I'm having the exact same issue with my iPhone 6 that all started with an upgrade to iOS 11.0.3. I've been in contact with Apple Customer Support over the past few days to try and resolve the issue--but nothing has changed in the slightest. Tonight, with support on the line, I went through a full factory restore of my phone, and did not use a backup (so no third-party apps were on the phone). With a factory restore (running iOS 11.1), I tried to use Maps, but with the same results as before. I then downloaded Waze (my preferred GPS app) and receive the same message as before--"Seeking GPS. Try going outdoors..."
Downloading GPSdiagnostic yields some interesting information. My lat/long coordinates are close--but not as accurate as they should be (+/-200 ft). Of course, as many of you have already noticed--while attempting to use a GPS program, the initial coordinates are somewhat close--however, GPS tracking does not work at all. The GPSdiagnostic app also states that Location Services have been started, enabled, and are functioning normally. HOWEVER, though lat/long coordinates are provided (as described above), the app also indicates that it does not have any communication with any GPS satellites. There is a Satellites vs. Quality bar chart that is completely blank (the x-axis is labeled "1", "2", "3", and ">=4" and y-axis indicates signal strength from 0% to 100%). Also, "No Satellites" is displayed in the chart where the bars should be.
I'm stating this because I think it affirms what we've known all along--this is entirely a software issue. Obviously, GPS data is being received because coordinates are being provided (I don't think the coordinates are based off of cellular data, right?), but there's apparently (buggy) code in the new update which incorrectly tells GPS-enabled apps that no satellites have been found. Ergo, those apps do not function as they should.
These are just my thoughts. I'm absolutely convinced it's a software/update issue (vice a hardware or settings issue), but I'm wondering why this wouldn't affect more people (e.g. other people with a factory fresh iPhone 6 running iOS 11.1).
Do you guys have any more updates on your end?