Sparse Bayesian information filters for localization and mapping

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008This thesis formulates an estimation framework for Simultaneous Localization and Mapping (SLAM) that addresses the problem of scalability in large environments. We describe an estimation-theoretic algorithm that achieves significant gains in computational efficiency while maintaining consistent estimates for the vehicle pose and the map of the environment. We specifically address the feature-based SLAM problem in which the robot represents the environment as a collection of landmarks. The thesis takes a Bayesian approach whereby we maintain a joint posterior over the vehicle pose and feature states, conditioned upon measurement data. We model the distribution as Gaussian and parametrize the posterior in the canonical form, in terms of the information (inverse covariance) matrix. When sparse, this representation is amenable to computationally efficient Bayesian SLAM filtering. However, while a large majority of the elements within the normalized information matrix are very small in magnitude, it is fully populated nonetheless. Recent feature-based SLAM filters achieve the scalability benefits of a sparse parametrization by explicitly pruning these weak links in an effort to enforce sparsity. We analyze one such algorithm, the Sparse Extended Information Filter (SEIF), which has laid much of the groundwork concerning the computational benefits of the sparse canonical form. The thesis performs a detailed analysis of the process by which the SEIF approximates the sparsity of the information matrix and reveals key insights into the consequences of different sparsification strategies. We demonstrate that the SEIF yields a sparse approximation to the posterior that is inconsistent, suffering from exaggerated confidence estimates. This overconfidence has detrimental effects on important aspects of the SLAM process and affects the higher level goal of producing accurate maps for subsequent localization and path planning. This thesis proposes an alternative scalable filter that maintains sparsity while preserving the consistency of the distribution. We leverage insights into the natural structure of the feature-based canonical parametrization and derive a method that actively maintains an exactly sparse posterior. Our algorithm exploits the structure of the parametrization to achieve gains in efficiency, with a computational cost that scales linearly with the size of the map. Unlike similar techniques that sacrifice consistency for improved scalability, our algorithm performs inference over a posterior that is conservative relative to the nominal Gaussian distribution. Consequently, we preserve the consistency of the pose and map estimates and avoid the effects of an overconfident posterior. We demonstrate our filter alongside the SEIF and the standard EKF both in simulation as well as on two real-world datasets. While we maintain the computational advantages of an exactly sparse representation, the results show convincingly that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the original Gaussian distribution as produced by the EKF, but at much less computational expense. The thesis concludes with an extension of our SLAM filter to a complex underwater environment. We describe a systems-level framework for localization and mapping relative to a ship hull with an Autonomous Underwater Vehicle (AUV) equipped with a forward-looking sonar. The approach utilizes our filter to fuse measurements of vehicle attitude and motion from onboard sensors with data from sonar images of the hull. We employ the system to perform three-dimensional, 6-DOF SLAM on a ship hull

Exactly Sparse Extended Information Filters for Feature-Based SLAM

Recent research concerning the Gaussian canonical form for Simultaneous Localization and Mapping (SLAM) has given rise to a handful of algorithms that attempt to solve the SLAM scalability problem for arbitrarily large environments. One such estimator that has received due attention is the Sparse Extended Information Filter (SEIF) proposed by Thrun et al., which is reported to be nearly constant time, irrespective of the size of the map. The key to the SEIF's scalability is to prune weak links in what is a dense information (inverse covariance) matrix to achieve a sparse approximation that allows for efficient, scalable SLAM. We demonstrate that the SEIF sparsification strategy yields error estimates that are overconfident when expressed in the global reference frame, while empirical results show that relative map consistency is maintained. In this paper, we propose an alternative scalable estimator based on an information form that maintains sparsity while preserving consistency. The paper describes a method for controlling the population of the information matrix, whereby we track a modified version of the SLAM posterior, essentially by ignoring a small fraction of temporal measurements. In this manner, the Exactly Sparse Extended Information Filter (ESEIF) performs inference over a model that is conservative relative to the standard Gaussian distribution. We compare our algorithm to the SEIF and standard EKF both in simulation as well as on two nonlinear datasets. The results convincingly show that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the EKF.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86031/1/mwalter-22.pd

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 non-sparsified 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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86045/1/reustice-31.pd

Laminated Object Manufacturing of Si3N4 With Enhanced Properties

The potential to fabricate near net-shape ceramic components of intricate shape is attractive and offers considerable savings in cost and time. The laminated architecture inherent in many Rapid Prototyping techniques can be utilized to enhance material properties by providing weak interfaces at regular intervals, oriented microstructures, and functionally graded compositions. By design and control of these variables it is possible to enhance the strength, toughness and performance of components fabricated from structural ceramics. A range of oriented microstructural features have been investigated in Laminated Object Manufacturing of Si3N4 materials. Changes in the mechanical properties can be related to specific architectures and microstructural developments which took place during sintering.Mechanical Engineerin

SAR-Based Vibration Estimation Using the Discrete Fractional Fourier Transform

A vibration estimation method for synthetic aperture radar (SAR) is presented based on a novel application of the discrete fractional Fourier transform (DFRFT). Small vibrations of ground targets introduce phase modulation in the SAR returned signals. With standard preprocessing of the returned signals, followed by the application of the DFRFT, the time-varying accelerations, frequencies, and displacements associated with vibrating objects can be extracted by successively estimating the quasi-instantaneous chirp rate in the phase-modulated signal in each subaperture. The performance of the proposed method is investigated quantitatively, and the measurable vibration frequencies and displacements are determined. Simulation results show that the proposed method can successfully estimate a two-component vibration at practical signal-to-noise levels. Two airborne experiments were also conducted using the Lynx SAR system in conjunction with vibrating ground test targets. The experiments demonstrated the correct estimation of a 1-Hz vibration with an amplitude of 1.5 cm and a 5-Hz vibration with an amplitude of 1.5 mm

Atom chips on direct bonded copper substrates

We present the use of direct bonded copper (DBC) for the straightforward fabrication of high power atom chips. Atom chips using DBC have several benefits: excellent copper/substrate adhesion, high purity, thick (> 100 microns) copper layers, high substrate thermal conductivity, high aspect ratio wires, the potential for rapid (< 8 hr) fabrication, and three dimensional atom chip structures. Two mask options for DBC atom chip fabrication are presented, as well as two methods for etching wire patterns into the copper layer. The wire aspect ratio that optimizes the magnetic field gradient as a function of power dissipation is determined to be 0.84:1 (height:width). The optimal wire thickness as a function of magnetic trapping height is also determined. A test chip, able to support 100 A of current for 2 s without failing, is used to determine the thermal impedance of the DBC. An assembly using two DBC atom chips to provide magnetic confinement is also shown.Comment: 8 pages, 5 figure

Utility of targeted gene sequencing to differentiate myeloid malignancies from other cytopenic conditions

The National Heart, Lung, and Blood Institute-funded National MDS Natural History Study (NCT02775383) is a prospective cohort study enrolling patients with cytopenia with suspected myelodysplastic syndromes (MDS) to evaluate factors associated with disease. Here, we sequenced 53 genes in bone marrow samples harvested from 1298 patients diagnosed with myeloid malignancy, including MDS and non-MDS myeloid malignancy or alternative marrow conditions with cytopenia based on concordance between independent histopathologic reviews (local, centralized, and tertiary to adjudicate disagreements when needed). We developed a novel 2-stage diagnostic classifier based on mutational profiles in 18 of 53 sequenced genes that were sufficient to best predict a diagnosis of myeloid malignancy and among those with a predicted myeloid malignancy, predict whether they had MDS. The classifier achieved a positive predictive value (PPV) of 0.84 and negative predictive value (NPV) of 0.8 with an area under the receiver operating characteristic curve (AUROC) of 0.85 when classifying patients as having myeloid vs no myeloid malignancy based on variant allele frequencies (VAFs) in 17 genes and a PPV of 0.71 and NPV of 0.64 with an AUROC of 0.73 when classifying patients as having MDS vs non-MDS malignancy based on VAFs in 10 genes. We next assessed how this approach could complement histopathology to improve diagnostic accuracy. For 99 of 139 (71%) patients (PPV of 0.83 and NPV of 0.65) with local and centralized histopathologic disagreement in myeloid vs no myeloid malignancy, the classifier-predicted diagnosis agreed with the tertiary pathology review (considered the internal gold standard)

Adjustable microchip ring trap for cold atoms and molecules

We describe the design and function of a circular magnetic waveguide produced from wires on a microchip for atom interferometry using deBroglie waves. The guide is a two-dimensional magnetic minimum for trapping weak-field seeking states of atoms or molecules with a magnetic dipole moment. The design consists of seven circular wires sharing a common radius. We describe the design, the time-dependent currents of the wires and show that it is possible to form a circular waveguide with adjustable height and gradient while minimizing perturbation resulting from leads or wire crossings. This maximal area geometry is suited for rotation sensing with atom interferometry via the Sagnac effect using either cold atoms, molecules and Bose-condensed systems