Finding longitude/latitude of a aircraft

Question

I have been scratching my head for a long time on this one so any help is apperciated. How would I find longitude and latitude points of a UAV given this:

• True Airspeed
• Roll rate, pitch rate, and yaw rate
• Time Stamps

Is it even possible?

Answer 1

No, it is not possible with that information.

The information you gave is not related to position at all. (It could be pitching, rolling, and yawing at the equator, the North pole, or anywhere in between.)

You need at least a starting position in order to apply speed, direction, wind, etc. to calculate a final position.

Answer 2

You don't have the required data to determine your position relatively to the ground (lat, lon). It's pure physics, nothing related to aviation in particular.

Ground velocity integration

To solve your problem you would need to break down your UAV motion into individual segments of some duration, e.g. 10 s, and associate a mean ground velocity vector to each segment. Velocity has two components: a magnitude, what we usually call speed, e.g. 100 kt, and a direction, e.g. 120°. If you know the individual mean velocities, then you can derive your displacement for each interval (blue). You can also sum them to get your total displacement (red).

Furthermore, if you know your starting position you also know your current position. Mathematically this operation is integrating the velocity over time. In practical the interval of time (sampling interval) is smaller than 10 s, but for any sample you must know the ground speed and direction of motion.

You're missing the two components of ground velocity: Airspeed is not ground speed, and attitude (yaw, roll, pitch) is not helpful to determine the direction of motion relatively to the ground.

Acceleration integration

The usual way to determine ground velocity is to use an inertial navigation system, which determines direction with gyroscopes and speed with accelerometers.

An INS actually first detects acceleration using accelerometers. Velocity magnitude is built by integrating acceleration and velocity direction by using direction measured by gyroscopes. Velocity is then integrated, as described above, to get the displacement:

Source. The rotation of coordinates is used because this block diagram is for a strap-down INS. The rotation recreates the absolute coordinates system of the stabilized-platform INS (first generation of INS).

GNSS

Of course there are other ways to determine a position, of which the GNSS (using the US GPS or other available satellite constellations like Galileo). Small GNSS receivers like the ones in smartphones, are easily deployed on UAV.