Parameter adaptive multivariable flight controller using a full autoregressive moving average (ARMA) model and recursive least squares (RLS) estimation

1991 ◽  
Author(s):  
DARYL HAMMOND ◽  
JOHN D'AZZO
Keyword(s):  
Least Squares ◽  
Moving Average ◽  
Arma Model ◽  
Recursive Least Squares ◽  
Autoregressive Moving Average ◽  
Parameter Adaptive

scholarly journals Data Filtering Based Recursive Least Squares Algorithm for Two-Input Single-Output Systems with Moving Average Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xianling Lu ◽  
Wei Zhou ◽  
Wenlin Shi
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Moving Average ◽  
Recursive Least Squares ◽  
Noise Model ◽  
Autoregressive Moving Average ◽  
Data Filtering ◽  
Noise Transfer Function ◽  
Single Output ◽  
Recursive Least Squares Method

This paper studies identification problems of two-input single-output controlled autoregressive moving average systems by using an estimated noise transfer function to filter the input-output data. Through data filtering, we obtain two simple identification models, one containing the parameters of the system model and the other containing the parameters of the noise model. Furthermore, we deduce a data filtering based recursive least squares method for estimating the parameters of these two identification models, respectively, by replacing the unmeasurable variables in the information vectors with their estimates. The proposed algorithm has high computational efficiency because the dimensions of its covariance matrices become small. The simulation results indicate that the proposed algorithm is effective.

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.

MEMS Gyro Random Drift Model Parameter Identification Based on Two-Stage Recursive Least Squares Method

2012 ◽  
Vol 220-223 ◽  
pp. 1044-1047 ◽  
Author(s):  
Zhao Hua Liu ◽  
Jia Bin Chen ◽  
Yu Liang Mao ◽  
Chun Lei Song
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Moving Average ◽  
Recursive Least Squares ◽  
Model Parameters ◽  
Random Drift ◽  
Two Stage ◽  
Autoregressive Moving Average Model ◽  
Drift Model ◽  
Recursive Least Squares Method

Autoregressive moving average model (ARMA) was usually used for gyro random drift modeling. Because gyro random drift was a non-stationary, weak non-linear and time-variant random signal, model parameters were random and time-variant, too. For improving precision of gyro and reducing effects of random drift, this paper adopted two-stage recursive least squares method for ARMA parameter estimation. This method overcame the shortcomings of the conventional recursive extended least squares (RELS) algorithm. At the same time, the forgetting factor was introduced to adapt the model parameters change. The simulation experimental results showed that this method is effective.

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.

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