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The Setting of IMU Parameters in Kalman Filtering-based Information Fusion
Qiang Hu, Yanhua Zou, Shuaiyi Huo, Haibo Ge, Wei Ouyang
TL;DR
IMU noise and bias-instability settings are difficult because static calibration may not represent broader operating conditions. The paper derives Allan-variance-based tuning within Kalman filtering, relating PSD to process uncertainty and testing it across three fusion systems. The reported experiments demonstrate feasibility, while the authors identify correlation-time uncertainty and limited online observability as practical boundaries.
Problem
IMU noise and bias-instability parameters are difficult to set because static calibration does not accommodate all sensor-fusion working conditions.
Method
The paper relates Allan-variance-calibrated specifications to power spectral density and uses that relationship to set continuous- and discrete-time process covariance matrices.
Results
The method is tested in INS/GNSS integration, LiDAR-inertial odometry, and visual-inertial odometry to demonstrate its feasibility and effectiveness.
Takeaways & Limitations
Allan-variance calibration provides the basis for tuning inertial Kalman-filter process parameters across the three evaluated fusion systems.
Takeaways & Limitations
Bias instability is less observable and difficult to estimate online for industrial-grade and consumer-grade inertial sensors, while correlation-time uncertainty affects PSD reliability.
Abstract
from arXiv · showhide
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.
1 Introduction
IMU noise and bias-instability parameters are difficult to set for Kalman filtering-based fusion because static calibration does not fully represent operating conditions. The paper proposes Allan-variance-based parameter tuning and evaluates it in three sensor-fusion systems.
- IMU noise and bias instability specify process-model uncertainty and balance propagation against measurement updates.
- Static Allan-variance calibration may not accommodate the more complex working conditions encountered during sensor fusion.
- The continuous-time PSD description of IMU uncertainty must be related to discrete-time filtering models used for covariance propagation.
- The paper revisits continuous- and discrete-time noise matrices and proposes setting process covariance from Allan-variance calibration.
- The proposed parameter-setting method is tested in INS/GNSS integration, LiDAR-inertial odometry, and visual-inertial odometry.
2 Continuous- to Discrete-Time Filtering Models
This section connects continuous-time inertial process models with discrete-time covariance propagation in error-state Kalman filtering. It establishes that discrete process-noise covariance is related to PSD through the sampling interval, motivating PSD tuning from Allan variance.
- Continuous-time model: The navigation state typically contains rotation, velocity, position, gyroscope bias, and accelerometer bias, with IMU measurements supplying angular velocity and specific force.
- Continuous-time model: Gyroscope and accelerometer noises enter the error-state model as additive process-noise inputs, while IMU biases follow first-order Gauss-Markov processes.
- Continuous-time model: Linearizing the nonlinear continuous-time system yields an error-state model with an input matrix G(t) for additive IMU process noises.
- Discretization: Continuous-time covariance propagation is discretized through the state-transition and noise-input matrices over each sampling interval.
- Discretization: The discrete-time formulation may instead discretize the dynamics first and then linearize, as adopted in FASTLIO2.
- Discretization: The discrete noise covariance matrix is related to the power spectral density by the sampling interval, making PSD tuning pivotal for fusion performance.
3 The Parameter Setting by Allan Variance
The paper relates Allan variance to power spectral density to set IMU process-noise parameters, modeling stochastic components and continuous bias processes. It also illustrates axis-specific tuning and warns that correlation-time uncertainty can substantially affect the resulting spectral-density values.
- Allan-variance model: Allan variance is computed from the power spectral density to obtain IMU noise random-walk and bias-instability specifications.These specifications are then used to set the power spectral density matrix.
- Allan-variance model: The stochastic signal is modeled as components including noise random walk, bias instability, and rate random walk, with coefficients N, B, and K.The power spectral density is represented as a series of frequency-dependent components.
- Bias-instability model: For bias instability, Allan variance is independent of τ and corresponds to a zero-slope Allan-variance plot.The continuous bias is represented using a first-order Gauss–Markov model whose driving noise has power spectral density S_B.
- Bias-instability model: When λ ≈ 1.89, F(1.89) ≈ 0.19, providing the relation used to derive the bias-process power spectral density.Here λ is the ratio τ/T_B, and σ_zB is obtained from the Allan-variance plot.
- Axis-specific tuning: For ADIS16465-1, the reported gyro and accelerometer parameters differ by axis, including T_B = 105.8s for selected X/Y axes and T_B = 529.1s for the Z gyro axis.The example reports S_Bg = 1.53e-08(°/s)^2/s for gyro X/Y and S_Bg = 3.06e-09(°/s)^2/s for gyro Z; accelerometer Z uses T_B = 42.3s and S_Ba = 1.6e-10(m/s2)^2/s.
- Axis-specific tuning: Uncertainty in each axis’s correlation time T_B affects the reliability of S_B, so specific tuning of S_B is necessary.The paper notes that the resulting power spectral density can differ substantially from the most appropriate value.
4 Experiments
Experiments evaluate Allan-variance-based IMU parameter tuning across INS/GNSS, LiDAR-inertial, and visual-inertial systems. Results show system-dependent benefits, including improved positioning accuracy in selected LiDAR sequences and a 41.3% OpenVINS position-RMSE improvement.
- INS/GNSS integration: The INS/GNSS system preferred the standard setting of calibrated parameters, while kgb = kab = 0.5 also achieved satisfactory positioning accuracy.The passage suggests suppressing bias divergence during GNSS outages may benefit positioning accuracy.
- LiDAR-inertial odometry: The LiDAR-inertial tuning approach improved positioning accuracy in Seq1, Seq4, and Seq7.The evaluation examined different kgb and kab values and reported maximum, minimum, and average RMSEs over ten runs.
- LiDAR-inertial odometry: For the most challenging Seq4, standard FASTLIO2 performed much worse than the tuned parameters.The standard discrete bias-instability covariances corresponded approximately to kgb ≈ 32.5 and kab ≈ 12.5 at 400 Hz, contrasting with the tuned parameters.
- Visual-inertial odometry: OpenVINS sequentially tuned accelerometer-noise, gyroscope-noise, and corresponding bias-instability coefficients.The search fixed previously selected coefficients while successively optimizing ka, kg, kab, and kgb.
- Visual-inertial odometry: 41.3% relative improvement reduced OpenVINS position RMSE from 1.483 m to 0.870 m with (ka, kg, kab, kgb) = (40, 90, 10, 10).This result supports incorporating measurement-noise tuning in addition to bias-instability tuning for the evaluated sequence.
5 Conclusion
The work formulates covariance process-noise matrices for continuous and discrete systems and uses Allan-variance calibration to tune inertial Kalman-filter parameters. Feasibility is demonstrated across INS/GNSS, LiDAR-inertial, and visual-inertial odometry, while more efficient tuning remains future work.
- The study formulates and analyzes covariance process-noise matrices for both discrete and continuous systems.
- The proposed tuning approach uses the relationship between power spectral density and calibrated Allan variance, focusing mainly on bias-instability parameters.The OpenVINS experiment also considers simultaneous tuning of IMU measurement-noise parameters.
- Feasibility is demonstrated in INS/GNSS integration, LiDAR-inertial odometry, and visual-inertial odometry.
- More efficient methods for tuning remain a stated direction for future work.