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The paper analyzes the properties of the full covariance simultaneous localization and map building problem (SLAM). We prove that, even for the special case of a stationary vehicle (with no process noise) which uses a range-bearing sensor and has non-zero angular uncertainty, the full covariance SLAM algorithm always yields an inconsistent map. We also show, through simulations, that these conclusions appear to extend to a moving vehicle with process noise. However, these inconsistencies only become apparent after several hundred beacon updates.