ekf_localization_node system model when fusing IMU and Odometry

edit

Hello,

I have found this great tutorial about Extended Kalman filter which made me wonder how does ekf_localization_node in ROS work (I found a similar question asked before, however it was not answered).

Firstly, Id like to understand model system of my robot (in this case, I am using Jackal robot which is originally a tank-like robot. However, with the help of teb_local_planner it was possible to limit the minimum turning radius and make it move more like a car. The purpose of ekf_localization_node in my case is just to fuse Odometry and IMU data, but how does it work? What is my system model in this case?

One more question regarding ekf_localization_node. I have read that EKF (in general) is capable of adding bias of a sensor. I havent found a parameter in the wiki regarding it. How does one smoothen sensor measurement noise then?

I have read couple of papers regarding model system, or in this case motion system (since its odometry?).

Is this what I am using? Am I looking the right way?

Clearly, I am a noobie here so any help is appreciated!

EDIT One more question. So I know my current kinematic model, but what is my system's observation model then? When I look at the code, I am focusing at this area (lines 109-144) where it builds the measurement matrices but how? What does it use to build it?

 for (size_t i = 0; i < updateSize; ++i)
{
  measurementSubset(i) = measurement.measurement_(updateIndices[i]);
  stateSubset(i) = state_(updateIndices[i]);

  for (size_t j = 0; j < updateSize; ++j)
  {
    measurementCovarianceSubset(i, j) = measurement.covariance_(updateIndices[i], updateIndices[j]);
  }

  // Handle negative (read: bad) covariances in the measurement. Rather
  // than exclude the measurement or make up a covariance, just take
  // the absolute value.
  if (measurementCovarianceSubset(i, i) < 0)
  {
    FB_DEBUG("WARNING: Negative covariance for index " << i <<
             " of measurement (value is" << measurementCovarianceSubset(i, i) <<
             "). Using absolute value...\n");

    measurementCovarianceSubset(i, i) = ::fabs(measurementCovarianceSubset(i, i));
  }

  // If the measurement variance for a given variable is very
  // near 0 (as in e-50 or so) and the variance for that
  // variable in the covariance matrix is also near zero, then
  // the Kalman gain computation will blow up. Really, no
  // measurement can be completely without error, so add a small
  // amount in that case.
  if (measurementCovarianceSubset(i, i) < 1e-9)
  {
    FB_DEBUG("WARNING: measurement had very small error covariance for index " << updateIndices[i] <<
             ". Adding some noise to maintain filter stability.\n");

    measurementCovarianceSubset(i, i) = 1e-9;
  }
}