Auto-zero/Auto-calibration

(Difference between revisions)

Revision as of 08:28, 14 August 2010

Let

$LaTeX: x_i\,$ be some environmental or control variables that need to be estimated
$LaTeX: \hat{x}_i$ be the estimates of $LaTeX: x_i\,$
$LaTeX: Q(x,\hat{x})$ be a quality measure of resulting estimation; for example $LaTeX: \sum{(x_i-\hat{x_i})^2}$ .
$LaTeX: y_j\,$ be the results of a measurement processes attempting to measure $LaTeX: x_i\,$
$LaTeX: p_k\,$ be uncertain parameters affecting the measurement
$LaTeX: e_k\,$ be the errors in $LaTeX: p_k\,$ referred to nominal.
$LaTeX: \hat{e}_k$ be the estimates of $LaTeX: e_k\,$

Then the problem can be formulated as:

@@ Line 1: / Line 1: @@
-==  Formulation ==
+==  Mathematical Formulation ==
 Let
-*<math>x_i</math> be some environmental or control variables that need to be estimated
+*<math> x_i\, </math> be some environmental or control variables that need to be estimated
-*<math>\hat{x}_i</math> be the estimates of <math>x_i</math>
+*<math>\hat{x}_i</math> be the estimates of <math>x_i\,</math>
-* <math>y_j</math> be the results of a measurement processes attempting to measure <math>x_i</math>
+*<math>Q(x,\hat{x})</math> be a quality measure of resulting estimation; for example <math>\sum{(x_i-\hat{x_i})^2}</math>.
-*<math>p_k</math> be uncertain parameters affecting the measurement
+* <math>y_j\,</math> be the results of a measurement processes attempting to measure <math>x_i\,</math>
-*<math>e_k</math> be the errors in <math>p_k</math> referred to nominal.
+*<math>p_k\,</math> be uncertain parameters affecting the measurement
-*<math>\hat{e}_k</math> be the estimates of <math>e_k</math>
+*<math>e_k\,</math> be the errors in <math>p_k\,</math> referred to nominal.
+*<math>\hat{e}_k</math> be the estimates of <math>e_k\,</math>
 Then the problem can be formulated as:
+*Given  <math>y_j\,</math>
+*Find a formula/process