Discrete-Time Least Squares, Minimum Mean Square Error, and Minimax Estimation

1966 ◽  
Vol 14 (3) ◽  
pp. 302-308 ◽  
Author(s):  
S. Alterman
Integers ◽  
2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Paul Shaman

AbstractThe Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson–Durbin sequence is also defined, and we note that binomial coefficients constitute a special case of such a sequence. Generalized Levinson–Durbin sequences obey formulas which generalize relations satisfied by binomial coefficients. Some of these results are extended to vector stationary processes.


Author(s):  
Luiz W. P. Biscainho ◽  
Paulo S. R. Diniz ◽  
Mauro F. de Carvalho

This paper addresses the effects of the quantization of an audio signal on the Least-Squares (LS) estimate of its autoregressive (AR) model. First, three topics are reviewed: the statistical description of the quantization error in terms of the number of bits used in fixed-point representation for a signal; the LS estimation of the AR model for a signal; and the relation between Minimum Mean-Square Error (MMSE) solutions for the AR model obtained from noisy and noiseless signals. The sensitivity of the associated generator filter poles localization (expressed by magnitudes and phases) to the deviation of the model parameters is examined. Through the interconnection of these aspects, the deviation of the model coefficients is described in terms of the number of bits used to represent the signal to be modeled, which allows for model correction. Conclusions about peculiarities of the pole deviation of the generator filter are drawn.


2019 ◽  
Vol 28 (1) ◽  
pp. 145-152
Author(s):  
Abd El-aziz Ebrahim Hsaneen ◽  
EL-Sayed M. El-Rabaei ◽  
Moawad I. Dessouky ◽  
Ghada El-bamby ◽  
Fathi E. Abd El-Samie ◽  
...  

2021 ◽  
Vol 11 (9) ◽  
pp. 3763
Author(s):  
Yunlong Zou ◽  
Jinyu Zhao ◽  
Yuanhao Wu ◽  
Bin Wang

Space object recognition in high Earth orbits (between 2000 km and 36,000 km) is affected by moonlight and clouds, resulting in some bright or saturated image areas and uneven image backgrounds. It is difficult to separate dim objects from complex backgrounds with gray thresholding methods alone. In this paper, we present a segmentation method of star images with complex backgrounds based on correlation between space objects and one-dimensional (1D) Gaussian morphology, and the focus is shifted from gray thresholding to correlation thresholding. We build 1D Gaussian functions with five consecutive column data of an image as a group based on minimum mean square error rules, and the correlation coefficients between the column data and functions are used to extract objects and stars. Then, lateral correlation is repeated around the identified objects and stars to ensure their complete outlines, and false alarms are removed by setting two values, the standard deviation and the ratio of mean square error and variance. We analyze the selection process of each thresholding, and experimental results demonstrate that our proposed correlation segmentation method has obvious advantages in complex backgrounds, which is attractive for object detection and tracking on a cloudy and bright moonlit night.


Author(s):  
Eiichi Yoshikawa ◽  
Naoya Takizawa ◽  
Hiroshi Kikuchi ◽  
Tomoaki Mega ◽  
Tomoo Ushio

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