Auto-zero/Auto-calibration

Revision as of 09:35, 14 August 2010 by Rrogers314 (Talk | contribs)

Mathematical Formulation

Let

$LaTeX: x\,$ a vector of some environmental or control variables that need to be estimated
$LaTeX: \bar{x}$ a vector of calibration points
$LaTeX: \hat{x}$ be the estimate of $LaTeX: x\,$
a vector of nominal values of uncertain parameters affecting the measurement
- Assumed constant or designed in
be the errors in
- Assumed to vary but constant in the intervals between calibrations and real measurements
be the results of a measurement processes attempting to measure
- $LaTeX: y=Y(x;p,e)\,$ where $LaTeX: e\,$ might be additive, multiplicative, or some other form.
- $LaTeX: \bar{y}=Y(\bar{x};p,e)$ the reading values at the calibration points
- Subsequently $LaTeX: p\,$ will be assumed fixed for the problem realm; and dropped from notation
be estimates of derived from
- $LaTeX: \hat{e}=E(\bar{x},\bar{y})$
be a quality measure of resulting estimation; for example
- Where $LaTeX: x\,$ is allowed to vary over a domain for fixed $LaTeX: \hat{x}$
- The example is oversimplified as will be demonstrated below.