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Journal articles on the topic 'Quantization error'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Dai, Xinyan, Xiao Yan, Kelvin K. W. Ng, Jiu Liu, and James Cheng. "Norm-Explicit Quantization: Improving Vector Quantization for Maximum Inner Product Search." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 01 (2020): 51–58. http://dx.doi.org/10.1609/aaai.v34i01.5333.

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Vector quantization (VQ) techniques are widely used in similarity search for data compression, computation acceleration and etc. Originally designed for Euclidean distance, existing VQ techniques (e.g., PQ, AQ) explicitly or implicitly minimize the quantization error. In this paper, we present a new angle to analyze the quantization error, which decomposes the quantization error into norm error and direction error. We show that quantization errors in norm have much higher influence on inner products than quantization errors in direction, and small quantization error does not necessarily lead to good performance in maximum inner product search (MIPS). Based on this observation, we propose norm-explicit quantization (NEQ) — a general paradigm that improves existing VQ techniques for MIPS. NEQ quantizes the norms of items in a dataset explicitly to reduce errors in norm, which is crucial for MIPS. For the direction vectors, NEQ can simply reuse an existing VQ technique to quantize them without modification. We conducted extensive experiments on a variety of datasets and parameter configurations. The experimental results show that NEQ improves the performance of various VQ techniques for MIPS, including PQ, OPQ, RQ and AQ.

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2

Qin, Li Juan. "Robustness Problem Argumentation from Image Quantization Errors in Vision Location." Advanced Materials Research 225-226 (April 2011): 1332–35. http://dx.doi.org/10.4028/www.scientific.net/amr.225-226.1332.

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In our vision location system, error is inevitable. Image quantization errors play an important role in computer vision field. Quantization errors are the primary sources that affect the precision of pose estimation and they are inherent and unavoidable. It is important to analysis on the effect of this error on compute process. In this paper, Robustness problem argumentation in vision location is presented in detail. Then we introduce image quantization error. Robustness mathematical model for vision location is set up at last.

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3

Blinn, J. F. "Quantization error and dithering." IEEE Computer Graphics and Applications 14, no. 4 (1994): 78–82. http://dx.doi.org/10.1109/38.291534.

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4

Zheng, Dong Xi. "The Realization and Comparison of Directly Fitting Method and Edge Extraction Method Used in Amending the Quantization Errors." Advanced Materials Research 546-547 (July 2012): 537–41. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.537.

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The quantization error is one of errors in 3D measuring, the method of amending the quantization errors includes directly fitting method and edge extraction method. Analyzed the source of quantization errors and the principle to amend the quantization errors, and analyzed the simulation test of directly fitting method and edge extraction method, and compared them with each other.

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5

Chen, Congliang, Li Shen, Haozhi Huang, and Wei Liu. "Quantized Adam with Error Feedback." ACM Transactions on Intelligent Systems and Technology 12, no. 5 (2021): 1–26. http://dx.doi.org/10.1145/3470890.

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In this article, we present a distributed variant of an adaptive stochastic gradient method for training deep neural networks in the parameter-server model. To reduce the communication cost among the workers and server, we incorporate two types of quantization schemes, i.e., gradient quantization and weight quantization, into the proposed distributed Adam. In addition, to reduce the bias introduced by quantization operations, we propose an error-feedback technique to compensate for the quantized gradient. Theoretically, in the stochastic nonconvex setting, we show that the distributed adaptive gradient method with gradient quantization and error feedback converges to the first-order stationary point, and that the distributed adaptive gradient method with weight quantization and error feedback converges to the point related to the quantized level under both the single-worker and multi-worker modes. Last, we apply the proposed distributed adaptive gradient methods to train deep neural networks. Experimental results demonstrate the efficacy of our methods.

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6

Ti-Chiun Chang and J. P. Allebach. "Quantization of accumulated diffused errors in error diffusion." IEEE Transactions on Image Processing 14, no. 12 (2005): 1960–76. http://dx.doi.org/10.1109/tip.2005.859372.

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7

Zhang, Qiu Ju, Yong Chang Wang, and Kai Liu. "The Theory of Using an Intensity-Correcting Algorithm to Overcome Quantization Error for Phase Measuring Profilometry." Advanced Materials Research 718-720 (July 2013): 1170–74. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.1170.

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In the image process, intensity differs from its true value because the quantization process restricts image pixels to lie on an integer grid, and phase quantization error is introduced. In this paper, we propose a theory of using an intensity-correcting to overcome phase quantization error. According to the distribution of the intensity error in some pixels, the mathematical model of the intensity error is reconstructed to correct intensity values and reduce phase quantization error. Using specific example deduct the intensity-correction algorithm. At last, we compare the uncorrected quantization error and the quantization error after correction, and prove that the principle of this algorithm is right.

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8

Saini, Deepika, and Sanjeev Kumar. "Quantization error in stereo imaging system with noise distributions." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 05 (2020): 2050042. http://dx.doi.org/10.1142/s1793962320500427.

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The problem of estimating quantization error in 2D images is an inherent problem in computer vision. The outcome of this problem is directly related to the error in reconstructed 3D position coordinates of an object. Thus estimation of quantization error has its own importance in stereo vision. Although the quantization error cannot be controlled fully, still statistical error analysis helps us to measure the performance of stereo systems that relies on the imaging parameters. Generally, it is assumed that the quantization error in 2D images is distributed uniformly that need not to be true from a practical aspect. In this paper, we have incorporated noise distributions (Triangular and Trapezoidal) for the stochastic error analysis of the quantization error in stereo imaging systems. For the validation of the theoretical analysis, the detailed simulation study is carried out by considering different cases.

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9

NAGASHIMA, Tomotaka, Makoto HASEGAWA, Takuya MURAKAWA, and Tsuyoshi KONISHI. "Quantization Error Improvement for Optical Quantization Using Dual Rail Configuration." IEICE Transactions on Electronics E98.C, no. 8 (2015): 808–15. http://dx.doi.org/10.1587/transele.e98.c.808.

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10

Cadiz, Rodrigo F., Camila Muñoz, Cristian Tejos, Marcelo E. Andia, Sergio Uribe, and Pablo Irarrazaval. "Quantization error in magnetic resonance imaging." Concepts in Magnetic Resonance Part A 43A, no. 3 (2014): 79–89. http://dx.doi.org/10.1002/cmr.a.21303.

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11

Balasubramanian, R., Sukhendu Das, S. Udayabaskaran, and K. Swaminathan. "Quantization Error in Stereo Imaging systems." International Journal of Computer Mathematics 79, no. 6 (2002): 671–91. http://dx.doi.org/10.1080/00207160211283.

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12

Szymanowski, R., R. Szplet, and P. Kwiatkowski. "Quantization error in precision time counters." Measurement Science and Technology 26, no. 7 (2015): 075002. http://dx.doi.org/10.1088/0957-0233/26/7/075002.

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13

Tripathi, Akanksha, and Sachin Kathuria. "Image Steganography based on Quantization Error." International Journal of Computer Applications 141, no. 9 (2016): 36–39. http://dx.doi.org/10.5120/ijca2016909804.

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14

Kamgar-Parsi, Behzad, and Behrooz Kamgar-Parsi. "Quantization error in hexagonal sensory configurations." IEEE Transactions on Pattern Analysis and Machine Intelligence 14, no. 6 (1992): 665–71. http://dx.doi.org/10.1109/34.141556.

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15

Rodriguez, J. J., and J. K. Aggarwal. "Stochastic analysis of stereo quantization error." IEEE Transactions on Pattern Analysis and Machine Intelligence 12, no. 5 (1990): 467–70. http://dx.doi.org/10.1109/34.55106.

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16

Borodachov, Sergiy, and Yang Wang. "Lattice quantization error for redundant representations." Applied and Computational Harmonic Analysis 27, no. 3 (2009): 334–41. http://dx.doi.org/10.1016/j.acha.2009.03.001.

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17

Xu, De Hong, Huan Xin Peng, and Bin Liu. "Non-Uniform Probabilistically Quantized Distributed Consensus Applied on Sensors Network." Applied Mechanics and Materials 577 (July 2014): 921–25. http://dx.doi.org/10.4028/www.scientific.net/amm.577.921.

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In order to improve the accuracy of distributed consensus under digital communication, in the paper, assuming the initial states of nodes following uniform distribution, a non-uniform quantization scheme based on probabilistic quantization is proposed, and the entire data range is divided based on µ-law non-uniform quantization scheme. The quantization step-size near the average of initial states is smaller, and the corresponding quantization errors are smaller. Base on the proposed quantization scheme, a non-uniform probabilistically quantized distributed consensus algorithm is proposed. The performance and the mean square errors of the non-uniform probabilistically quantized distributed consensus algorithm is analyzed, by analyses and simulations, the results show the non-uniform probabilistically quantized distributed consensus can reach a consensus, and the mean square error is far smaller than that of probabilistically quantized distributed consensus.

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18

Mena-Parra, J., K. Bandura, M. A. Dobbs, J. R. Shaw, and S. Siegel. "Quantization Bias for Digital Correlators." Journal of Astronomical Instrumentation 07, no. 02n03 (2018): 1850008. http://dx.doi.org/10.1142/s2251171718500083.

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In radio interferometry, the quantization process introduces a bias in the magnitude and phase of the measured correlations which translates into errors in the measurement of source brightness and position in the sky, affecting both the system calibration and image reconstruction. In this paper, we investigate the biasing effect of quantization in the measured correlation between complex-valued inputs with a circularly symmetric Gaussian probability density function (PDF), which is the typical case for radio astronomy applications. We start by calculating the correlation between the input and quantization error and its effect on the quantized variance, first in the case of a real-valued quantizer with a zero mean Gaussian input and then in the case of a complex-valued quantizer with a circularly symmetric Gaussian input. We demonstrate that this input-error correlation is always negative for a quantizer with an odd number of levels, while for an even number of levels, this correlation is positive in the low signal level regime. In both cases, there is an optimal interval for the input signal level for which this input-error correlation is very weak and the model of additive uncorrelated quantization noise provides a very accurate approximation. We determine the conditions under which the magnitude and phase of the measured correlation have negligible bias with respect to the unquantized values: we demonstrate that the magnitude bias is negligible only if both unquantized inputs are optimally quantized (i.e. when the uncorrelated quantization error model is valid), while the phase bias is negligible when (1) at least one of the inputs is optimally quantized, or when (2) the correlation coefficient between the unquantized inputs is small. Finally, we determine the implications of these results for radio interferometry.

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19

Yang, Haigen, Linqun Zhu, Zhun Xia, et al. "Research on Quantization Error Influence of Millimeter-Wave Phased Array Antenna." International Journal of Antennas and Propagation 2021 (September 24, 2021): 1–19. http://dx.doi.org/10.1155/2021/1874537.

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The millimeter-wave phased array antenna is a higher integration system that is composed of different subarray modules, and in actual engineering, the existing amplitude, phase errors, and structural errors will change the performance of the array antenna. This paper studies the influence of the random amplitude and phase errors of the antenna array in the actual assembly process and the actual position errors between the subarrays on the electrical performance of the antenna. Based on the planar rectangular antenna array-electromagnetic coupling model, we propose a method of verifying the effect of random errors on the phased array antenna. The simulation result shows that the method could obtain the critical value of the error generated by the antenna subarray during processing and assembly. To reduce the error factor, it is necessary to ensure that the random phase and amplitude error should not exceed 10 ° , 0.5 dB . The error in the X-direction during assembly should be ≤ 0.05 λ , and the error in the Y-direction should be ≤ 0.1 λ . When symmetrical deformation occurs, the maximum deformation should be less than 0.05 λ .

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20

Hulle, Marc M. Van, and Dominique Martinez. "On an Unsupervised Learning Rule for Scalar Quantization following the Maximum Entropy Principle." Neural Computation 5, no. 6 (1993): 939–53. http://dx.doi.org/10.1162/neco.1993.5.6.939.

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A novel unsupervised learning rule, called Boundary Adaptation Rule (BAR), is introduced for scalar quantization. It is shown that the rule maximizes information-theoretic entropy and thus yields equiprobable quantizations of univariate probability density functions. It is shown by simulations that BAR outperforms other unsupervised competitive learning rules in generating equiprobable quantizations. It is also shown that our rule can do better or worse than the Lloyd I algorithm in minimizing average mean square error, depending on the input distribution. Finally, an application to adaptive non-uniform analog to digital (A/D) conversion is considered.

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21

Wang, Dong Xing, and Su Chen. "Improved Subdivision Based Halftoning Algorithm." Advanced Materials Research 267 (June 2011): 368–71. http://dx.doi.org/10.4028/www.scientific.net/amr.267.368.

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The subdivision based halftoning algorithm works in a statistical way. Analysis of its output shows that, error accumulation and rounding operation may produce big quantization error, and there may be artifacts in its output. Some improvements have been proposed. First, a procedure is added to find cases with big quantization error, and to solve the problem. Second, instead of propagating error sequentially as in the algorithm, propagating error along random directions has been tested to reduce the artifacts in the output. Third, propagating error along a direction, in which the quantization error of each subpart is the minimum, has also been tested to improve the output quality. Halftoning tests show that the improved algorithm produces clearer output than the original.

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22

EISAKA, Toshio, and Ryozaburo TAGAWA. "DDC Algorithm with Small Quantization Output Error." Transactions of the Society of Instrument and Control Engineers 23, no. 7 (1987): 692–98. http://dx.doi.org/10.9746/sicetr1965.23.692.

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23

PÖTZELBERGER, KLAUS. "The quantization error of self-similar distributions." Mathematical Proceedings of the Cambridge Philosophical Society 137, no. 3 (2004): 725–40. http://dx.doi.org/10.1017/s0305004104007765.

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24

Leijon, Arne. "Quantization Error in Clinical Pure-Tone Audiometry." Scandinavian Audiology 21, no. 2 (1992): 103–8. http://dx.doi.org/10.3109/01050399209045989.

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25

Fan, Zhigang. "Improved quantization methods in color error diffusion." Journal of Electronic Imaging 8, no. 4 (1999): 430. http://dx.doi.org/10.1117/1.482711.

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26

Liberman, Y. L. "Reduction of quantization error in position encoders." IOP Conference Series: Materials Science and Engineering 709 (January 3, 2020): 022062. http://dx.doi.org/10.1088/1757-899x/709/2/022062.

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27

Bryngdahl, Olof. "Quantization noise and the error diffusion algorithm." Journal of Electronic Imaging 3, no. 1 (1994): 37. http://dx.doi.org/10.1117/12.165062.

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28

Hardwick, John C., and Jae S. Lim. "Methods for speech quantization and error correction." Journal of the Acoustical Society of America 95, no. 6 (1994): 3687. http://dx.doi.org/10.1121/1.409888.

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29

Kamgar-Parsi, B., and B. Kamgar-Parsi. "Quantization error in regular grids: triangular pixels." IEEE Transactions on Image Processing 7, no. 10 (1998): 1496–500. http://dx.doi.org/10.1109/83.718490.

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30

Lai, J. Z. C., and J. Y. Yen. "Inverse error-diffusion using classified vector quantization." IEEE Transactions on Image Processing 7, no. 12 (1998): 1753–58. http://dx.doi.org/10.1109/83.730390.

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31

Kamgar-Parsi, Behrooz, and Behzad Kamgar-Parsi. "Evaluation of quantization error in computer vision." IEEE Transactions on Pattern Analysis and Machine Intelligence 11, no. 9 (1989): 929–40. http://dx.doi.org/10.1109/34.35496.

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32

Efraim, Hadar, Ori Shental, Nadav Yacov, and Ido Kanter. "Can quantization improve error performance in CDMA?" Journal of Physics A: Mathematical and Theoretical 41, no. 36 (2008): 365004. http://dx.doi.org/10.1088/1751-8113/41/36/365004.

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33

Broja, Manfred, Kristina Michalowski, and Olof Bryngdahl. "Error diffusion concept for multi-level quantization." Optics Communications 79, no. 5 (1990): 280–84. http://dx.doi.org/10.1016/0030-4018(90)90069-6.

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34

Nadarajah, Saralees. "An Expression for the Average Quantization Error." Wireless Personal Communications 49, no. 4 (2008): 575–85. http://dx.doi.org/10.1007/s11277-008-9578-y.

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35

Pawlus, Paweł, Rafał Reizer, and Dominik Czach. "The effect of vertical resolution on measurement errors of machined surfaces topography." Mechanik 91, no. 11 (2018): 988–91. http://dx.doi.org/10.17814/mechanik.2018.11.177.

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The effect of the quantization error on values of surface topography parameters was examined. Surface topography was measured using an optical profilometer of 0.01 nm vertical resolution. Twenty isotropic and anisotropic, one- and two-process, random and deterministic surfaces were objects of investigations. The vertical resolution was changed using TalyMap software. Tendencies of changes of three surfaces due to quantization errors were analyzed in details. Parameters of the highest and the smallest sensitivity on errors were selected.

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36

Hasso, Alaaldin, and Karwan Jacksi. "Effects of Rounding and Truncating Methods of Quantization Error and SQNR for Sine Signal." Journal of Applied Science and Technology Trends 1, no. 1 (2020): 08–12. http://dx.doi.org/10.38094/jastt113.

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Within the Analog to Digital Conversion (ADC), quantization noise is a duplicate of a Quantization Error (QE) which is introduced by quantization. In signal processing and telecommunication systems, the noise is non-linear and depends on the signal type. During the analog, Sine signal converts to the digital (ADC) process, the two methods are used Rounding and Truncating in-order to eliminate the error produced in the digitization process. The rounding method quantize assigns each sample of sine signal to the nearest quantization level. However, making the Truncating would have assigned each sample of sine signal to the quantization level below it. This paper compares the rounding and truncating methods of QE for sine signal, signal to quantization noise ratio, correlation coefficient, and regression equation of a line for both methods. Then, it calculates the residual sum of squares and compares it to the regression equations of the lines.

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37

Bugrov, V. "Dynamic Quantization of Digital Filter Coefficients." Proceedings of Telecommunication Universities 7, no. 2 (2021): 8–17. http://dx.doi.org/10.31854/1813-324x-2021-7-2-8-17.

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The possibility of quantizing the coefficients of a digital filter in the concept of dynamic mathematical programming, as a dynamic process of step-by-step quantization of coefficients with their discrete optimization at each step according to the objective function, common to the entire quantization process, is considered. Dynamic quantization can significantly reduce the functional error when implementing the required characteristics of a lowbit digital filter in comparison with classical quantization. An algorithm is presented for step-by-step dynamic quantization using integer nonlinear programming methods, taking into account the specified signal scaling and the radius of the poles of the filter transfer function. The effectiveness of this approach is illustrated by dynamically quantizing the coefficients of a cascaded high-order IIR bandpass filter with a minimum bit depth to represent integer coefficients. A comparative analysis of functional quantization errors is carried out, as well as a test of the quantized filter performance on test and real signals.

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38

Jeon, Gwang Gil. "A New Error-Diffusion Dithering Kernel for Image Halftoning." Advanced Materials Research 717 (July 2013): 506–10. http://dx.doi.org/10.4028/www.scientific.net/amr.717.506.

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Signal image halftoning approach quantizes each pixel to one bit binary pixel. During the process of error diffusion, the quantization difference at each pixel is fed back to the input to diffuse the quantization difference among the adjacent color or gray-level pixels. This paper proposes a new kernel for error diffusion to enhance halftoning quality by minimizing average error after the process. Simulation results section confirms that the obtained color and green channel result images are satisfactory.

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39

Hu, Bin, Zhiping Shen, and Weizhou Su. "An upper bound of mean-square error in state estimation with quantized measurements." Transactions of the Institute of Measurement and Control 41, no. 2 (2018): 582–90. http://dx.doi.org/10.1177/0142331218765297.

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In this paper, we study the state estimation for a linear time-invariant (LTI) discrete-time system with quantized measurements. The quantization law under consideration has a time-varying data rate. To cope with nonlinearities in quantization laws and to analyse stability in the state estimation problem, a Kalman-filter-based sub-optimal state estimator is developed and an upper bound of its estimation error covariance is minimized. It turns out that, to guarantee the convergence of the upper bound, the averaged data rate of the quantization law must be greater than a minimum rate. This minimum data rate for the quantization law is presented in terms of the poles of the system and design parameters in the state estimator. Numerical examples are presented to illustrate the results in this work.

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40

PÖTZELBERGER, KLAUS. "The quantization dimension of distributions." Mathematical Proceedings of the Cambridge Philosophical Society 131, no. 3 (2001): 507–19. http://dx.doi.org/10.1017/s0305004101005357.

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We show that the asymptotic behaviour of the quantization error allows the definition of dimensions for probability distributions, the upper and the lower quantization dimension. These concepts fit into standard geometric measure theory, as the upper quantization dimension is always between the packing and the upper box-counting dimension, whereas the lower quantization dimension is between the Hausdorff and the lower box-counting dimension.

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41

Goto, Yutaka. "Effects of Noise on the Interpolation Accuracy for Apodized FFT Spectra of Time-Domain Damped Signals." Applied Spectroscopy 49, no. 12 (1995): 1776–80. http://dx.doi.org/10.1366/0003702953966037.

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Interpolation formulas for the apodized magnitude-mode fast Fourier transformed (FFT) spectra determine accurately the frequency, damping constant, and amplitude of time-domain damped signals. However, additive noise causes a large amount of error in interpolation. In this paper, we obtain, theoretically, the frequency-domain signal-to-noise (S/N) ratio due to windowing by the function of sinα( X) and quantization with finite bit-length analog-to-digital (A/D) converters. Then, with the use of the squared ratios between three magnitudes nearest to the peak maximum on the apodized FFT spectrum, we derive the relationship equation between the frequency error and the S/N ratio. The results obtained by computer simulation of experimental conditions (i.e., sampling, quantization, windowing, FFT, and interpolation) for the Hanning window (α = 2) agree well with the theoretical calculations; the frequency errors decrease with increasing bit-length of the A/D converter. These observed errors are unavoidable because A/D converters are indispensable for measurements with Fourier transform spectrometers. Furthermore, as shown theoretically, the observed accuracy of interpolation is inversely proportional to the S/N ratio, provided that the S/N ratio is below the value due to quantization and windowing.

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42

Fisher, P. D., and J. W. Pyhtila. "Timing quantization error in lidar speed-measurement devices." IEEE Transactions on Vehicular Technology 49, no. 1 (2000): 276–80. http://dx.doi.org/10.1109/25.820720.

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43

Sun, Yi. "On quantization error of self-organizing map network." Neurocomputing 34, no. 1-4 (2000): 169–93. http://dx.doi.org/10.1016/s0925-2312(00)00292-7.

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44

Graf, Siegfried, and Harald Luschgy. "Rates of convergence for the empirical quantization error." Annals of Probability 30, no. 2 (2002): 874–97. http://dx.doi.org/10.1214/aop/1023481010.

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45

Horváth, G. "Coefficient Quantization Error in FFT-Based Spectrum Analysis." IFAC Proceedings Volumes 20, no. 5 (1987): 251–56. http://dx.doi.org/10.1016/s1474-6670(17)55509-3.

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46

Hung, A. C., E. K. Tsern, and T. H. Meng. "Error-resilient pyramid vector quantization for image compression." IEEE Transactions on Image Processing 7, no. 10 (1998): 1373–86. http://dx.doi.org/10.1109/83.718479.

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47

Hsi-Wen Nein and Chin-Teng Lin. "Incorporating error shaping technique into LSF vector quantization." IEEE Transactions on Speech and Audio Processing 9, no. 2 (2001): 73–86. http://dx.doi.org/10.1109/89.902275.

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48

Ludwig, T., K. Volk, W. Barth, and H. Klein. "Quantization error of slit‐grid emittance measurement devices." Review of Scientific Instruments 65, no. 4 (1994): 1462–64. http://dx.doi.org/10.1063/1.1144946.

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49

Zhu, Xiaolong, Sitong Xiang, and Jianguo Yang. "Novel thermal error modeling method for machining centers." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 8 (2014): 1500–1508. http://dx.doi.org/10.1177/0954406214545661.

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Thermal deformation is one of the main contributors to machining errors in machine tools. In this paper, a novel approach to build an effective thermal error model for a machining center is proposed. Adaptive vector quantization network clustering algorithm is conducted to identify the temperature variables, and then one temperature variable is selected from each cluster to represent the same cluster. Furthermore, a non-linear model based on output-hidden feedback Elman neural network is adopted to establish the relationship between thermal error and temperature variables. The output-hidden feedback Elman network is adopted to predict the thermal deformation of the machining center. Back propagation (BP) neural network is introduced for comparison. A verification experiment on the machining center is carried out to validate the efficiency of the newly proposed method. Experimental verification shows that the adaptive vector quantization network clustering algorithm and output-hidden feedback Elman neural network is an accurate and effective method.

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50

Sato, Takao, Hironobu Sakaguchi, Nozomu Araki, and Yasuo Konishi. "Reduction of Quantization Error in Multirate Output Feedback Control." Journal of Robotics and Mechatronics 28, no. 5 (2016): 640–45. http://dx.doi.org/10.20965/jrm.2016.p0640.

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[abstFig src='/00280005/04.jpg' width='250' text='Multirate output feedback control' ] In the new design method we propose for a multirate output feedback control system, the hold interval of control input is longer than the sampling interval of plant output. In this system, unknown state variables are calculated using control input and plant output without observers. The multirate output feedback control system has been extended by introducing new design parameters that are designed independent of the calculation of the state variable. To our knowledge, however, no systematic design scheme has ever been proposed for design parameters in this case. In this study, quantization error is dealt with statistically and design parameters are decided to minimize quantization error.

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