Auto-zero/Auto-calibration

(Difference between revisions)

Revision as of 07:39, 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 $LaTeX: x_i$
$LaTeX: y_j$ 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: @@
-I have been working on creating a robust design structure for the design of Auto-Zero/Auto-calibration
+==  Formulation ==
-implementations.  I have a lot of moving parts in my head; but I believe I need outside viewpoints and knowledge in  order to construct a general approach.
+Let
-If anybody is interested please respond here.  It is a bit more complicated than it would seem on the surface IMHO. I somewhat think it falls within convex optimization.  On the other hand I sometimes think it doesn't.
+*<math>x_i</math> be some environmental or control variables that need to be estimated
-I do have a particular example that illustrates the various problems that can arise.  Although the ideas should be applicable to Scientific measurements; the applications I have in mind relate to autonomous embedded software and hardware implementations.
+*<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>
-Ray
+*<math>p_k</math> be uncertain parameters affecting the measurement
+*<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: