This one has some neat Bayesian takes on mesueement error. https://www.crcpress.com/The-BUGS-Book-A-Practical-Introduction-to-Bayesian-Analysis/Lunn-Jackson-Best-Thomas-Spiegelhalter/p/book/9781584888499 … Alternatively BDA3 by Gelman et al. Simply put: model the measurement error process, and use Stan or Jags to estimate.
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Personally I find the Bugs book very readable. BDA3 is the proper, updated version with newer software. All works from R, btw.
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