An air carrier CRJ-700 Pilot reported a loss of GPS on departure.

Narrative

I was Pilot Flying during the takeoff on ZZZ Runway XX. During the initial phase of climb; the Captain and I noted that the Flight Director/AutoPilot was initiating a turn to the right. The SID called for a straight out and then a left hand turn after a fix. I disengaged the AutoPilot and started hand flying the aircraft on the present heading. During the climb out we noted that the FMS (Flight Management System) was displaying an error and had lost its position. We conferred with ATC who gave us a heading and I continued to hand fly while the Captain tried to sort out the problem. Once we were at a safe altitude; we advised ATC we had lost GPS and needed an updated flight plan for VOR based navigation to ZZZ1. We programmed in the new plan and continued the flight in green needles. During the flight; the Captain was able to reinitialize the FMS position and we switched back to white needles while periodically checking our position against VORs and a General Aviation application on my phone.