alone or by smoothing alone, as done in previous studies. To validate this, elevation estimates from the different stages of the pipeline were each compared statistically to Google elevations. The Pearson correlation coefficient and the Mean Absolute Error were calculated for (i) raw DEM elevations, (ii) the intermediate interpolated elevations and (iii) the final elevations produced by the pipeline against Google elevations and are shown in Figures 8 and 9. The high correlation of 0.9971 between the Google elevations and
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Fig. 5. Elevation profiles obtained from raw DEM elevations (in black) compared to final smoothed elevations (in red).
Fig. 8. Correlation between Google elevations and elevations from (i) raw SRTM data, (ii) SRTM data after interpolation and (iii) SRTM data after interpolation and smoothing. Each bar represents the correlation of the particular series with Google elevations.
Fig. 6. Road Grade profiles derived from raw DEM elevations (in black) and from final smoothed elevations (in red). Fig. 9. Mean Absolute Error (MAE) between elevations derived from Google data and those derived from (i) raw SRTM data, (ii) SRTM data after interpolation and (iii) SRTM data after interpolation and smoothing. Each bar represents the MAE of the particular series as compared to Google elevations.
Fig. 7. Google API elevation profiles (in black) compared to the final smoothed elevations (in red). elevations resulting from the pipeline supports the usefulness of the methodology implemented in the current study. Fig. 7 shows the smoothed elevation profile in close correspondence with Google elevations. Discrepancies between the profiles may be due to the presence of bridges, overpasses or similar structures (Magrath and Brady, 2017). 8. CONCLUSION The work presented demonstrates that road grade profiles and elevation profiles can be derived on a large scale from GPS trace data combined with DEM information. 432
A pipeline of methods for data cleansing, route averaging, elevation interpolation and smoothing was implemented and evaluated. The pipeline worked successfully and individual elevation profiles and road grade profiles were generated for all 120 routes of Dublin Bus network for which data was available. An overview of combined citywide road grade maps is presented in Fig. 10. The staged, modular nature of the pipeline enabled the separate stages of processing to be developed and validated independently. The pipeline does not rely on commercial services. A number of data cleansing schemes were developed and evaluated. A relatively strict scheme for removing anomalous trip data – Algorithm 3 – gave the best results. A number of methods for averaging GPS position estimates from different trips of a route were evaluated. A 4-point moving average filter performed best in smoothing route profiles. An analysis of interpolation methods for DEM elevations showed that an Advanced Bilinear Interpolation method
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Fig. 10. Bus routes in the Dublin area with road grades. Grades from zero to one degree are shown in black. Grades between one and two degrees are shown in blue, and grades greater than two degrees are depicted in red. (Henriques and Bento, 2013) was most effective, producing best agreement with Google elevation data. A combination of interpolation and smoothing techniques yielded results in better agreement with Google data than either one individually. A Pearson correlation of 0.9971 between the final elevations and Google elevations indicates a high degree of accuracy and underscores the viability of the pipeline approach. Since the pipeline and associated techniques worked well for the Dublin Bus route data, it would be interesting indeed to use it on data from other locations. REFERENCES Boroujeni, B.Y. and Frey, H.C. (2014). Road grade quantification based on global positioning system data obtained from real-world vehicle fuel use and emissions measurements. Atmospheric Environment, 85, 179–186. Boroujeni, B.Y., Frey, H.C., and Sandhu, G.S. (2013). Road grade measurement using in-vehicle, stand-alone GPS with barometric altimeter. Journal of Transportation Engineering, 139(6), 605–611. Frey, H.C., Zhang, K., and Rouphail, N.M. (2008). Fuel use and emissions comparisons for alternative routes, time of day, road grade, and vehicles based on in-use measurements. Environmental Science & Technology, 42(7), 2483–2489. Henriques, N. and Bento, C. (2013). Integration of GPS Traces and Digital Elevation Maps for Improving Bicycle Traffic Simulation Behavior. In Transportation Research Board 92nd Annual Meeting, Transportation Research Board. Jet Propulsion Laboratory (1999). Aster: Advanced spaceborne thermal emission and reflection radiometer. URL https://asterweb.jpl.nasa.gov/. Accessed on October 2017. John, S., Hahmann, S., Rousell, A., L¨ owner, M.O., and Zipf, A. (2017). Deriving incline values for street networks from voluntarily collected gps traces. Cartography and Geographic Information Science, 44(2), 152–169. Levin, M.W., Duell, M., and Waller, S.T. (2014). The effect of road elevation on network wide vehicle energy consumption and eco-routing. Transportation Research Record: Journal of the Transportation Research Board. Magrath, J. and Brady, M. (2017). Evaluating different methods for determining road grade best suited to 433
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ITS. In IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI 2017). National Transport Authority (2013). Public Transport Route Networks. URL https://data.dublinked.ie/ dataset/public-transport-route-networks/. Accessed July 2017. Sahlholm, P. (2008). Iterative road grade estimation for heavy duty vehicle control. Ph.D. thesis, KTH. Sahlholm, P. and Johansson, K.H. (2010). Road grade estimation for look-ahead vehicle control using multiple measurement runs. Control Engineering Practice, 18(11), 1328–1341. Sheng, T. (1990). Watershed management field manual. FAO conservation guide, 13(6). USGS (2009). Shuttle radar tomography mission (SRTM). URL https://pubs.usgs.gov/fs/2009/3087/. Accessed on October 2017. Wood, E., Burton, E., Duran, A., Gonder, J., et al. (2014a). Appending high resolution elevation data to GPS speed traces for vehicle energy modeling and simulation. National Renewable Energy Laboratory. Wood, E., Burton, E., Duran, A., and Gonder, J. (2014b). Contribution of road grade to the energy use of modern automobiles across large datasets of real-world drive cycles. Technical report, SAE Technical Paper. Wood, E., Duran, A., Burton, E., Gonder, J., and Kelly, K. (2015). EPA GHG Certification of Medium-and Heavy-Duty Vehicles: Development of Road Grade Profiles Representative of US Controlled Access Highways. Technical report, National Renewable Energy Laboratory (NREL), Golden, CO (United States). Yamaguchi, Y., Kahle, A.B., Tsu, H., Kawakami, T., and Pniel, M. (1998). Overview of advanced spaceborne thermal emission and reflection radiometer (ASTER). IEEE Transactions on geoscience and remote sensing, 36(4), 1062–1071. Zhang, K. and Frey, H.C. (2006). Road grade estimation for on-road vehicle emissions modeling using light detection and ranging data. Journal of the Air & Waste Management Association, 56(6), 777–788. Zhou, M., Jin, H., and Wang, W. (2016). A review of vehicle fuel consumption models to evaluate ecodriving and eco-routing. Transportation Research Part D: Transport and Environment, 49, 203–218.