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GPS Tuple

Description

GPS 센서를 부착한 선수의 시점별 위도, 경도, 속력의 측정값을 GPS tuple이라 한다.

Formal Definition

A GPS sensor attached to a player measures the player's location and speed for each time. The measured data is represented as a time-series

\mathbf{x}^{\mathsf{GPS}}

consisting of

•

latitudes  lat:P×T[λGPS]→[−90,90]\text{lat}: \mathscr{P} \times \mathbb{T}[\lambda^{\mathsf{GPS}}] \rightarrow [-90, 90]lat:P×T[λGPS]→[−90,90] (deg),

•

longitudes  long:P×T[λGPS]→[−180,180]\text{long}: \mathscr{P} \times \mathbb{T}[\lambda^{\mathsf{GPS}}] \rightarrow [-180, 180]long:P×T[λGPS]→[−180,180] (deg),

•

speeds  vgps:P×T[λGPS]→Vv^{gps}: \mathscr{P} \times \mathbb{T}[\lambda^{\mathsf{GPS}}] \rightarrow \mathbb{V}vgps:P×T[λGPS]→V (=[0,∞)= [0, \infty)=[0,∞) (km/h)

where the domain

\mathbb{T}[\lambda^{\mathsf{GPS}}] \subset \mathbb{T}

denotes the

\lambda^{\mathsf{GPS}}

-time axis. Here the data point

\textbf{x}^{\mathsf{GPS}}(P,t) = (\text{lat}(P,t), \text{long}(P,t), v^{\mathsf{GPS}}(P,t))

for a player

P \in \mathscr{P}

and a time

t \in \mathbb{T}[\lambda^{\mathsf{GPS}}]

is called a GPS tuple of

P

at

t

.

Parameter Setting

•

[1.8.3] λGPS=0.1 s\lambda^{\mathsf{GPS}} = 0.1\,\text{s}λGPS=0.1s (10 Hz)