Auto-zero/Auto-calibration
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(Difference between revisions)
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- | == Formulation == | + | == Mathematical Formulation == |
Let | 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: | Then the problem can be formulated as: | ||
+ | *Given <math>y_j\,</math> | ||
+ | *Find a formula/process |
Revision as of 08:28, 14 August 2010
Mathematical Formulation
Let
- be some environmental or control variables that need to be estimated
- be the estimates of
- be a quality measure of resulting estimation; for example .
- be the results of a measurement processes attempting to measure
- be uncertain parameters affecting the measurement
- be the errors in referred to nominal.
- be the estimates of
Then the problem can be formulated as:
- Given
- Find a formula/process