Random Error Reduction Algorithms for MEMS Inertial Sensor Accuracy Improvement—A Review
Abstract
:1. Introduction
2. Materials and Methods
3. Results
3.1. Simple Filter Algorithms
3.1.1. Fading Memory Filter (FMF)
3.1.2. Morphological Filter (MF)
3.1.3. Moving Average Filter (MAF)
3.1.4. Variable Bandwidth Filter (VBF)
3.2. Kalman-Based Algorithms
3.2.1. Kalman Filter (KF)
3.2.2. Extended Kalman Filter (EKF)
3.2.3. Incremental Kalman Filter (IKF)
3.2.4. Strong Tracking Kalman Filter (STKF)
3.2.5. Discrete Time Kalman Filter (DTKF)
3.3. Wavelet-Based Algorithms
3.3.1. Wavelet Threshold (WT)
3.3.2. Improved Wavelet Threshold (IWT)
3.3.3. Adaptive Stationary Wavelet Threshold (ASWT)
3.3.4. EMD-Based Wavelet Threshold (EMD-WT)
3.4. Sensor Fusion Algorithms
3.4.1. Virtual Gyroscope (VG)
3.4.2. Heterogeneous Fusion (HF)
3.4.3. Combination Sensors (CS)
3.5. Machine Learning
3.5.1. Back Propagation Neural Network (BP)
3.5.2. Radial Basis Function Neural Network (RBF)
3.5.3. Support Vector Machine (SVM)
3.5.4. Relevance Vector Machine (RVM)
3.6. Deep Learning
3.6.1. Wiener-Type Recurrent Neural Network (WRNN)
3.6.2. Neural Architecture Search Recurrent Neural Network (NAS-RNN)
3.6.3. Long Short Term Memory (LSTM)
3.6.4. Gate Recurrent Unit (GRU)
3.6.5. Simple Recurrent Unit (SRU)
3.7. Adaptive-Based Algorithms
3.7.1. Recursive Least Squares (RLS)
3.7.2. Least Mean Squares (LMS)
3.7.3. Adaptive Sliding Mode Controller (ASMC)
3.7.4. Adaptive Kalman Filter (AKF)
3.7.5. Adaptive Filtering Based on Dynamic Variance Model (AF-DVM)
3.8. Comparative Analysis of Existing Algorithms
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Algorithm | # of Papers | Task Analysis | Real-Time and Online/Offline | Working Environment | Remark |
---|---|---|---|---|---|
FMF | 1 | Raw data noise reduction [33] | Online | AMD-Quadcore FX-8800pCPU platform | The results show that the proposed filter can effectively reduce the sensor’s noise. |
MF | 2 | Noise suppression in the MEMS gyroscope [36]; MEMS gyroscope output signal denoising [37] | Real time | MATLAB | The simulation is better achieved in the static state and dynamic state; the principle is simple and has much less calculation in real time. |
MAF | 1 | Suppress the signal’s unstable periods [38] | Collect data online and process the data offline | NA | Single and multiple rate dynamic experiment analysis, and synthetic signal denoising analysis. |
VBF | 1 | Reduce the low frequency vibration and sensor noise [39] | Real time | MATLAB | Adaptive bandwidth filter provides smooth data in harsh environments and eliminates the low frequency vibration effects (<10 Hz). |
KF | 3 | Random drift compensation [41]; Temperature drift compensation [42,44] | Offline | MATLAB | The proposed method can effectively reduce random drift and temperature drift not only on the conditions but also at constant rates. |
EKF | 1 | Damping and stiffness imperfections compensation [43] | Offline | MATLAB and DSP | Numeric simulation and experiment EKF show consistent results. |
IKF | 1 | To reduce large errors and improve the convergence of the KF [44] | Offline | MATLAB | Comparison of KF/AKF/AIKF |
STKF | 2 | To compensate the temperature drift [42]; Error compensation and accuracy improvement [45] | Real time | DSP | Static and dynamic experiments; the algorithm is easily implemented; the measurement noise of the MEMS gyroscope in static and dynamic states can be reduced by 93.6% and 63.9%, respectively. |
DTKF | 1 | Bias drift and noise reduction [46] | Real time | DSP | The greatest feature is the direct modeling for true angular rate to obtain an optimal estimate. |
WT | 2 | Large noise reduction for low-precision MEMS gyroscope [47,50] | Real time | DSP | A large number of the constant and dynamic rates experiments were tested. |
IWT | 2 | Error compensation [48]; High frequency noise reduction and random drift suppression [49] | Offline | NA | Experimental results indicate that the improved wavelet threshold is effective. |
ASWT | 1 | High frequency noise restraint [50] | Real time | DSP | Experimental results show that the adaptive stationary wavelet threshold is better than traditional wavelet threshold denoising methods. |
EMD-WT | 1 | To improve the performance of the high-G MEMS accelerometer [51] | Offline | NA | Experiment and verification in the Hopkinson Bar calibration system, and it decreases the noise of the original signal by 96%. |
VG | 2 | To reduce the noise and improve the accuracy of the individual gyroscope [52,53] | Online | MATLAB/Simulink | Dynamic simulations and experiments with a six-gyroscope array were carried out. |
HF | 1 | Real time calibration and long-term drift compensation [54] | Real time/Online | MATLAB | Intelligent Real-Time MEMS Sensor Fusion and Calibration. |
CS | 1 | To eliminate the drift and offset [55] | Real time | DSP and FRGA | Various simulation and experimental results are presented demonstrating its effectiveness. |
BP | 2 | Null drift, temperature compensation [57]; Compensation of temperature and acceleration effects [58] | Real time | NA | Bias instability shows 57% improvement; Temperature test from −40 to −80 °C; BP NN yields accurate temperature compensation. |
RBF | 3 | Random error compensating [48]; Temperature compensation [60,63] | Real time [60] Offline [48,63] | NA | Good generalization ability, higher precision prediction, and compensation ability; A new fusion algorithm is proposed and proved in temperature test equipment. |
SVM | 3 | Modeling and compensation [63,65]; Error modeling [64] | Offline | MATLAB/LibSVM | SVM has high precision and good generalization ability; thus, experimental results proved that the SVM approach reduced the noise standard deviation by 10–35% for gyroscopes and 61–76% for accelerometers. |
RVM | 1 | Random drift compensation [67] | Offline | NA | Static and dynamic experiments were conducted. |
WRNN | 2 | Random drift modeling and compensation [68,69] | Real time | MCU | The effectiveness of the proposed WRNN-based random drift modeling and compensation scheme for the MEMS-based gyroscopes was successfully validated. |
NAS-RNN | 1 | Noise suppressing [71] | Offline | NA | The NAS-RNN was effective for MEMS gyroscope noise suppressing. |
GRU | 1 | Noise suppressing [74] | Offline | Python | The mixed deep recurrent neural networks outperformed GRU-GRU and LSTM-LSTM. |
SRU | 1 | Signal denoising [77] | Offline | Python | The results surely demonstrated the effectiveness of the employed SRU in this application. |
RLS | 2 | Random noise reduction [78]; Online dynamic estimation of inertial sensor error model [79]; | Online | STM32 microcontroller [78]; DSP [79] | The results show that RLS can effectively reduce the prediction error compared with non-recursive estimation. |
LMS | 1 | Signal error processing [80] | Online | DSP Builder/FPGA | The results show that it is reliable and has high precision. |
ASMC | 2 | Estimate the angular velocity and the damping and stiffness coefficients [81,82] | Offline | MATLAB/Simulink | It has satisfactory performance and robustness in the presence of model uncertainty and external disturbance. |
AKF | 4 | Noise reduction [78]; Static and dynamic noise reduction [83]; The drift error and random noise restraint [84]; Navigation precision improvement [85] | Real time [78,84,85] | STM32 microcontroller [78]; DSP [84,85] | It is shown that AKF has a better performance rather than conventional KF. |
AF-DVM | 1 | Dynamic random error compensation [86] | Online | DSP | The proposed method was verified through a constant angular rate and continuous variable angular rate turntable experiments. |
Group | Algorithms | Structure Characteristics | Advantages | Disadvantages | Strength in Application Domain |
---|---|---|---|---|---|
Simple filter algorithms | FMF | The FMF structure is very similar to KF | Very low computational overhead and KF divergence suppression | The optimal filter gain is not easy to find | To reduce the sensor’s noise and track moving objects in radar applications and medical devices |
MF | Four basic operators as follows: dilation, erosion, opening, and closing | It is simple, fast, and real-time | MF generally suffers from different output biases and the scale selection problems of structural elements | In order to filter out the noise of the MEMS gyroscope in vehicle mobile satellite communication | |
MAF | MAF is the first choice of time domain signal, and is the most common in DSP | Fast convergence rate and small steady-state errors | MAF shows certain lag | It is applicable for signal denoising under arbitrary motion state conditions | |
VBF | VBF processes data by sinusoidal data estimation | It can be implemented real-time | As the bandwidth decreases, the time delay increases | Real flight conditions | |
KF | Filter computation loop and gain computation loop | Small amount of calculation | It can only fit linear Gaussian systems. | Sensor data fusion | |
EKF | EKF is a kind of pseudo nonlinear KF | Small and fast calculations | Less effective for highly nonlinear problems and poor robustness | Unmanned aerial vehicles | |
Kalman-based algorithms | IKF | IKF also is a nonlinear KF | Better estimation accuracy and more robust to the unstable system | It has a larger calculation amount, but still can satisfy the real-time requirement. | In the airborne strapdown inertial navigation system application |
STKF | Nonlinear adaptive filter | Strong robustness | The sequence of residuals should be orthogonal at all times | With potential to be used in adaptive control of flexible robot | |
DTKF | A type of optimal KF | Direct modeling for angular rate signal | The filtered rate signal has an auto-correlation | Aviation and aerospace navigation | |
WT | Hard threshold and soft threshold | No need to establish accurate error model; Fast computation, and broad adaptability | The Pseudo-Gibbs will appear at the discontinuity of the signal | Primarily applicable in the case of white noise in the signal processing | |
Wavelet-based algorithms | IWT | In addition to soft and hard threshold function, a new threshold function is added | Better adaptability | It is very difficult to find an ideal threshold | Indoor inertial navigation systems |
ASWT | Redundancy, translation-invariance, and more approximate estimation | Time invariance; simple and more smoothing | The computation load will increase | Application in the case of dynamic signal with high frequency noise restraining | |
EMD-WT | Combination of two algorithms | Suitable for nonlinear and non-stationary signals; Faster, more reliable, and efficient than single methods | It is quite difficult to remove noise in real time | Monitoring natural disasters and various navigation control | |
Sensor fusion algorithms | VG | Gyroscope array | Accuracy of virtual gyro is higher than single gyro | It still needs KF filter | Navigation and guidance |
HF | Fusion of gyroscopes, accelerometers, and magnetometers | Faster dynamic response; Converges faster and take less computational time | Higher CPU load | Attitude and heading reference systems | |
CS | Combines rotary encoders and gyroscopes; Low computational demands and negligible parameter tuning effort | A viable alternative to high-resolution encoders; | It still needs to further restrain the disturbance | Servo motors or robot joints | |
BP | Input layer, hidden layer, and output layer | Nonlinear function relationship model | Time-consuming and its denoising accuracy depends on personal experience | To effectively improve the accuracy and practicability of flight attitude angle calculation | |
Machine Learning | RBF | Input layer, hidden layer, and output layer | The training speed and convergence speed of the RBF are faster than BP | Need to combine with other algorithms for high accuracy | High-G MEMS accelerometer temperature compensation; Application in navigation, defense, and impact measurement. |
SVM | It is a two-classification algorithm that classifies samples by constructing a hyperplane function | Better generalization ability for small samples | It is difficult to learn and predict large samples | North-seeking, navigation, pedestrian step estimation, pattern recognition, and many other fields | |
RVM | It is a sparse probability model | The generalization ability of RVM is better than SVM | The training time is a little long | Guidance, navigation, and control systems for space vehicles | |
WRNN | A dynamic linear model cascaded by a static nonlinear model | The algorithm is integrated into the real application | It still needs to integrate a lowpass filter | Handwriting Trajectory Reconstruction | |
Deep Learning | NAS-RNN | Neural networks with reinforcement learning | The NAS-RNN superiority compared with the LSTM-RNN | More heavy computation load | Various vehicles, carriers, and smart devices |
LSTM | A type of RNN | LSTM performs better in longer sequences | More parameters and more difficult training | Image processing, nature language processing, and sequential signal processing | |
GRU | A type of RNN | GRU is much easier to train than LSTM and can greatly improve training efficiency | GRU parameters are fewer and therefore, easier to converge, but LSTM expression performance is better for large datasets | Image processing, nature language processing, and sequential signal processing | |
SRU | A new type of RNN based on LSTM and GRU | The SRU has faster training speed than LSTM and GRU | It still needs further research | Image processing, nature language processing and sequential signal processing | |
RLS | A type of adaptive filter | Convergence speed is very fast | Different inertial sensors need different forgetting factor | Automobile industry, flight vehicle, and robotics | |
LMS | A widely used type of adaptive filter | Simple principle, few parameters, fast convergence speed and easy implementation | Need to combine other algorithms for good performance | It can be integrated into the FPGA for various real applications. | |
Adaptive-based algorithms | ASMC | Sliding mode controller | More high robustness | The simulations are only performed | Environment variations and external disturbances from the real system |
AKF | NA | AKF performs better than traditional KF | NA | Land vehicle applications | |
AF-DVM | Algorithm combination | Adaptive dynamic random error compensation is validated | NA | Inertial measurement and inertial stabilization |
Group | Main Tasks | Advantages | Disadvantages | Number of Studies |
---|---|---|---|---|
Simple filter algorithms |
|
|
| 5 |
Kalman-based algorithms |
|
|
| 8 |
Wavelet-based algorithms |
|
|
| 6 |
Sensor fusion algorithms |
|
|
| 4 |
Machine Learning |
|
|
| 9 |
Deep Learning |
|
|
| 7 |
Adaptive-based algorithms |
|
|
| 10 |
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Han, S.; Meng, Z.; Omisore, O.; Akinyemi, T.; Yan, Y. Random Error Reduction Algorithms for MEMS Inertial Sensor Accuracy Improvement—A Review. Micromachines 2020, 11, 1021. https://doi.org/10.3390/mi11111021
Han S, Meng Z, Omisore O, Akinyemi T, Yan Y. Random Error Reduction Algorithms for MEMS Inertial Sensor Accuracy Improvement—A Review. Micromachines. 2020; 11(11):1021. https://doi.org/10.3390/mi11111021
Chicago/Turabian StyleHan, Shipeng, Zhen Meng, Olatunji Omisore, Toluwanimi Akinyemi, and Yuepeng Yan. 2020. "Random Error Reduction Algorithms for MEMS Inertial Sensor Accuracy Improvement—A Review" Micromachines 11, no. 11: 1021. https://doi.org/10.3390/mi11111021