scholarly journals Multi-targets localization based on ARMA and GA in WSNs

2018 ◽  
Vol 189 ◽  
pp. 04015
Author(s):  
Heng Zhang ◽  
Zhongming Pan
Keyword(s):  
Objective Function ◽  
Moving Average ◽  
Linear Equations ◽  
Optimal Solution ◽  
Arma Model ◽  
Target Localization ◽  
Autoregressive Moving Average ◽  
Arma Process ◽  
Popular Subject ◽  
Noise Sequence

Multi-target localization methods for locating of the movingtarget in interested area monitored by Wireless Sensor Networks (WSNs) are nowadays a popular subject of study. The methods can be classified into two categories: range-free algorithm and range-based algorithm. In this work, we propose a novel multi-target localization method, which belongs to the category of range-based algorithm, by using a genetic algorithm (GA) for searching optimal solution of the objective function of multi-target localization. The objective function is only a group of linear equations with independent variables of acoustic energies calculated at each sensor-node in a WSN. However, application of the method, the accuracy of multi-target localization is sensitive to the SNR of the measured sound signals at each node, thus a denoising strategy should be inserted into the method. It turned out that the measured sound noise, comparing intrinsic sensor noise and environmental noise, may be considered as an Autoregressive Moving Average (ARMA) process. Thus, by building the ARMA model, the noise sequence commingled with the target signals can be predicted. As a consequence, the power of the noises can be subtracted from the measured sound signals for revealing the target signal's power. The results in present work demonstrate the advantage of the proposed method.

ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

1985 ◽  
Vol 17 (04) ◽  
pp. 810-840 ◽  
Author(s):  
Jürgen Franke
Keyword(s):  
Time Series ◽  
Impulse Response ◽  
Moving Average ◽  
Autoregressive Process ◽  
Natural Generalization ◽  
Maximal Entropy ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
Arma Process ◽  
Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

Application of Kalman Filtering for Natural Gray Image Denoising

2011 ◽  
Vol 187 ◽  
pp. 92-96 ◽  
Author(s):  
Zhi Kai Huang ◽  
De Hui Liu ◽  
Xing Wang Zhang ◽  
Ling Ying Hou
Keyword(s):  
Kalman Filter ◽  
Image Denoising ◽  
Kalman Filtering ◽  
Moving Average ◽  
Arma Model ◽  
Adaptive Method ◽  
Natural Image ◽  
Autoregressive Moving Average ◽  
Processing Step ◽  
Reduction Methods

Image denoising is one of the classical problems in digital image processing, and has been studied for nearly half a century due to its important role as a pre-processing step in various image applications. In this work, a denoising algorithm based on Kalman filtering was used to improve natural image quality. We have studied noise reduction methods using a hybrid Kalman filter with an autoregressive moving average (ARMA) model that the coefficients of the AR models for the Kalman filter are calculated by solving for the minimum square error solutions of over-determined linear systems. Experimental results show that as an adaptive method, the algorithm reduces the noise while retaining the image details much better than conventional algorithms.

scholarly journals Testing and modelling autoregressive conditional heteroskedasticity of streamflow processes

2005 ◽  
Vol 12 (1) ◽  
pp. 55-66 ◽  
Author(s):  
W. Wang ◽  
P. H. A. J. M Van Gelder ◽  
J. K. Vrijling ◽  
J. Ma
Keyword(s):  
Seasonal Variation ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Conditional Heteroskedasticity ◽  
Daily Streamflow ◽  
Arch Effect ◽  
Monthly Streamflow ◽  
Autoregressive Conditional Heteroskedasticity ◽  
Residual Series

Abstract. Conventional streamflow models operate under the assumption of constant variance or season-dependent variances (e.g. ARMA (AutoRegressive Moving Average) models for deseasonalized streamflow series and PARMA (Periodic AutoRegressive Moving Average) models for seasonal streamflow series). However, with McLeod-Li test and Engle's Lagrange Multiplier test, clear evidences are found for the existence of autoregressive conditional heteroskedasticity (i.e. the ARCH (AutoRegressive Conditional Heteroskedasticity) effect), a nonlinear phenomenon of the variance behaviour, in the residual series from linear models fitted to daily and monthly streamflow processes of the upper Yellow River, China. It is shown that the major cause of the ARCH effect is the seasonal variation in variance of the residual series. However, while the seasonal variation in variance can fully explain the ARCH effect for monthly streamflow, it is only a partial explanation for daily flow. It is also shown that while the periodic autoregressive moving average model is adequate in modelling monthly flows, no model is adequate in modelling daily streamflow processes because none of the conventional time series models takes the seasonal variation in variance, as well as the ARCH effect in the residuals, into account. Therefore, an ARMA-GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) error model is proposed to capture the ARCH effect present in daily streamflow series, as well as to preserve seasonal variation in variance in the residuals. The ARMA-GARCH error model combines an ARMA model for modelling the mean behaviour and a GARCH model for modelling the variance behaviour of the residuals from the ARMA model. Since the GARCH model is not followed widely in statistical hydrology, the work can be a useful addition in terms of statistical modelling of daily streamflow processes for the hydrological community.

Representations of continuous-time ARMA processes

2004 ◽  
Vol 41 (A) ◽  
pp. 375-382 ◽  
Author(s):  
Peter J. Brockwell
Keyword(s):  
Continuous Time ◽  
Moving Average ◽  
Asymptotic Properties ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
Arma Process ◽  
Simple Modification ◽  
Arma Processes ◽  
Kernel Representation ◽  
Autoregressive Moving Average Process

Using the kernel representation of a continuous-time Lévy-driven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévy-driven Ornstein–Uhlenbeck processes employed by Barndorff-Nielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévy-driven continuous-time ARMA processes obtained by a simple modification of the kernel of the continuous-time ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.

ADAPTIVE, FREQUENCY DOMAIN, 2-D MODELING USING SPATIOTEMPORAL SIGNALS

1996 ◽  
Vol 06 (04) ◽  
pp. 351-358
Author(s):  
WASFY B. MIKHAEL ◽  
HAOPING YU
Keyword(s):  
Frequency Domain ◽  
Moving Average ◽  
System Modeling ◽  
Arma Model ◽  
Model Parameters ◽  
Two Dimensional ◽  
Convergence Factor ◽  
Arma Process ◽  
Auto Regressive ◽  
Unknown System

In this paper, an adaptive, frequency domain, steepest descent algorithm for two-dimensional (2-D) system modeling is presented. Based on the equation error model, the algorithm, which characterizes the 2-D spatially linear and invariant unknown system by a 2-D auto-regressive, moving-average (ARMA) process, is derived and implemented in the 3-D spatiotemporal domain. At each iteration, corresponding to a given pair of input and output 2-D signals, the algorithm is formulated to minimize the error-function’s energy in the frequency domain by adjusting the 2-D ARMA model parameters. A signal dependent, optimal convergence factor, referred to as the homogeneous convergence factor, is developed. It is the same for all the coefficients but is updated once per iteration. The resulting algorithm is called the Two-Dimensional, Frequency Domain, with Homogeneous µ*, Adaptive Algorithm (2D-FD-HAA). In addition, the algorithm is implemented using the 2-D Fast Fourier Transform (FFT) to enhance the computational efficiency. Computer simulations demonstrate the algorithm’s excellent adaptation accuracy and convergence speed. For illustration, the proposed algorithm is successfully applied to modeling a time varying 2-D system.

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

A Novel Adaptive Integrated Navigation Filtering Method Based on ARMA/GARCH Model

2013 ◽  
Vol 462-463 ◽  
pp. 259-266
Author(s):  
Xin Zhao ◽  
Hong Lei Qin ◽  
Li Cong
Keyword(s):  
Moving Average ◽  
Garch Model ◽  
Main Idea ◽  
Arma Model ◽  
Statistical Characteristics ◽  
Autoregressive Moving Average ◽  
Integrated Navigation ◽  
Conditional Mean ◽  
Filtering Method ◽  
Residual Series

This paper proposes a novel adaptive integrated navigation filtering method based on autoregressive moving average (ARMA) model and generalized autoregressive conditional heteroscedasticity (GARCH) model. The main idea in this study is to employ ARMA/GARCH model to estimate statistical characteristics of filtering residual series online, namely, the conditional mean and conditional standard deviation, and then the filter parameters are adaptively adjusted based on forecasted results of ARMA/GARCH model in order to improve the reliability of the system when there are abnormal disturbance and other uncertain factors in real condition. On this basis, experiment is used to verify the validity of the method. The simulation results demonstrate that the ARMA/GARCH model can well capture the unusual condition of GPS receiver output, and this adaptive filtering method can effectively improve the reliability of the system.

Parameter Identification of Time Varying System Using Basic Function Expansion

2011 ◽  
Vol 403-408 ◽  
pp. 2800-2804
Author(s):  
En Wei Chen ◽  
Yi Min Lu ◽  
Zheng Shi Liu ◽  
Yong Wang
Keyword(s):  
High Efficiency ◽  
Moving Average ◽  
Arma Model ◽  
Basic Function ◽  
Least Square ◽  
Autoregressive Moving Average ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Time Invariant

Time-varying parameters identification in linear system is considered, which can be changed into time-invariant coefficient polynomials after Taylor expansion. Using response data to establish the time-varying autoregressive moving average (TV-ARMA) model, then utilizing least-square algorithm to obtain time-invariant coefficients of time-varying parameters. According to error analysis, to reduce errors and improve accuracy, the estimation time is divided into small internals and the above method is used in each interval. Simulation shows that, under certain error condition, the time-varying parameters obtained by the method have good agreement with the theoretical values; the measures taken have strong anti-interference and high efficiency.

scholarly journals Minimum Message Length in Hybrid ARMA and LSTM Model Forecasting

2021 ◽  
Author(s):  
Zheng Fang ◽  
David L. Dowe ◽  
Shelton Peiris ◽  
Dedi Rosadi
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Short Term Memory ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Information Theoretic ◽  
Minimum Message Length ◽  
Message Length ◽  
Long Short Term Memory

We investigate the power of time series analysis based on a variety of information-theoretic approaches from statistics (AIC, BIC) and machine learning (Minimum Message Length) - and we then compare their efficacy with traditional time series model and with hybrids involving deep learning. More specifically, we develop AIC, BIC and Minimum Message Length (MML) ARMA (autoregressive moving average) time series models - with this Bayesian information-theoretic MML ARMA modelling already being new work. We then study deep learning based algorithms in time series forecasting, using Long Short Term Memory (LSTM), and we then combine this with the ARMA modelling to produce a hybrid ARMA-LSTM prediction. Part of the purpose of the use of LSTM is to seek capture any hidden information in the residuals left from the traditional ARMA model. We show that MML not only outperforms earlier statistical approaches to ARMA modelling, but we further show that the hybrid MML ARMA-LSTM models outperform both ARMA models and LSTM models.

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