Levinson Algorithm Research Articles

Performance of signal-to-noise ratio estimation for scanning electron microscope using autocorrelation Levinson-Durbin recursion model.

A new technique to quantify signal-to-noise ratio (SNR) value of the scanning electron microscope (SEM) images is proposed. This technique is known as autocorrelation Levinson-Durbin recursion (ACLDR) model. To test the performance of this technique, the SEM image is corrupted with noise. The autocorrelation function of the original image and the noisy image are formed. The signal spectrum based on the autocorrelation function of image is formed. ACLDR is then used as an SNR estimator to quantify the signal spectrum of noisy image. The SNR values of the original image and the quantified image are calculated. The ACLDR is then compared with the three existing techniques, which are nearest neighbourhood, first-order linear interpolation and nearest neighbourhood combined with first-order linear interpolation. It is shown that ACLDR model is able to achieve higher accuracy in SNR estimation.

INTRODUCING AN INTERPOLATION METHOD TO EFFICIENTLY IMPLEMENT AN APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATOR FOR THE HURST EXPONENT

The efficiency and accuracy of estimating the Hurst exponent have been two inevitable considerations. Recently, an efficient implementation of the maximum likelihood estimator (MLE) (simply called the fast MLE) for the Hurst exponent was proposed based on a combination of the Levinson algorithm and Cholesky decomposition, and furthermore the fast MLE has also considered all four possible cases, including known mean, unknown mean, known variance, and unknown variance. In this paper, four cases of an approximate MLE (AMLE) were obtained based on two approximations of the logarithmic determinant and the inverse of a covariance matrix. The computational cost of the AMLE is much lower than that of the MLE, but a little higher than that of the fast MLE. To raise the computational efficiency of the proposed AMLE, a required power spectral density (PSD) was indirectly calculated by interpolating two suitable PSDs chosen from a set of established PSDs. Experimental results show that the AMLE through interpolation (simply called the interpolating AMLE) can speed up computation. The computational speed of the interpolating AMLE is on average over 24 times quicker than that of the fast MLE while remaining the accuracy very close to that of the MLE or the fast MLE.

Modify Levinson algorithm for symmetric positive definite Toeplitz system

This paper describes a new O(N32log(N))$O(N^{\frac {3}{2}}\log (N))$ solver for the symmetric positive definite Toeplitz system TNxN = bN. The method is based on the block QR decomposition of TN accompanied with Levinson algorithm and its generalized version for solving Schur complements Sm of size m. In our algorithm we use a formula for displacement rank representation of the Sm in terms of generating vectors of the matrix TN, and we assume that N = lm with l,m?N$l, m\in \mathbb {N}$. The new algorithm is faster than the classical O(N2)-algorithm for N > 29. Numerical experiments confirm the good computational properties of the new method.

Configurational entropy theory for streamflow forecasting

This study develops configurational entropy theory (CET) for monthly streamflow forecasting. The theory is comprised of three main parts: (1) determination of spectral density (2) determination of parameters by cepstrum analysis, and (3) extension of autocorrelation function. Comparison with the Burg entropy theory (BET) shows that CET yields higher resolution spectral density with more accurate location of spectral peaks. Cepstrum analysis yields more accurate parameters than the Levinson algorithm in the autoregressive (AR) method and the Levinson–Burg algorithm in BET. CET is tested using monthly streamflow data from 19 river basins covering a broad range of physiographic characteristics. Testing shows that CET captures streamflow seasonality and satisfactorily forecasts both high and low flows. High flows are satisfactorily forecasted with the coefficient of determination (r2) higher than 0.92 for one year ahead of time, with r2 higher than 0.85 for two years ahead of time, and up to 60 months ahead with r2 higher than 0.80. However, low flows are forecasted with r2 higher than 0.50 for one year ahead time. When relative drainage area is considered for analyzing streamflow characteristics and spectral patterns, it is found that upstream streamflow is forecasted more accurately (r2 = 0.84) than downstream streamflow (r2 = 0.75). Residuals of forecasted values relative to observed values are found to follow normal distribution.

Forecasting Daily Variations of Stock Index Returns with a Multifractal Model of Realized Volatility

ABSTRACTMultifractal models have recently been introduced as a new type of data‐generating process for asset returns and other financial data. Here we propose an adaptation of this model for realized volatility. We estimate this new model via generalized method of moments and perform forecasting by means of best linear forecasts derived via the Levinson–Durbin algorithm. Its out‐of‐sample performance is compared against other popular time series specifications. Using an intra‐day dataset for five major international stock market indices, we find that the the multifractal model for realized volatility improves upon forecasts of its earlier counterparts based on daily returns and of many other volatility models. While the more traditional RV‐ARFIMA model comes out as the most successful model (in terms of the number of cases in which it has the best forecasts for all combinations of forecast horizons and evaluation criteria), the new model performs often significantly better during the turbulent times of the recent financial crisis. Copyright © 2014 John Wiley & Sons, Ltd.

An efficient estimator of Hurst exponent through an autoregressive model with an order selected by data induction.

The discrete-time fractional Gaussian noise (DFGN) has been proven to be a regular process. Therefore, an autoregressive (AR) model of an infinite order can describe DFGN based on Wold and Kolmogorov theorems. A fast estimation algorithm on the Hurst exponent of DFGN or discrete-time fractional Brownian motion (DFBM) has been proposed, but the algorithm did not consider the order selection of AR model. Recently, a Hurst exponent estimator based on an AR model with six existing methods of order selection has been proposed to raise the accuracy of estimating the Hurst exponent. Although the estimation accuracy has been confirmed to be better than the one without order selection, the estimator still requires computing all parameter sets through the Levinson algorithm. In order to lower computational cost, this paper proposes an efficient method of order selection, simply called data induction, which uses simulation data to induce an appropriate threshold of terminating the Levinson algorithm before computing all parameter sets. Experimental results show that the proposed data-induction method has a competitive advantage over six existing methods of order selection in terms of lowering computational cost and raising the accuracy.

Efficiently Implementing the Maximum Likelihood Estimator for Hurst Exponent

This paper aims to efficiently implement the maximum likelihood estimator (MLE) for Hurst exponent, a vital parameter embedded in the process of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN), via a combination of the Levinson algorithm and Cholesky decomposition. Many natural and biomedical signals can often be modeled as one of these two processes. It is necessary for users to estimate the Hurst exponent to differentiate one physical signal from another. Among all estimators for estimating the Hurst exponent, the maximum likelihood estimator (MLE) is optimal, whereas its computational cost is also the highest. Consequently, a faster but slightly less accurate estimator is often adopted. Analysis discovers that the combination of the Levinson algorithm and Cholesky decomposition can avoid storing any matrix and performing any matrix multiplication and thus save a great deal of computer memory and computational time. In addition, the first proposed MLE for the Hurst exponent was based on the assumptions that the mean is known as zero and the variance is unknown. In this paper, all four possible situations are considered: known mean, unknown mean, known variance, and unknown variance. Experimental results show that the MLE through efficiently implementing numerical computation can greatly enhance the computational performance.

Simultaneous confidence bands for sequential autoregressive fitting

Let {Xk,k∈Z} be a zero mean causal AR(∞) process with parameter Θ∈R∞. A very common fitting procedure is to employ the Yule–Walker equations in connection with the Durbin–Levinson algorithm, which yields the (recursive) sequence of estimators Θ̂m:=(θ̂m,1,…,θ̂m,m)⊤, m=1,2,….. Under mild conditions, simultaneous confidence bands for Θ̂m, Θ̂m+1,… are derived. More precisely, it is shown that maxdn−κn≤m≤dnmax1≤h≤m|θ̂m,h−θh| converges to an extreme value distribution, where dn=O(nδ), δ>0, and n denotes the sample size. The relation of κn and dn depends on the bias term ∑i=dn−2κn∞|θi|. This significantly extends a recent result in Jirak (2012). Moreover, extensions of results of An et al. (1982) and Bhansali (1978) are obtained. In addition, the behavior of Information criteria in the AR(∞) setting is briefly discussed.

Development of simple fixed linear predictors for use in speech compression

The need to compress digitised signals like speech for more efficient transmission and storage while still maintaining considerable amount of information that they convey is highly desirable. A very popular method used for compression is Linear Prediction Coding (LPC), by using the Linear Prediction Model. The development of simple fixed linear prediction filters for speech signal compression is therefore carried out in this work. The prediction filters- an analysis filter on one side and a reconstruction filter on the other are designed to have 11 fixed coefficients each. The Levinson-Durbin algorithm, derived from the Linear Prediction Model of speech is used to calculate the coefficients of the filter. Various speech signals are used to test the performance of both filters within a DPCM system. The output signals are then tested using objective and subjective quality tests. Results from these tests presented in later sections show satisfactory filter performance.

Detection of obstructive sleep apnea by estimation of oral and nasal cavity cross-section areas from acoustic recordings of snore

Obstructive sleep apnea (OSA) refers to the condition in which a person’s breathing is paused while asleep, or the airflow is decreased, due to obstruction in the upper respiratory airway. In severe cases, OSA can cause complete arousals and deprive the patient from normal sleep. Surgical intervention is sometimes recommended, but accurate identification of the site of obstruction can be difficult. In the present study, we devised signal processing methods to estimate the site and the severity of airflow obstruction from recordings of sounds of snore. The vocal tract, the oral and the nasal cavity are modeled as three branches joining at the pharynx. Each branch consists of cylindrical segments whose cross-section areas can vary during snoring. Estimation of these cross-section areas consists of two steps: First, an auto-regressive moving-average method is applied to find the linear coefficients of a pole-zero model that optimally accounts for the recorded sound. Then, the Levinson-Durbin algorithm is applied to convert the coefficients to ratios of cross-section areas between adjacent segments. The present method is applied to a set of recorded snore samples during clinically confirmed apnea episodes, and results are compared with those of simple snore. Effectiveness of the method is analyzed statistically.

FPGA/NIOS Implementation of an Adaptive FIR Filter Using Linear Prediction to Reduce Narrow-Band RFI for Radio Detection of Cosmic Rays

We present the FPGA/NIOS implementation of an adaptive finite impulse response (FIR) filter based on linear prediction to suppress radio frequency interference (RFI). This technique will be used for experiments that observe coherent radio emission from extensive air showers induced by ultra-high-energy cosmic rays. These experiments are designed to make a detailed study of the development of the electromagnetic part of air showers. Therefore, these radio signals provide information that is complementary to that obtained by water-Cherenkov detectors which are predominantly sensitive to the particle content of an air shower at ground. The radio signals from air showers are caused by the coherent emission due to geomagnetic and charge-excess processes. These emissions can be observed in the frequency band between 10-100 MHz. However, this frequency range is significantly contaminated by narrow-band RFI and other human-made distortions. A FIR filter implemented in the FPGA logic segment of the front-end electronics of a radio sensor significantly improves the signal-to-noise ratio. In this paper we discuss an adaptive filter which is based on linear prediction. The coefficients for the linear predictor (LP) are dynamically refreshed and calculated in the embedded NIOS processor, which is implemented in the same FPGA chip. The Levinson recursion, used to obtain the filter coefficients, is also implemented in the NIOS and is partially supported by direct multiplication in the DSP blocks of the logic FPGA segment. Tests confirm that the LP can be an alternative to other methods involving multiple time-to-frequency domain conversions using an FFT procedure. These multiple conversions draw heavily on the power consumption of the FPGA and are avoided by the linear prediction approach. Minimization of the power consumption is an important issue because the final system will be powered by solar panels. The FIR filter has been successfully tested in the Altera development kits with the EP4CE115F29C7 from the Cyclone IV family and the EP3C120F780C7 from the Cyclone III family at a 170 MHz sampling rate, a 12-bit I/O resolution, and an internal 30-bit dynamic range. Most of the slow floating-point NIOS calculations have been moved to the FPGA logic segments as extended fixed-point operations, which significantly reduced the refreshing time of the coefficients used in the LP. We conclude that the LP is a viable alternative to other methods such as non-adaptive methods involving digital notch filters or multiple time-to-frequency domain conversions using an FFT procedure.

High‐frequency sampling and kernel estimation for continuous‐time moving average processes

Interest in continuous‐time processes has increased rapidly in recent years, largely because of high‐frequency data available in many applications. We develop a method for estimating the kernel function g of a second‐order stationary Lévy‐driven continuous‐time moving average (CMA) process Y based on observations of the discrete‐time process YΔ obtained by sampling Y at Δ, 2Δ, …, nΔ for small Δ. We approximate g by gΔ based on the Wold representation and prove its pointwise convergence to g as Δ → 0 for continuous‐time autoregressive moving average (CARMA) processes. Two non‐parametric estimators of gΔ, on the basis of the innovations algorithm and the Durbin–Levinson algorithm, are proposed to estimate g. For a Gaussian CARMA process, we give conditions on the sample size n and the grid spacing Δ(n) under which the innovations estimator is consistent and asymptotically normal as n → ∞. The estimators can be calculated from sampled observations of any CMA process, and simulations suggest that they perform well even outside the class of CARMA processes. We illustrate their performance for simulated data and apply them to the Brookhaven turbulent wind speed data. Finally, we extend results of Brockwell et al. (2012) for sampled CARMA processes to a much wider class of CMA processes.

Estimation of Observer Parameters for Dynamic Positioning Ships

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.

ROOM ACOUSTIC RESPONSE MODELING AND EQUALIZATION WITH LINEAR PREDICTIVE CODING AND PARAMETRIC FILTERS

A method for determining coefficients of a family of cascaded second order Infinite Impulse Response (IIR) parametric filters used for equalizing a room response. The method includes determining parameters of each IIR parametric filter from poles or roots of a reasonably high-order Linear Predictive Coding (LPC) model. The LPC model is able to accurately model the low-frequency room response modes providing better equalization of loudspeaker and room acoustics, particularly at the low frequencies. Advantages of the method include fast and efficient computation of the LPC model using a Levinson-Durbin recursion to solve the normal equations that arise from the least squares formulation. Due to possible band interactions between the cascaded IIR parametric filters, the method further includes optimizing the Q value of each filter to better equalize the room response.

Global feed-forward vibration isolation in a km scale interferometer

Using a network of seismometers and sets of optimal filters, we implemented a feed-forward control technique to minimize the seismic contribution to multiple interferometric degrees of freedom of the Laser Interferometer Gravitational-wave Observatory interferometers. The filters are constructed by using the Levinson–Durbin recursion relation to approximate the optimal Wiener filter. By reducing the RMS of the interferometer feedback signals below ∼10 Hz, we have improved the stability and duty cycle of the joint network of gravitational wave detectors. By suppressing the large control forces and mirror motions, we have dramatically reduced the rate of non-Gaussian transients in the gravitational wave signal stream.

Maximum likelihood estimation of structural VARFIMA models

This paper considers the maximum likelihood estimation of a class of structural vector autoregressive fractionally integrated moving-average (VARFIMA) models. The structural VARFIMA model includes the fractional cointegration model as one of its special cases. We show that the conditional likelihood Durbin–Levinson (CLDL) algorithm of Tsay (2010a) is a fast and reliable approach to estimate the long-run effects as well as the short- and long-term dynamics of a structural VARFIMA process simultaneously. In particular, the computational cost of the CLDL algorithm is much lower than that proposed in Sowell (1989) and Dueker and Startz (1998). We apply the CLDL method to the Congressional approval data of Durr et al. (1997) and find that the long-run effect of economic expectations on Congressional approval is at least 0.5718, which is over twice the estimate of 0.24 found in Table 2 of Box-Steffensmeier and Tomlinson (2000). This paper also tests the divided party government hypothesis with the CLDL algorithm.

AR model whitening and signal detection based on GLD algorithm in the non-Gaussian reverberation

The paper analyzes the characteristics of shallow sea reverberation such as divergent variance and heavy tails in probability density distribution and matches it to symmetric alpha stable (SαS) distribution. After analyzing the AR model whitening method based on Gaussian distribution and Levinson–Durbin algorithm, the paper proposes and derives the generalized Levinson–Durbin (GLD) algorithm based on covariation theory of alpha stable distribution. The GLD algorithm can estimate the order and parameters of AR SαS model by iterations which are fast and effective in calculating, and then the performance tests by simulations are given. The AR model whitening method using GLD algorithm has a faster speed and a better detection performance than AR Gaussian whitening method in impulsive reverberation. At last the Monte Carlo simulating tests are used to validate the validity of the new method.

Modeling Research of Background Noise in Low-Voltage Power Line Communication Channel

Background noise interference is one of the most important factors for low-voltage power line communication’s reliability. By analyzing the background noise of low-voltage power line communication’s channel, the background noise’s measuring circuit is set up and the AR model of the measured background noise is established. Both of them are respectively using singular value decomposition and Levinson-Durbin (LD) recursive method to calculate the AR model’s parameters and a comparative analysis of the simulation is made. The results induct: parameters acquired from the methods of singular value decomposition and LD recursive method are feasible, the parameter model from singular value decomposition is relatively complex, but extremely accurate, which is suitable for the off-line calculation and analysis of the low-voltage power line’s background noise; the parameter model from LD recursive method is very simple, but has a greater loss of accuracy, fitting for online quickly generation of the low-voltage power line’s background noise.

Parameter estimation and forecasting for multiplicative log-normal cascades

We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian and log normally distributed random variables yields time series with intermittent bursts of activity. Due to the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been estimated mostly by fitting the numerical approximation of the associated non-Gaussian probability density function to empirical data, cf. Castaing et al. [Physica D 46, 177 (1990)]. More recently, alternative estimators based upon various moments have been proposed by Beck [Physica D 193, 195 (2004)] and Kiyono et al. [Phys. Rev. E 76, 041113 (2007)]. In this paper, we pursue this moment-based approach further and develop a more rigorous generalized method of moments (GMM) estimation procedure to cope with the documented difficulties of previous methodologies. We show that even under uncertainty about the actual number of cascade steps, our methodology yields very reliable results for the estimated intermittency parameter. Employing the Levinson-Durbin algorithm for best linear forecasts, we also show that estimated parameters can be used for forecasting the evolution of the turbulent flow. We compare forecasting results from the GMM and Kiyono et al.'s procedure via Monte Carlo simulations. We finally test the applicability of our approach by estimating the intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange markets.

Voice Prediction Based On All-Poles Signals

The paper has discussed the voice prediction research based on biological and medical research. From all-pole model, we create speech transform model and predicate voice signal. The Levinson recursion was introduce to this model, the experiment proved the method is feasible and effective.