Reference control points（RCPs） used to establish the regression model in registration are commonly assumed "perfect".However

this assumption is often violated in practice due to the reason that RCPs actually always containing errors.Moreover

the errors in RCPs are one of main sources lowering the accuracy of image registration of uncorrected image.In this case Ordinary least squares（OLS） estimator

widely used in the image registration of remotely sensed data

is biased and does not have the ability to handle explanatory variables with error and to propagate appropriately errors from RCPs to the corrected image.In this paper

we introduce the consistent adjusted least squares（CALS） estimator and propose a relaxed consistent adjusted least squares（RCALS） method

which can be applied to more general relationship

for registration.These estimators have good capability in correcting errors contained in the RCPs

and to propagate correctly errors of the RCPs to the corrected image with and without prior information.The objective of the CALS and our proposed RCALS estimators is to improve the accuracy of measurement value by weakening the measurement errors.For validating CALS and RCALS estimators

we employ the CALS and RCALS estimators using real-life remotely sensed data.It has been argued and demonstrated that CALS and RCALS estimators give superior overall performances in estimating the regression coefficients and variance of measurement error.