Random Noise Suppression Method for Inertial Sensors Based on Complexing an AR Model and Adaptive SRUKF Kalman Filter under the PINS Alignment on a Stationary Platform

Introduction. In the gyrocompassing mode, the initial heading angle of a platformless inertial navigation system (PINS) is determined based on the data obtained from accelerometers and gyroscopes that measure the projections of the gravitational acceleration vector and the Earth’s angular velocity vector on the axes of the body coordinates system in the PINS initial stationary mode. Due to unavoidable circumstances, such as bias instability and random noise in the accelerometer and gyroscope signals, much time is required to obtain the sufficient amount of sensor data for achieving the necessary accuracy of useful measurement values by the averaging method. In this context, in order to reduce the time of the gyrocompassing mode, data processing methods should be used to eliminate the bias instability and random noise in the signals received from PINS inertial sensors.
Aim. To develop a method for suppressing random noise and reducing bias instability in the signals of inertial sensors, thereby reducing the time of the gyrocompassing mode of PINS and providing for the required accuracy of its initial heading angle determination.
Materials and methods. An autoregressive (AR) model was used to simulate random noise in the measured sensor signals followed by its filtering using a Sage-window square-root unscented Kalman filter (SW-SRUKF).
Results. A mathematical model describing random noise in the PINS inertial sensors in the stationary mode was derived. A methodology for suppressing random noise was proposed. The effectiveness of the proposed method was tested on actual data, with the results presented in the form of figures and tables.
Conclusion. A method for eliminating the bias instability and random noise of PINS accelerometers and gyroscopes was proposed based on AR model and SW-SRUKF. The accuracy and effectiveness of the proposed method was confirmed by processing actual inertial sensor data. The results obtained are significant for reducing the initial alignment time of a PINS in the gyrocompassing mode.

1. Boronakhin A. M., Lukyanov D. P., Filatov Yu. V. Opticheskie i mikromekhanicheskie inertsial'nye pribory [Optical and Micromechanical Inertial Devices]. SPb, Ehlmor, 2008, 400 p. (In Russ.)

2. Matveev V. V., Raspopov V. Ya. Osnovy postroeniya besplatformennykh inertsial'nykh navigatsionnykh system [Basics of Building Strapdown Inertial Navigation Systems]. SPb, RNTS RF OAO «Kontsern «TSNII «EhlektropriboR», 2009, 208 p. (In Russ.)

3. Han Sh., Meng Zh., Omisore O., Akinyemi T., Yan Yu. Random Error Reduction Algorithms for MEMS Inertial Sensor Accu-racy Improvement. A Review. Micromachines. 2020, vol. 11, iss. 11, p. 1021. doi:10.3390/mi11111021

4. Huang L. Auto Regressive Moving Average (ARMA) Modeling Method for Gyro Random Noise Using a Robust Kalman Filter. Sensors. 2015, vol. 15, iss. 10, pp. 25277–25286. doi:10.3390/s151025277

5. Narasimhappa M., Mahindrakar A. D., Guizilini V. C., Terra M. H., Sabat S. L. An improved Sage Husa Adaptive Robust Kalman Flter for DeNoising the MEMS IMU Drift Signal. Proc. of the IEEE Conf. on Indian Control Conf. (ICC). Kanpur, India, 04–06 January 2018. IEEE, 2018, pp. 229–234. doi:10.1109/INDIANCC.2018.8307983

6. Duan D. Study on Modeling and Filtering of Random Drift on FOG // Proc. of SPIE. 2011, vol. 8191, p. 81912G. doi:10.1117/12.90323

7. Narasimhappa M., Nayak J., Terra M. H., Sabat S. L. ARMA Model Based Adaptive Unscented Fading Kalman Filter for Reducing Drift of Fiber Optic Gyroscope. Sensor and Actuator A. 2016, vol. 251, pp. 42–51. doi:10.1016/j.sna.2016.09.036

8. Sage, A.P.; Husa, W. Adaptive Filtering with Unknown Prior Statistics. Proc. of the Joint Automatic Control Conf., Washington, DC, USA, 22–24 June 1969, pp. 760–769.

9. Sun J., Xu X., Liu Y., Zhang T., Li Y. FOG Random Drift Signal Denoising Based on the Improved AR Model and Modified Sage-Husa Adaptive Kalman Filter. Sensors. 2016, vol. 16, no. 7, pp. 1–19. doi:10.3390/s16071073

10. Julier S. J., Uhlmann J. K. Unscented Filtering and Nonlinear Estimation. Proc. of the IEEE. 2004, vol. 92, no. 3, pp. 401–422. doi:10.1109/JPROC.2003.823141

11. Viswanathan M. Wireless Com-munication Systems in Matlab, 2nd Ed. Independently published, 2020, 382 p.

12. Wang P., Li G., Gao Ya. A Compensation Method for Gyroscope Random Drift Based on Unscented Kalman Filter and Support Vector Regression Optimized by Adaptive Beetle Antennae Search Algorithm. Applied Intelligence. 2022, vol. 53, pp. 4350–4365. doi:10.1007/s10489-022-03734-7

13. Yang Yu, Gao W. Comparison of Adaptive Factors in Kalman Filters on Navigation Re-sults. The J. of Navigation. 2005, vol. 58, iss. 3, pp. 471–478. doi:10.1017/S0373463305003292

14. Yang Y., Xu T. An Adaptive Kalman Filter Based on Sage Windowing Weights and Variance Components. The J. of Navigation. 2003, vol. 56, iss. 2, pp. 231–240. doi:10.1017/S0373463303002248

15. Gao Sh., Wei W., Zhong Yo., Subic A. Sage Windowing and Random Weighting Adaptive Filtering Method for Kinematic Model Error. IEEE Transactions on Aerospace and Electronic Systems. 2015, vol. 51, no. 2, pp. 1488–1500. doi:10.1109/TAES.2015.130656

16. Gao Sh., Hu G., Zhong Yo. Windowing and Random Weighting-Based Adaptive Un-Scented Kalman Filter. Int. J. Adapt. Control Signal Process. 2015, vol. 29, iss. 2, pp. 201–223. doi:10.1002/acs.2467

17. ARIMA models for time series forecasting. Available at: https://people.duke.edu/~rnau/411arim3.htm (accessed 10.04.2022)

18. Merwe R. Van der, Wan E. A. The Square-Root Unscented Kalman Filter for State and ParameterEstimation. 2001 IEEE Intern. Conf. on Acoustics, Speech, and Signal Processing. Proc. (Cat. No.01CH37221). Salt Lake City, USA, 07–11 May 2001. IEEE, 2001, vol. 6, pp. 3461–3464 doi:10.1109/ICASSP.2001.940586

19. Qiao Sh., Fan Yu., Wang G., Mu D., He Zh. Radar Target Tracking for Unmanned Surface Vehicle Based on Square Root Sage–Husa Adaptive Robust Kalman Filter. Sensors. 2022, vol. 22, iss. 8, p. 2924. doi:10.3390/s22082924

20. Moving Average Proofs. Available at: https://real-statistics.com/time-series-analysis/movingaverage-processes/moving-average-proofs/ (accessed 16.03.2022)

21. Chang L., Hu B., Li A., Qin F. Unscented Kalman Filter: Limitation and Combination. IET Signal Process. 2013, vol. 7, iss. 3, pp. 167–176. doi:10.1049/iet-spr.2012.0330

22. Datasheet SINS-2M. Electrooptika. Available at: http://www.electrooptika.ru/index.php/bins/binsmezhvidovogo-primeneniya (accessed 15.02.2022)