From 86aa572fc080affe541d702ed9d56edf7be3ed54 Mon Sep 17 00:00:00 2001 From: Michael Fleig Date: Tue, 12 Jan 2021 16:52:34 +0100 Subject: [PATCH 1/7] init --- ...c-transit-map-matching-with-graphHopper.md | 179 ++++++++++++++++++ .../hmm.png | Bin 0 -> 61014 bytes .../inter_hop_turn_restrictions.png | Bin 0 -> 30286 bytes .../road_network.png | Bin 0 -> 184900 bytes .../stuttgart.accuracy.png | Bin 0 -> 16797 bytes .../stuttgart.al.png | Bin 0 -> 18031 bytes .../stuttgart.an.png | Bin 0 -> 21175 bytes .../stuttgart.avg_fd.png | Bin 0 -> 32047 bytes .../vg.accuracy.png | Bin 0 -> 16622 bytes .../vg.al.png | Bin 0 -> 16957 bytes .../vg.an.png | Bin 0 -> 16761 bytes .../vg.avg_fd.png | Bin 0 -> 31922 bytes 12 files changed, 179 insertions(+) create mode 100644 content/post/project-public-transit-map-matching-with-graphHopper.md create mode 100644 static/img/project_public_transit_map_matching/hmm.png create mode 100644 static/img/project_public_transit_map_matching/inter_hop_turn_restrictions.png create mode 100644 static/img/project_public_transit_map_matching/road_network.png create mode 100644 static/img/project_public_transit_map_matching/stuttgart.accuracy.png create mode 100644 static/img/project_public_transit_map_matching/stuttgart.al.png create mode 100644 static/img/project_public_transit_map_matching/stuttgart.an.png create mode 100644 static/img/project_public_transit_map_matching/stuttgart.avg_fd.png create mode 100644 static/img/project_public_transit_map_matching/vg.accuracy.png create mode 100644 static/img/project_public_transit_map_matching/vg.al.png create mode 100644 static/img/project_public_transit_map_matching/vg.an.png create mode 100644 static/img/project_public_transit_map_matching/vg.avg_fd.png diff --git a/content/post/project-public-transit-map-matching-with-graphHopper.md b/content/post/project-public-transit-map-matching-with-graphHopper.md new file mode 100644 index 0000000..e29f1c0 --- /dev/null +++ b/content/post/project-public-transit-map-matching-with-graphHopper.md @@ -0,0 +1,179 @@ +--- +title: "Project Public Transit Map Matching With GraphHopper" +date: 2021-01-04T11:16:35+01:00 +author: "Michael Fleig" +authorAvatar: "img/ada.jpg" +tags: [] +categories: [] +image: "img/writing.jpg" +draft: true +--- + +some abstract lorem... + +# Contents + +1. Introduction + 1. General Transit Feed Specification GTFS +1. Our map matching approach + 1. Limitations of the GraphHopper Map Matching Library + 1. Finding Candidates + 1. Path finding between candidates + 1. Hidden Markov Model HMM + 1. Turn restrictions +1. Evaluation + 1. Metrics + 1. Results Stuttgart + 1. Results Victoria-Gasteiz +1. Further research + + +# Introduction + +*TransitRouter* is a tool for generating shapes of GTFS feeds for bus routes using the map matching approach described in the paper [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). + +*TransitRouter* uses the OSM routing engine [GraphHopper]() and a modified version the [GraphHopper Map Matching library](). + +The quality of the results are compared with the original GraphHopper Map Matching (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the university of Freiburg. + +## General Transit Feed Specification GTFS + +TODO: Add text + + +# Our map matching approach +Given a trip \\(T\\) with a ordered sequence of stations \\(S = (s_0, s_1, s_2, ..., s_n)\\) we want to find its path \\(P\\) through our street network graph \\(G=(V, E)\\). + +## Limitations of the GraphHopper Map Matching library +- removes stations that are to close +- no turn restrictions / costs +- no support for inter hop turns restrictions + +## GraphHopper Map Matching base line (*GHMM*) +The GraphHopper Map Matching is a one to one implementation of [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). +To be used as a base line we removed the filtering of close observations described in chapter 4.1 as this removes consecutive stations that are to close to one another. + + +## Finding candidates +The GPS positions of our stations might not be accurate so we cannot use them directly to find our path. + +For each station \\(s_i\\) we want to find a set of possible candidates \\(C_i\\). To construct \\(C_i\\) we use the following approach: + +For every edge \\(e_j \in E\\) within a radius \\(r\\) around \\(s_i\\) calculate the projection \\(p_{i,j}\\) of \\(s_i\\) on \\(e_j\\). Then for each outgoing edge \\(e_k\\) of \\(p_{i,j}\\) we add a candidate \\(c_i^{k} = (p_{i,j}, e_k)\\) to \\(C_i\\). So a candidate consists of a position in out road network and a direction in which we can drive. + +Note that we could have used *orientation less* candidates consisting only of the projection \\(p_{i,j}\\) but we need the direction to enable turn restrictions which we will see at a later point. + +![text](/../../img/project_public_transit_map_matching/road_network.png) + +## Path finding between candidates +As a path finding strategy either shortest or fastest routing can be used. Note that turn costs do not work properly with shortest routing because of the way GraphHopper calculates the turn penalties. + +For feeds with short distances between stations shortest routing might produce better results that fastest routing. An example can be seen in the evaluation chapter. + +## Hidden Markov Model *HMM* +To find the most likely sequence of candidates we use a Hidden Markov Model (*HMM*) with our stations \\(s_i\\) as observations and our candidates \\(C_i\\) as observations. The approach is based on **TODO** + +### Emission probability +The emission probability \\(p(s_i | c_i^k)\\) describes the likelihood that we observed \\(s_i\\) given that \\(c_i^k\\) is a matching candidate. + +We use the great circle distance \\(d\\) between the station\\(s_i\\) and its candidate node\\(c^i_k\\) and apply a weighting function with the tuning parameter\\(\sigma\\). + +$$d=\|s_i - c_i^k\|_{\text{great circle}}$$ +$$p(s_i | c_i^k) = \frac{1}{\sqrt{2\pi}\sigma}e^{0.5(\frac{d}{\sigma})^2}$$ + + + +### Transition probability +For the transition probability \\(p(c_i^k \rightarrow c_{i+1}^j)\\) describes the likelihood that our next state will be \\(c_{i+1}\\) given our current state is \\(c_i^k\\). +We use the distance difference \\(d_t\\) between the great circle distance of the two stations \\(s_i, s_{i+1}\\) and the length of the road path between the two candidates \\(c_i^k, c_{i+1}^j\\) and apply out weighting function with tuning parameter \\(\beta\\). + +$$d_t = | \|s_i - s_{i+1}\|_{\text{great circle}} - \| c_i^k - c_{i-1}^j \|_{\text{route}} |$$ +$$p(c_i^k \rightarrow c_{i+1}^j)=\frac{1}{\beta}e^{\frac{d_t}{\beta}}$$ + +![text](/../../img/project_public_transit_map_matching/hmm.png "title here") + + + +## Turn restrictions +For our bus routes we want to prevent forbidden and unlikely turns. GraphHopper has built in support for turn restrictions based on osm meta data and for turn costs. But if we calculate the path between candidates only using there position we run into the problem of inter hop turns. + +Consider the following example: + +![text](/../../img/project_public_transit_map_matching/inter_hop_turn_restrictions.png) + +Having no information from which direction we arrived at candidate \\(c^0_1\\) the most likely path to \\(c^0_2\\) would include a full turn which is unlikely for busses and might even be forbidden at that position by traffic rules. + +In GraphHopper we can specify a start and end edge when finding the path between two nodes. We use this to enable turn restrictions between hops. +Given two candidates \\(c_1 = (u_1, e_1), c_2 = (u_2, e_2)\\). Let \\(v\\) be the neighbor of \\(u_2\\) connected by \\(e_2\\). Then we calculate the path \\(P_1\\) from \\(u_1\\) starting with edge \\(e_2\\) to \\(v\\) ending with \\(e_2\\). +When we combine the most likely paths \\(P_i\\) to get the whole path \\(P\\) we remove the last edge from every \\(P_i\\). + + +# Evaluation + +## Metrics + +To evaluate the quality of our generated shapes we use three different metrics where we compare a generated path P with the corresponding path Q of the ground truth. + +### Average Frèchet Distance \\(\delta_{a_F}\\) +We split the paths \\(P\\) and \\(Q\\) into an equal number of segments such that the segments in \\(P\\) have a length of 1m. Then \\(\delta_{a_F}\\) is the average of the Frèchet Distance between the segments in \\(P\\) and \\(Q\\). + + +### Percentage of unmatched hop segments \\(A_N\\) +A *hop segment* is the path between two station / hops. +A *hop segment* is mismatched its Frèchet Distance is \\(\geq\\) 20m. +$$A_N = \frac{\text{\#unmatched hop segments}}{\text{\#hop segments}}$$ + +### Percentage of length of unmatched hop segments \\(A_L\\) +$$A_L = \frac{\text{length of unmatched segments}}{\text{length ground truth}}$$ + + +## Stuttgart + +![](/../../img/project_public_transit_map_matching/stuttgart.avg_fd.png) + +*Average Frèchet Distance \\(\delta_{a_F}\\) histogram* + +![](/../../img/project_public_transit_map_matching/stuttgart.accuracy.png) + +*Accuracy* + +![](/../../img/project_public_transit_map_matching/stuttgart.an.png) + +*Percentage of unmatched hop segments \\(A_N\\)* + +![](/../../img/project_public_transit_map_matching/stuttgart.al.png) + +*Percentage of length of unmatched hop segments \\(A_L\\)* + + +## Victoria-Gasteiz + +![](/../../img/project_public_transit_map_matching/vg.avg_fd.png) + +*Average Frèchet Distance \\(\delta_{a_F}\\) histogram* + +![](/../../img/project_public_transit_map_matching/vg.accuracy.png) + +*Accuracy* + +![](/../../img/project_public_transit_map_matching/vg.an.png) + +*Percentage of unmatched hop segments \\(A_N\\)* + +![](/../../img/project_public_transit_map_matching/vg.al.png) + +*Percentage of length of unmatched hop segments \\(A_L\\)* + + +## Current problems and further research + +### Inter-hop turn restrictions are not properly reflected in the HMM +GraphHopper uses a time based penalty to prevent unnecessary turns but this is not reflected in our transition weight function where we only use the distance of our path. So inter hop turns are not always prevented. + +### Path finding difficulties with turn restrictions +With turn restrictions enabled for some trips GraphHopper is not able to find any path between the candidates of two stations. If this happens we disable turn restrictions for that particular trip. For Stuttgart this affects around \\(10\\%\\) of all trips. For Victoria-Gasteiz none of the trips is affected. + +At the moment we were not able to find the reasons why GraphHopper is not able to find any path. This issue needs further investigation. + +### Use OSM metadata +OSM provides useful information about public transit routes which might increase the quality of the generated shapes. \ No newline at end of file diff --git a/static/img/project_public_transit_map_matching/hmm.png b/static/img/project_public_transit_map_matching/hmm.png new file mode 100644 index 0000000000000000000000000000000000000000..55ed52f90f6726e021b24849f93b606a7af24c5f GIT binary patch literal 61014 zcmbq)1yq&m*XKdHyStHYl#WA4NQ#Jvgmfz1NQZ!kNP{3q2m%Tc(y53b-K`)cC@DGn z-20#T*36nU>sxEQOD`S|=Y8Mj+0XvfCRXpJIw2k%9s+?NyrF?KKp@a#5ePI-94vSx zu{rP~0zpyeZ)DaVN!P$nz)6d<8#m3jc7J=}cuE=zF_MkL1^74J0`IQyS z7oGOwGT;83%GBTH6?;=?oN-mQqjycVzLVB>X+YuPsPS@%`-tJ5VC@~Ly|Z1lq;T%9 zA;BjfiRD{Qk474G7kone7RJtk==?@m^Ev|=^LmASThGM59Whv5oU}MC=vti;?VpD} zUeF!RI0(Fyy)mDZccgMbG&;Bzdte-ryKzQT(}LYn8hH69$sveofBO878mHz*_X3KQ z8?1kQ7Uab=PVgOeOHSKF{B31*uht(KpA)Gm2H%-yPMW`DczHkUtXJ$PV87xrW=N<# zX(a%8BJkocfmHY6Pq%C8wE14sxmh)choqzPH3mCNXVy7pqbyID& 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b/content/post/project-public-transit-map-matching-with-graphHopper.md index e29f1c0..a2a6e55 100644 --- a/content/post/project-public-transit-map-matching-with-graphHopper.md +++ b/content/post/project-public-transit-map-matching-with-graphHopper.md @@ -9,14 +9,10 @@ image: "img/writing.jpg" draft: true --- -some abstract lorem... - # Contents 1. Introduction - 1. General Transit Feed Specification GTFS 1. Our map matching approach - 1. Limitations of the GraphHopper Map Matching Library 1. Finding Candidates 1. Path finding between candidates 1. Hidden Markov Model HMM @@ -34,24 +30,12 @@ some abstract lorem... *TransitRouter* uses the OSM routing engine [GraphHopper]() and a modified version the [GraphHopper Map Matching library](). -The quality of the results are compared with the original GraphHopper Map Matching (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the university of Freiburg. - -## General Transit Feed Specification GTFS - -TODO: Add text +The quality of the results are compared with the original GraphHopper Map Matching library (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the university of Freiburg. -# Our map matching approach +# Approach Given a trip \\(T\\) with a ordered sequence of stations \\(S = (s_0, s_1, s_2, ..., s_n)\\) we want to find its path \\(P\\) through our street network graph \\(G=(V, E)\\). - -## Limitations of the GraphHopper Map Matching library -- removes stations that are to close -- no turn restrictions / costs -- no support for inter hop turns restrictions - -## GraphHopper Map Matching base line (*GHMM*) -The GraphHopper Map Matching is a one to one implementation of [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). -To be used as a base line we removed the filtering of close observations described in chapter 4.1 as this removes consecutive stations that are to close to one another. +First we discuss how we can find possible candidates in G for every \\(s_i\\) and how we find a path between candidates. Then how we can find the most likely sequence of candidates and finally how we enable turn restrictions. ## Finding candidates @@ -76,7 +60,7 @@ To find the most likely sequence of candidates we use a Hidden Markov Model (*HM ### Emission probability The emission probability \\(p(s_i | c_i^k)\\) describes the likelihood that we observed \\(s_i\\) given that \\(c_i^k\\) is a matching candidate. -We use the great circle distance \\(d\\) between the station\\(s_i\\) and its candidate node\\(c^i_k\\) and apply a weighting function with the tuning parameter\\(\sigma\\). +We use the great circle distance \\(d\\) between the station\\(s_i\\) and its candidate node \\(c^i_k\\) and apply a weighting function with the tuning parameter \\(\sigma\\). $$d=\|s_i - c_i^k\|_{\text{great circle}}$$ $$p(s_i | c_i^k) = \frac{1}{\sqrt{2\pi}\sigma}e^{0.5(\frac{d}{\sigma})^2}$$ @@ -108,8 +92,12 @@ Given two candidates \\(c_1 = (u_1, e_1), c_2 = (u_2, e_2)\\). Let \\(v\\) be th When we combine the most likely paths \\(P_i\\) to get the whole path \\(P\\) we remove the last edge from every \\(P_i\\). + # Evaluation +We evaluate *TransitRouter* and *GHMM* on the GTFS feeds of Stuttgart (S) and Victoria-Gasteiz (VG) with both fastest and shortest routing and following tuning parameters: +$$\sigma=10, \\: \beta=1.0, \\: \text{candidate search radius } r = 10$$ + ## Metrics To evaluate the quality of our generated shapes we use three different metrics where we compare a generated path P with the corresponding path Q of the ground truth. @@ -127,6 +115,17 @@ $$A_N = \frac{\text{\#unmatched hop segments}}{\text{\#hop segments}}$$ $$A_L = \frac{\text{length of unmatched segments}}{\text{length ground truth}}$$ +## GraphHopper Map Matching base line +The GraphHopper Map Matching (*GHMM*) library is a one to one implementation of [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). + +To be used as a base line we removed the filtering of close observations described in chapter 4.1 as this removes consecutive stations that are to close to one another. To compare the speed with *TransitRouter* we made the implementation thread safe to allow parallel execution. + +The differences to TransitRouter are: +- uses orientationless candidates +- no support for turn restrictions and turn costs +- no support for inter hop turn restrictions + + ## Stuttgart ![](/../../img/project_public_transit_map_matching/stuttgart.avg_fd.png) From 58263837f1483711bbb83ba23f789fe693b8610e Mon Sep 17 00:00:00 2001 From: Michael Fleig Date: Mon, 18 Jan 2021 11:35:07 +0100 Subject: [PATCH 3/7] pathfinding & new profiles --- ...project-public-transit-map-matching-with-graphHopper.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/content/post/project-public-transit-map-matching-with-graphHopper.md b/content/post/project-public-transit-map-matching-with-graphHopper.md index a2a6e55..43c9810 100644 --- a/content/post/project-public-transit-map-matching-with-graphHopper.md +++ b/content/post/project-public-transit-map-matching-with-graphHopper.md @@ -54,6 +54,8 @@ As a path finding strategy either shortest or fastest routing can be used. Note For feeds with short distances between stations shortest routing might produce better results that fastest routing. An example can be seen in the evaluation chapter. +GraphHopper uses vehicle profiles to control access and travel costs for edges and nodes. Traffic rules for public transit differ significantly from personal transit, so we use our own public transit optimized bus profile for *TransitRouter* and *GHMM*. + ## Hidden Markov Model *HMM* To find the most likely sequence of candidates we use a Hidden Markov Model (*HMM*) with our stations \\(s_i\\) as observations and our candidates \\(C_i\\) as observations. The approach is based on **TODO** @@ -175,4 +177,7 @@ With turn restrictions enabled for some trips GraphHopper is not able to find an At the moment we were not able to find the reasons why GraphHopper is not able to find any path. This issue needs further investigation. ### Use OSM metadata -OSM provides useful information about public transit routes which might increase the quality of the generated shapes. \ No newline at end of file +OSM provides useful information about public transit routes which might increase the quality of the generated shapes. + +### Enable other vehicle types +Currently *TransitRouter* only supports bus routes. With new vehicle profiles we could add support for tram, subway and rail public transit. \ No newline at end of file From cf241554989521f8a95ca5b7ee07a0455df0f666 Mon Sep 17 00:00:00 2001 From: Michael Fleig Date: Mon, 18 Jan 2021 14:26:14 +0100 Subject: [PATCH 4/7] introduction and other minor changes --- ...c-transit-map-matching-with-graphHopper.md | 39 ++++++++++--------- 1 file changed, 21 insertions(+), 18 deletions(-) diff --git a/content/post/project-public-transit-map-matching-with-graphHopper.md b/content/post/project-public-transit-map-matching-with-graphHopper.md index 43c9810..5c8c198 100644 --- a/content/post/project-public-transit-map-matching-with-graphHopper.md +++ b/content/post/project-public-transit-map-matching-with-graphHopper.md @@ -26,11 +26,14 @@ draft: true # Introduction -*TransitRouter* is a tool for generating shapes of GTFS feeds for bus routes using the map matching approach described in the paper [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). +*TransitRouter* is a web tool for generating shapes of GTFS feeds for bus routes using the map matching approach described in the paper [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). -*TransitRouter* uses the OSM routing engine [GraphHopper]() and a modified version the [GraphHopper Map Matching library](). +*TransitRouter* uses the OSM routing engine [GraphHopper]() and a modified version the [GraphHopper Map Matching library]() that enables turn restrictions and tries to prevent inter hop turns. + +*GraphHopper* is a fast and memory efficient routing engine written in Java. It has built in support for different weighting strategies (e.g. fastest and shortest path routing), turn restrictions (based on OSM meta data) and turn costs and most important the ability to specify custom routing profiles. As public transit has quit different traffic rules we created a specialized *bus profile*. + +The quality of the results are compared with the original GraphHopper Map Matching library (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the university of Freiburg. -The quality of the results are compared with the original GraphHopper Map Matching library (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the university of Freiburg. # Approach @@ -54,10 +57,12 @@ As a path finding strategy either shortest or fastest routing can be used. Note For feeds with short distances between stations shortest routing might produce better results that fastest routing. An example can be seen in the evaluation chapter. -GraphHopper uses vehicle profiles to control access and travel costs for edges and nodes. Traffic rules for public transit differ significantly from personal transit, so we use our own public transit optimized bus profile for *TransitRouter* and *GHMM*. +We use our own public transit optimized bus profile for *TransitRouter* and *GHMM*. ## Hidden Markov Model *HMM* -To find the most likely sequence of candidates we use a Hidden Markov Model (*HMM*) with our stations \\(s_i\\) as observations and our candidates \\(C_i\\) as observations. The approach is based on **TODO** +To find the most likely sequence of candidates we use a Hidden Markov Model (*HMM*) with our stations \\(s_i\\) as observations and our candidates \\(C_i\\) as observations. The approach is based on the paper [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). + +Given a optimal sequence of candidates we construct our final path \\(P\\) by combining the paths between the candidates in our sequence. ### Emission probability The emission probability \\(p(s_i | c_i^k)\\) describes the likelihood that we observed \\(s_i\\) given that \\(c_i^k\\) is a matching candidate. @@ -113,6 +118,9 @@ A *hop segment* is the path between two station / hops. A *hop segment* is mismatched its Frèchet Distance is \\(\geq\\) 20m. $$A_N = \frac{\text{\#unmatched hop segments}}{\text{\#hop segments}}$$ +### Accuracy +The accuracy is the percentage of trips that are below a given threshold of \\(A_N\\). + ### Percentage of length of unmatched hop segments \\(A_L\\) $$A_L = \frac{\text{length of unmatched segments}}{\text{length ground truth}}$$ @@ -130,40 +138,35 @@ The differences to TransitRouter are: ## Stuttgart +Average Frèchet Distance \\(\delta_{a_F}\\) histogram ![](/../../img/project_public_transit_map_matching/stuttgart.avg_fd.png) -*Average Frèchet Distance \\(\delta_{a_F}\\) histogram* - +Accuracy ![](/../../img/project_public_transit_map_matching/stuttgart.accuracy.png) -*Accuracy* - +Percentage of unmatched hop segments \\(A_N\\) ![](/../../img/project_public_transit_map_matching/stuttgart.an.png) -*Percentage of unmatched hop segments \\(A_N\\)* - +Percentage of length of unmatched hop segments \\(A_L\\) ![](/../../img/project_public_transit_map_matching/stuttgart.al.png) -*Percentage of length of unmatched hop segments \\(A_L\\)* - ## Victoria-Gasteiz +Average Frèchet Distance \\(\delta_{a_F}\\) histogram ![](/../../img/project_public_transit_map_matching/vg.avg_fd.png) -*Average Frèchet Distance \\(\delta_{a_F}\\) histogram* - +Accuracy ![](/../../img/project_public_transit_map_matching/vg.accuracy.png) -*Accuracy* +Percentage of unmatched hop segments \\(A_N\\) ![](/../../img/project_public_transit_map_matching/vg.an.png) -*Percentage of unmatched hop segments \\(A_N\\)* +Percentage of length of unmatched hop segments \\(A_L\\) ![](/../../img/project_public_transit_map_matching/vg.al.png) -*Percentage of length of unmatched hop segments \\(A_L\\)* ## Current problems and further research From 9df3631a510cdd1642ca029fa0839970dd961e7b Mon Sep 17 00:00:00 2001 From: Michael Fleig Date: Thu, 21 Jan 2021 11:15:14 +0100 Subject: [PATCH 5/7] added street graph and fixed toc --- ...c-transit-map-matching-with-graphHopper.md | 66 ++-- .../street_graph.png | Bin 0 -> 177278 bytes .../street_graph.svg | 336 ++++++++++++++++++ 3 files changed, 370 insertions(+), 32 deletions(-) create mode 100644 static/img/project_public_transit_map_matching/street_graph.png create mode 100644 static/img/project_public_transit_map_matching/street_graph.svg diff --git a/content/post/project-public-transit-map-matching-with-graphHopper.md b/content/post/project-public-transit-map-matching-with-graphHopper.md index 5c8c198..b84b23c 100644 --- a/content/post/project-public-transit-map-matching-with-graphHopper.md +++ b/content/post/project-public-transit-map-matching-with-graphHopper.md @@ -11,37 +11,39 @@ draft: true # Contents -1. Introduction -1. Our map matching approach - 1. Finding Candidates - 1. Path finding between candidates - 1. Hidden Markov Model HMM - 1. Turn restrictions -1. Evaluation - 1. Metrics - 1. Results Stuttgart - 1. Results Victoria-Gasteiz -1. Further research +1. [Introduction](#introduction) +1. [Our map matching approach](#approach) + 1. [Finding Candidates](#finding-candidates) + 1. [Path finding between candidates](#path-finding-between-candidates) + 1. [Hidden Markov Model HMM](#hidden-markov-model) + 1. [Turn restrictions](#turn-restrictions) +1. [Evaluation](#evaluation) + 1. [Metrics](#metrics) + 1. [Results Stuttgart](#results-stuttgart) + 1. [Results Victoria-Gasteiz](#results-victoria-gasteiz) +1. [Further research](#current-problems-and-further-research) -# Introduction +# Introduction -*TransitRouter* is a web tool for generating shapes of GTFS feeds for bus routes using the map matching approach described in the paper [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). +*TransitRouter* is a web tool for generating shapes of GTFS (*General Transit Feed Specification*) feeds for bus routes using the map matching approach described in the paper [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). *TransitRouter* uses the OSM routing engine [GraphHopper]() and a modified version the [GraphHopper Map Matching library]() that enables turn restrictions and tries to prevent inter hop turns. -*GraphHopper* is a fast and memory efficient routing engine written in Java. It has built in support for different weighting strategies (e.g. fastest and shortest path routing), turn restrictions (based on OSM meta data) and turn costs and most important the ability to specify custom routing profiles. As public transit has quit different traffic rules we created a specialized *bus profile*. +*GraphHopper* is a fast and memory efficient routing engine written in Java. It has built in support for different weighting strategies (e.g. fastest and shortest path routing), turn restrictions (based on OSM meta data), turn costs and most important the ability to specify custom routing profiles. As public transit has quite different traffic rules we created a specialized *bus profile*. The quality of the results are compared with the original GraphHopper Map Matching library (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the university of Freiburg. -# Approach +# Approach Given a trip \\(T\\) with a ordered sequence of stations \\(S = (s_0, s_1, s_2, ..., s_n)\\) we want to find its path \\(P\\) through our street network graph \\(G=(V, E)\\). First we discuss how we can find possible candidates in G for every \\(s_i\\) and how we find a path between candidates. Then how we can find the most likely sequence of candidates and finally how we enable turn restrictions. +![text](/../../img/project_public_transit_map_matching/street_graph.svg) +Stations \\(s_0, s_1, ..., s_6\\). Red: candidates within radius \\(r\\) around \\(s_i\\). Blue: Path of the bus. -## Finding candidates +## Finding candidates The GPS positions of our stations might not be accurate so we cannot use them directly to find our path. For each station \\(s_i\\) we want to find a set of possible candidates \\(C_i\\). To construct \\(C_i\\) we use the following approach: @@ -50,21 +52,21 @@ For every edge \\(e_j \in E\\) within a radius \\(r\\) around \\(s_i\\) calculat Note that we could have used *orientation less* candidates consisting only of the projection \\(p_{i,j}\\) but we need the direction to enable turn restrictions which we will see at a later point. -![text](/../../img/project_public_transit_map_matching/road_network.png) -## Path finding between candidates + +## Path finding between candidates As a path finding strategy either shortest or fastest routing can be used. Note that turn costs do not work properly with shortest routing because of the way GraphHopper calculates the turn penalties. For feeds with short distances between stations shortest routing might produce better results that fastest routing. An example can be seen in the evaluation chapter. We use our own public transit optimized bus profile for *TransitRouter* and *GHMM*. -## Hidden Markov Model *HMM* +## Hidden Markov Model *HMM* To find the most likely sequence of candidates we use a Hidden Markov Model (*HMM*) with our stations \\(s_i\\) as observations and our candidates \\(C_i\\) as observations. The approach is based on the paper [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). Given a optimal sequence of candidates we construct our final path \\(P\\) by combining the paths between the candidates in our sequence. -### Emission probability +### Emission probability The emission probability \\(p(s_i | c_i^k)\\) describes the likelihood that we observed \\(s_i\\) given that \\(c_i^k\\) is a matching candidate. We use the great circle distance \\(d\\) between the station\\(s_i\\) and its candidate node \\(c^i_k\\) and apply a weighting function with the tuning parameter \\(\sigma\\). @@ -74,7 +76,7 @@ $$p(s_i | c_i^k) = \frac{1}{\sqrt{2\pi}\sigma}e^{0.5(\frac{d}{\sigma})^2}$$ -### Transition probability +### Transition probability For the transition probability \\(p(c_i^k \rightarrow c_{i+1}^j)\\) describes the likelihood that our next state will be \\(c_{i+1}\\) given our current state is \\(c_i^k\\). We use the distance difference \\(d_t\\) between the great circle distance of the two stations \\(s_i, s_{i+1}\\) and the length of the road path between the two candidates \\(c_i^k, c_{i+1}^j\\) and apply out weighting function with tuning parameter \\(\beta\\). @@ -85,7 +87,7 @@ $$p(c_i^k \rightarrow c_{i+1}^j)=\frac{1}{\beta}e^{\frac{d_t}{\beta}}$$ -## Turn restrictions +## Turn restrictions For our bus routes we want to prevent forbidden and unlikely turns. GraphHopper has built in support for turn restrictions based on osm meta data and for turn costs. But if we calculate the path between candidates only using there position we run into the problem of inter hop turns. Consider the following example: @@ -100,32 +102,32 @@ When we combine the most likely paths \\(P_i\\) to get the whole path \\(P\\) we -# Evaluation +# Evaluation We evaluate *TransitRouter* and *GHMM* on the GTFS feeds of Stuttgart (S) and Victoria-Gasteiz (VG) with both fastest and shortest routing and following tuning parameters: $$\sigma=10, \\: \beta=1.0, \\: \text{candidate search radius } r = 10$$ -## Metrics +## Metrics To evaluate the quality of our generated shapes we use three different metrics where we compare a generated path P with the corresponding path Q of the ground truth. -### Average Frèchet Distance \\(\delta_{a_F}\\) +### Average Frèchet Distance \\(\delta_{a_F}\\) We split the paths \\(P\\) and \\(Q\\) into an equal number of segments such that the segments in \\(P\\) have a length of 1m. Then \\(\delta_{a_F}\\) is the average of the Frèchet Distance between the segments in \\(P\\) and \\(Q\\). -### Percentage of unmatched hop segments \\(A_N\\) +### Percentage of unmatched hop segments \\(A_N\\) A *hop segment* is the path between two station / hops. A *hop segment* is mismatched its Frèchet Distance is \\(\geq\\) 20m. $$A_N = \frac{\text{\#unmatched hop segments}}{\text{\#hop segments}}$$ -### Accuracy +### Accuracy The accuracy is the percentage of trips that are below a given threshold of \\(A_N\\). -### Percentage of length of unmatched hop segments \\(A_L\\) +### Percentage of length of unmatched hop segments \\(A_L\\) $$A_L = \frac{\text{length of unmatched segments}}{\text{length ground truth}}$$ -## GraphHopper Map Matching base line +## GraphHopper Map Matching base line The GraphHopper Map Matching (*GHMM*) library is a one to one implementation of [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). To be used as a base line we removed the filtering of close observations described in chapter 4.1 as this removes consecutive stations that are to close to one another. To compare the speed with *TransitRouter* we made the implementation thread safe to allow parallel execution. @@ -136,7 +138,7 @@ The differences to TransitRouter are: - no support for inter hop turn restrictions -## Stuttgart +## Results Stuttgart Average Frèchet Distance \\(\delta_{a_F}\\) histogram ![](/../../img/project_public_transit_map_matching/stuttgart.avg_fd.png) @@ -151,7 +153,7 @@ Percentage of length of unmatched hop segments \\(A_L\\) ![](/../../img/project_public_transit_map_matching/stuttgart.al.png) -## Victoria-Gasteiz +## Results Victoria-Gasteiz Average Frèchet Distance \\(\delta_{a_F}\\) histogram ![](/../../img/project_public_transit_map_matching/vg.avg_fd.png) @@ -169,7 +171,7 @@ Percentage of length of unmatched hop segments \\(A_L\\) -## Current problems and further research +## Current problems and further research ### Inter-hop turn restrictions are not properly reflected in the HMM GraphHopper uses a time based penalty to prevent unnecessary turns but this is not reflected in our transition weight function where we only use the distance of our path. 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a/static/img/project_public_transit_map_matching/street_graph.svg b/static/img/project_public_transit_map_matching/street_graph.svg new file mode 100644 index 0000000..d3c6ce1 --- /dev/null +++ b/static/img/project_public_transit_map_matching/street_graph.svg @@ -0,0 +1,336 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From cf545d93cd5fce79d09a50bf0a239cd10b879f25 Mon Sep 17 00:00:00 2001 From: Michael Fleig Date: Tue, 20 Apr 2021 11:31:45 +0200 Subject: [PATCH 6/7] blog post --- ...t-public-transit-map-matching-with-graphHopper.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/content/post/project-public-transit-map-matching-with-graphHopper.md b/content/post/project-public-transit-map-matching-with-graphHopper.md index b84b23c..24d3de8 100644 --- a/content/post/project-public-transit-map-matching-with-graphHopper.md +++ b/content/post/project-public-transit-map-matching-with-graphHopper.md @@ -37,7 +37,7 @@ The quality of the results are compared with the original GraphHopper Map Matchi # Approach -Given a trip \\(T\\) with a ordered sequence of stations \\(S = (s_0, s_1, s_2, ..., s_n)\\) we want to find its path \\(P\\) through our street network graph \\(G=(V, E)\\). +Given a trip \\(T\\) with an ordered sequence of stations \\(S = (s_0, s_1, s_2, ..., s_n)\\) we want to find its path \\(P\\) through our street network graph \\(G=(V, E)\\). First we discuss how we can find possible candidates in G for every \\(s_i\\) and how we find a path between candidates. Then how we can find the most likely sequence of candidates and finally how we enable turn restrictions. ![text](/../../img/project_public_transit_map_matching/street_graph.svg) @@ -48,14 +48,14 @@ The GPS positions of our stations might not be accurate so we cannot use them di For each station \\(s_i\\) we want to find a set of possible candidates \\(C_i\\). To construct \\(C_i\\) we use the following approach: -For every edge \\(e_j \in E\\) within a radius \\(r\\) around \\(s_i\\) calculate the projection \\(p_{i,j}\\) of \\(s_i\\) on \\(e_j\\). Then for each outgoing edge \\(e_k\\) of \\(p_{i,j}\\) we add a candidate \\(c_i^{k} = (p_{i,j}, e_k)\\) to \\(C_i\\). So a candidate consists of a position in out road network and a direction in which we can drive. +For every edge \\(e_j \in E\\) within a radius \\(r\\) around \\(s_i\\) calculate the projection \\(p_{i,j}\\) of \\(s_i\\) on \\(e_j\\). Then for each outgoing edge \\(e_k\\) of \\(p_{i,j}\\) we add a candidate \\(c_i^{k} = (p_{i,j}, e_k)\\) to \\(C_i\\). So a candidate consists of a position in our road network and a direction in which we can drive. Note that we could have used *orientation less* candidates consisting only of the projection \\(p_{i,j}\\) but we need the direction to enable turn restrictions which we will see at a later point. ## Path finding between candidates -As a path finding strategy either shortest or fastest routing can be used. Note that turn costs do not work properly with shortest routing because of the way GraphHopper calculates the turn penalties. +As a path finding strategy either shortest or fastest routing can be used. For feeds with short distances between stations shortest routing might produce better results that fastest routing. An example can be seen in the evaluation chapter. @@ -88,7 +88,7 @@ $$p(c_i^k \rightarrow c_{i+1}^j)=\frac{1}{\beta}e^{\frac{d_t}{\beta}}$$ ## Turn restrictions -For our bus routes we want to prevent forbidden and unlikely turns. GraphHopper has built in support for turn restrictions based on osm meta data and for turn costs. But if we calculate the path between candidates only using there position we run into the problem of inter hop turns. +For our bus routes we want to prevent forbidden and unlikely turns. GraphHopper has built in support for turn restrictions based on osm meta data. But if we calculate the path between candidates only using there position we run into the problem of inter hop turns. Consider the following example: @@ -130,7 +130,7 @@ $$A_L = \frac{\text{length of unmatched segments}}{\text{length ground truth}}$$ ## GraphHopper Map Matching base line The GraphHopper Map Matching (*GHMM*) library is a one to one implementation of [Hidden Markov Map Matching Through Noise and Sparseness](https://www.ismll.uni-hildesheim.de/lehre/semSpatial-10s/script/6.pdf). -To be used as a base line we removed the filtering of close observations described in chapter 4.1 as this removes consecutive stations that are to close to one another. To compare the speed with *TransitRouter* we made the implementation thread safe to allow parallel execution. +To be used as a base line we removed the filtering of close observations described in chapter 4.1 as this removes consecutive stations that are to close to one another. The differences to TransitRouter are: - uses orientationless candidates @@ -185,4 +185,4 @@ At the moment we were not able to find the reasons why GraphHopper is not able t OSM provides useful information about public transit routes which might increase the quality of the generated shapes. ### Enable other vehicle types -Currently *TransitRouter* only supports bus routes. With new vehicle profiles we could add support for tram, subway and rail public transit. \ No newline at end of file +Currently *TransitRouter* only supports bus routes. With new vehicle profiles we could add support for tram, subway and rail public transit routes. \ No newline at end of file From a8606d57670dbcbfdd9f39f6dc8c0c986394470f Mon Sep 17 00:00:00 2001 From: Michael Fleig Date: Sun, 2 May 2021 14:42:38 +0200 Subject: [PATCH 7/7] final version --- ...ic-transit-map-matching-with-graphHopper.md | 17 +++++++++-------- .../webapp.png | Bin 0 -> 282878 bytes 2 files changed, 9 insertions(+), 8 deletions(-) create mode 100644 static/img/project_public_transit_map_matching/webapp.png diff --git a/content/post/project-public-transit-map-matching-with-graphHopper.md b/content/post/project-public-transit-map-matching-with-graphHopper.md index 24d3de8..4521bae 100644 --- a/content/post/project-public-transit-map-matching-with-graphHopper.md +++ b/content/post/project-public-transit-map-matching-with-graphHopper.md @@ -3,10 +3,10 @@ title: "Project Public Transit Map Matching With GraphHopper" date: 2021-01-04T11:16:35+01:00 author: "Michael Fleig" authorAvatar: "img/ada.jpg" -tags: [] -categories: [] -image: "img/writing.jpg" -draft: true +tags: ["map-matching", "GTFS", "OSM", "public transit", "schedule data"] +categories: ["project"] +image: "img/project_public_transit_map_matching/webapp.png" +draft: false --- # Contents @@ -32,8 +32,9 @@ draft: true *GraphHopper* is a fast and memory efficient routing engine written in Java. It has built in support for different weighting strategies (e.g. fastest and shortest path routing), turn restrictions (based on OSM meta data), turn costs and most important the ability to specify custom routing profiles. As public transit has quite different traffic rules we created a specialized *bus profile*. -The quality of the results are compared with the original GraphHopper Map Matching library (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the university of Freiburg. +The quality of the results are compared with the original GraphHopper Map Matching library (*GHMM*) and [*pfaedle*](https://github.com/ad-freiburg/pfaedle) a similar tool developed by the chair of Algorithms and Data Structures at the University of Freiburg. +The source code of TransitRouter is available on [GitHub](https://github.com/fleigm/TransitRouter). # Approach @@ -72,7 +73,7 @@ The emission probability \\(p(s_i | c_i^k)\\) describes the likelihood that we o We use the great circle distance \\(d\\) between the station\\(s_i\\) and its candidate node \\(c^i_k\\) and apply a weighting function with the tuning parameter \\(\sigma\\). $$d=\|s_i - c_i^k\|_{\text{great circle}}$$ -$$p(s_i | c_i^k) = \frac{1}{\sqrt{2\pi}\sigma}e^{0.5(\frac{d}{\sigma})^2}$$ +$$p(s_i | c_i^k) = \frac{1}{\sqrt{2\pi}\sigma}e^{-0.5(\frac{d}{\sigma})^2}$$ @@ -81,7 +82,7 @@ For the transition probability \\(p(c_i^k \rightarrow c_{i+1}^j)\\) describes th We use the distance difference \\(d_t\\) between the great circle distance of the two stations \\(s_i, s_{i+1}\\) and the length of the road path between the two candidates \\(c_i^k, c_{i+1}^j\\) and apply out weighting function with tuning parameter \\(\beta\\). $$d_t = | \|s_i - s_{i+1}\|_{\text{great circle}} - \| c_i^k - c_{i-1}^j \|_{\text{route}} |$$ -$$p(c_i^k \rightarrow c_{i+1}^j)=\frac{1}{\beta}e^{\frac{d_t}{\beta}}$$ +$$p(c_i^k \rightarrow c_{i+1}^j)=\frac{1}{\beta}e^{-\frac{d_t}{\beta}}$$ ![text](/../../img/project_public_transit_map_matching/hmm.png "title here") @@ -94,7 +95,7 @@ Consider the following example: ![text](/../../img/project_public_transit_map_matching/inter_hop_turn_restrictions.png) -Having no information from which direction we arrived at candidate \\(c^0_1\\) the most likely path to \\(c^0_2\\) would include a full turn which is unlikely for busses and might even be forbidden at that position by traffic rules. +Having no information from which direction we arrived at candidate \\(c^0_1\\) the most likely path to \\(c^0_2\\) would include a full turn which is unlikely for a bus and might even be forbidden at that position by traffic rules. 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