**A.N. Grekov ^{1,2}, A.A. Kabanov^{2}, S.**

**Yu.**

**Alekseev**

^{1}^{1}Institute of Natural and Technical Systems, RF, Sevastopol, Lenin St., 28

^{2}Sevastopol State University, RF, Sevastopol, Universitetskaya St., 33

*E-mail: oceanmhi@ya.ru *

**DOI: 10.33075/2220-5861-2021-4-134-142**

**UDC 004.852**

**Abstract:**

The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. The information obtained from the developed laboratory setup with MEMS sensors installed on a sealed platform with the ability to adjust its tilt angles and placed in an aquarium with water was used as input data for the classifier. To assess the effectiveness of the models, test curves were constructed with different values of the parameters of these models for three kernels: linear, polynomial, and radial-basis function. As a parameter, the inverse regularization parameter was used, a higher value of which corresponded to large penalties for errors, while choosing a lower value means less severity with respect to misclassification errors.

Applying the complex nonlinear architecture of the SVM-based machine learning method, which has been used in many applications, the ML algorithm is implemented to improve the determination of Euler angles (roll, pitch and yaw) from MEMS sensor data. For this, the problem of overfitting and undertraining is solved by choosing the optimal values of hyperparameters.

The proposed algorithm based on MO has demonstrated its ability to correctly classify in the presence of noise typical for MEMS sensors, where good classification results were obtained when choosing the optimal values

Further research will be directed to the application of other algorithms for the classification of ML, as well as to increase the types of input data.

**Keywords: **navigation, accelerometer, acceleration, gyroscope, magnetometer, error, autonomous underwater vehicles, machine learning, algorithm.

**To quote:**

**REFERENCES**

*Shishkin Y.E. and Grekov A.N.*Koncepcija intellektual’noj sistemy avtomatizirovannogo jekologicheskogo monitoringa na baze malogabaritnyh avtonomnyh robotov (The concept of automated environmental monitoring intellectual system based on compact autonomous robots). Sistemy kontrolja okruzhajushhej sredy, 2018, No. 4(34), pp. 63–69.*Shishkin Y.E., Grekov A.N., and Nikishin V.V.*Intelligent decision support system for detection of anomalies and unmanned surface vehicle inertial navigation correction. 2019 International Russian Automation Conference (RusAutoCon). IEEE, 2019, pp. 1–6.*Duong D.Q., Nguyen T.P., Sun J., and Luo L.*Attitude estimation by using MEMS IMU with Fuzzy Tuned Complementary Filter. Computer Science. 2016 IEEE International Conference on Electronic Information and Communication Technology (ICEICT), 2016, DOI:10.1109/ICEICT.2016.7879720*Siciliano B. and Khatib O.*(eds.): Springer Handbook of Robotics. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32552-1*Malmstrom J.*Robust Navigation with GPS/INS and Adaptive Beamforming. Swedish Defence Research Agency System Technology Division SE-172 90 STOCKHOLM Sweden, 2003.*Grekov A.N., Alekseev S.Y., and Bashkirov V.Y.*Rezul’taty laboratornyh ispytanij podvodnoj navigacionnoj sistemy dlja apparatov jekologicheskogo kontrolja (The results of laboratory tests underwater navigation system for environmental monitoring devices). Sistemy kontrolja okruzhajushhej sredy, 2020, No. 3 (41), pp. 65–74. DOI:10.33075/2220-5861-2020-3-65-74- An Introduction to Machine Learning with Python (O’Reilly) by Andreas C. Mueller and Sarah Guido. Copyright 2017 Sarah Guido and Andreas Mueller, 978-1-449-36941-5
*Klein I. and Asraf O.*StepNet – Deep Learning Approaches for Step Length Estimation. IEEE Access, 2020, Vol. 8, pp. 85706–85713.*Jamil F., Iqbal N., Ahmad S., and Kim D.H.*Toward Accurate Position Estimation Using Learning to Prediction Algorithm in Indoor Navigation. Sensors, 2020, Vol. 20, pp. 4410.*Deng J., Xu Q., Ren A., Duan Y., Zahid A., and Abbasi Q.H.*Machine Learning Driven Method for Indoor Positioning Using Inertial Measurement Unit. In Proceedings of the International Conference on UK-China Emerging Technologies (UCET), Glasgow, UK, 20-21 August 2020, pp. 1-4.*Wang H.N., Yi G.X., Wang C.H., and Guan Y.*Nonlinear Initial Alignment of Strapdown Inertial Navigation System Using CSVM. In Applied Mechanics and Materials, Trans Tech Publications: StafaZurich, Switzerland, 2012, Vol. 148-149, pp. 616–620.*Cortés S., Solin A., and Kannala J.*Deep learning based speed estimation for constraining strapdown inertial navigation on smartphones. In Proceedings of the IEEE 28th International Workshop on Machine Learning for Signal Processing, Aalborg, Denmark, 17–20 September 2018, pp. 1–6.*Chen H., Aggarwal P., Taha T.M., and Chodavarapu V.P.*Improving Inertial Sensor by Reducing Errors using Deep Learning Methodology. In Proceedings of the NAECON 2018-IEEE National Aerospace and Electronics Conference, Dayton, OH, USA, 23–26 July 2018, pp. 197–202.*Pukhov E. and Cohen H.I.*Novel Approach to Improve Performance of Inertial Navigation System Via Neural Network. In Proceedings of the 2020 IEEE/ION Position, Location and Navigation Symposium, Portland, OR, USA, 20–23 April 2020, pp. 746–754.*Raschka S. and Mirjalili V.*Python Machine Learning, Third Edit. Packt, 2019, 725 p. ISBN: 978-1-78995-575-0.*Wolpert D.H*. The lack of a priori distinctions between learning algorithms. Neural computation, 1996, Vol. 8, No. 7, pp. 1341–1390.- Scikit-learn: Machine Learning in Python, Pedregosa et al., JMLR 12, 2011, pp. 2825–2830.
*Witten Ian H., Frank Eibe, Hall Mark A.,and Pal Christopher J.*Data Mining: Practical Machine Learning Tools and Techniques. Amsterdam; Paris: Elsevier. 2017. https://doi.org/10.1016/C2015-0-02071-8*Brunton S.L. and Kutz J.N.*Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2019.*Bishop C.M.*Pattern recognition. Machine learning, 2006, Vol. 128, No. 9.*Smola A.J. and Schölkopf B.*A tutorial on support vector regression. Statistics and computing, 2004, Vol. 14, No. 3, pp. 199–222.*Vapnik V.*The nature of statistical learning theory. Springer science & business media, 2013.- Burges C.J.C. A tutorial on support vector machines for pattern recognition. Data mining and knowledge discovery, 1998, Vol. 2, No. 2, pp. 121–167.
*Boser Bernhard E., Guyon Isabelle M., and Vapnik Vladimir N.*A training algorithm for optimal margin classifiers. In Proceedings of the Fifth Annual Workshop on Computational Learning Theory, 1992, ACM, pp. 144–152.*Cortes C. and Vapnik V.*Support-vector networks. Machine Learning, 1995, Vol. 20 (3), pp. 273–297.*Albon C.*Machine learning with python cookbook: Practical solutions from preprocessing to deep learning. O’Reilly Media, Inc., 2018.