scholarly journals Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 572
Author(s):  
Todd K. Moon ◽  
Jacob H. Gunther
Keyword(s):  
Weighted Least Squares ◽  
Estimation Algorithm ◽  
Ar Model ◽  
Parameter Estimates ◽  
Spectrum Estimation ◽  
Vector Autoregressive ◽  
Performance Improvements ◽  
Weighted Least Squares Estimation ◽  
Noisy Measurements ◽  
Unknown Covariance

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation.

The Power Spectrum Estimation of the AR Model Based on Motor Imagery EEG

2013 ◽  
Vol 706-708 ◽  
pp. 1923-1927 ◽  
Author(s):  
Li Zhao ◽  
Yang He
Keyword(s):  
Power Spectrum ◽  
Motor Imagery ◽  
Ar Model ◽  
Spectrum Estimation ◽  
Power Spectrum Estimation ◽  
Estimation Algorithms ◽  
Model Based

This paper uses three common AR model power spectrum estimation algorithms which are the Yule-Walker method, the burg method and the improved covariance method. Taking Matlab as a tool, the corresponding algorithms are used to carry out the power spectrum estimation of motor imagery EEG, the relationships and distinctions between the spectrum charts are compared in order to find the relatively appropriate algorithm for analyzing the EEG, which aims at providing a theoretical guidance for processing the motor imagery EEG and laying a foundation for further research.

Effects of errors-in-variables on weighted least squares estimation

2014 ◽  
Vol 88 (7) ◽  
pp. 705-716 ◽  
Author(s):  
Peiliang Xu ◽  
Jingnan Liu ◽  
Wenxian Zeng ◽  
Yunzhong Shen
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Least Squares Estimation ◽  
Errors In Variables ◽  
Weighted Least Squares Estimation

scholarly journals Robust and Fast State Estimation for Poorly-Observable Low Voltage Distribution Networks Based on the Kalman Filter Algorithm

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4457 ◽  
Author(s):  
Antončič ◽  
Papič ◽  
Blažič
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Low Voltage ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Estimation Algorithm ◽  
Distribution Networks ◽  
Voltage Distribution ◽  
State Estimator

This paper presents a novel approach for the state estimation of poorly-observable low voltage distribution networks, characterized by intermittent and erroneous measurements. The developed state estimation algorithm is based on the Extended Kalman filter, where we have modified the execution of the filtering process. Namely, we have fixed the Kalman gain and Jacobian matrices to constant matrices; their values change only after a larger disturbance in the network. This allows for a fast and robust estimation of the network state. The performance of the proposed state-estimation algorithm is validated by means of simulations of an actual low-voltage network with actual field measurement data. Two different cases are presented. The results of the developed state estimator are compared to a classical estimator based on the weighted least squares method. The comparison shows that the developed state estimator outperforms the classical one in terms of calculation speed and, in case of spurious measurements errors, also in terms of accuracy.

scholarly journals A New Online Dynamic Testing Method for Noise of Broadcast Transmitter

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shan-Shan Li ◽  
Jian Zhou ◽  
Xuan Wang
Keyword(s):  
Real Time ◽  
Data Storage ◽  
Dynamic Testing ◽  
Noise Figure ◽  
Estimation Algorithm ◽  
Test Method ◽  
Noise Estimation ◽  
Experimental Simulation ◽  
Spectrum Estimation ◽  
Low Efficiency

Aiming at the shortcomings of traditional broadcast transmitter noise test methods, such as low efficiency, inconvenient data storage, and high requirements for testers, a dynamic online test method for transmitter noise is proposed. The principle of system composition and test method is given. The transmitter noise is real-time changing. The Voice Active Detection (VAD) noise estimation algorithm cannot track the transmitter noise change in real time. This paper proposes a combined noise estimation algorithm for VAD and dynamic estimation. By setting the threshold of the double-threshold VAD detection to be low, it can accurately detect the silent segment. The silent segment is used as a noise signal for noise estimation. For the nonsilent segment detected by the VAD, a minimum value search dynamic spectrum estimation algorithm based on the existence probability of the speech (IMCRA) is used for noise estimation. Transmitter noise is measured by calculating the noise figure (NF).The test method collects the input and output data of the transmitter in real time, which has better accuracy and real-time performance, and the feasibility of the method is verified by experimental simulation.

scholarly journals Analysis of algebraic weighted least-squares estimators for enzyme parameters

1992 ◽  
Vol 288 (2) ◽  
pp. 533-538 ◽  
Author(s):  
M E Jones
Keyword(s):  
Least Squares ◽  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Weighted Least Squares ◽  
Simulated Data ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Spreadsheet Program ◽  
Least Squares Estimators ◽  
Constant Coefficient Of Variation

An algorithm for the least-squares estimation of enzyme parameters Km and Vmax. is proposed and its performance analysed. The problem is non-linear, but the algorithm is algebraic and does not require initial parameter estimates. On a spreadsheet program such as MINITAB, it may be coded in as few as ten instructions. The algorithm derives an intermediate estimate of Km and Vmax. appropriate to data with a constant coefficient of variation and then applies a single reweighting. Its performance using simulated data with a variety of error structures is compared with that of the classical reciprocal transforms and to both appropriately and inappropriately weighted direct least-squares estimators. Three approaches to estimating the standard errors of the parameter estimates are discussed, and one suitable for spreadsheet implementation is illustrated.

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