This paper presents an optimized algorithm for real-time implementation of the Simultaneous Localization and Map Building (SLAM) algorithm. The algorithm reduces computational requirements while maintaining accuracy. It introduces a compressed filter that stores and maintains information from a local area with a cost proportional to the square of the number of landmarks in that area. This information can then be transferred to the global map with a cost similar to full SLAM but in one iteration. The algorithm is validated with experimental results from a standard vehicle operating in an unstructured outdoor environment. The paper discusses the challenges of SLAM, including computational complexity and the need for efficient algorithms. It presents an optimized SLAM algorithm that reduces the complexity from O(M³) to O(M²), where M is the number of landmarks plus the number of vehicle states. A compressed filter is introduced to further reduce computational requirements, making the algorithm efficient for real-time applications. The paper also presents a sub-optimal simplification of the SLAM algorithm that reduces computational requirements by considering a subset of navigation landmarks. This approach is conservative and consistent, and can generate results close to optimal when combined with an appropriate relative map representation. The paper introduces a relative map representation that groups landmarks into constellations, each with an associated frame based on two landmarks. This representation reduces cross-correlations between landmarks of different regions, making the algorithm less conservative. The experimental results show that the optimized SLAM algorithm can effectively navigate in an unstructured outdoor environment. The algorithm maintains accurate localization and map building while significantly reducing computational requirements. The results demonstrate the effectiveness of the proposed algorithms in real-time applications.This paper presents an optimized algorithm for real-time implementation of the Simultaneous Localization and Map Building (SLAM) algorithm. The algorithm reduces computational requirements while maintaining accuracy. It introduces a compressed filter that stores and maintains information from a local area with a cost proportional to the square of the number of landmarks in that area. This information can then be transferred to the global map with a cost similar to full SLAM but in one iteration. The algorithm is validated with experimental results from a standard vehicle operating in an unstructured outdoor environment. The paper discusses the challenges of SLAM, including computational complexity and the need for efficient algorithms. It presents an optimized SLAM algorithm that reduces the complexity from O(M³) to O(M²), where M is the number of landmarks plus the number of vehicle states. A compressed filter is introduced to further reduce computational requirements, making the algorithm efficient for real-time applications. The paper also presents a sub-optimal simplification of the SLAM algorithm that reduces computational requirements by considering a subset of navigation landmarks. This approach is conservative and consistent, and can generate results close to optimal when combined with an appropriate relative map representation. The paper introduces a relative map representation that groups landmarks into constellations, each with an associated frame based on two landmarks. This representation reduces cross-correlations between landmarks of different regions, making the algorithm less conservative. The experimental results show that the optimized SLAM algorithm can effectively navigate in an unstructured outdoor environment. The algorithm maintains accurate localization and map building while significantly reducing computational requirements. The results demonstrate the effectiveness of the proposed algorithms in real-time applications.