Currently, most runners use GPS data to estimate where they ran. However, as seen in the image below, this tracking of distances can be inaccurate, especially around a smaller geographical footprint like a track. The track is a known shape and thus it is clear to see that the logged GPS running path is not consistent with the physical path that is known. While GPS data is generally accurate enough for recreational running, this accuracy drops sharply on trails and where there is a lot of turning. This makes track-based runs especially susceptible to path errors. In the picture below, the GPS data suggests that the runner went out beyond the outer lanes of the track when the subject was in the innermost lane for the duration of the run [Bloss, 2022].

We seek to:

perform state estimation around a track that is more accurate than GPS data that popular running apps like Strava use

Input measurements:

x direction acceleration, heading velocity, GPS latitude and longitude

Where our input measurements come from:

iPhone accelerometer and gyroscope, running smartwatch

State variables being estimated:

x and y position, x and y velocity, heading

State variables we REALLY care about:

x and y position

Shown below is a figure detailing the definition of heading for this project. Heading is calculated as the arctan of the change in y position over the change in x position at every time step. Also included is the definition of where (0,0) is located on the track.