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Excalibur is a non-parametric, hierarchical framework for precisionwavelength-calibration of spectrographs. It is designed with the needs ofextreme-precision radial velocity (EPRV) in mind, which require thatinstruments be calibrated or stabilized to better than $10^{-4}$ pixels.Instruments vary along only a few dominant degrees of freedom, especially EPRVinstruments that feature highly stabilized optical systems and detectors.Excalibur takes advantage of this property by using all calibration data toconstruct a low-dimensional representation of all accessible calibration statesfor an instrument. Excalibur also takes advantage of laser frequency combs oretalons, which generate a dense set of stable calibration points. This densitypermits the use of a non-parametric wavelength solution that can adapt to anyinstrument or detector oddities better than parametric models, such as apolynomial. We demonstrate the success of this method with data from theEXtreme PREcision Spectrograph (EXPRES), which uses a laser frequency comb.When wavelengths are assigned to laser comb lines using excalibur, the RMS ofthe residuals is about five times lower than wavelengths assigned usingpolynomial fits to individual exposures. Radial-velocity measurements of HD34411 showed a reduction in RMS scatter over a 10-month time baseline from$1.17$ to $1.05\, m\,s^{-1}$.

Excalibur: A Non-Parametric, Hierarchical Wavelength-Calibration Method for a Precision Spectrograph