Mixed‐phase wavelet estimation using fourth‐order cumulants

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 1042-1051 ◽  
Author(s):  
Gregory D. Lazear
Keyword(s):  
Fourth Order ◽  
Mean Squared Error ◽  
Moving Average ◽  
High Order ◽  
Mixed Phase ◽  
Order Moment ◽  
Covariance Functions ◽  
Minimum Mean Squared Error ◽  
Air Gun ◽  
Fourth Order Cumulant

In recent years methods have been developed in the field of high‐order statistics that can reliably estimate a mixed‐phase wavelet from the noisy output of a convolutional process. These methods use high‐order covariance functions of the data called cumulants, which retain phase information and allow recovery of the wavelet. The assumption is that the reflection coefficient series is a non‐Gaussian, stationary, and statistically independent random process. The method described in this paper uses the fourth‐order cumulant of the data, and a moving‐average, noncausal parametric model for the wavelet. The fourth‐order moment function of this wavelet matches the fourth‐order cumulant of the data in a minimum mean‐squared error sense. Numerical simulations demonstrate that the method can accurately estimate mixed‐phase wavelets, even when the reflectivity has a distribution close to Gaussian. Three seismic data examples demonstrate possible uses of the method. In the first two, an average source wavelet is estimated from marine shot records acquired with air gun and water gun sources, respectively. These wavelets compare favorably with recorded far‐field signatures modified for receiver ghosting. In the third example, a wavelet estimate from marine stacked data is used to correct the phase of the stacked section, resulting in zero‐phase water bottom and salt top reflections.

Simulated annealing wavelet estimation via fourth‐order cumulant matching

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1939-1948 ◽  
Author(s):  
Danilo R. Velis ◽  
Tadeusz J. Ulrych
Keyword(s):  
Simulated Annealing ◽  
Fourth Order ◽  
Simulated Annealing Algorithm ◽  
Numerical Solutions ◽  
Mean Squared Error ◽  
Real Data ◽  
Hybrid Strategy ◽  
Minimum Mean Squared Error ◽  
Highly Nonlinear ◽  
Fourth Order Cumulant

The fourth‐order cumulant matching method has been developed recently for estimating a mixed‐phase wavelet from a convolutional process. Matching between the trace cumulant and the wavelet moment is done in a minimum mean‐squared error sense under the assumption of a non‐Gaussian, stationary, and statistically independent reflectivity series. This leads to a highly nonlinear optimization problem, usually solved by techniques that require a certain degree of linearization, and that invariably converge to the minimum closest to the initial model. Alternatively, we propose a hybrid strategy that makes use of a simulated annealing algorithm to provide reliability of the numerical solutions by reducing the risk of being trapped in local minima. Beyond the numerical aspect, the reliability of the derived wavelets depends strongly on the amount of data available. However, by using a multidimensional taper to smooth the trace cumulant, we show that the method can be used even in a trace‐by‐trace implementation, which is very important from the point of view of stationarity and consistency. We demonstrate the viability of the method under several reflectivity models. Finally, we illustrate the hybrid strategy using marine and field real data examples. The consistency of the results is very encouraging because the improved cumulant matching strategy we describe can be effectively used with a limited amount of data.

MATRIX FORMULAS FOR NONSTATIONARY ARIMA SIGNAL EXTRACTION

2008 ◽  
Vol 24 (4) ◽  
pp. 988-1009 ◽  
Author(s):  
Tucker McElroy
Keyword(s):  
Time Series ◽  
Mean Squared Error ◽  
Moving Average ◽  
Signal Extraction ◽  
Error Signal ◽  
Autoregressive Integrated Moving Average ◽  
General Matrix ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Moving Average Processes

The paper provides general matrix formulas for minimum mean squared error signal extraction for a finitely sampled time series whose signal and noise components are nonstationary autoregressive integrated moving average processes. These formulas are quite practical; in addition to being simple to implement on a computer, they make it possible to easily derive important general properties of the signal extraction filters. We also extend these formulas to estimates of future values of the unobserved signal, and we show how this result combines signal extraction and forecasting.

scholarly journals Inherent Complexity Research on the Bullwhip Effect in Supply Chains with Two Retailers: The Impact of Three Forecasting Methods Considering Market Share

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Junhai Ma ◽  
Binshuo Bao ◽  
Xiaogang Ma
Keyword(s):  
Supply Chain ◽  
Market Share ◽  
Mean Squared Error ◽  
Moving Average ◽  
Bullwhip Effect ◽  
Minimum Mean Squared Error ◽  
Forecasting Methods ◽  
Effect Measure ◽  
Demand Variability ◽  
The Impact

An important phenomenon in supply chain management which is known as the bullwhip effect suggests that demand variability increases as one moves up a supply chain. This paper contrasts the bullwhip effect for a two-stage supply chain consisting of one supplier and two retailers under three forecasting methods based on the market share. We can quantify the correlation coefficient between the two retailers clearly, in consideration of market share. The two retailers both employ the order-up-to inventory policy for replenishments. The bullwhip effect is measured, respectively, under the minimum mean squared error (MMSE), moving average (MA), and exponential smoothing (ES) forecasting methods. The effect of autoregressive coefficient, lead time, and the market share on a bullwhip effect measure is investigated by using algebraic analysis and numerical simulation. And the comparison of the bullwhip effect under three forecasting methods is conducted. The conclusion suggests that different forecasting methods and various parameters lead to different bullwhip effects. Hence, the corresponding forecasting method should be chosen by the managers under different parameters in practice.

scholarly journals A Comparison of Bullwhip Effect under Various Forecasting Techniques in Supply Chains with Two Retailers

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Junhai Ma ◽  
Xiaogang Ma
Keyword(s):  
Mean Squared Error ◽  
Moving Average ◽  
Market Competition ◽  
Bullwhip Effect ◽  
Demand Forecast ◽  
Autoregressive Moving Average Model ◽  
Minimum Mean Squared Error ◽  
Forecasting Methods ◽  
The Impact ◽  
Forecasting Techniques

We examine the impact of three forecasting methods on the bullwhip effect in a two-stage supply chain with one supplier and two retailers. A first order mixed autoregressive-moving average model (ARMA(1, 1)) performs the demand forecast and an order-up-to inventory policy characterizes the inventory decision. The bullwhip effect is measured, respectively, under the minimum mean-squared error (MMSE), moving average (MA), and exponential smoothing (ES) forecasting techniques. The effect of parameters on the bullwhip effect under three forecasting methods is analyzed and the bullwhip effect under three forecasting methods is compared. Conclusions indicate that different forecasting methods lead to different bullwhip effects caused by lead time, underlying parameters of the demand process, market competition, and the consistency of demand volatility between two retailers. Moreover, some suggestions are present to help managers to select the forecasting method that yields the lowest bullwhip effect.

Multi-AUV Aided Cooperative 3D-localization for Underwater Sensor Networks

2020 ◽  
Vol 13 (1) ◽  
pp. 80-90 ◽  
Author(s):  
Meiyan Zhang ◽  
Wenyu Cai
Keyword(s):  
Sensor Networks ◽  
Mean Squared Error ◽  
Autonomous Underwater Vehicles ◽  
Estimation Method ◽  
Location Estimation ◽  
Underwater Sensor Networks ◽  
Coverage Ratio ◽  
Minimum Mean Squared Error ◽  
3D Localization ◽  
Localization Scheme

Background: Effective 3D-localization in mobile underwater sensor networks is still an active research topic. Due to the sparse characteristic of underwater sensor networks, AUVs (Autonomous Underwater Vehicles) with precise positioning abilities will benefit cooperative localization. It has important significance to study accurate localization methods. Methods: In this paper, a cooperative and distributed 3D-localization algorithm for sparse underwater sensor networks is proposed. The proposed algorithm combines with the advantages of both recursive location estimation of reference nodes and the outstanding self-positioning ability of mobile AUV. Moreover, our design utilizes MMSE (Minimum Mean Squared Error) based recursive location estimation method in 2D horizontal plane projected from 3D region and then revises positions of un-localized sensor nodes through multiple measurements of Time of Arrival (ToA) with mobile AUVs. Results: Simulation results verify that the proposed cooperative 3D-localization scheme can improve performance in terms of localization coverage ratio, average localization error and localization confidence level. Conclusion: The research can improve localization accuracy and coverage ratio for whole underwater sensor networks.

scholarly journals How to improve infectious disease prediction by integrating environmental data: an application of a novel ensemble analysis strategy to predict HFMD

2021 ◽  
Vol 149 ◽  
Author(s):  
Junwen Tao ◽  
Yue Ma ◽  
Xuefei Zhuang ◽  
Qiang Lv ◽  
Yaqiong Liu ◽  
...  
Keyword(s):  
Variable Selection ◽  
Mean Squared Error ◽  
Moving Average ◽  
Dynamic Bayesian Networks ◽  
Environmental Data ◽  
Control Measures ◽  
Coefficient Of Determination ◽  
Percentage Error ◽  
Analysis Strategy ◽  
Ensemble Analysis

Abstract This study proposed a novel ensemble analysis strategy to improve hand, foot and mouth disease (HFMD) prediction by integrating environmental data. The approach began by establishing a vector autoregressive model (VAR). Then, a dynamic Bayesian networks (DBN) model was used for variable selection of environmental factors. Finally, a VAR model with constraints (CVAR) was established for predicting the incidence of HFMD in Chengdu city from 2011 to 2017. DBN showed that temperature was related to HFMD at lags 1 and 2. Humidity, wind speed, sunshine, PM10, SO2 and NO2 were related to HFMD at lag 2. Compared with the autoregressive integrated moving average model with external variables (ARIMAX), the CVAR model had a higher coefficient of determination (R2, average difference: + 2.11%; t = 6.2051, P = 0.0003 < 0.05), a lower root mean-squared error (−24.88%; t = −5.2898, P = 0.0007 < 0.05) and a lower mean absolute percentage error (−16.69%; t = −4.3647, P = 0.0024 < 0.05). The accuracy of predicting the time-series shape was 88.16% for the CVAR model and 86.41% for ARIMAX. The CVAR model performed better in terms of variable selection, model interpretation and prediction. Therefore, it could be used by health authorities to identify potential HFMD outbreaks and develop disease control measures.

scholarly journals Attack-resilient minimum mean-squared error estimation

2014 ◽  
Author(s):  
James Weimer ◽  
Nicola Bezzo ◽  
Miroslav Pajic ◽  
Oleg Sokolsky ◽  
Insup Lee
Keyword(s):  
Error Estimation ◽  
Mean Squared Error ◽  
Minimum Mean Squared Error ◽  
Squared Error

scholarly journals Multi-Channel Singular Spectrum Analysis on Geocenter Motion and Its Precise Prediction

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1403
Author(s):  
Xin Jin ◽  
Xin Liu ◽  
Jinyun Guo ◽  
Yi Shen
Keyword(s):  
Solid Earth ◽  
Spectrum Analysis ◽  
Mean Squared Error ◽  
Moving Average ◽  
Singular Spectrum Analysis ◽  
Singular Spectrum ◽  
Autoregressive Moving Average Model ◽  
Seasonal Characteristics ◽  
Geocenter Motion ◽  
Moving Average Model

Geocenter is the center of the mass of the Earth system including the solid Earth, ocean, and atmosphere. The time-varying characteristics of geocenter motion (GCM) reflect the redistribution of the Earth’s mass and the interaction between solid Earth and mass loading. Multi-channel singular spectrum analysis (MSSA) was introduced to analyze the GCM products determined from satellite laser ranging data released by the Center for Space Research through January 1993 to February 2017 for extracting the periods and the long-term trend of GCM. The results show that the GCM has obvious seasonal characteristics of the annual, semiannual, quasi-0.6-year, and quasi-1.5-year in the X, Y, and Z directions, the annual characteristics make great domination, and its amplitudes are 1.7, 2.8, and 4.4 mm, respectively. It also shows long-period terms of 6.09 years as well as the non-linear trends of 0.05, 0.04, and –0.10 mm/yr in the three directions, respectively. To obtain real-time GCM parameters, the MSSA method combining a linear model (LM) and autoregressive moving average model (ARMA) was applied to predict GCM for 2 years into the future. The precision of predictions made using the proposed model was evaluated by the root mean squared error (RMSE). The results show that the proposed method can effectively predict GCM parameters, and the prediction precision in the three directions is 1.53, 1.08, and 3.46 mm, respectively.

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