Covariance Intersection Fusion Smoothers for Multichannel ARMA Signal with Colored Measurement Noises

2013 ◽  
Vol 373-375 ◽  
pp. 716-722 ◽  
Author(s):  
Wen Juan Qi ◽  
Peng Zhang ◽  
Zi Li Deng ◽  
Yuan Gao
Keyword(s):  
Moving Average ◽  
State Space Model ◽  
Minimum Variance ◽  
Autoregressive Moving Average ◽  
Matrix Weights ◽  
Weighted Fusion ◽  
Accuracy Comparison ◽  
Covariance Intersection ◽  
Measurement Noises ◽  
Augmented State

For multichannel autoregressive moving average (ARMA) signal with colored measurement noises, based on classical Kalman filtering theory, a covariance intersection (CI) fusion smoother without cross-covariances is presented by the augmented state space model. It has the advantage that the computation of cross-covariances is avoid, so it can significantly reduce the computational burden, and it can solve the fusion problem for multi-sensor systems with unknown cross-covariances. Under the unbiased linear minimum variance (ULMV) criterion, three optimal weighted fusion smoothers with matrix weights, scalar weights and diagonal weights are also presented respectively. The accuracy comparison of the CI fuser with the other three weighted fusers is given. It is shown that its accuracy is higher than that of each local smoother, and is lower than or close to that of the optimal fuser weighted by matrices. So the presented fusion smoother is better in performance.

Multisensor Covariance Intersection Fusion Kalman Filters

2013 ◽  
Vol 373-375 ◽  
pp. 946-952
Author(s):  
Wen Juan Qi ◽  
Peng Zhang ◽  
Zi Li Deng ◽  
Yuan Gao
Keyword(s):  
Kalman Filter ◽  
Kalman Filters ◽  
Tracking System ◽  
Minimum Variance ◽  
Geometric Interpretation ◽  
Weighted Fusion ◽  
Covariance Intersection ◽  
The Common ◽  
Measurement Biases ◽  
Theoretical Accuracy

For multisensor system with colored measurement noises, the common disturbance noises and measurement biases, the batch covariance intersection fusion (BCI) Kalman filter and the sequential covariance intersection fusion (SCI) Kalman filter are presented, which can avoid the computation of the local filtering errors and reduce the computational burden significantly. Under the linear unbiased minimum variance (ULMV) criterion, the three weighted fusion Kalman filters (weighted by matrices, scalars or diagonal matrices) are also presented. Their accuracy relations are analyzed and compared. Specially, the accuracy of the proposed covariance intersection fusion Kalman filters are higher than that of each local Kalman filters, and is lower than that of optimal fuser weighted by matrices. The geometric interpretation of the accuracy relations is given by the covariance ellipses. A Monte-Carlo simulation example for a tracking system verifies the correctness of the theoretical accuracy relations.

Statistical properties of breath-to-breath variations in ventilation at constant Pet CO2 and Pet O2 in humans

1996 ◽  
Vol 81 (5) ◽  
pp. 2274-2286 ◽  
Author(s):  
Pei-Ji Liang ◽  
Jaideep J. Pandit ◽  
Peter A. Robbins
Keyword(s):  
State Space ◽  
Spectral Power ◽  
Moving Average ◽  
State Space Model ◽  
Statistical Properties ◽  
Autoregressive Moving Average ◽  
Data Sets ◽  
Arma Models ◽  
Space Model ◽  
End Tidal

Liang, Pei-Ji, Jaideep J. Pandit, and Peter A. Robbins. Statistical properties of breath-to-breath variations in ventilation at constant Pet CO2 and Pet O2 in humans. J. Appl. Physiol. 81(5): 2274–2286, 1996.—The purpose of this study was to provide a statistical description of the breath-to-breath variations in ventilation during steady breathing in both rest and during light exercise, with the end-tidal gases controlled by using an end-tidal forcing system. Sixty data sets were studied, only one of which was white (i.e., did not show autocorrelation). Three simple autoregressive moving average (ARMA) models, i.e., AR1, AR2, and AR1MA1, and one simple state-space model were fitted to the data and resulted in white residuals in 15, 31, 46, and 48 out of 60 occasions, respectively. Evolutionary spectral analysis revealed that only 13 data sets had a constant power spectrum, although 50 were uniformly modulated. An autoregressive estimate of variance could be used to “demodulate” the data in most cases, but the results were not significantly affected by fitting the model to the demodulated data. The results indicate that 1) both simple ARMA models and a simple state-space model can describe the autocorrelation present; 2) variations in spectral power were present in the data that cannot be described by these models; and 3) these variations were often due to a uniform modulation and did not significantly affect the coefficients for the models. For these kinds of data, a heteroscedastic form of state-space model provides an attractive theoretical structure for the noise processes.

Optimal Estimation for Multiple Packet Dropouts Systems with Colored Measurement Noise

2011 ◽  
Vol 135-136 ◽  
pp. 649-654
Author(s):  
Li Xin Yang ◽  
Li Jun Zhang ◽  
Li Dong Guo ◽  
He Ming Jia
Keyword(s):  
State Space Model ◽  
Optimal Estimation ◽  
Measurement Noise ◽  
Packet Dropouts ◽  
Space Model ◽  
Innovation Analysis ◽  
Measurement Noises ◽  
Simulation Results ◽  
Augmented State ◽  
Optimal Estimators

This paper is concerned with the optimal estimation problem for multiple packet dropouts systems with colored measurement noise. Using the latest received measurement value to replace the current missing data. Then, based on the augmented state space model, the optimal estimators including filter, predictor and smoother are developed via an innovation analysis approach for multiple packet dropouts systems with white and colored measurement noises. Finally, simulation results show the effectiveness and superiority of the proposed estimators.

scholarly journals A Time-Varying MIMO Generalized Minimum Variance Controller for Servo Application

2013 ◽  
Vol 321-324 ◽  
pp. 1593-1596 ◽  
Author(s):  
Zheng Li ◽  
Guo Li Wang
Keyword(s):  
Performance Index ◽  
Moving Average ◽  
Minimum Variance ◽  
Autoregressive Moving Average ◽  
Time Varying ◽  
Average Model ◽  
Autoregressive Moving Average Model ◽  
Multiple Input ◽  
Control Objective ◽  
Moving Average Model

A generalized minimum variance controller is developed for multiple input and multiple output systems having time-varying dynamics. The plant to be controlled is described using a controlled autoregressive moving average model and the control objective is to minimize a generalized minimum variance performance index for servo applications.

scholarly journals Value-at-Risk and Minimum Variance in the Investment Portfolio with Non Constant Volatility

2019 ◽  
Vol 8 (2S7) ◽  
pp. 197-202
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Moving Average ◽  
Minimum Variance ◽  
Capital Allocation ◽  
Autoregressive Moving Average ◽  
Investment Portfolio ◽  
Minimum Risk ◽  
Asset Return ◽  
Weighted Composition

One of the criteria for efficient portofilio is that it produces the same level of profit, but with minimum risk.This paper discusses the estimates Value-at-Risk and minimum variance on an investment portfolio.In this case it is assumed that the asset return follows the time series model. Therefore, non-constant meanis estimated using autoregressive moving average (ARMA) models.While non constant volatility is estimated using generalized autoregressive conditionaly heteroscedasticity (GARCH) models. To determine the minimum variance is done using Markowitz's model optimization. Furthermore, Value-at-Risk is calculated based on the values of the mean and minimum variance. The result of return analysis of assets of BBRI, INCI, LPBN, and MPPA, obtained the minimum variance value of 0.011734775, and at the 95% confidence level obtained Value-at-Risk of 0.017873889.The minimum variance and Value-at-Risk are obtained on the vector of the investment weighted composition as x' = (0.092827551, 0.212180907, 0.14631804, 0.548673502). So to get a minimum risk on the investment portfolio consisting of the four assets, the capital allocation must follow the vector of weighted composition produced

scholarly journals Semiparametric estimation of the canonical permanent‐transitory model of earnings dynamics

2019 ◽  
Vol 10 (4) ◽  
pp. 1495-1536 ◽  
Author(s):  
Yingyao Hu ◽  
Robert Moffitt ◽  
Yuya Sasaki
Keyword(s):  
Moving Average ◽  
State Space Model ◽  
Estimation Method ◽  
Higher Order ◽  
Autoregressive Moving Average ◽  
Earnings Mobility ◽  
Arma Process ◽  
Earnings Dynamics ◽  
Prior Literature ◽  
Transitory Component

This paper presents identification and estimation results for a flexible state space model. Our modification of the canonical model allows the permanent component to follow a unit root process and the transitory component to follow a semiparametric model of a higher‐order autoregressive‐moving‐average (ARMA) process. Using panel data of observed earnings, we establish identification of the nonparametric joint distributions for each of the permanent and transitory components over time. We apply the identification and estimation method to the earnings dynamics of U.S. men using the Panel Survey of Income Dynamics (PSID). The results show that the marginal distributions of permanent and transitory earnings components are more dispersed, more skewed, and have fatter tails than the normal and that earnings mobility is much lower than for the normal. We also find strong evidence for the existence of higher‐order ARMA processes in the transitory component, which lead to much different estimates of the distributions of and earnings mobility in the permanent component, implying that misspecification of the process for transitory earnings can affect estimated distributions of the permanent component and estimated earnings dynamics of that component. Thus our flexible model implies earnings dynamics for U.S. men different from much of the prior literature.

Optimal Control of Time-Varying Systems with Multiple Delays for Servo Appplications

2014 ◽  
Vol 496-500 ◽  
pp. 1556-1559
Author(s):  
Zheng Li ◽  
Steven X. Ding
Keyword(s):  
Optimal Control ◽  
Linear Time ◽  
Moving Average ◽  
Minimum Variance ◽  
Autoregressive Moving Average ◽  
Multiple Delays ◽  
Time Varying ◽  
Autoregressive Moving Average Model ◽  
Time Varying Systems ◽  
Moving Average Model

We study the problem of optimal control of linear time-varying systems for servo applications and develop a generalized minimum variance controller for a multi-input and multi-output controlled autoregressive moving average model with multiple delays. The controller is applicable to a large class of stochastic linear time-varying systems regardless variation speed in plant parameters.

Using The Fully Modified M Method In Estimating The Effect Of Cultivated Area On Barley Production In Iraq For The Period 1970-2018

2020 ◽  
Vol 2020 (66) ◽  
pp. 101-110
Author(s):  
. Azhar Kadhim Jbarah ◽  
Prof Dr. Ahmed Shaker Mohammed
Keyword(s):  
Regression Model ◽  
Moving Average ◽  
Estimation Method ◽  
Estimation Methods ◽  
Autoregressive Moving Average ◽  
Moving Average Models ◽  
Error Terms ◽  
Relationship Of ◽  
The Relationship ◽  
Barley Crop

The research is concerned with estimating the effect of the cultivated area of barley crop on the production of that crop by estimating the regression model representing the relationship of these two variables. The results of the tests indicated that the time series of the response variable values is stationary and the series of values of the explanatory variable were nonstationary and that they were integrated of order one ( I(1) ), these tests also indicate that the random error terms are auto correlated and can be modeled according to the mixed autoregressive-moving average models ARMA(p,q), for these results we cannot use the classical estimation method to estimate our regression model, therefore, a fully modified M method was adopted, which is a robust estimation methods, The estimated results indicate a positive significant relation between the production of barley crop and cultivated area.

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