iSAM is an incremental smoothing and mapping algorithm that efficiently solves the simultaneous localization and mapping (SLAM) problem using fast incremental matrix factorization. It updates a QR factorization of the naturally sparse smoothing information matrix, recalculating only the matrix entries that change. This approach is efficient even for robot trajectories with many loops, as it avoids unnecessary fill-in in the factor matrix by periodic variable reordering. iSAM also enables real-time data association by efficiently accessing estimation uncertainties based on the factored information matrix. The algorithm works by incrementally updating the square root information matrix with new measurements as they arrive, reusing previously calculated components and only performing calculations for entries affected by new measurements. This results in a local and constant time operation for exploration tasks. For trajectories with loops, periodic variable reordering prevents unnecessary fill-in in the square root factor, which would otherwise slow down incremental updates and back-substitution. Incremental mapping also requires online data association, so iSAM provides efficient algorithms to access relevant estimation uncertainties from the incrementally updated square root factor. The key insight is that only some entries of the full covariance matrix are needed, and iSAM focuses on the relevant parts by exploiting the sparsity of the square root factor. It also provides conservative estimates derived from the square root factor. iSAM is evaluated on simulated and real-world datasets for both landmark-based and pose-only settings. The pose-only setting is a special case where no landmarks are used, but general pose constraints between pairs of poses are considered. Results show that iSAM provides an efficient and exact solution for both types of SLAM settings, with the square root factor remaining sparse even for large-scale environments with many loops. The paper presents iSAM as an incremental solution to SLAM, using QR matrix factorization to solve the least squares problem. It discusses how iSAM handles loops in the robot trajectory and nonlinear sensor measurement functions. The algorithm is efficient for both landmark-based and pose constraint-based SLAM, with performance evaluated on simulated and real-world datasets. The results show that iSAM is significantly faster than real-time for large-scale environments, with the square root factor remaining sparse and efficient for computation.iSAM is an incremental smoothing and mapping algorithm that efficiently solves the simultaneous localization and mapping (SLAM) problem using fast incremental matrix factorization. It updates a QR factorization of the naturally sparse smoothing information matrix, recalculating only the matrix entries that change. This approach is efficient even for robot trajectories with many loops, as it avoids unnecessary fill-in in the factor matrix by periodic variable reordering. iSAM also enables real-time data association by efficiently accessing estimation uncertainties based on the factored information matrix. The algorithm works by incrementally updating the square root information matrix with new measurements as they arrive, reusing previously calculated components and only performing calculations for entries affected by new measurements. This results in a local and constant time operation for exploration tasks. For trajectories with loops, periodic variable reordering prevents unnecessary fill-in in the square root factor, which would otherwise slow down incremental updates and back-substitution. Incremental mapping also requires online data association, so iSAM provides efficient algorithms to access relevant estimation uncertainties from the incrementally updated square root factor. The key insight is that only some entries of the full covariance matrix are needed, and iSAM focuses on the relevant parts by exploiting the sparsity of the square root factor. It also provides conservative estimates derived from the square root factor. iSAM is evaluated on simulated and real-world datasets for both landmark-based and pose-only settings. The pose-only setting is a special case where no landmarks are used, but general pose constraints between pairs of poses are considered. Results show that iSAM provides an efficient and exact solution for both types of SLAM settings, with the square root factor remaining sparse even for large-scale environments with many loops. The paper presents iSAM as an incremental solution to SLAM, using QR matrix factorization to solve the least squares problem. It discusses how iSAM handles loops in the robot trajectory and nonlinear sensor measurement functions. The algorithm is efficient for both landmark-based and pose constraint-based SLAM, with performance evaluated on simulated and real-world datasets. The results show that iSAM is significantly faster than real-time for large-scale environments, with the square root factor remaining sparse and efficient for computation.