Robust identification of non-stationary objects with nongaussian interference
DOI:
https://doi.org/10.15587/1729-4061.2019.181256Keywords:
Markov model, gradient algorithm, mixing parameter, recurrent procedure, asymptotic estimate, identification accuracyAbstract
The problem of identification of non-stationary parameters of a linear object, which can be described by the first-order Markov model, with non-Gaussian interference is considered. The identification algorithm is a gradient minimization procedure of the combined functional. The combined functional, in turn, consists of quadratic and modular functionals, the weights of which are set using the mixing parameter. Such a combination of functionals makes it possible to obtain estimates with robust properties. The identification algorithm does not require knowledge of the degree of non-stationarity of the investigated object. It is the simplest, since information about only one measurement cycle (step) is used in model construction. The use of the Markov model is quite effective, as it allows obtaining analytical estimates of the properties of the algorithm.
Conditions of mean and mean-square convergence of the gradient algorithm in the estimation of non-stationary parameters and with non-Gaussian measurement interference are determined.
The obtained estimates are quite general and depend both on the degree of object non-stationarity and statistical characteristics of useful signals and interference. In addition, expressions are determined for the asymptotic values of the parameter estimation error and asymptotic accuracy of identification. Since these expressions contain a number of unknown parameters (values of signal and interference dispersion, dispersion characterizing non-stationarity), estimates of these parameters should be used for their practical application. For this purpose, any recurrent procedure for evaluating these unknown parameters should be applied and the resulting estimates should be used to refine the parameters included in the algorithms. In addition, the asymptotic values of the estimation error and identification accuracy depend on the choice of mixing parameterReferences
- Kaczmarz, S. (1993). Approximate solution of systems of linear equations†. International Journal of Control, 57 (6), 1269–1271. doi: https://doi.org/10.1080/00207179308934446
- Raybman, N. S., Chadeev, V. M. (1966). Adaptivnye modeli v sistemah upravleniya. Moscow: Sovetskoe radio, 156.
- Aved'yan, E. D. (1978). Modified Kaczmarz algorithms for estimating the parameters of linear plants. Avtomatika i telemehanika, 5, 64–72.
- Liberol', B. D., Rudenko, O. G., Timofeev, V. A. (1995). Modifitsirovanniy algoritm Kachmazha dlya otsenivaniya parametrov nestatsionarnyh obektov. Problemy upravleniya i informatiki, 3, 81–89.
- Liberol', B. D., Rudenko, O. G., Bessonov, A. A. (2018). Issledovanie shodimosti odnoshagovyh adaptivnyh algoritmov identifikatsii. Problemy upravleniya i informatiki, 5, 19–32.
- Strohmer, T., Vershynin, R. (2009). Comments on the Randomized Kaczmarz Method. Journal of Fourier Analysis and Applications, 15 (4), 437–440. doi: https://doi.org/10.1007/s00041-009-9082-0
- Rudenko, O., Bezsonov, O., Romanyk, O., Lebediev, V. (2019). Analysis of convergence of adaptive singlestep algorithms for the identification of nonstationary objects. Eastern-European Journal of Enterprise Technologies, 1 (4 (97)), 6–14. doi: https://doi.org/10.15587/1729-4061.2019.157288
- Rudenko, O. G., Bezsonov, O. O. (2019). The Regularized Adaline Learning Algorithm for the Problem of Evaluation of Non-Stationary Parameters. Control Systems and Computers, 1, 22–30. doi: https://doi.org/10.15407/usim.2019.01.022
- Shao, T., Zheng, Y. R., Benesty, J. (2010). An Affine Projection Sign Algorithm Robust Against Impulsive Interferences. IEEE Signal Processing Letters, 17 (4), 327–330. doi: https://doi.org/10.1109/lsp.2010.2040203
- Shin, J., Yoo, J., Park, P. (2012). Variable step-size affine projection sign algorithm. Electronics Letters, 48 (9), 483. doi: https://doi.org/10.1049/el.2012.0751
- Lu, L., Zhao, H., Li, K., Chen, B. (2015). A Novel Normalized Sign Algorithm for System Identification Under Impulsive Noise Interference. Circuits, Systems, and Signal Processing, 35 (9), 3244–3265. doi: https://doi.org/10.1007/s00034-015-0195-1
- Huang, H.-C., Lee, J. (2012). A New Variable Step-Size NLMS Algorithm and Its Performance Analysis. IEEE Transactions on Signal Processing, 60 (4), 2055–2060. doi: https://doi.org/10.1109/tsp.2011.2181505
- Casco-Sánchez, F. M., Medina-Ramírez, R. C., López-Guerrero, M. (2011). A New Variable Step-Size NLMS Algorithm and its Performance Evaluation in Echo Cancelling Applications. Journal of Applied Research and Technology, 9 (3), 302–313.
- Huber, P. J. (1977). Robust methods of estimation of regression coefficients. Series Statistics, 8 (1), 41–53. doi: https://doi.org/10.1080/02331887708801356
- Huber, P. J. (1964). Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics, 35 (1), 73–101. doi: https://doi.org/10.1214/aoms/1177703732
- Hampel, F. R. (1974). The Influence Curve and its Role in Robust Estimation. Journal of the American Statistical Association, 69 (346), 383–393. doi: https://doi.org/10.1080/01621459.1974.10482962
- Adamczyk, T. (2017). Application of the Huber and Hampel M-estimation in real estate value modeling. Geomatics and Environmental Engineering, 11 (1), 15. doi: https://doi.org/10.7494/geom.2017.11.1.15
- Andrews, D. F. (1974). A Robust Method for Multiple Linear Regression. Technometrics, 16 (4), 523. doi: https://doi.org/10.2307/1267603
- Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. The Annals of Statistics, 15 (2), 642–656. doi: https://doi.org/10.1214/aos/1176350366
- Croux, C., Rousseeuw, P. J., Hossjer, O. (1994). Generalized S-Estimators. Journal of the American Statistical Association, 89 (428), 1271. doi: https://doi.org/10.2307/2290990
- Rudenko, O. G., Bessonov, A. A. (2011). Robastnoe obuchenie radial'no-bazisnyh setey. Kibernetika i sistemniy analiz, 6, 38–46.
- Rudenko, O. G., Bessonov, A. A. (2014). Robust neuroevolutionary identification of nonlinear nonstationary objects. Kibernetika i sistemniy analiz, 50 (1), 21–36.
- Rudenko, O. G., Bessonov, A. A., Rudenko, C. O. (2013). Robastnaya identifikatsiya nelineynyh obektov s pomoshch'yu evolyutsioniruyushchey radial'no-bazisnoy seti. Kibernetika i sistemniy analiz, 2, 15–26.
- Rudenko, O., Bezsonov, O. (2011). Function Approximation Using Robust Radial Basis Function Networks. Journal of Intelligent Learning Systems and Applications, 03 (01), 17–25. doi: https://doi.org/10.4236/jilsa.2011.31003
- Walach, E., Widrow, B. (1984). The least mean fourth (LMF) adaptive algorithm and its family. IEEE Transactions on Information Theory, 30 (2), 275–283. doi: https://doi.org/10.1109/tit.1984.1056886
- Bershad, N. J., Bermudez, J. C. M. (2011). Mean-square stability of the Normalized Least-Mean Fourth algorithm for white Gaussian inputs. Digital Signal Processing, 21 (6), 694–700. doi: https://doi.org/10.1016/j.dsp.2011.06.002
- Eweda, E., Zerguine, A. (2011). New insights into the normalization of the least mean fourth algorithm. Signal, Image and Video Processing, 7 (2), 255–262. doi: https://doi.org/10.1007/s11760-011-0231-y
- Eweda, E. (2012). Global Stabilization of the Least Mean Fourth Algorithm. IEEE Transactions on Signal Processing, 60 (3), 1473–1477. doi: https://doi.org/10.1109/tsp.2011.2177976
- Eweda, E., Bershad, N. J. (2012). Stochastic Analysis of a Stable Normalized Least Mean Fourth Algorithm for Adaptive Noise Canceling With a White Gaussian Reference. IEEE Transactions on Signal Processing, 60 (12), 6235–6244. doi: https://doi.org/10.1109/tsp.2012.2215607
- Hubscher, P. I., Bermudez, J. C. M., Nascimento, Ví. H. (2007). A Mean-Square Stability Analysis of the Least Mean Fourth Adaptive Algorithm. IEEE Transactions on Signal Processing, 55 (8), 4018–4028. doi: https://doi.org/10.1109/tsp.2007.894423
- Chambers, J. A., Tanrikulu, O., Constantinides, A. G. (1994). Least mean mixed-norm adaptive filtering. Electronics Letters, 30 (19), 1574–1575. doi: https://doi.org/10.1049/el:19941060
- Rakesh, P., Kumar, T. K., Albu, F. (2019). Modified Least-Mean Mixed-Norm Algorithms For Adaptive Sparse System Identification Under Impulsive Noise Environment. 2019 42nd International Conference on Telecommunications and Signal Processing (TSP). doi: https://doi.org/10.1109/tsp.2019.8768813
- Chambers, J., Avlonitis, A. (1997). A robust mixed-norm adaptive filter algorithm. IEEE Signal Processing Letters, 4 (2), 46–48. doi: https://doi.org/10.1109/97.554469
- Papoulis, E. V., Stathaki, T. (2004). A Normalized Robust Mixed-Norm Adaptive Algorithm for System Identification. IEEE Signal Processing Letters, 11 (1), 56–59. doi: https://doi.org/10.1109/lsp.2003.819353
- Arenas-García, J., Figueiras-Vidal, A. R. (2005). Adaptive combination of normalised filters for robust system identification. Electronics Letters, 41 (15), 874. doi: https://doi.org/10.1049/el:20051936
- Wagner, K. T., Doroslovacki, M. I. (2008). Towards analytical convergence analysis of proportionate-type nlms algorithms. 2008 IEEE International Conference on Acoustics, Speech and Signal Processing. doi: https://doi.org/10.1109/icassp.2008.4518487
- Price, R. (1958). A useful theorem for nonlinear devices having Gaussian inputs. IEEE Transactions on Information Theory, 4 (2), 69–72. doi: https://doi.org/10.1109/tit.1958.1057444
- Feuer, A., Weinstein, E. (1985). Convergence analysis of LMS filters with uncorrelated Gaussian data. IEEE Transactions on Acoustics, Speech, and Signal Processing, 33 (1), 222–230. doi: https://doi.org/10.1109/tassp.1985.1164493
- Gladyshev, E. G. (1965). On Stochastic Approximation. Theory of Probability & Its Applications, 10 (2), 275–278. doi: https://doi.org/10.1137/1110031
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 Oleg Rudenko, Oleksandr Bezsonov, Oleh Lebediev, Nataliia Serdiuk
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.