Online IMU Intrinsic Calibration: Is It Necessary?

Yulin Yang, Patrick Geneva, Xingxing Zuo, Guoquan Huang


This paper addresses the problem of visual-inertial self-calibration while focusing on the necessity of online IMU intrinsic calibration. To this end, we perform observability analysis for visual-inertial navigation systems (VINS) with four different inertial model variants containing intrinsic parameters that encompass one commonly used IMU model for low-cost inertial sensors. The analysis theoretically confirms what is intuitively believed in the literature, that is, the IMU intrinsics are observable given fully-excited 6-axis motion. Moreover, we, for the first time, identify 6 primitive degenerate motions for IMU intrinsic calibration. Each degenerate motion profile will cause a set of intrinsic parameters to be unobservable and any combinations of these degenerate motions are still degenerate. This result holds for all four inertial model variants and has significant implications on the necessity to perform online IMU intrinsic calibration in many robotic applications. Extensive simulations and real-world experiments are performed to validate both our observability analysis and degenerate motion analysis.

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Review 3

The observability analysis for the model in [21] is valuable, since the identification of degenerate motions is important to avoid filter inconsistency and other problems. The authors describe four different IMU models in Section II.B, but the reviewer is uncertain why models 'imu3' and 'imu4' are valuable? The use of matrices containing nine parameters does not seem to be physically motivated? The model in [21] already captures known axis scale factor and axis misalignment effects (that are physical) - adding more degrees of freedom would seem only to make the problem much harder / more prone to degeneracies. Can the authors comment on this? The observability analysis is also based on linearization - a fully nonlinear analysis might provide further insight. It it not surprising that the results in Table III show that an IMU with fixed, 'bad' calibration leads to estimator inconsistency (as seen in the NEES scores). What is surprising, to the reviewer, is that inconsistency does not appear to manifest in the simulation results shown in Figures 4 and 5; although the three-sigma bounds do not decrease much for several of the parameters, all of the estimates appear to stay within their respective bounds. Typically, for unobservable states/parameters, the values wander outside of the bounds - perhaps the motion was not sufficiently 'degenerate'? Section IV.D can be removed - it is already very clear from the models presented in Section II.B (and is otherwise known) that an over-parameterization with an additional rotation makes the system unobservable/unidentifiable (because the kinematic chain then has three redundant DOFs that are arbitrary). It is not necessary to provide simulation results that show this - the space would likely be better dedicated to other aspects of the problem Minor notes: there are a few grammatical errors in the paper that should be fixed, e.g., in the first sentence of the Introduction, "visual-inertial navigation system (VINS) [10] has gained great popularity" is not correct. Also, in Section II.C, the authors use the phrase "denotes JPL quaternion" - I believe they mean that the JPL quaternion convention is uses but this should be clarified (and the sentence is not grammatically correct).