While we're looking for a backup to the pitot-static systems, I could not resist a high tech backup that wasn't so high tech 40 years ago.
First, you must have a decent inertial system, GPS-aided or not.
Then you need a decent computer to provide movement across the earth - velocity and position.
If your nav computer notices that with your heading, that your course is not on the same heading, and also notices that your speed across the earth does not agree with the inertial/nav system numbers if you had zero "wind", then what's up? . Duh? We're flying in the "wind", the air mass. So a fairly simple computer uses actual velocity across the earth and heading with what it should be with no "wind"/air mass movement. You can now compute airspeed. Kinda the reverse of what we used to do way back with "forecast" winds and airspeed indicators and so forth to get course/groundspeed.
Back when the earth was still cooling, I flew a plane with that capability. It was very accurate, and ATC center controllers would frequently ask us what the winds were at our altitude/position. We didn't need actual indicated speed, but we could have easily reversed the equation. Mach could also be calculated using "system altitude" versus the pitot-static system altitude.
In short, if you have the modern systems and a few software folks, it is not that hard to provide "airspeed" thru the airmass without the pitot-static sensors AoA is a different matter.