T3

### Investigation: Procerus claims Coriolis force correction for IMU...

1. http://www.procerusuav.com/Downloads/DataSheets/Kestrel_2.2x.pdf

"

Roll and pitch estimation corrected for coriolis forces

(10% to 25% improved roll and pitch estimates)

"

According to

http://en.wikipedia.org/wiki/Coriolis_effect

$\boldsymbol{ a}_C = -2 \, \boldsymbol{ \Omega \times v}$

|omega_earth|=2*PI/day=2*3.14/(24*60*60)=7.27e-5[rad/s]

assume aircraft diving at 20m/s in earth reference frame

|ac|=2*7.27e-5*20=0.003[m/s^2]=3e-4[G]

assume we have 16bit ADC which covers 100% range of the useful voltage (overly optimistic),

and the accelerometer is quite sensitive with 6G full span (+/-3G) (overly optimistic, procerus claims +/-10G).

Therefore 6G is divided into 65536 counts.

3e-4G equals then to around 3 ADC counts which is below noise level of most

accelerometers which would be around 2^4, by eye.

Therefore coriolis acceleration is barely detectable (you can attach a plane to the rails, push it down, and the only deviating force will be at most those poor 2-4 counts on extremely sensitive ADC, overswamped by natural sensor noise).

How did they come to 10%/25%?

Where is an arorr in my calculation?

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#### Comments

• pqr is roll/pitch/yaw rates (rotational velocities), and uvw are x, y, z velocities
• T3
I am not quite familiar with all those conventions of naming the angles. What are p,q,r vectors? distance from IMU to COG? u' says ax is a result of change of speed vector component u along the axis of movement.
but qw-rv numerator in the first line... not sure.
• Developer
Yeah, they are referring to the centripetal acceleration in the NED reference frame. Nothing significant or new here. And they also significantly over simplify the probelm using fixed wing aircraft assumptions.
-Beall

• BAAAAACK TO WOOOOOORK!!!!!!!
• As a corollary to this, I was taught in school that, in addition to affecting toilets, canon balls, and weather systems, Coriolis Force makes drunk engineers always fall over to the right.

;)

Tom
• T3
Ahhah of course they talk bout the correction for noncentral IMU location, still, a small effect but measurable (mostly for 30cm UAS in a spin).
I am rarely thinking in non-inertial reference frames unless it's as big as earth, therefore I have attached Coriolis to a very large scale (coriolis is a clever name to imaginary force when you want to those simple Newton laws work when you are in rotating reference frame).
• I don't think that they're necessarily speaking of the Coriolis effect of the earth. The spec sheet says Coriolis Force, which is general, and could apply to any rotating frame of reference.

My guess is that they are including something in the algorithm to compensate for an IMU not being placed at the center of rotation of the aircraft.
• Our sensors aren't good enough yet to worry about this. Unless you have a fiber optic ring gyro or something.
• 3D Robotics
Most likely they threw an algorithm in there that is supposed to do this correction, but in reality it does nothing.
This reply was deleted.