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In INS (Inertial navigation system) sensors, is there a distinction between the following?

  • Orientation (heading, pitch and roll)
  • Position (latitude, longitude and altitude)

Is the orientation relative to a specific axis while the position is absolute? If yes, what is the axis?

Federico
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ransh
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3 Answers3

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Yes there is a distinction, pitch, roll and heading are angles [unit = radian] and latitude, longitude and altitude are linear distances [unit = meter]. Together, these six parameters define the six Degrees of Freedom that define the momentary state of a rigid object with reference to the earth.

All six are defined relative to earth axes. For the linear dimensions this is clear, we just need to define a suitable zero point. For the angles:

  • Pitch is the nose up/down angle relative to the gravity field of the earth.
  • Roll is the wingtip up/down angle relative to the gravity field of the earth.
  • Heading is the angle relative to a suitable earth reference, usually magnetic north or geographical north.

Conversion of aircraft axes into earth axes is a non-trivial matter and the cause of much confusion, for instance in questions comparing lift to weight: lift is always coupled to aircraft axes, weight to earth axes. The axes sets are defined as follows:

Aircraft axes

  • Origin: Centre of Gravity of aircraft
  • X-axis: in the symmetry plane of the aircraft, + = forward to the aircraft nose
  • Y-axis: in the span wise direction of the aircraft, + = to the right wingtip
  • Z-axis: perpendicular to the XOY-plane, + = down into the floor.

Earth axes

  • Origin: Centre of Gravity at the start of the response
  • X-axis: In the horizontal plane (relative to gravity), + = pointing north.
  • Y-axis: Perpendicular to XOZ-plane, + = pointing east.
  • Z-axis: Pointing to the centre of the earth = +

Edit

Yes navigation lat/lon is given in [degrees] - the INS sensor ultimately converts displacement into proper navigational definitions of course. But for measuring 3-D aircraft inertial effects the SI system is used, and displacement is internally treated as a linear motion, units [metres].

Koyovis
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  • I think Yaw should be the third point... Along with Pitch and Roll, it forms the 'Big-3' Rotations of an aircraft, or the 3 Degrees of Freedom... : ) –  Nov 15 '17 at 07:50
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    Yes the aircraft pitches, rolls and yaws - but relative to what? – Koyovis Nov 15 '17 at 07:58
  • I think you misunderstood - I meant replacing the 'Heading' point with 'Yaw', as it sounds more complete... : ) –  Nov 15 '17 at 14:57
  • Down is positive Z? That seems backwards. – Monty Harder Nov 15 '17 at 18:51
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    I hate to be pedantic, but latitude and longitude, are angles not linear distances...just angles relative to the centre of the earth though the Greenwich Meridian. – Trevor_G Nov 15 '17 at 18:56
  • @MontyHarder It is counterintuitive for aeronauticers, but it is defined this way to comply with the corkscrew rule: twist a corkscrew from X to Y-axis and you find positive Z – Koyovis Nov 15 '17 at 21:38
  • @Trevor yes indeed, lon and lat are angles. There are a couple of assumptions made so that they can be treated as linear distances, following the curvature of the earth. – Koyovis Nov 15 '17 at 21:42
  • @Koyovis Hmm... I wonder if this convention varies by area. I don't recall positive z ever pointing towards the center of Earth in any of the math, physics, or engineering classes I took in the U.S. Granted, I didn't take any aerospace engineering classes. +z pointing to the origin in a spherical coordinate system doesn't make much sense. Literally all coordinates (except the origin itself) would have negative z, which is kind of silly. The corkscrew reasoning seems weird, since that's an equally-arbitrary convention. – reirab Nov 15 '17 at 23:28
  • @reirab Any sign convention will work, one will just need to remember to carry over appropriate minus signs. In the US, people are more used to carrying over constants etc due to the non- metric system so that is where the difference may be. If I remember correctly, the corkscrew definition is a requirement when Euler transforms are done - which is what you do when transforming from aircraft to earth axes. You are free to choose 2 of the three axes, sign of the 3rd one is then determined. And yes I have made a few errors with this counter-intuitive definition as well, it doesn't look right. – Koyovis Nov 15 '17 at 23:46
  • @Koyovis By "an equal arbitrary convention," I meant that you can just as easily design a corkscrew that turns either way. Which way a corkscrew turns is just an arbitrary convention, just as which way an engine turns is an arbitrary convention. Granted, with a corkscrew a decent argument could be made that designing it one way is better for most people (the right-handed ones,) but either way is certainly possible. – reirab Nov 16 '17 at 06:11
  • @reirab it most certainly is possible to define it any way you desire, as long as you state the sign conventions etc in the docs. One can also have the x-axis point in any other convenient way than north. – Koyovis Nov 16 '17 at 07:35
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Position is where you are; orientation is which way you're pointing (including any roll).

David Richerby
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"position" is absolute. You can think of it as the x, y, z coordinates of the aircraft in the 3D space.

"orientation" is the state of the aircraft relative to its own axes:

enter image description here

Image from https://en.wikipedia.org/wiki/Aircraft_principal_axes

"position" (coordinates) - https://en.wikipedia.org/wiki/Geographic_coordinate_system

orientation - https://en.wikipedia.org/wiki/Aircraft_principal_axes

DeepSpace
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    Sorry, but position is never absolute, and orientation is not a state, but a set of angles. – bogl Nov 15 '17 at 08:24
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    @bogl An object's orientation in a specific point of time definitely describes its state. – DeepSpace Nov 15 '17 at 08:28
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    A state is a complete description of a system. The position, orientation, speed vector, and angular speed vector together describe the state of a rigid body. Orientation alone is far away from completely describing the state of a plane. – bogl Nov 15 '17 at 08:35
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    Also it's not really accurate to say orientation is the state of the aircraft relative to its own axes: relative to its own axes, it doesn't move at all! – psmears Nov 15 '17 at 13:49
  • @psmears It doesn't move at all relative to its axes? This is totally wrong. – DeepSpace Nov 15 '17 at 13:51
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    @DeepSpace: No, it's 100% correct, because when the plane moves (pitches, rolls, yaws), its axes move too. – psmears Nov 15 '17 at 13:55
  • @psmears Don't be so picky. https://en.wikipedia.org/wiki/Moving_frame – DeepSpace Nov 15 '17 at 13:58
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    @DeepSpace: I'm not being picky - sorry if it seems that way - but this is an important point. You can express change in the aircraft's orientation relative to its axes, but you can't usefully specify its current orientation that way - you need to relate it to some other, external reference. To clarify: can you give an example of how would you give the current orientation of an aircraft relative to its own axes? – psmears Nov 15 '17 at 14:14