Adaptive linear estimation of dynamic measurement error

The problem of the dynamic measurement error estimation and compensation is considered. This type of error is determined by two components. The first one is due to dynamic properties (inertia) of a sensor. The second one is due to the presence of an additive noise at the sensor output. An approach to estimate and reduce the dynamic measurement error based on the signals adaptive linear prediction or adaptive line enhancement principle is proposed. The approach consists in generating a dynamic measurement error estimation signal based on comparing a delayed copy of the recovered signal with the recovered signal passed through an adaptive non-recursive filter with a linear phase characteristic. The structure of a measuring system with an adaptive linear estimator of the dynamic measurement error based on this approach has been developed. A computer simulation of the proposed measuring system for the second-order sensor is carried out. Optimal (in the sense of the mean squared deviation of the dynamic error) orders of the restoring adaptive filter are obtained in the presence of additive harmonic noise of variable frequency at the sensor output. The properties of the proposed measuring system with the dynamic measurement error estimator adaptive to the noise parameter are demonstrated. The application field of the results obtained is the measurement data processing of fast-changing processes (including real-time mode), when the component of the dynamic measurement error, caused by dynamic properties (inertia) of the sensor, as well as additive noises at its output, is dominant. The solution of such a problem is relevant, for example, when processing the results of ground tests of space technology.

1. Volosnikov A. S., Measurement Techniques, 2023, vol. 65, no. 10, pp. 720–728. https://doi.org/10.1007/s11018-023-02144-6

2. Elster C., Link A., Bruns, T., Measurement Science and Technology, 2007, vol. 18(12), pp. 3682–3687. https://doi.org/10.1088/0957-0233/18/12/002

3. Link A., Elster C., Measurement Science and Technology, 2009, vol. 20(5), 055104. https://doi.org/10.1088/0957-0233/20/5/055104

4. Eichstädt S., Link A., Elster C., Sensors, 2010, vol. 10(8), pp. 7621–7631. https://doi.org/10.3390/s100807621

5. Eichstädt S., Elster C., Smith I. M., Esward T. J., Journal of Sensors and Sensor Systems, 2017, vol. 6(1), pp. 97–105. https://doi.org/10.5194/jsss-6-97-2017

6. Eichstädt S., Elster C., Esward T. J., Hessling J. P., Metrologia, 2010, vol. 47(5), pp. 522–533. https://doi.org/10.1088/0026-1394/47/5/003

7. Eichstädt S., Link A., Harris P., Elster C., Metrologia, 2012, vol. 49(3), pp. 401–410. https://doi.org/10.1088/0026-1394/49/3/401

8. Esward T. J., tm – Technisches Messen, 2016, vol. 83(10), pp. 557–564. https://doi.org/10.1515/teme-2015-0128

9. Fujii Y., Maru K., Experimental Techniques, 2011, vol. 35(3), pp. 5–20. https://doi.org/10.1111/j.1747-1567.2009.00594.x

10. Hessling J. P., Measurement Science and Technology, 2006, vol. 17(10), pp. 2740–2750. https://doi.org/10.1088/0957-0233/17/10/028

11. Markovsky I., IEEE Signal Processing Letters, 2015, vol. 22(8), pp. 1094–1097. https://doi.org/10.1109/LSP.2014.2388369

12. Monti A., Ponci F., IEEE Transactions on Instrumentation and Measurement, 2010, vol. 59(11), pp. 2825–2833. https://doi.org/10.1109/TIM.2010.2060913

13. Shestakov A. L., IEEE Transactions on Instrumentation and Measurement, 1996, vol. 45(1), pp. 250–255. https://doi.org/10.1109/19.481342

14. Shestakov A. L., Dynamic Measurements Based on Automatic Control Theory Approach, in Advanced Mathematical and Computational Tools in Metrology and Testing X, 2015, pp. 66–77. https://doi.org/10.1142/9789814678629_0008

15. Shestakov A. L., Metody teorii avtomaticheskogo upravlenija v dinamicheskih izmereniyah, a monograph, Chelyabinsk, SUSU Publ., 2013, 257 p. (In Russ.)

16. Granovskiy V. A., Dinamicheskie izmereniya: Osnovy metrologicheskogo obespecheniya, Leningrad, Energoatomizdat Publ., 1984. 224 p. (In Russ.)

17. Roshahliza M. Ramli, Ali O. Abid Noor, Salina Abdul Samad, A Review of Adaptive Line Enhancers for Noise Cancellation, Australian Journal of Basic and Applied Sciences, 2012, vol. 6(6), pp. 337–352.

18. Hayes M. H., Adaptive filtering, in Statistical digital signal processing and modeling, John Wiley & Sons, 1996, pp. 493–570.

19. Diniz P., Adaptive Filtering: Algorithms and Practical Implementation (fourth edition), Springer New York, 2008, 652 p.