Pixhawk and autonomous flight

So, I’m working on a small project of mine, the idea is to have the quadcopter fly to specifics location autonomously without human interaction.
I’m thinking of having a sensor with a GPS build in when triggered no matter how make the sensor send the GPS coordinates to the pixhawk so that the quadcopter go there.
Can we make this happen, maybe using onboard computer (Arduino or raspberry pi …)
I would really appreciate any help, Thank you in advance.

This is basic functionality with a Pixhawk running Arducopter. You do not need a companion computer.
http://ardupilot.org/copter/docs/auto-mode.html

Lets say that I want to put movement sensor outside my house, once there is a movement the sensor should trigger the ardocopter( which is in standby mode) to go and check what over there.
Can I do that?

I don’t know what you mean by standby mode but read this for sending guided mode commands. You will have to write the code to accomplish what you want to do.

http://ardupilot.org/dev/docs/copter-commands-in-guided-mode.html

Thank you for the help!