I delivered a 20-minute presentation on September 20th at iOSDC Japan 2025.

If you prefer video:

  • Japanese (conference): YouTube
  • English (post-conference recording): YouTube

Other materials:

This post is a deconstructed version of the talk with the slide images above and my speaker notes in English below.

  • Lately I’ve been working on an app called Eki Live.
  • Today I’m going to talk about a part of that app.
  • So what do I mean by train tracking algorithm?
  • Well, when riding a train, it’s useful to know the upcoming station.

  • On the train, we can see the train information display or listen for announcements.
  • But would it also be useful to see this information in your Dynamic Island?

  • In my talk, we’ll first review the data prerequisites we’ll need for the algorithm.
  • Then, we’ll write each part of the algorithm, improving it step-by-step.

  • We need two types of data for the train tracking algorithm:
  • Static data that describes the railway system of greater Tokyo.
  • And Live GPS data from the iPhone user.

  • Railways are ordered groups of Stations.
  • In this example, we can see that the Minatomirai Line is made up of 6 stations.

  • Trains travel in both Directions on a Railway.
  • Coordinates make up the path of a Railway’s physical tracks.

  • This map shows the Railway data we’ll be using.

  • We collect live GPS data from an iPhone using the Core Location framework.
  • We store the data in a local SQLite database.

  • A Location has all data from CLLocation.
  • Latitude, longitude, speed, course, accuracy, etc.

  • A Session is an ordered list of Locations.
  • A Session represents a possible journey.
  • Green is for fast and red is for stopped.

  • I created a macOS app to visualize the raw data.
  • In the left sidebar there is a list of Sessions.
  • In the bottom panel there is a list of ordered Locations for a Session.
  • Clicking on a Location shows its position and course on the map.

  • Our goal is to write an algorithm that determines 3 types of information:
  • The Railway, the direction of the train, and the next Station.

  • Here is a brief overview of the system.

  • The app channels Location values to the algorithm.

  • The algorithm reads the Location and gathers information from its memory.

  • The algorithm updates its understanding of the device’s location in the world.

  • The algorithm calculates a new result set of railway, direction, and station phase.
  • The result is used to update the app UI and Live Activity.

  • Let’s start by considering a single Location.
  • I captured this Location while riding the Tokyu Toyoko Line close to Tsunashima Station.

  • Can we determine the Railway from just this Location?

  • We do have coordinates that outline the railway…

  • First, we find the closest RailwayCoordinate to the Location for each Railway.
  • Then, we order the Railways by which RailwayCoordinate is nearest.

  • Here are our results.

  • The closest RailwayCoordinate is from the Toyoko Line at only 12 meters away.
  • The next closest RailwayCoordinate is from the Shin-Yokohama Line at 177 meters away.
  • We did it!
  • Our algorithm works well for this case.
  • But…

  • Let’s consider another Location.
  • This Location was also captured on the Toyoko Line.

  • But in this section of the railway track, the Toyoko Line and Meguro Line run parallel.
  • It’s not possible to determine whether the correct line is Toyoko or Meguro from just this one Location.

  • The algorithm needs to use all Locations from the journey.
  • The example journey follows the Toyoko Line for longer than the Meguro Line.

  • First, we convert the distance between the Location and the nearest RailwayCoordinate to a score.
  • The score is high if close and exponentially lower when far.
  • Then, we add the scores over time.

  • The score from Nakameguro to Hiyoshi is now higher for the Toyoko Line than the Meguro Line.
  • We did it!
  • Our algorithm works well for this case.
  • But…

  • Let’s consider a third Location.
  • This Location was captured on the Keihin-Tohoku Line which runs the east corridor of Tokyo.

  • Several lines run parallel in this corridor.
  • The Tokaido Line follows the same track as the Keihin-Tohoku Line

  • But the Tokaido Line skips many stations.

  • If we only compare railway coordinate proximity scores, the scores will be the same.

  • Let’s add a small penalty to the score if a station is passed.
  • If a station is passed, that indicates the iPhone may be on a parallel express railway.
  • Let’s also add a small penalty to the score if a train stops between stations.
  • If a train stops between stations, that indicates the iPhone may be on a parallel local railway.

  • Using this algorithm, the Keihin-Tohoku score is now slightly larger than the Tokaido score.

  • Let’s consider two example trips to better understand penalties.
  • For an example trip 1 that starts at Tokyo station…

  • The train stops at the second Keihin-Tohoku station.
  • The Tokaido score receives a penalty since the stop occurs between stations.

  • As we continue…

  • The Tokaido score receives many penalties.
  • Therefore, the algorithm determines the trip was on the Keihin-Tohoku Line.

  • For an example trip 2 that also starts at Tokyo…

  • The train passes the 2nd Keihin-Tohoku station.
  • And the Keihin-Tohoku score receives a penalty.

  • As we continue…

  • The Keihin-Tohoku score receives many penalties.
  • Therefore, the algorithm determines the trip was on the Tokaido Line.
  • We did it!
  • Our algorithm works well for this case.
  • There are many more edge cases.
  • However, let’s continue.

  • For each potential railway, we will determine which direction the train is moving.

  • Every railway has 2 directions.
  • We’re used to seeing separate timetables on the departure board at a non-terminal station.

  • For example, the Toyoko Line goes inbound towards Shibuya and outbound towards Yokohama.

  • Let’s consider a Location captured on the Toyoko Line going inbound to Shibuya.

  • Once we have visited two stations, we can compare the temporal order the station visits.
  • If the visit order matches the order of the stations in the database, we say that the iPhone is heading in the “ascending” direction.

  • The iPhone visited Kikuna and then Okurayama.

  • This ordering does not match the database, so we consider it “descending”.
  • In the database, “descending” maps to inbound.
  • Therefore, we know the iPhone is heading inbound to Shibuya.
  • We did it!
  • Our algorithm works well for this case.
  • But…
  • It could take 5 minutes to determine the train direction.
  • Can we do better?

  • Let’s use the Location’s course.
  • Remember that course is included with some CLLocations by Core Location.
  • Several points moving at a decent speed are required before Core Location adds course to a CLLocation.
  • And course itself has its own accuracy value included.

  • Core Location provides an estimate of the iPhone’s course in degrees.

  • Note that this is not the iPhone’s orientation using the compass.
  • The course value should be the same regardless of whether the iPhone is in a pocket or held in a hand facing the rear of the train.

  • The course for the example Location is 359.6 degrees.
  • It’s almost directly North.

  • First, we find the 2 closest stations to the Location

  • Next, we calculate the vector between the 2 closest stations for the “ascending” direction in our database.
  • For the Toyoko line, the “ascending” direction is outbound (as mentioned earlier).
  • Therefore the vector goes from Tsunashima to Okurayama.

  • We need to take a quick sidebar to talk about the dot product.
  • Do you remember the dot product from math class?
  • We can compare the direction of unit vectors with the dot product.
  • Two vectors facing the same direction have a positive dot product.
  • Two vectors facing in opposite directions have a negative dot product.

  • Next, we calculate the dot product between the Location’s course vector and the stations vector.
  • If the dot product is positive, then the railway direction is “ascending”.
  • If the dot product is negative, then the railway direction is “descending”.

  • The dot product is -0.95.
  • It’s negative.
  • Negative means “descending”.
  • And “descending” in our database maps to inbound for the Toyoko Line.
  • Therefore, the iPhone is heading to Shibuya.
  • We did it!
  • Our algorithm works well.
  • Let’s move on to the last part of the algorithm.

  • Finally, we can determine the next station.

  • The next station is shown on the train information display.
  • We’ll call this the “focus station phase” going forward.
  • This includes the station name (e.g. Kikuna) and its phase (e.g. Next).

  • The display cycles through next, soon, and now phases for each station.

  • On a map, here is where we will show each phase.

  • We calculate the distance d and direction vector c from the Location to the closest station.
  • We show the closest station S or the next station in the travel direction S+1 depending on d and c.

  • When the closest station is in the travel direction, the phase will be “next”.

  • A Location less than 500m from the station will be “soon”.

  • A Location less than 200m from the station will be “now”.

  • Even though the Location is within 500m from the closest station, the station is not in the travel direction.
  • Therefore, the phase will be “next” for the next station in the travel direction.
  • We did it!
  • Our algorithm works well.
  • But…

  • GPS data is unreliable.
  • Especially within big stations.
  • Especially when not moving.
  • Here is an example Location stopped inside Kawasaki station that has an abysmal 1 km accuracy.

  • Let’s create a history of Locations for each station.
  • For each station, let’s categorize each Location according to its distance and direction.

  • In this example, “approaching” points are orange, “visiting” points are green, and the departure point is “red”.

  • Focus station algorithm version 2 has 3 steps.

  • In step 1, we categorize a Location as “visiting” or “approaching” if it lies within the bounds of a Station.
  • Our rule is that only 1 Station per Railway will store a unique Location in the visitingLocations or approachingLocations array.
  • Usually, this is not an issue, but some Stations on the same Railway are within 200m of each other.
  • To disambiguate, we always choose the closest Station.

  • If the Location is outside the bounds of any Station that already has visitingLocations or approachingLocations as non-empty, we set the firstDepartureLocation for that Station.
  • It’s okay for a Location to be set as firstDepartureLocation for Station A while also being in a visitingLocations or approachingLocations array of Station B.
  • Additionally, there is special handling for the startup case where a railway has no Locations set yet. In this case, we try to find the closest Station opposite the travel direction and set its firstDepartureLocation.
  • We can then consider that Station the user’s departure station and use it to determine the focus station.

  • In step 2, we use the station history to calculate the phase for each station.

  • This is a departure phase for Minami-Senju station.
  • The StationDirectionalLocationHistory has only a firstDepartureLocation.

  • This is an approaching phase for Kita-Senju station.
  • Note: this would still count as an approaching phase even if there were only 1 Location in the approachingLocations array.

  • This is a visiting phase.
  • Note: this would still count as a visiting phase even if there were only 1 Location in the visitingLocations array.

  • This is a visited phase.
  • You can see the firstDepartureLocation in red.

  • In step 3, we look through the station phase history for all stations to determine the focus station phase.

  • In an example, when the latest phase for Kawasaki station is visited, then the focus phase is “Next: Kamata”

  • In another example, when the latest station phase for Musashi-Kosugi station is visited and Motosumiyoshi station is approaching, then the focus phase is “Soon: Motosumiyoshi”

  • Using a state machine gives us more stable results.
  • We did it!
  • Our algorithm works well…

  • But can we tell the difference between a visited station and a passed station?
  • Remember, we need this information to calculate a potential penalty for the railway score.

  • If the train is stopped within a station’s bounds for more than 20 seconds then we consider it visited.

  • If the train is moving within a station’s bounds for more than 70 seconds then we also consider it visited.
  • This case is for stations with bad GPS reception.

  • Otherwise we consider the station as passed.
  • Now I’d like to demo the SessionViewer macOS app I created.
  • I’ll show a journey from Kannai station to Kawasaki station on the Keihin-Tohoku line.
  • It takes some time for all Locations to be processed by the algorithm (top right).
  • But while it’s processing, I can start playback to see the journey at 10x speed (top right).
  • In the inspector (right sidebar), you can see the algorithm’s results updating.
  • Keihin-Tohoku line has the highest score (top right).
  • The direction is northbound (top right).
  • The latest phase for each station is shown (middle right).
  • When we reach the last Location in the Session, we can see the full Station history (middle right).
  • We can see the phase history for any station by clicking its current phase.
  • When I click on a station, I can see on the map the Locations that were used to calculate its phase.

  • The 5 iOS apps I created to collect this data are open source on GitHub.
  • The macOS app and algorithm are included as well.

  • The algorithm is still being improved!

  • But if you want to try it, Eki Live is on the App Store now.
  • The app starts up automatically in the background and shows the next station in the Dynamic Island.

  • Thanks for reading this presentation.
  • If you have questions or comments, feel free to reach out.