Given the GPS data with longitude and latitude, it is very common to determine the distance for location information of these data.In order to do that, you need first transform those gps data into x-y plane. It is always not so simple to achieve that, there are many materials about map projection and UTM.
When the area is small, you can use a very simple equirectangular projection to
approximate the projection. If you use the horizontal axis x to map longitude, and the vertical axis y to map latitude,
then you can use the following formula to approximate the projection:
- \( x = r\phi \cos(\psi_0) \)
- \( y = r\psi \)
Note that: the \( \phi \) denotes longitude and the \( \psi \) denotes the latitude, they are both in radian, and the \( \psi_0 \) is the average value of latitudes, and \( r \) denotes the radius of the Earth, which is about 6371km..
Applying this simple map projection with the gps data of Shanghai, it proves to be a good approximation. For example, computing the distance between (121.05E, 30.73N) and (121.05E, 31.447N) by using this method gives the result 79.7km, while querying that from the website gives 80.5km. That means the loss of the distance along the latitude across the whole Shanghai is almost 1%, which is good enough for approximation.
Another thing might be useful is to make some shift by adding 0.0044 degree in longitude and minus 0.00205 degree in latitude, which can helps align the gps data on the google map. Although the raw gps data aligns satellite view perfectly, the map does not align the satellite view for some unfathomable reason. So to align gps data with the map in Shanghai, you need to do the above shifting.
