There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator (MEAE), whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator (SEAE), whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE,and simulation results demonstrate the efficacy of the presented algorithm.