Noise Reduction of MEMS Gyroscope Based on Direct Modeling for an Angular Rate Signal
Abstract
:1. Introduction
2. Modeling of Stochastic Error for MEMS Gyroscope
Noise Terms | Allan Variance | Slope | Coefficient | Unit |
---|---|---|---|---|
ARW | N2/τ | −1/2 | N = σ(1) | °/h0.5 |
Bias instability | (0.6643B)2 | 0 | B = σ(f0)/0.6643 | °/h |
RRW | K2τ/3 | +1/2 | K = σ(3) | °/h1.5 |
3. Optimal KF Algorithm for Gyroscope Noise Reduction
3.1. KF State and Measurement Equation
3.2. Analysis of KF Observability
3.3. Discrete-Time KF for True Rate Signal Estimate
- Step 1: Form the covariance matrices Q and R by the ARW and RRW noise variance and variance qω;
- Step 2: Analyze the steady-state filtering gain Ks off-line by using of Equations (9)–(11), ;
- Step 3: Perform the eigenvalue decomposition of matrix m, ;
- Step 4: Extract the eigenvectors matrix S and eigenvalues λ1 and λ2;
- Step 5: Calculate the matrices A and B,
- Step 6: Perform the discrete-time KF equation,
3.4. Analysis of KF Bandwidth
4. Experiment and Discussion
4.1. Static Drift Test Result
Terms | Noise (°/s/Hz0.5) | ARW (°/h0.5) | Bias drift (°/h) |
---|---|---|---|
Original gyro | 0.150 | 4.8668 | 44.4129 |
BW = 10 Hz | 0.013 | 0.4006 | 4.1344 |
BW = 20 Hz | 0.040 | 1.2037 | 12.1383 |
BW = 30 Hz | 0.061 | 1.8879 | 19.7388 |
4.2. Constant Rate Test Result
Rate (°/s) | Mean of Estimated Error (°/s) | STD of Estimated Error (°/s) | ||
---|---|---|---|---|
Original Gyro | After Filtering | Original Gyro | After Filtering | |
10 | 0.0413 | −0.0421 | 1.9378 | 0.1120 |
30 | 0.0197 | −0.0209 | 2.0195 | 0.1075 |
50 | 0.0582 | −0.0607 | 1.9751 | 0.1069 |
80 | 0.0776 | −0.0812 | 2.6189 | 0.1407 |
4.3. Swing Rate Test Result
Frequency f (Hz) | Amplitude (°/s) | STD Error (°/s) | ||
---|---|---|---|---|
Original Gyro | After Filtering | Original Gyro | After Filtering | |
0.1 | 22.4481 | 20.0973 | 1.6749 | 0.3836 |
0.3 | 22.6760 | 20.1926 | 1.6242 | 0.5510 |
0.5 | 23.1104 | 20.7806 | 1.7234 | 0.6866 |
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
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Xue, L.; Jiang, C.; Wang, L.; Liu, J.; Yuan, W. Noise Reduction of MEMS Gyroscope Based on Direct Modeling for an Angular Rate Signal. Micromachines 2015, 6, 266-280. https://doi.org/10.3390/mi6020266
Xue L, Jiang C, Wang L, Liu J, Yuan W. Noise Reduction of MEMS Gyroscope Based on Direct Modeling for an Angular Rate Signal. Micromachines. 2015; 6(2):266-280. https://doi.org/10.3390/mi6020266
Chicago/Turabian StyleXue, Liang, Chengyu Jiang, Lixin Wang, Jieyu Liu, and Weizheng Yuan. 2015. "Noise Reduction of MEMS Gyroscope Based on Direct Modeling for an Angular Rate Signal" Micromachines 6, no. 2: 266-280. https://doi.org/10.3390/mi6020266