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When IMU is gravity aligned, yaw is not observable from linear acceleration data.

However, when IMU has non null pitch, the sensor is not gravity aligned anymore and the gravity acceleration gets remapped on other axes.

Question: how do you compute the yaw angle from linear acceleration data when the pitch is not null (and therefore yaw is observable)?

Thank you in advance

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Yaw is not observable from gravity regardless of pitch.

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  • $\begingroup$ How can you be so sure? The gravity acceleration if pitch is not null, gets remapped on other axes. So the yaw information should be there. $\endgroup$ – Employee Jan 7 at 1:19
  • $\begingroup$ This paper elaborates on yaw extraction from linear acceleration data - ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=893168 (page of interest is page 4) $\endgroup$ – Employee Jan 7 at 1:45
  • $\begingroup$ Close your eyes and spin around. You can not tell which way you were originally facing by tilting your head. Yaw is not observable from gravity. $\endgroup$ – holmeski Jan 7 at 11:39
  • $\begingroup$ Thanks for your answer @holmeski but we are looking for comprehensive answers that provide some explanation and context. Very short answers cannot do this, so please edit your answer to explain why it is right, ideally with citations. Answers that don't include explanations may be removed. $\endgroup$ – Mark Booth Jan 8 at 2:25
  • $\begingroup$ Also, it is better to edit your answer to add information requested in comments, rather than adding more comments. Comments are for helping to improve questions and answers, and are distracting, so we try to keep them to a minimum. If all of the information needed to answer the question is contained within it, the comments can be tidied up (deleted). $\endgroup$ – Mark Booth Jan 8 at 2:25
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When you want to detect the Yaw of a robot, you want to use an IMU.

An IMU is an Inertial Measurement Unit. A standard IMU consists of an accelerometer, gyroscope, and magnetometer, each with 3 degrees of measurement (XYZ). A standard IMU contains these 3 sensors, together, such that the combined sensor data can be fused together to create an accurate estimate of the RPY (Roll Pitch Yaw) of the robot's frame.

Now, why does this matter?

Well, in your question, you are asking to find the robot's Yaw from only the accelerometer. This is generally bad practice because you can only measure the second derivative of linear position, whereas Yaw is (0th derivative? - bad notation) the original, non-differentiated function, which is a measurement of orientation, not translation. This means that, in summary, you cannot measure Yaw with an accelerometer.

TL;DR => You don't

@holmeski is correct

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  • $\begingroup$ I know that I can not extract absolute yaw information. I think anyway that I can extract relative yaw information. As an example, think of being a robot on stairs. The gravity acceleration will be partially remapped on x and y axes. From this, we can extract the yaw. Could you check this paper and tell me what is your idea about it? They extract robot/stair relative yaw from linear acceleration data - ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=893168 $\endgroup$ – Employee Jan 10 at 20:10
  • $\begingroup$ That paper uses the "vision sensor" to align itself with the stairs - this is, in a way, yaw control. Also, to quote the paper: "The above formulae assume that the Urbie is moving under constant velocity, so that the acceleration is purely a function of gravity" This is why you cannot rely on the accelerometer, if you are basing your work on this paper. I suggest you spend $10~ or so and get an IMU from Sparkfun and this will no longer be an issue. Again, you are trying to measure a rotational property with a linear sensor. This is a one-way road to Very inaccurate readings. $\endgroup$ – thatrobotguy Jan 10 at 22:29
  • $\begingroup$ I've tested the approach, and it actually works fantastic. If pitch is non null, gravity acceleration gets remapped on other axis and the relative yaw of the sensor in respect to the inclined plane where it is lying on is beautifully observable. $\endgroup$ – Employee Jan 21 at 17:59

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