I'm just starting up with IMU's and I really want to work on my own flight controller, but a question always hits my mind and I am not able to find answer anywhere, so I'm here.

Will multiple IMUs will help improving stability of a quadcopter? averaging out the values of all the multiple IMUs should reduce the drift, which is a function of time, but I have no experience with IMUs and just cant figure out about the amount of error correction by adding one extra IMU, will it be just additive? or Exponential?

This question was also posted on the Robotics Stack Exchange site.

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    \$\begingroup\$ Simple averaging will improve it a little bit (given both sensors are comparable quality). But a better idea would be to fuse the data with a Kalman filter (properly designed, of course). \$\endgroup\$
    – Eugene Sh.
    May 8 '17 at 15:21
  • \$\begingroup\$ Yes, but the main problem is I'm not able to imagine the number of IMUs vs improve in accuracy graph, as I haven't worked with them yet. \$\endgroup\$ May 8 '17 at 15:24
  • 1
    \$\begingroup\$ This is something you better find empirically. \$\endgroup\$
    – Eugene Sh.
    May 8 '17 at 15:25
  • 1
    \$\begingroup\$ If you have an access to IEEE library, you can check out this paper: ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6214600 (or get it from other sources by name "Combining Numerous Uncorrelated MEMS Gyroscopes for Accuracy Improvement Based on an Optimal Kalman Filter") \$\endgroup\$
    – Eugene Sh.
    May 8 '17 at 15:51
  • \$\begingroup\$ The Allen variance in AD's IMU with one IMU achieves the same 6 deg/h drift of 6 IMU's in this old 2012 research paper \$\endgroup\$ May 8 '17 at 16:07

Yes, you can use multiple sensor units to improve the data, but only if their errors — biases, scale factors, noise, etc. — are independent (uncorrelated). In that case, you can expect the RMS error to decrease in proportion to the square root of the number of units used. For example, if you have four units, the random errors will be roughly cut in half.

  • \$\begingroup\$ this neglect common mode errors which do not average out. \$\endgroup\$ May 8 '17 at 16:02
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    \$\begingroup\$ @TonyStewart.EEsince'75: Which part of "only if ... independent/uncorrelated" do you find confusing? \$\endgroup\$
    – Dave Tweed
    May 8 '17 at 16:11
  • \$\begingroup\$ .. the part that neglects correlated CM errors that are impossible to null. \$\endgroup\$ May 8 '17 at 16:19
  • \$\begingroup\$ @TonyStewart.EEsince'75: So what is your actual point? \$\endgroup\$
    – Dave Tweed
    May 8 '17 at 16:23
  • \$\begingroup\$ older worse technology like Eugene's paper benefit from averaging with IMU's that have more noise than DC error to the same extent that AD's recent article in my answer achieve with no references to multiple IMU's but improved noise, calibration and Allen Variance averaging on one IMU. .. Multiple IMU's cannot improve their results, since residual drift DC error is integrated. Did you provide references with better than 6 deg/h using redundancy \$\endgroup\$ May 8 '17 at 16:27

​ An IMU is a single unit in the electronics module which collects angular velocity and linear acceleration data which is sent to the main processor. An IMU housing contains two separate sensors.

The first sensor is the accelerometer triad. It generates three analog signals describing the accelerations along each of its axes produced by, and acting on the vehicle. Due to thruster system and physical limitations, the most significant of these sensed accelerations is caused by gravity.

The second sensor is the angular rate sensor triad. It also outputs three analog signals. These signals describe the vehicle angular rate about each of the sensor axes. Even though the IMU is not located at the vehicle center of mass, the angular rate measurements are not effected by linear or angular accelerations.

The data from these sensors is collected by the IMU and returned to a main processor.

Because position is integral of velocity, and double integral of acceleration, minute offset voltages after calibration still accumulate relative position range or coordinate errors.

Without a GPS, or visual feedback, the flight time and integrated errors cannot be eliminated. Calibration is critical for longer flights and acceptable position error to get "home"

Thus averaging multiple IMU's only reduces the error by rms (n) or not much. (best case assuming random offsets)

"The Allan variance curves provides a tool for understanding the trade-off between repeatability (noise) and the averaging time.". Ref http://www.analog.com/media/en/analog-dialogue/volume-49/number-2/articles/mems-imu-gyroscope-alignment.pdf

  • 1
    \$\begingroup\$ This is an intro to IMUs. Not an answer to the question. \$\endgroup\$
    – Eugene Sh.
    May 8 '17 at 15:45
  • \$\begingroup\$ The answer is obvious, NO, the details explain why \$\endgroup\$ May 8 '17 at 15:46
  • \$\begingroup\$ The answer is actually YES. Commercial high-end MEMS devices from vendors such as Analog Devices use this technique to reduce measurement noise. \$\endgroup\$
    – Dave Tweed
    May 8 '17 at 15:49
  • \$\begingroup\$ yes rms(n) is possible as we agree on this if random!! but not if they all experience thermal offset. and more $$ \$\endgroup\$ May 8 '17 at 15:51
  • \$\begingroup\$ (-1) to those who cannot understand, no better explanation possible , except analog devices ref in my answer. Dave pls show ref. \$\endgroup\$ May 8 '17 at 15:57

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