Precision Measurement of Audio Frequency Voltage Based on the Least Squares Method and Application of the Method for Voltage Ratio Measurement

1996 ◽  
Vol 116 (5) ◽  
pp. 430-438 ◽  
Author(s):  
Toshihiko Yoshioka ◽  
Megumi Sato ◽  
Touru Yamazaki
Keyword(s):  
Least Squares ◽  
Precision Measurement ◽  
Least Squares Method ◽  
Audio Frequency ◽  
Ratio Measurement ◽  
Voltage Ratio

A Complex Voltage Ratio Measurement System for the Audio Frequency Range

2012 ◽  
Vol 239-240 ◽  
pp. 278-282
Author(s):  
Chang Xi Yue ◽  
Enrico Mohns ◽  
Feng Zhou ◽  
Min Lei ◽  
Shu Han Zhang ◽  
...  
Keyword(s):  
Measurement System ◽  
Input Voltage ◽  
Test Results ◽  
Audio Frequency ◽  
Frequency Range ◽  
Channel Switching ◽  
Ratio Measurement ◽  
Response Characteristics ◽  
Voltage Ratio ◽  
Audio Frequency Range

This paper describes the setup of a complex voltage ratio measurement system for the audio frequency range. A wideband two-channel digitizer and a differential analogue channel switching front-end are used as the heart of the system. The complex error, frequency response characteristics and short term stability of the system are tested in this paper. The errors range from 1×10-7at 50 Hz to 10×10-6at 200 kHz in ratio 1:1 test with 6 V input voltages. And errors are below ±8×10-7and ±0.06 μrad in ratio 1:1 test with a 4V power line (50 Hz) input voltage over 64 hours. The test results and comparisons between with and without channel exchange mode confirm the remarkable improvement regarding the suppression of the static mismatch errors of the digitizer and show the usefulness of the system at 50 Hz too.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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