Sparse extended information filters: insights into sparsification

Recently, there have been a number of variant simultaneous localization and mapping (SLAM) algorithms that have made substantial progress towards large-area scalability by parameterizing the SLAM posterior within the information (canonical/inverse covariance) form. Of these, probably the most well known and popular approach is the sparse extended information filter (SEIF) by Thrun et al. While SEIFs have been successfully implemented with a variety of challenging real world datasets and have led to new insights into scalable SLAM, open research questions remain regarding the approximate sparsification procedure and its effect on map error consistency. In this paper, we examine the constant time SEIF sparsification procedure in depth and offer new insight into issues of consistency. In particular, we show that exaggerated map inconsistency occurs within the global reference frame where estimation is performed, but that empirical testing shows that relative local map relationships are preserved. We then present a slightly modified version of their sparsification procedure, which is shown to preserve sparsity while also generating both local and global map estimates comparable to those obtained by the nonsparsified SLAM filter. While this modified approximation is no longer constant time, it does serve as a theoretical benchmark against which to compare SEIFs constant time results. We demonstrate our findings by benchmark comparison of the modified and original SEIF sparsification rule using simulation in the linear Gaussian SLAM case and real world experiments for a nonlinear dataset.