I need to create the trajectory of respondents according to the their collected GPS data (including X and Y).
I am familiar with python programming, but I am a beginner in ArcGIS.
I want to write a script to automate this process.
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The Points To Line tool in the Data Management toolbox may meet your requirements so perhaps look at that before Python.
Use the Sketch ("pencil") tool to draw, but instead of 1st point right click and select "Absolute x,y " or press F6 to enter your GPS points in window provided.