Reference control points (RCPs) used in establishing the regression model in the regis-tration or geometric correction of remote sensing images are generally assumed to be “perfect”. That is, the RCPs, as explanatory variables in the regression equation, are accurate and the coordinates of their locations have no errors. Thus ordinary least squares (OLS) estimator has been applied exten-sively to the registration or geometric correction of remotely sensed data. However, this assumption is often invalid in practice because RCPs always contain errors. Moreover, the errors are actually one of the main sources which lower the accuracy of geometric correction of an uncorrected image. Under this situation, the OLS estimator is biased. It cannot handle explanatory variables with errors and cannot propagate appropriately errors from the RCPs to the corrected image. Therefore, it is essential to develop new feasible methods to overcome such a problem. This paper introduces a consistent adjusted least squares (CALS) estimator and proposes relaxed consistent adjusted least squares (RCALS) estimator, with the latter being more general and flexible, for geometric correction or regis-tration. These estimators have good capability in correcting errors contained in the RCPs, and in propagating appropriately errors of the RCPs to the corrected image with and without prior information. The objective of the CALS and proposed RCALS estimators is to improve the accuracy of measure-ment value by weakening the measurement errors. The conceptual arguments are substantiated by a real remotely sensed data. Compared to the OLS estimator, the CALS and RCALS estimators give a superior overall performance in estimating the regression coefficients and variance of measurement errors. Reference control points (RCPs) used in establishing the regression model in the regis-tration or geometric correction of remote sensing images are generally assumed to be “perfect.” That is, the RCPs, as explanatory variables in the regression equation, are accurate and However, this coordinates of their locations have no errors. As ordinary least squares (OLS) estimator has been applied exten-sively to the registration or geometric correction of remotely sensed data. However, this assumption is often invalid in practice because RCPs always contain inaccuracies. , the errors are actually one of the main sources which lower the accuracy of geometric correction of an uncorrected image. Under this situation, the OLS estimator is biased. image. Therefore, it is essential to develop new feasible methods to overcome such a problem. This paper introduces a consistent adju These estimators have good capabilities in correcting errors contained in the RCPs, and in propagating appropriately errors of the RCPs to the corrected image with and without prior information. The objective of the CALS and proposed RCALS estimators is to improve the accuracy of measure-ment value by weakening the measurement errors. The conceptual arguments are substantiated by a real Compared to the OLS estimator, the CALS and RCALS estimators give a superior overall performance in estimating the regression coefficients and variance of measurement errors.