Fast information matrix process of SEIF based on tri-diagonal matrix splitting

Abstract

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. The most well-known and popular approach is the Sparse Extended Information Filter (SEIF) by Thrun et al. SEIF has been successfully implemented with a variety of challenging real-world data sets and has lead to new insights into scalable SLAM. The paper presents a new approach based upon tri-diagonal matrix splitting for solving the computational complexity problem of inverse information matrix. In this paper, by analyzing the every steps of information matrix update in SEIF process, we find that the most computational cost is in recovery information matrix (inverse matrix). According to this characteristics which the normalized information matrix exhibits a natural sparseness and the many of the off-diagonal elements are relatively weak (nearly to zero) in information matrix, we enforce the elements into zero according to setting a threshold and computer inverse information matrix with the method of tri-diagonal matrix splitting. As the new processing does not need direct matrix inversion, the computational complexity is much lower. The Computer simulation results indicate that SEIF process is faster and localization precision is no influence.