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The purpose of this note is to derive alternative formulae for parameter estimation in partial errors-in-variables models to those given in Xu et al. (J Geod 86:661-675, ). We show that these new formulae are more compact and more straightforward to interpret the corrections of the random elements of the design matrix. Nevertheless, each formula has its own computational advantage, depending on the relationship between the number of measurements y and that of the independent random elements of the design matrix. The original formula is computationally more efficient, if the number of measurements y is significantly larger than that of the independent random elements of the design matrix; otherwise, the new alternative formula is much more efficient. [ABSTRACT FROM AUTHOR]