# IMU covariance matrix setting for robot_localization [closed]

Hi guys :)

I'm trying to fuse an odometry source with the data coming from an IMU. To do this, I'm using robot_localization. I'm having difficulties in understanding how to set the covariance matrix for the IMU. At the moment, I have a covariance matrix filled with zeros. As you can read from here ( http://docs.ros.org/kinetic/api/robot... ) this is an error:

-> Missing covariances. If you have configured a given sensor to fuse a given variable into the state estimation node, then the variance for that value (i.e., the covariance matrix value at position (i,i), where i is the index of that variable) **should not be 0**. If a 0 variance value is encountered for a variable that is being fused, the state estimation nodes will add a small epsilon value (1eā6) to that value. A better solution is for users to set covariances appropriately.

Ok, so let's set the covariances appropriately. I think I only have two options: calculate it or get the values from the datasheet.

So, let's look at the datasheet. I'm using the X-NUCLEO-IKS01A1 board with LSM6DS0 IMU. The datasheet is here https://www.st.com/resource/en/datash... . As you can see there's a table on page 9 that talks about noise, like 'Gyroscope RMS noise in normal/low-power mode', etc. But how can I relate these values to variances? I didn't find anything on the web apart from this answer here https://robotics.stackexchange.com/qu... where they say: "If you haven't got a background in random processes and signal analysis then you're going to have a rough time relating this back to real-world numbers, particularly if you're doing any kind of sensor fusion. Even the "big boys" in the sensor fusion game can't easily map sensor noise to system behavior without lots of simulation and head-scratching."

The other option is to calculate it. Again, I didn't find any standard approach to do it. I came up with the idea to just collect data for a while placing the IMU in a very firm way, then calculating the variance (so assuming the covariance matrix diagonal). Does it make sense an approach like this?

Moreover, do you know if there's a standard approach to set the covariance matrix? What's the complete spectrum of the alternatives?

Thanks

EDIT 26/05/19: I have temporarily postponed solving the problem with a sound approach in a favor to a trial and error one as proposed here: https://github.com/methylDragon/ros-s...

I have also found some interesting material that I still didn't have time to look at, but I would like to share with the readers hoping to be helpful:

Allan variance method (Allan DW (1966) Statistics of atomic frequency standards. Proceedings of the IEEE 54(2): 221ā230): https://github.com/GAVLab/allan_variance

My experience is that, if the sensor vendor doesn't provide the information, computing it can be black magic. Your approach seems reasonable to me. You could rotate the IMU through N full rotations in a given axis, manually integrate the velocities, and see what the final error is, and then back out the values from that.

I understand that at the end of "n" rotations, we'll end up with some error. Are you saying there's a way to back out a variance for the rotational rate from this? If so, can you explain a little more how to go about doing this?

Off the top of my head, rotating

`N`

times means you have an expected rotation of`2pi * N`

radians (ground truth, expected value). Your integrated IMU velocity data measures`M`

radians. So your error per measurement in`(M - 2pi * N) / C`

, where`C`

is the number measurements. So maybe try`[(M - 2pi * N) / C]^2`

?I was proposing to calculate the data variance just placing the IMU in a static position. With your approach, @Tom Moore, aren't you introducing an error that depends on the numerical integration, thus, depending on the frequency of measurement?

@ricber you could also normalize by the number of seconds elapsed for your N rotations, which gives you the error/sec, which is really what you wanted anyway.

If the gyro is not actively rotating, I'm not sure that you can characterize the error in it. But I'm not an expert in such things.

If you

doend up solving this, please update this question and accept the answer, or just close it.No one of the reasons to close a question applies to my case.

@ricber did you ever figure out how to convert the values in the datasheet to variance?

I have noticed page 9 in the datasheet like you mentioned and it has RMS noise rate for the gyro and RMS noise value for the acceleration.

Given that noise has a mean of zero then RMS is equivalent to standard deviation and variance is the square of the standard deviation so the variance for the acceleration values can be easily found through that.

The issue I am stuck with is the gyro variance because the datasheet provides noise density for the gyro and to calulate rms from noise density, bandwidth is needed and the datasheet is unclear as to what the value of the bandwidth for the gyro is.