Handle SE(3) measurement by invariant EKF

[narutojxl]

Hello doctor @artivis,
I learned invariant EKF has some advantages, e.g. consistent and guaranteed convergence etc, over traditional EKF recently in paper [The Invariant Extended Kalman filter as a stable observer, Axel Barrau, Silvere Bonnabel]. But the measurement model must is Left-invariant observations, zt = x * d or Right-invariant observations, zt = x.inv * d. I want to loosely couple imu with a lio(lidar-inertial-odometry) system, which can give SE(3) measurement. But it seems that lio measurement can not statisfy invariant EKF measurement, right ?
From your experience, In kalmanif lib , Square Root Extended Kalman Filter (SEKF) or Unscented Kalman Filter on manifolds (UKFM), which one should i to try in terms of accuracy and stability? Thanks for your help and time a lot!

Best regards
narutojxl