Technically, if you know everything that the plane is doing, you’ve got an accurate 3D coordinate for the plane, and an accurate vector of movement relative to the ground then anything the plane is doing that you can’t predict from the ground-relative vector, the engine power, and the angles on all the flaps is air direction and velocity.
If you know everything the plane is doing, why not plug the airspeed indicator into the computer as well, while you are at it?
I’m just a dumb pilot. Care to dumb that down for me?
Sounds like you’re saying you could disregard indicated airspeed, which would be news to me. But I am very likely not understanding your point.
Say I’m using WAAS data on an approach, which would give me a 3D position based on the geometry provided by the vertical guidance. And I’d have the groundspeed. That still doesn’t take into account the “parcel of air” that the plane is inside. As you say, I could make a guess based on what I know of engine settings and configuration, but I still don’t see how I could safely not know indicated airspeed.
So as to not fight the hypothetical.
Say that you have a toy car that has a set velocity of 2 mph. I can track its position accurately and I know that it’s moving directly forward on a treadmill.
If the position of the car is moving forward at 1 mph then the treadmill is going backwards at 1 mph.
If the position of the car is moving forward at 5 mph then the treadmill is going forwards at 3 mph.
If you know where an airplane is and what it would do on its own then you can calculate what the environment around it is doing through some math.
Aviation and treadmills… I don’t think that’s ever come up before. What could go wrong? 
Again, just a dumb pilot… But indicated airspeed and groundspeed can be very different, even with known engine and configuration settings. Wind, temperature, etc.
I have landed airplanes with no indicated airspeed for various reasons, and I would indeed reference GPS groundspeed in that situation. But I would also be reacting to how the airplane was handling, what the wind was doing and so on. Without understanding more about what you’re proposing, I would trust my pilot training and experience over doing some math.
I see this mentioned a lot.
To me this means aviation is forever stuck as it is. No one will spend the money to improve what is there. What we have works well enough so…who will spend money to find something better?
Here’s another way of looking at it…
The FAA is extremely careful about new systems. And IMHO, as they should be. But they have also been known to move fairly quickly. When I began flying over 20 years ago GPS existed, but wasn’t widely used. In just a few short years it completely changed how we fly, particularly in the IFR system. The FAA managed that transition very effectively, safely, and quickly by their standards.
But think of the safety record we have now. It’s incredible. And the changes that brought about that safety have largely been in how the humans behave. The ILS is still the gold standard in approaches, and has been for many decades. GPS is great, and is utilized, but I’m not sure what would be gained in the short term if we made a soup-to-nuts change to accommodate the latest and greatest avionics advances.
I remember reading that on the space shuttle they used older laptops for various things, not newer, cutting edge tech. They wanted it to work, reliably. That’s where we are now, I think. Advances are being undertaken, but the system is so safe it pays to do it carefully and sometimes slowly.
I’m with you. I agree the FAA should be very cautious and their caution has worked. Air travel safety is so much better than it was when I was a kid in the 70s.
Yet, many (most?) GA planes still use leaded fuel. There is no shortage of engines that use unleaded gasoline. They’ve been around for 40+ years. Yet they keep making planes that use leaded fuel.
I’d say that’s more of a money issue. If you own a prop plane, do you want to pay to convert it to turbine? There’s a shop near me that specializes in turning a certain flavor of Cessna into a turboprop, and the price tag is well into multiple six-figures.
Imagine the outcry from the GA community if that were mandated, even with the understandable zeal to get rid of leaded fuel. Unfortunately, those engines are what we have for the moment.
Edit: I think you added to your post while I was responding. It’s true, there are more and more engines that burn something other than leaded fuel. But any newer airplane is very likely more expensive than a legacy plane that already exists. I wish it were otherwise, believe me.
Grandfather in all the current planes.
Why not mandate all new piston engine planes use unleaded gas?
I’m not disagreeing with the wisdom that autonomous take off and landing is 20 or more year’s away, but I’ve heard that the Garmin system is expected to be one of the first fully autonomous GPS based landing systems to be certified:
If Dad is flying the family to Vail and suddenly keels over, one of these would be nice to have in the plane…
Psst, mentioned in post #4 
That’s the sort of thing that is possible in principle but it’s not practical, particularly when you have a perfectly good airspeed indicated that can give an input to the flight computer. Also, we need to be careful talking about what “GPS” can do. GPS is dumb. It is just a position triangulated from satellites. Navigation systems using GPS, or more correctly GNSS, can do all sorts of things but that all depends on what other functions and inputs it has in addition to a GPS position.
GPS altitude is relatively bad information, so barometric altitude and radar altitude are used at various points instead. GPS heading can be derived using change of position over time, but it is not as good as having a heading input from a dedicated system. True airspeed could be calculated using attitude / thrust / configuration formulas, but it is much better to have a dedicated system that measures it more directly and provides that information to the flight computer. Even the position itself is more accurately provided by an additional input to the system. GPS has an error that is not known. A ground station knows exactly what its own position is and also knows what its calculated GPS position is so it can calculate the error and transmit a correction value to aircraft in the area. This is the principle of the various augmentation systems.
The take-away is that GPS is great but it has limitations and it is only by working around the limitations that you can get something accurate enough to land a plane. Which is to say, planes can and do land all by themselves, but GPS is only a very small part of what makes that possible.
That’s got to be dual-band GPS; regular old GPS is only good for 3 meter accuracy.
It’s complicated. Just because the system is only accurate to 3m doesn’t mean you will always be 3m from your actual position, it just means the system has a certain confidence level that you are within 3m of your actual position. As I understand it the predicted accuracy is based on summing of the various errors in the system. In reality a lot of the errors negate each other rather than compounding and so your position may be more accurate than expected, but the system can’t guarantee that accuracy. That’s why I say it is accurate enough to put you on the centreline (I was being slight hyperbolic, I meant safely on the runway) most of the time. Most of the time is just fine when you can see the runway with your eyes or have other better systems available. It is absolutely not good enough if you have to rely on it to safely deliver people to their destination.
I think we’re agreeing, more or less. I was thinking that 3 meters is fantastic in terms of navigation from one place to another, and even in terms of getting a pilot roughly lined up with the runway, but not enough to actually land a plane.
Maybe the dual-band GPS improves enough on that to make it feasible- I’ve seen claims of “centimeter level accuracy” for dual-band GPS.
Dual band is the mechanism used to correct for ionospheric delay. The atmosphere is slightly dispersive, and different frequencies travel at different speeds. Comparing the delay between the two bands allows the ionospheric delta to be estimated, and thus mitigate this source of error. However the local accuracy augmentation system can get you much better accuracy.
If a local GPS receiver station knows that it is stationary, it can provide a position delta that corrects for error in the instantaneous GPS location received versus its known position - if the station and the aircraft are close they both see the same conditions, and so the delta is good, usually very good. Like I wrote above. If I was using a local accuracy augmentation system to auto land a plane, I would want to hear a really solid story about proof against jamming and especially spoofing of the augmentation system. That scene in Die Hard 2 where they hack the glidescope system was rubbish. But it would be almost spot on if you were hacking a local accuracy augmentation system.
Any GPS can get you centimetre accuracy. So long as you wait long enough in one place. It makes a huge difference if you can tell the GPS receiver that it isn’t moving. This isn’t an option for a landing plane.
Velocity calculation can be done from two sources in a GPS receiver. You can calculate position deltas. This is not so good if you want a fast answer. Great if you are post processing the data. Or you can use Doppler shifts on the received signals. The accuracy isn’t as good, but you get the numbers in real time. You choose.
I’m not sure why everyone is separating out augmentation systems. DGNSS, WAAS, SBAS, RTK, PPP are just ways of improving accuracy. Whether I’m measuring carrier cycles or using the difference between the L1 and the L2 frequencies to determine ionospheric interference I’m still using GPS. The OP specifies the best money can buy. A data connection to a RTK network should get you real-time sub centimeter accuracy. You could use multiple antenna on the wingtips, nose and tail. I guess I read the OP as more theoretical.
I have set up an RTK system. It improves accuracy immensely. But maybe the OP means a GPS system self contained to the aircraft. No ground based RTK at the airfield he is landing at. Even our Terrastar GPS license may not be good enough to land an aircraft reliably in all conditions and number of times. Using the Ublox UCenter software to monitor a Ublox RTK system in house, I felt it accurate and stable enough to use as a very accurate drone flight pattern positioning system. The quad copter drone landing scheme is far simpler than a fixed wing aircraft. And only a very close observer might suffer damage.
I tested some rover units that were in contact with an RTK base station connected to our States DOT reference network. The rover units were basically high end antennas driven by smartphones. They seemed to deliver amazing accuracy within multiple miles of the base station. I’m not sure of how real time the data would be. You seem to have more experience.