I have seen the car speedometer and the GPS speed (Waze) differ when going up or down a steep hill. Is this real ?
If it’s real, can you estimate the slope of a straight road that goes up a hill by :
Theta (angle of incline) = Inv. COS (Vgps/Vspd)
where
Vgps = speed shown by gps
Vspd = speedometer speed
GPS is more precise for horizontal position than vertical, so I wouldn’t be surprised if some GPS programs report only the horizontal component of velocity. But even a “steep” hill will usually be a fairly small angle, which will make any discrepancies from this effect very small.
GPS error is about three times higher for altitude than it is for position on the surface. Many dedicated GPS receivers (including iPhones) use a supplemental ambient pressure sensor to get a handle on altitude.
A really steep hill will increase or decrease the effective diameter of the wheel the speedometer uses to count revolutions. I suspect that the uncertainty in all these factors (and others) would make it impractical to measure slope in the way you propose. Just using your phone’s 3-axis accelerometer would probably give better results.
ETA: partially ninja’d!
How does it do that?
Let’s assume that the speedometer reads the rate of rotation of the left front wheel. When going up a steep hill, the rear tires bear more of the car’s mass than on the flat and the front tires bear less.
So the front tires’ contact patch decreases in area and the tires’ effective radius increases. The opposite happens going down a steep hill.
I don’t actually believe that’s a significant factor either way; it was partly meant to illustrate all of the small variables that come into play.
Don’t GPS systems use doppler-shift for speed measurement? And not position. So this should be independent of any slope?
That is differential GPS and they are available and are used when the accuracy of GPS is not enough. Since the introduction of the WAAS satellites which I believe was launched by the FAA for the purpose of giving aircraft better accuracy then GPS would, differential GPS has become less important for many applications that once used them. That and Pres Clinton stopping the intentional scrambling (which WAAS also sort of undoes anyway).
Just to put a number on this: the ratio of ground distance to horizontal difference is √(1 + (grade)[sup]2[/sup]), where the grade is expressed as a decimal. For example, for a 10% grade (which is a rather steep road for a highway), the ground distance is √(1 + (0.10)[sup]2[/sup]) ≈ 1.005. In other words, the two distances only differ by about 0.5%.
I’ve watched my navigator’s reported altitude bounce up and down more than ten feet – while sitting at a light.
Also, in the west there’s a sign with the altitude at a lot of the summits. I check the sign vs. the navigator when I sail by and there’s often a discrepancy of more than fifty feet even allowing for the fact that the sign is presumably at the road’s surface and the navigator more than three feet above it.
Either the DOT engineers haven’t figured out how to use a transit to measure from a benchmark of the nav is just plain wrong. My money is on the latter.
You’re right—speed is measured by Doppler shift.
That’s not true. Doppler-shift velocity calcs do not require differential GPS. Cite:
It’s usually not even that precise for horizontal position, and there is a considerable amount of “assume that you are driving on a road” processing. Some of this is available as a GCP api.
Smartphones (which are what most folks use for GPS nowadays) get location info from the relative strengths of cell phone towers, the relative strengths of known WiFi signals, inertial guidance, and assumptions from maps, in addition to GPS proper. I’ve heard that WiFi is responsible for the largest part of the information.
Are you talking about the Lincoln Navigator (big suv)? Altimeters need calibrating for air pressure. Not sure if the car even has allowance for it. Airline pilots get the local pressure when landing to correct readings.
“Pressure with Height: pressure decreases with increasing altitude. The pressure at any level in the atmosphere may be interpreted as the total weight of the air above a unit area at any elevation. At higher elevations, there are fewer air molecules above a given surface than a similar surface at lower levels.”
Hmm. You seem to be conflating GPS proper with land navigation apps/devices.
The former gives speed and “raw” position. The latter use other datasets (including road maps, topographic maps and all the things Chronos listed) to tweak the raw position in a way that’s useful for land navigation.
Marine and aviation GPS units tend not to assume that you’re driving on a road, if you catch my drift.
That’s nice to know. Is the speed displayed by the smartphone corrected for the all the different location information ? Or while the location is corrected by the information from the different sources you mention, the speed is computed using just the gps info?
I expect that the phone uses data from all sources to compute everything it shows you, but different sources would have different weights for different purposes. GPS velocity is extremely precise, but sometimes you can’t get a signal, and even when you can get a signal, sometimes it takes a little time. For a Kansas freeway in clear weather, the GPS velocity can’t be beat. For flooring it after the light turns green, the accelerometer probably gives better data.
I’m not sure what a phone would do if you gave it multiple input streams that all seem reliable, but which disagree significantly. Probably just throw out an error message that says “Location data lost. Searching.”, or something like that.
My GPS is a TomTom, and it definitely thinks in two dimensions. When I go downtown and enter the area with tall buildings, it basically freaks out. The display shows my car traveling on top of the buildings which, though pretty cool looking, makes it useless for navigation. The next time I go downtown, I’m going to input the destination into Google Maps and see if it behaves in the same way.
Just to add to EdelweissPirate’s comment:
https://www.gpsworld.com/gnss-systemalgorithms-methodsinnovation-doppler-aided-positioning-11601/
https://www.e-education.psu.edu/geog862/node/1786
As per Chronos’ post on other data, I have a utility on my phone which shows altitude from GPS signal and next to it from map data over mobile or WiFi signal (where available).
But I don’t think WiFi is responsible for most of the data, especially when up in a forest where the signal is weak 
One reason it freaks out is that those buildings interfere a whole lot with the signal from GPS satellites. They’re not very strong—when I ride my mountain bike under leafy tree cover, my bike’s GPS display shows a much less precise position than when I do the same ride in the fall with no leaves.
Also, I’d speculate that the tall buildings play havoc with Doppler speed calculations due to multipath propagation.
The error of the automobile speedometer is about 5-7 km/h, so there may be a difference with the GPS navigators