scholarly journals A distributed minimum variance estimator for sensor networks

2008 ◽  
Vol 26 (4) ◽  
pp. 609-621 ◽  
Author(s):  
A. Speranzon ◽  
C. Fischione ◽  
K. Johansson ◽  
A. Sangiovanni-Vincentelli
Keyword(s):  
Sensor Networks ◽  
Minimum Variance ◽  
Variance Estimator ◽  
Minimum Variance Estimator

Fast minimum variance estimator for limited angle CT image reconstruction

1981 ◽  
Vol 8 (5) ◽  
pp. 695-702 ◽  
Author(s):  
Michael H. Buonocore ◽  
William R. Brody ◽  
Albert Macovski
Keyword(s):  
Image Reconstruction ◽  
Minimum Variance ◽  
Ct Image ◽  
Variance Estimator ◽  
Minimum Variance Estimator ◽  
Ct Image Reconstruction ◽  
Limited Angle

scholarly journals Error Propagation of Capon’s Minimum Variance Estimator

2021 ◽  
Vol 9 ◽  
Author(s):  
S. Toepfer ◽  
Y. Narita ◽  
D. Heyner ◽  
U. Motschmann
Keyword(s):  
Measurement Errors ◽  
Error Propagation ◽  
Minimum Variance ◽  
Least Square ◽  
Variance Estimator ◽  
Position Errors ◽  
Minimum Variance Estimator ◽  
Least Square Fit ◽  
Special Case ◽  
Key Parameter

The error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix which describes the location depence of the measurement positions is the key parameter for the error propagation, since the condition number of the shape matrix determines how the errors are amplified. Furthermore, the error resulting from a finite number of data samples is derived by regarding Capon’s estimator as a special case of the maximum likelihood estimator.

The Gauss Markov Theorem: A Pedagogical Note

2001 ◽  
Vol 45 (1) ◽  
pp. 92-94 ◽  
Author(s):  
Ralph C. Allen ◽  
Jack H. Stone
Keyword(s):  
Least Squares ◽  
Ordinary Least Squares ◽  
Minimum Variance ◽  
Variance Estimator ◽  
Unique Minimum ◽  
Unbiased Estimators ◽  
Markov Theorem ◽  
Minimum Variance Estimator ◽  
Per Se

When stating the Gauss-Markov theorem, undergraduate econometric textbooks generally imply that the ordinary least squares (OLS) estimator has minimum variance. However, the proof of the Gauss Markov theorem indicates that the weights produced by the OLS estimator–not the formula per se–produce the unique minimum–variance estimator. An example demonstrates that other linear unbiased estimators can yield the same variance as the OLS estimator; however, the weights from such formulas are identical to the OLS weights. To avoid this pedagogical confusion, the statement of the theorem should emphasize the weights rather than the estimator itself.

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