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This paper deals with the theoretical investigation of the importance of cross-correlation in mobile robot localization. Two different case studies were conducted to examine the effects of crosscorrelation terms on the estimation. The first case refers to a situation when a mobile robot moves and calculates its position relative to a landmark, while in the second case the mobile robot is independent of the landmark position. The preliminary results obtained have indicated that the updated state covariance of the mobile robot that is independent of the landmark position could decrease or increase compared to that of the mobile robot that depends on the landmark position. The results are then evaluated through simulation which is consistently agrees with the theoretical results.