The Setting of IMU Parameters in Kalman Filtering-based Information Fusion

Qiang Hu; Yanhua Zou; Shuaiyi Huo; Haibo Ge; Wei Ouyang

cs.ROAug 17, 2026

The Setting of IMU Parameters in Kalman Filtering-based Information Fusion

Authors: Qiang Hu, Yanhua Zou, Shuaiyi Huo, Haibo Ge, Wei Ouyang

Organizations: Tongji University, Shanghai, China, 200092

Abstract

The setting or tuning of specifications for the inertial measurement unit (IMU) is tricky in sensor fusion. The underneath conundrum is caused by the fact that the working condition of IMU is more complex than the stationary calibration scenario. Since the noises and biases instabilities calibrated under static condition cannot accommodate other cases, the effective tuning of IMU parameters largely hinges on the experience or profound understanding of the system. In the current work, the setting method of IMU parameters based on Allan variance calibration is delved into within the Kalman filtering framework. Specifically, the relationship between the power sepctral density and Allan variance is leveraged in formulating the process uncertainty in continuous-time filtering. Three typical IMU-based sensor fusion systems, including INS/GNSS integration, LiDAR-inertial odometry, and visual-inertial odometry are considered to show the feasibility and effectiveness of this parameter setting process.

Figures & tables

Figure 1: The variation of

\sigma_{{z_{B}}}^{2}(\tau)

with the ratio

\lambda

Figure 2: The Allan deviation plot of ADIS16465-1 (see footnote 1).

Tuning	Attitude (deg, [Roll Pitch Yaw])	Position (m, [N, U, E])
Built-in	[0.035 0.053 0.385]	[0.387 0.711 0.383]
$k_{gb}=k_{ab}=0.5$	[0.027 0.052 0.367]	[0.236 0.463 0.409]
$k_{gb}=k_{ab}=1$	[0.027 0.052 0.367]	[0.246 0.484 0.409]
$k_{gb}=k_{ab}=3$	[0.028 0.052 0.380]	[0.318 0.569 0.409]
$k_{gb}=k_{ab}=5$	[0.031 0.053 0.402]	[0.362 0.653 0.408]

Table 1: RMSEs of states for built-in and tuned parameters KF-GINS

Tuning	Seq1([Max Min Average]m)	Seq2 ([Max Min Average]m)
FASTLIO2	[2.166 1.535 1.845]	[ 0.511 0.470 0.490 ]
$k_{gb}=k_{ab}=10$	[ 1.587 1.409 1.490]	[0.600 0.542 0.572]
$k_{gb}=k_{ab}=25$	[1.617 1.360 1.458 ]	[0.689 0.575 0.644]
$k_{gb}=k_{ab}=50$	[1.691 1.456 1.553]	[0.693 0.633 0.678]
	Seq4([Max Min Average]m)	Seq7 ([Max Min Average]m)
FASTLIO2	[22.643 6.901 11.709]	[0.211 0.144 0.188]

Table 2: RMSEs of position errors for FASTLIO2 and tuned parameters

Tuning	Seq1([Max Min Average]m)	Seq2 ([Max Min Average]m)
FASTLIO2	[2.166 1.535 1.845]	[ 0.511 0.470 0.490 ]
$k_{gb}=20,k_{ab}=40$	[ 1.662 1.506 1.580 ]	[0.689 0.563 0.637]
	Seq4([Max Min Average]m)	Seq7 ([Max Min Average]m)
FASTLIO2	[22.643 6.901 11.709]	[0.211 0.144 0.188]
$k_{gb}=20,k_{ab}=40$	[ 4.264 2.528 3.261 ]	[ 0.189 0.173 0.183 ]
	Seq8([Max Min Average]m)

Table 3: RMSEs of position errors for FASTLIO2 with tuned parameters

Dataset	$k_{a}$	$k_{g}$	$k_{ab}$	$k_{gb}$	RMSE (m)
building02	OpenVINS	OpenVINS	OpenVINS	OpenVINS	1.483
	40	1	1	1	1.443
	40	90	1	1	0.874
	40	90	10	1	0.872
	40	90	10	10	0.870

Table 4: Position RMSEs of OpenVINS with tuned IMU parameters

Parameter Estimation

Parameter estimation studies how to infer unknown quantities in statistical, physical, and machine-learning models from observed data.

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Radar-Inertial Odometry (RIO) based on the Extended Kalman Filter (EKF) relies on accurate extrinsic calibration between the radar and the Inertial Measurement Unit (IMU) and is sensitive to disturbances, as large linearization errors can degrade performance or even cause divergence. To address these limitations, this letter proposes an Equivariant Filter (EqF) for RIO based on a Lie group symmetry that geometrically couples navigation states and IMU biases, extending it to incorporate radar-IMU extrinsic calibration and multi-state constraint updates. This equivariant formulation inherently preserves consistency and enhances robustness, enabling reliable state estimation even under poor or completely wrong initialization of calibration states. Real-world experiments on two different Uncrewed Aerial Vehicles (UAVs) show that the proposed EqF-RIO achieves state-of-the-art accuracy under correct extrinsic calibration and offers improved convergence under large calibration errors, where the conventional EKF-RIO fails. Evaluation code is open-sourced.

Abstract

Parameter Estimation

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