The role of the integration covariance

[goldenhazard]

Hello, I am recently navigating through imu_preintegration factor
While scrutinizing ImuFactor and CombinedImuFactor , I bumped into the presence of so-called integration_covariance or biasAccOmegaInt. The two terms appear while propagating uncertainty as follows,

ImuFactor.cpp :: integrateMeasurement

  const Matrix3& iCov = p().integrationCovariance;
  preintMeasCov_ = A * preintMeasCov_ * A.transpose();
  preintMeasCov_.noalias() += B * (aCov / dt) * B.transpose();
  preintMeasCov_.noalias() += C * (wCov / dt) * C.transpose();

  // NOTE(frank): (Gi*dt)*(C/dt)*(Gi'*dt), with Gi << Z_3x3, I_3x3, Z_3x3
  preintMeasCov_.block<3, 3>(3, 3).noalias() += iCov * dt;

CombinedImuFactor.cpp :: integrateMeasurement

  // BLOCK DIAGONAL TERMS
  D_t_t(&G_measCov_Gt) = dt * iCov;
  D_v_v(&G_measCov_Gt) = (1 / dt) * vel_H_biasAcc
      * (aCov + p().biasAccOmegaInt.block<3, 3>(0, 0))
      * (vel_H_biasAcc.transpose());
  D_R_R(&G_measCov_Gt) = (1 / dt) * theta_H_biasOmega
      * (wCov + p().biasAccOmegaInt.block<3, 3>(3, 3))
      * (theta_H_biasOmega.transpose());
  D_a_a(&G_measCov_Gt) = dt * p().biasAccCovariance;
  D_g_g(&G_measCov_Gt) = dt * p().biasOmegaCovariance;`

At first, I thought this was designed in heuristic to preclude some numerical failure while integrating measurement covariance. But found out it is the value that can be analytically derived, referring to your comment G*CovMeas*GT.

What is the role of it and how can I use it?

[varunagrawal]

I am writing this up actually. Refer to #879.

[goldenhazard]

Oh looking forward to the release of the docs. Thank you for your answer

[varunagrawal]

@goldenhazard #874 has the full documentation of the integration covariance.