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Journal articles on the topic 'Yule-Walker equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Kallas, M., P. Honeine, C. Francis, and H. Amoud. "Kernel autoregressive models using Yule–Walker equations." Signal Processing 93, no. 11 (November 2013): 3053–61. http://dx.doi.org/10.1016/j.sigpro.2013.03.032.

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2

Davila, C. E. "On the noise-compensated Yule-Walker equations." IEEE Transactions on Signal Processing 49, no. 6 (June 2001): 1119–21. http://dx.doi.org/10.1109/78.923293.

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3

Martinelli, G., G. Orlandi, and P. Burrascano. "Yule - Walker equations and Bartlett's bisection theory." IEEE Transactions on Circuits and Systems 32, no. 10 (October 1985): 1074–76. http://dx.doi.org/10.1109/tcs.1985.1085615.

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4

Hui-Min Zhang and P. Duhamel. "On the methods for solving Yule-Walker equations." IEEE Transactions on Signal Processing 40, no. 12 (1992): 2987–3000. http://dx.doi.org/10.1109/78.175742.

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5

Wang, Hai-Bin, and Bo-Cheng Wei. "Separable lower triangular bilinear model." Journal of Applied Probability 41, no. 01 (March 2004): 221–35. http://dx.doi.org/10.1017/s0021900200014169.

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The aim of this paper is to analyze the probabilistic structure for a rather general class of bilinear models systematically. First, the sufficient and necessary conditions for stationarity are given with a concise expression. Then both the autocovariance function and the spectral density function are obtained. The Yule–Walker-type difference equations for autocovariances are derived by means of the spectral density function. Concerning the second-order probabilistic structure, the model is similar to an ARMA model. The third-order probabilistic structure for the model is discussed and a group of Yule–Walker-type difference equations for third-order cumulants are discovered.

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6

Wang, Hai-Bin, and Bo-Cheng Wei. "Separable lower triangular bilinear model." Journal of Applied Probability 41, no. 1 (March 2004): 221–35. http://dx.doi.org/10.1239/jap/1077134680.

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The aim of this paper is to analyze the probabilistic structure for a rather general class of bilinear models systematically. First, the sufficient and necessary conditions for stationarity are given with a concise expression. Then both the autocovariance function and the spectral density function are obtained. The Yule–Walker-type difference equations for autocovariances are derived by means of the spectral density function. Concerning the second-order probabilistic structure, the model is similar to an ARMA model. The third-order probabilistic structure for the model is discussed and a group of Yule–Walker-type difference equations for third-order cumulants are discovered.

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7

Dimitriou-Fakalou, Chrysoula. "Yule-Walker Estimation for the Moving-Average Model." International Journal of Stochastic Analysis 2011 (August 14, 2011): 1–20. http://dx.doi.org/10.1155/2011/151823.

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The standard Yule-Walker equations, as they are known for an autoregression, are generalized to involve the moments of a moving-average process indexed on any number of dimensions. Once observations become available, new moments estimators are set to imitate the theoretical equations. These estimators are not only consistent but also asymptotically normal for any number of indexes. Their variance matrix resembles a standard result from maximum Gaussian likelihood estimation. A simulation study is added to conclude on their efficiency.

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8

Vergara-Dominguez, L. "New insights into the high-order Yule-Walker equations." IEEE Transactions on Acoustics, Speech, and Signal Processing 38, no. 9 (1990): 1649–51. http://dx.doi.org/10.1109/29.60088.

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9

Chen, Weitian, Brian D. O. Anderson, Manfred Deistler, and Alexander Filler. "Solutions of Yule-Walker equations for singular AR processes." Journal of Time Series Analysis 32, no. 5 (January 27, 2011): 531–38. http://dx.doi.org/10.1111/j.1467-9892.2010.00711.x.

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10

Tismenetsky, Miron. "Some properties of solutions of Yule-Walker type equations." Linear Algebra and its Applications 173 (August 1992): 1–17. http://dx.doi.org/10.1016/0024-3795(92)90419-b.

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11

Mahmoudi, Alimorad. "Adaptive Algorithm for Estimation of Two-Dimensional Autoregressive Fields from Noisy Observations." International Journal of Stochastic Analysis 2014 (December 25, 2014): 1–5. http://dx.doi.org/10.1155/2014/247274.

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This paper deals with the problem of two-dimensional autoregressive (AR) estimation from noisy observations. The Yule-Walker equations are solved using adaptive steepest descent (SD) algorithm. Performance comparisons are made with other existing methods to demonstrate merits of the proposed method.

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12

Zhang, Er Yan, and Xiao Feng Zhu. "The Recursive Algorithms of Yule-Walker Equation in Generalized Stationary Prediction." Advanced Materials Research 756-759 (September 2013): 3070–73. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.3070.

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Toeplitz matrix arises in a remarkable variety of applications such as signal processing, time series analysis, image processing. Yule-Walker equation in generalized stationary prediction is linear algebraic equations that use Toeplitz matrix as coefficient matrix. Making better use of the structure of Toeplitz matrix, we present a recursive algorithm of linear algebraic equations from by using Toeplitz matrix as coefficient matrix , and also offer the proof of the recursive formula. The algorithm, making better use of the structure of Toeplitz matrices, effectively reduces calculation cost. For n-order Toeplitz coefficient matrix, the computational complexity of usual Gaussian elimination is about , while this algorithm is about , decreasing of one order of magnitude.

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13

Jentsch, Carsten, and Lena Reichmann. "Generalized Binary Time Series Models." Econometrics 7, no. 4 (December 14, 2019): 47. http://dx.doi.org/10.3390/econometrics7040047.

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The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule–Walker equations hold that facilitate parameter estimation of gbAR models. Yule–Walker type equations are also derived for gbARMA processes.

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14

Correia, P. F., and J. M. Ferreira de Jesus. "Solving the Yule–Walker equations to generate synthetic, correlated wind speed variates." Electric Power Systems Research 93 (December 2012): 76–82. http://dx.doi.org/10.1016/j.epsr.2012.07.001.

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15

Shishebor, Z., A. R. Nematollahi, and A. R. Soltani. "On covariance generating functions and spectral densities of periodically correlated autoregressive processes." Journal of Applied Mathematics and Stochastic Analysis 2006 (May 4, 2006): 1–17. http://dx.doi.org/10.1155/jamsa/2006/94746.

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Periodically correlated autoregressive nonstationary processes of finite order are considered. The corresponding Yule-Walker equations are applied to derive the generating functions of the covariance functions, what are called here the periodic covariance generating functions. We also provide closed formulas for the spectral densities by using the periodic covariance generating functions, which is a new technique in the spectral theory of periodically correlated processes.

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16

Bhaskar, U., and J. B. Anderson. "A Lattice Structured Algorithm for Recursive Solution of the Extended Yule-Walker Equations." IFAC Proceedings Volumes 18, no. 5 (July 1985): 1431–35. http://dx.doi.org/10.1016/s1474-6670(17)60766-3.

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17

Mahmoudi, Alimorad. "Adaptive Algorithm for Multichannel Autoregressive Estimation in Spatially Correlated Noise." Journal of Stochastics 2014 (June 19, 2014): 1–7. http://dx.doi.org/10.1155/2014/502406.

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This paper addresses the problem of multichannel autoregressive (MAR) parameter estimation in the presence of spatially correlated noise by steepest descent (SD) method which combines low-order and high-order Yule-Walker (YW) equations. In addition, to yield an unbiased estimate of the MAR model parameters, we apply inverse filtering for noise covariance matrix estimation. In a simulation study, the performance of the proposed unbiased estimation algorithm is evaluated and compared with existing parameter estimation methods.

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18

Stoica, Petre, and Torsten Söderström. "High-order Yule-Walker equations for estimating sinusoidal frequencies: The complete set of solutions." Signal Processing 20, no. 3 (July 1990): 257–63. http://dx.doi.org/10.1016/0165-1684(90)90015-q.

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19

Chen, Zhi Qing, and You Shen Xia. "A Fast Algorithm for Vector ARMA Parameter Estimation." Advanced Materials Research 433-440 (January 2012): 4475–81. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.4475.

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In this paper, a fast algorithm for vector autoregressivemoving-average (ARMA) parameter estimation under noise environments is proposed. Based on an equivalent AR parameter model technique and a Yule-Walker equation technique, solving the parameter estimation problem of the VARMA model is well converted into solving linear equations. Therefore, the proposed algorithm has a lower computational complexity and a faster speed than conventional algorithms. Application examples with application to Lorenz systems confirm that the proposed algorithm can obtain a good solution.

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20

Zou, Jin, and Dong Han. "Yule–Walker Equations Using a Gini Covariance Matrix for the High-Dimensional Heavy-Tailed PVAR Model." Mathematics 9, no. 6 (March 15, 2021): 614. http://dx.doi.org/10.3390/math9060614.

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Gini covariance plays a vital role in analyzing the relationship between random variables with heavy-tailed distributions. In this papaer, with the existence of a finite second moment, we establish the Gini–Yule–Walker equation to estimate the transition matrix of high-dimensional periodic vector autoregressive (PVAR) processes, the asymptotic results of estimators have been established. We apply this method to study the Granger causality of the heavy-tailed PVAR process, and the results show that the robust transfer matrix estimation induces sign consistency in the value of Granger causality. Effectiveness of the proposed method is verified by both synthetic and real data.

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21

Lin, Xiaogong, Yehai Xie, Dawei Zhao, and Shusheng Xu. "Estimation of Observer Parameters for Dynamic Positioning Ships." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/173603.

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Considering the problem of dynamic positioning systems for the slowly varying disturbances, a parametrically adaptive observer is presented. The peak frequency of observer is adjusted on-line by autoregressive (AR) spectral estimation; other parameters of observer are optimized using particle swarm optimization (PSO). The peak frequency can be calculated by spectral analysis of the pitch, roll, and heave measurements. In the spectral estimation, Levinson-Durbin algorithm is used to solve the Yule-Walker equations. Finally, the computer simulation is given to demonstrate the effectiveness of the proposed method.

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22

Choi, ByoungSeon. "A recursive algorithm for solving the spatial Yule-Walker equations of causal spatial AR models." Statistics & Probability Letters 33, no. 3 (May 1997): 241–51. http://dx.doi.org/10.1016/s0167-7152(96)00133-2.

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23

Choi, ByoungSeon. "On the block lu decomposition of block toeplitz matrices using the vector yule-walker equations." Communications in Statistics - Theory and Methods 19, no. 8 (January 1990): 2815–27. http://dx.doi.org/10.1080/03610929008830350.

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24

Parrish, Joan, Steven M. Crunk, and Bee Leng Lee. "The Yule–Walker equations as a weighted least-squares problem and the association with tapering." Communications in Statistics - Theory and Methods 45, no. 17 (July 5, 2016): 5112–22. http://dx.doi.org/10.1080/03610926.2014.936941.

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25

Champagnat, F., and J. Idier. "On the correlation structure of unilateral AR processes on the plane." Advances in Applied Probability 32, no. 02 (June 2000): 408–25. http://dx.doi.org/10.1017/s0001867800010004.

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In, Tory and Pickard show that a simple subclass of unilateral AR processes identifies with Gaussian Pickard random fields on Z 2. First, we extend this result to the whole class of unilateral AR processes, by showing that they all satisfy a Pickard-type property, under which correlation matching and maximum entropy properties are assessed. Then, it is established that the Pickard property provides the ‘missing’ equations that complement the two-dimensional Yule-Walker equations, in the sense that the conjunction defines a one-to-one mapping between the set of AR parameters and a set of correlations. It also implies Markov chain conditions that allow exact evaluation of the likelihood and an exact sampling scheme on finite lattices.

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26

Champagnat, F., and J. Idier. "On the correlation structure of unilateral AR processes on the plane." Advances in Applied Probability 32, no. 2 (June 2000): 408–25. http://dx.doi.org/10.1239/aap/1013540171.

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In, Tory and Pickard show that a simple subclass of unilateral AR processes identifies with Gaussian Pickard random fields on Z2. First, we extend this result to the whole class of unilateral AR processes, by showing that they all satisfy a Pickard-type property, under which correlation matching and maximum entropy properties are assessed. Then, it is established that the Pickard property provides the ‘missing’ equations that complement the two-dimensional Yule-Walker equations, in the sense that the conjunction defines a one-to-one mapping between the set of AR parameters and a set of correlations. It also implies Markov chain conditions that allow exact evaluation of the likelihood and an exact sampling scheme on finite lattices.

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27

Sesay, S. A. O., and T. Subba Rao. "YULE-WALKER TYPE DIFFERENCE EQUATIONS FOR HIGHER-ORDER MOMENTS AND CUMULANTS FOR BILINEAR TIME SERIES MODELS." Journal of Time Series Analysis 9, no. 4 (July 1988): 385–401. http://dx.doi.org/10.1111/j.1467-9892.1988.tb00478.x.

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28

Bezerra, Manoel I. Silvestre, Fernando Antonio Moala, and Yuzo Iano. "A Bayesian Analysis of Spectral ARMA Model." Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/565894.

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Bezerra et al. (2008) proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967). The Bayesian computations, simulation via Markov Monte Carlo (MCMC) is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.

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29

Byoung-Seon Choi. "An algorithm for solving the extended Yule- Walker equations of an autoregressive moving-average time series (Corresp.)." IEEE Transactions on Information Theory 32, no. 3 (May 1986): 417–19. http://dx.doi.org/10.1109/tit.1986.1057181.

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30

ByoungSeon Choi. "An order-recursive algorithm to solve the 3-D Yule-Walker equations of causal 3-D AR models." IEEE Transactions on Signal Processing 47, no. 9 (1999): 2491–502. http://dx.doi.org/10.1109/78.782192.

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31

Anderson, Brian D. O., Manfred Deistler, Elisabeth Felsenstein, Bernd Funovits, Lukas Koelbl, and Mohsen Zamani. "MULTIVARIATE AR SYSTEMS AND MIXED FREQUENCY DATA: G-IDENTIFIABILITY AND ESTIMATION." Econometric Theory 32, no. 4 (April 2, 2015): 793–826. http://dx.doi.org/10.1017/s0266466615000043.

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This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these population second moments. These structural results are obtained using two alternative tools viz. extended Yule Walker equations and blocking of the output process. The cases of stock and flow variables, as well as of general linear transformations of high frequency data, are treated. Finally, we briefly discuss how our constructive identifiability results can be used for parameter estimation based on the sample second moments.

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32

Nakhaei, Arash Ashtari, Mohammad Sadegh Helfroush, Habibollah Danyali, and Mohammed Ghanbari. "Subjectively correlated estimation of noise due to blurriness distortion based on auto-regressive model using the Yule–Walker equations." IET Image Processing 12, no. 10 (October 1, 2018): 1788–96. http://dx.doi.org/10.1049/iet-ipr.2017.0916.

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33

Krumin, Michael, and Shy Shoham. "Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains." Computational Intelligence and Neuroscience 2010 (2010): 1–9. http://dx.doi.org/10.1155/2010/752428.

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Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden’’ Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method.

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34

Alkarni, S. H. "Statistical applications for equivariant matrices." International Journal of Mathematics and Mathematical Sciences 25, no. 1 (2001): 53–61. http://dx.doi.org/10.1155/s016117120100446x.

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Solving linear system of equationsAx=benters into many scientific applications. In this paper, we consider a special kind of linear systems, the matrixAis an equivariant matrix with respect to a finite group of permutations. Examples of this kind are special Toeplitz matrices, circulant matrices, and others. The equivariance property ofAmay be used to reduce the cost of computation for solving linear systems. We will show that the quadratic form is invariant with respect to a permutation matrix. This helps to know the multiplicity of eigenvalues of a matrix and yields corresponding eigenvectors at a low computational cost. Applications for such systems from the area of statistics will be presented. These include Fourier transforms on a symmetric group as part of statistical analysis of rankings in an election, spectral analysis in stationary processes, prediction of stationary processes and Yule-Walker equations and parameter estimation for autoregressive processes.

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35

Porsani, Milton J., and Bjorn Ursin. "Mixed‐phase deconvolution." GEOPHYSICS 63, no. 2 (March 1998): 637–47. http://dx.doi.org/10.1190/1.1444363.

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We describe a new algorithm for mixed‐phase deconvolution. It is valid only for pulses whose Z-transform has no zeros on the unit circle. That is, the amplitude spectrum cannot be zero for any frequency. Using the Z-transform of a discrete‐time signal, and assuming that the signal has α zeros inside the unit circle, the inverse of its minimum‐delay component may be estimated by solving the extended Yule‐Walker (EYW) system of equations with the lag α of the autocorrelation function (ACF) on diagonal of the coefficient matrix. This property of the solution of EYW equations is exploited to derive mixed‐phase inverse filters and their corresponding mixed‐phase pulses. For different values of α, a suite of inverse filters is generated using the same ACF. To choose the best decomposition and its corresponding mixed‐phase inverse filter, we have used the value of α which gives the maximum value of the Lp norm of the filtered signal. The optimal value of α does not seem to be very sensitive to the choice of norm as long as p > 2. In the numerical examples, we have used p = 5. The mixed‐phase deconvolution filter performs better than minimum‐phase deconvolution on the synthetic and real data examples shown.

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36

Korte, Johannes, Till Schubert, Jan Martin Brockmann, and Wolf-Dieter Schuh. "A Mathematical Investigation of a Continuous Covariance Function Fitting with Discrete Covariances of an AR Process." Engineering Proceedings 5, no. 1 (June 28, 2021): 18. http://dx.doi.org/10.3390/engproc2021005018.

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In this paper, we want to find a continuous function fitting through the discrete covariance sequence generated by a stationary AR process. This function can be determined as soon as the Yule–Walker equations are found. The procedure consists of two steps. At first the inverse zeros of the characteristic polynomial of the AR process must be fixed. The second step is based on the fact that an AR process can also be seen as a difference equation. By solving this difference equation, it is possible to determine a class of functions from which a candidate for a continuous covariance function can be determined. To analyze if this function is applicable as a positive definite covariance function, it is analyzed mathematically in view of the power spectral density compared to the characteristics of the power spectral density for the discrete covariances. Then it is shown that this function is positive semi-definite. At the end, a simulation of a stationary AR(3) process is elaborated to illustrate the derived properties.

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37

Wu, Hsiao-Chun, Shih Yu Chang, Tho Le-Ngoc, and Yiyan Wu. "Efficient Rank-Adaptive Least-Square Estimation and Multiple-Parameter Linear Regression Using Novel Dyadically Recursive Hermitian Matrix Inversion." International Journal of Antennas and Propagation 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/891932.

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Least-square estimation (LSE) and multiple-parameter linear regression (MLR) are the important estimation techniques for engineering and science, especially in the mobile communications and signal processing applications. The majority of computational complexity incurred in LSE and MLR arises from a Hermitian matrix inversion. In practice, the Yule-Walker equations are not valid, and hence the Levinson-Durbin algorithm cannot be employed for general LSE and MLR problems. Therefore, the most efficient Hermitian matrix inversion method is based on the Cholesky factorization. In this paper, we derive a new dyadic recursion algorithm for sequential rank-adaptive Hermitian matrix inversions. In addition, we provide the theoretical computational complexity analyses to compare our new dyadic recursion scheme and the conventional Cholesky factorization. We can design a variable model-order LSE (MLR) using this proposed dyadic recursion approach thereupon. Through our complexity analyses and the Monte Carlo simulations, we show that our new dyadic recursion algorithm is more efficient than the conventional Cholesky factorization for the sequential rank-adaptive LSE (MLR) and the associated variable model-order LSE (MLR) can seek the trade-off between the targeted estimation performance and the required computational complexity. Our proposed new scheme can benefit future portable and mobile signal processing or communications devices.

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38

Yang, Jun, Dongsheng Zhang, Bin Feng, Xuesong Mei, and Zhenbang Hu. "Thermal-Induced Errors Prediction and Compensation for a Coordinate Boring Machine Based on Time Series Analysis." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/784218.

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To improve the CNC machine tools precision, a thermal error modeling for the motorized spindle was proposed based on time series analysis, considering the length of cutting tools and thermal declined angles, and the real-time error compensation was implemented. A five-point method was applied to measure radial thermal declinations and axial expansion of the spindle with eddy current sensors, solving the problem that the three-point measurement cannot obtain the radial thermal angle errors. Then the stationarity of the thermal error sequences was determined by the Augmented Dickey-Fuller Test Algorithm, and the autocorrelation/partial autocorrelation function was applied to identify the model pattern. By combining both Yule-Walker equations and information criteria, the order and parameters of the models were solved effectively, which improved the prediction accuracy and generalization ability. The results indicated that the prediction accuracy of the time series model could reach up to 90%. In addition, the axial maximum error decreased from 39.6 μm to 7 μm after error compensation, and the machining accuracy was improved by 89.7%. Moreover, theX/Y-direction accuracy can reach up to 77.4% and 86%, respectively, which demonstrated that the proposed methods of measurement, modeling, and compensation were effective.

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39

Gruzdev, A. N. "Аccounting for autocorrelation in a linear regression problem on an example of analysis of atmospheric column NO2 content." Известия Российской академии наук. Физика атмосферы и океана 55, no. 1 (April 16, 2019): 73–82. http://dx.doi.org/10.31857/s0002-351555173-82.

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A method is proposed for taking into account a serial correlation (an autocorrelation) of data in a linear regression problem, which allows accounting for the autocorrelation on long scales. A residual series is presented as an autoregressive process of an order, k, that can be much larger than 1, and the autocorrelation function of the processes is calculated by solving the system of the Yule–Walker equations. Given the autocorrelation function, the autocorrelation matrix is constructed which enters the formulas for estimates of regression coefficients and their errors. The efficiency of the method is demonstrated on the base of the multiple regression analysis of data of 26-year measurements of the column NO2 contents at the Zvenigorod Research Station of the Institute of Atmospheric Physics. Estimates of regression coefficients and their errors depend on the autoregression order k. At first the error increases with increasing k. Then it approaches its maximum and thereafter begins to decrease. In the case of NO2 at the Zvenigorod Station the error more than doubled in its maximum compared to the beginning value. The decrease in the error after approaching the maximum stops if k approaches the value such that the autoregressive process of this order allows accounting for important features of the autocorrelation function of the residual series. Estimates have been obtained of seasonally dependent linear trends and effects on NO2 of nature factors such that the 11-year solar cycle, the quasi-biennial oscillation, the North Atlantic Oscillation and other.

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40

"A Compact Gradient Based Neural Network for Capon Spectral Estimation." International Journal of Neural Networks and Advanced Applications 7 (December 18, 2020). http://dx.doi.org/10.46300/91016.2020.7.7.

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This paper describes the use of a novel gradient based recurrent neural network to perform Capon spectral estimation. Nowadays, in the fastest algorithm proposed by Marple et al., the computational burden still remains significant in the calculation of the autoregressive (AR) Parameters. In this paper we propose to use a gradient based neural network to compute the AR parameters by solving the Yule-Walker equations. Furthermore, to reduce the complexity of the neural network architecture, the weights matrixinputs vector product is performed efficiently using the fast Fourier transform. Simulation results show that proposed neural network and its simplified architecture lead to the same results as the original method which prove the correctness of the proposed scheme.

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