## Sparse extended information filters: Insights into sparsification (2005)

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Venue: | in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems |

Citations: | 32 - 8 self |

### BibTeX

@INPROCEEDINGS{Eustice05sparseextended,

author = {Ryan Eustice and Woods Hole Ma},

title = {Sparse extended information filters: Insights into sparsification},

booktitle = {in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems},

year = {2005},

pages = {641--648}

}

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### Abstract

Abstract — Recently, there have been a number of variant Simultaneous Localization and Mapping (SLAM) algorithms which 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 data sets and have lead to new insights into scalable SLAM, open research questions remain regarding the approximate sparsification procedure and its effect on map error and 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 non-sparsified SLAM filter; this modified approximation, however, is no longer constant-time. 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. I.

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Citation Context ... the particular value of α we choose modifies the posterior approximation. Equations (5)–(8) summarize the SEIF sparsified posterior (4) as expressed in both covariance and information form (refer to =-=[14]-=- for a full derivation). For ease of comparison we use the same notation as [4] where S denotes a projection matrix over the state space ξt (e.g., xt = S⊤ xtξt extracts the robot pose). Note that the ... |

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Citation Context ...6], [7] — all based upon the canonical-form which has the nice interpretation as a Gaussian graphical model [5], [8]. As Thrun et al. [4] empirically first showed, and Frese later analytically proved =-=[9]-=-, the inverse covariance matrix Matthew Walter and John Leonard Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology Cambridge, MA, USA {mwalter,jleonard}@mit.... |

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Citation Context ... is limited to relatively small environments (e.g., less than than 100 landmarks). Recently, a new class of scalable SLAM algorithms have been proposed by Thrun et al. [4], Paskin [5], and Frese [6], =-=[7]-=- — all based upon the canonical-form which has the nice interpretation as a Gaussian graphical model [5], [8]. As Thrun et al. [4] empirically first showed, and Frese later analytically proved [9], th... |

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Exactly sparse delayed state filters
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Citation Context ...n of xt (see Table I for details of marginalization in the information form) while passive features remain unaffected; for a more in depth discussion of this phenomenon the reader is referred to [5], =-=[12]-=-. Insightfully, as Fig. 2(b) shows, we can control the active feature fill-in of the information matrix by bounding the number of links connected to xt before marginalization occurs. This key insight ... |

1 | culminating advance in the theory and practice of data fusion, filtering, and decentralized estimation,” Covariance Intersection Working Group (CIWG
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Citation Context ...c ρacρbcσaσb σ 2 b ρbcσbσc ρacσaσc ρbcσbσc σ 2 c ⎤⎞ ⎦⎠. (17) A necessary and sufficient condition for the approximation to be consistent is that the covariance matrices obey the inequality ˜Σ − Σ ≥ 0 =-=[15]-=-. A sufficient condition test for positive semi-definiteness is that the determinant of all upper left sub-matrices must be positive [16]. Applying this test we see that (17) is inconsistent since in ... |