Jacobian
Definition: The matrix of partial derivatives that maps small input changes into output changes.
Why it matters here: In Uncertainty Propagation and Calibration, Jacobian is needed to reason about Jacobians, covariance, systematic offsets, and calibration transfer rather than merely label the phenomenon.
Relationship: It is interpreted alongside Covariance and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The propagation is local; the offset is shared and is not independent noise.
\(C_y=J C_x J^T+C_sys\)
Covariance
Definition: The joint variation of two quantities, including correlated measurement or calibration errors.
Why it matters here: In Uncertainty Propagation and Calibration, Covariance is needed to reason about Jacobians, covariance, systematic offsets, and calibration transfer rather than merely label the phenomenon.
Relationship: It is interpreted alongside Systematic offset and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The propagation is local; the offset is shared and is not independent noise.
Systematic offset
Definition: A shared displacement from the target scale that does not average away with more measurements.
Why it matters here: In Uncertainty Propagation and Calibration, Systematic offset is needed to reason about Jacobians, covariance, systematic offsets, and calibration transfer rather than merely label the phenomenon.
Relationship: It is interpreted alongside Calibration transfer and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The propagation is local; the offset is shared and is not independent noise.
Calibration transfer
Definition: The propagation of a reference standard through an instrument or analysis chain to science measurements.
Why it matters here: In Uncertainty Propagation and Calibration, Calibration transfer is needed to reason about Jacobians, covariance, systematic offsets, and calibration transfer rather than merely label the phenomenon.
Relationship: It is interpreted alongside Uncertainty budget and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The propagation is local; the offset is shared and is not independent noise.
Uncertainty budget
Definition: A structured accounting of statistical, calibration, selection, and model contributions to uncertainty.
Why it matters here: In Uncertainty Propagation and Calibration, Uncertainty budget is needed to reason about Jacobians, covariance, systematic offsets, and calibration transfer rather than merely label the phenomenon.
Relationship: It is interpreted alongside Jacobian and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: The propagation is local; the offset is shared and is not independent noise.