Applying the Cramer-Rao Lower Bound to Spectroscopic Measurements

Details Applying the Cramer-Rao Lower Bound to Spectroscopic Measurements Applying the Cramer-Rao Lower Bound to Spectroscopic Measurements

May 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004aas...204.7608i&link_type=abstract

American Astronomical Society Meeting 204, #76.08; Bulletin of the American Astronomical Society, Vol. 36, p.807

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Solar spectra, through emission line models, can provide detailed diagnostics on the state of their emitting volume. Estimates of the emission line model parameters are found by fitting the model to the data. It is shown, via the application of Cramer-Rao lower bounds, that there are calculable lower limits to the achievable precision with which we can know the parameter estimates. The limits depend on how much is known about the spectrum prior to the fit, the spectral line model, the model spectrometer and the noise in the data.
A Cramer-Rao lower bound analysis introduces a theoretical framework in which questions of line fitting in particular, and spectrometers in general, may be posed. Some example applications are given and their implication for the design of spectrometric observations are discussed. This work is funded by NASA, contract number NNH04CC31C.

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