How is heading calculated by GPS?

Question

This is a simple question that I would have rather chatted with someone about but here it is:

How is heading calculated? I can't figure it out visually.

If the heading is calculated in regards to the Earth's Geographic North, does that mean a top view of the Earth? So when you are standing on top of the surface of the Earth somewhere, how can you get a heading direction on a digital device? What are the calculations? Does it involve the sphere at all or does the device ignore the existence of the sphere and simply keep in mind a simple coordinate eg. 90.000 N and 0.000 W?

I don't know why I can't seem to grasp the concept of heading mathematically...

Edit: I think I figured it out. You are treated as a point, on the surface; north is always directly above you figuratively- you may deviate from this point 360 degrees potentially, that's as you as a point on the surface of the Earth.

Nonconformity

Answer 1

Precisly a GPS receiver does not calculate heading.
heading is the direction where you are looking to.
The more correct term is course or course over ground.
But modern APIs often intermix heading, course and bearing.

heading and course is the same for a vehicle, But not for a ship (due drift).

But the main point is that one could think a GPS chip calculates the course/heading by evaluiating old and new position. But this is not true. This would be by far to inaccurate.

GPS receiver use Doppler Shift for speed and probably also for heading calculation.

And yes course and heading is the angle clockwise measured from geographical north (0°)

Merrythought

Alex, I was looking for your remark on heading and the method to determine it. However: could you provide a proof-link please? At the speed of 10 km/h the Doppler shift would be 10 ppb (1/100e6), and I cannot imagine a portable device capable of measuring such frequency drift with any reasonable accuracy. – Rondelle

Only the manufacturer of a specific GPS device can answer how it is implemented: Here a paper that presents a technic for speed and heading: Jun-ichi Meguro: Positioning Technique Based on Vehicle Trajectory, Using GPS Raw Data and Low-cost IMU . You find that as pdf in google – Merrythought

The paper doesn't go into detail, and the original one (DOI: 10.1080/00423114.2011.602697) is not publicly available. I still don't understand how it is possible to measure the Doppler shift with any reasonable accuracy. But it would be quite exciting if it was! – Rondelle

That GPS speed is calculated using doppler shift is a well known fact, so obviously it is possible, at least for high speeds (> 30 km/h) . Whether heading, is also calculated via doppler, is unknown. There are even RAW messages containing the doppler values (RINEX format, or uBlox binary) – Merrythought

If you're in a vehicle whose heading and bearing are not the same, better hold on because you're in trouble! – Regulation

The link to Jun-ichi Meguro: Positioning Technique Based on Vehicle Trajectory, Using GPS Raw Data and Low-cost IMU that @Merrythought refers to above is here. – Reprobative

Answer 2

There's no concept of "heading" in a coordinate, only in a procession of coordinates generated as something moves, in which case the heading is calculated based on the differences between the coordinates.
So if your first coordinate was at 10N50E and the second at 11N50E your device calculates you as traveling due north, thus on a northerly heading.

Tantra

+1.. small addition, newer GPS receivers tend to have different types of algorithms to keep heading working for a while even if signal is lost or signal quality reduced. Something like 'dead reckoning'.. As well an expensive receivers could have an integrated compass module, which is obviously not a heading but also should be taken into account (although it's used it's own NMEA messages) – Metachromatism

GPS receives do not deliver (only coordinate) they deliver a navigation solution (short name "fix") and the solution contains course over ground – Merrythought

Unfortunatley your answer is wrong, GPS reciever do not use the positions to calculate the heading, they use Doppler shift for heading (course) and speed, which is much more accurate. The faster you move, themore accurate is heaidng and speed – Merrythought

unfortunately, you'd be wrong as doppler shift can only calculate speed, not direction. – Tantra

I don't understand, I thought heading was related to the position of the device and geographic north? You are treated as a central point on a circle and the top of the circle is north. Isn't that what it is? I'm talking specifically about accessing the heading function in touchdevelop which outputs numbers between 0 and 360 degrees. – Nonconformity

position, yes. Direction of travel, no. That requires 2 data points at least, can't be calculated solely from current position. – Tantra

Answer 3

More than one question on this one :)

The heading (or yaw angle, in aeronautics), is defined as the angle between the North and the direction faced by the nose of the plane, when the plane is horizontal (pitch and roll angle at zero). This is also what you could read on a compass (North = 0°, East = 90°, etc.)

Wherever you are on the globe, you should be able to lay on the ground a protractor whose 0° is aligned with your current meridian, pointing north, and the 90° is aligned on the local parallel, toward the east. Hence you can read your heading everywhere (except on poles)

In a car, the heading is deduced from the trajectory, by looking at the previously recorded points (Doppler based speed measurement is not widespread on cheap devices). And, as stated in other answers, this is not the heading but the track which is displayed (the direction you are moving to, compared to the direction you are facing). Luckily, cars don't drift (most of the time) and so, the track is equal to the heading.

In a smartphone, the display of the heading may be assisted by the internal compass.

So a GPS, as this, is not able to assess your heading, unless you use more than one antenna, like in this device. Where the phase difference measured between the two antennas enable the device to deduce a pure, GPS based, heading.

Unemployed

Answer 4

Similar to the method suggested in another answer - One way would be to have 2 GPS antennas and knowing their relative position to each other. Then you have the location of a straight line on the earth and you have a solid direction (perpendicular to this straight line). You can now calculate your orientation with respect to any datum (e.g. true north, or a reference GPS location).

Allerus