Please see my papers:

Article Spatial models for non-Gaussian data with covariate measurement error

and

Article Non-Gaussian Covariate-Dependent Spatial Measurement Error M...

Hi. You have asked a question about what are called errors in variables models, i.e. regression models where both the Y and Xi are measured with error not just Y. there is a literature on proposed solutions. The following article may get you started. Then Google things like errors in variables regression for a lead in to the literature. This is a difficult but interesting area. Best wishes, David

https://en.wikipedia.org/wiki/Errors-in-variables_models

For software google errors in variables models R

Hi, I know what are errors in variables. What I look for is the specific solution to the problem stated above. Can you provide me with any specific sollution to my problem?

If the model is linear in the coefficients of the respective variables and the error distribution is symmetric, then the estimates of a standard linear regression model will be unbiased. Otherwise, things are quite complicated anyway and need a special consideration of your model and your error structure.

Thanks for your answer Jochen Wilhelm. Could you recommend any literature?

The proper choice of a model depends on the situation that you are modeling. Out of the set of possible models choose the one that best matches your situation. No model works for everything.