Allan Variance Analysis & Noise Parameter Estimation
Characterize inertial measurement unit (IMU) performance using Allan variance analysis.
Extract noise parameters including angle random walk, bias instability, and rate random walk.
Sensor Parameters
ARW (N)
0.10
°/√hr
Bias Inst. (B)
5.0
°/hr
RRW (K)
0.50
°/hr^3/2
BI Correlation
100
s
Allan Deviation (Log-Log)
Simulated Gyro Output
Noise Component Breakdown
Allan Variance Theory
What is Allan Variance?
Allan variance (AVAR) is a statistical tool used to characterize the stability and noise characteristics
of inertial sensors. It analyzes how sensor output varies over different averaging times, revealing
distinct noise processes that affect sensor performance.
Allan Deviation Calculation
The Allan deviation σ(τ) is computed by averaging sensor data over intervals of duration τ, then
computing the variance of consecutive averaged values:
σ²(τ) = (1 / (2(M-1))) × Σ[(Ω̄ₖ₊₁(τ) - Ω̄ₖ(τ))²]
where:
- τ is the averaging time (cluster time)
- Ω̄ₖ(τ) is the average of sensor data over interval k
- M is the number of clusters
Noise Components
The Allan deviation plot reveals multiple noise processes, each with a characteristic slope on a
log-log plot:
Quantization Noise (Q): Slope -1, appears at short τ. Due to ADC resolution limits.
Angle Random Walk (N): Slope -1/2, white noise from electronics. Read at τ = 1s.
Bias Instability (B): Slope 0 (flat), minimum of curve. Long-term drift, critical for INS.
Rate Random Walk (K): Slope +1/2, increasing uncertainty over time. Due to random walk processes.
σ(τ) = √[Q²/τ² + N²/τ + B² + (K²×τ)/3]
Extracting parameters:
- N = σ(τ=1) for ARW region
- B = minimum of σ(τ) curve
- K = σ(τ) × √3/√τ for RRW region
IMU Performance Grades
Tactical Grade: ARW ~ 0.01-0.1 °/√hr, BI ~ 0.1-10 °/hr
Navigation Grade: ARW ~ 0.001-0.01 °/√hr, BI ~ 0.01-0.1 °/hr
Automotive Grade: ARW ~ 0.1-1.0 °/√hr, BI ~ 10-100 °/hr
MEMS Grade: ARW ~ 1-10 °/√hr, BI ~ 100-1000 °/hr