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11
Square Root SAM: Simultaneous localization and mapping via square root information smoothing
 International Journal of Robotics Reasearch
, 2006
"... Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filterbased solutions to the problem. In particular, we look at approaches that factorize either th ..."
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Cited by 144 (39 self)
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Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filterbased solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement Jacobian into square root form. Such techniques have several significant advantages over the EKF: they are faster yet exact, they can be used in either batch or incremental mode, are better equipped to deal with nonlinear process and measurement models, and yield the entire robot trajectory, at lower cost for a large class of SLAM problems. In addition, in an indirect but dramatic way, column ordering heuristics automatically exploit the locality inherent in the geographic nature of the SLAM problem. In this paper we present the theory underlying these methods, along with an interpretation of factorization in terms of the graphical model associated with the SLAM problem. We present both simulation results and actual SLAM experiments in largescale environments that underscore the potential of these methods as an alternative to EKFbased approaches. 1
McMC Data Association and Sparse Factorization Updating for Real Time Multitarget Tracking with Merged and Multiple Measurements
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—In several multitarget tracking applications, a target may return more than one measurement per target and interacting targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially applied to radar tracking, do not adequate ..."
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Cited by 37 (1 self)
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Abstract—In several multitarget tracking applications, a target may return more than one measurement per target and interacting targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially applied to radar tracking, do not adequately address these types of measurements. Here, we introduce a probabilistic model for interacting targets that addresses both types of measurements simultaneously. We provide an algorithm for approximate inference in this model using a Markov chain Monte Carlo (MCMC)based auxiliary variable particle filter. We RaoBlackwellize the Markov chain to eliminate sampling over the continuous state space of the targets. A major contribution of this work is the use of sparse least squares updating and downdating techniques, which significantly reduce the computational cost per iteration of the Markov chain. Also, when combined with a simple heuristic, they enable the algorithm to correctly focus computation on interacting targets. We include experimental results on a challenging simulation sequence. We test the accuracy of the algorithm using two sensor modalities, video, and laser range data. We also show the algorithm exhibits real time performance on a conventional PC. Index Terms—Markov chain Monte Carlo, QR factorization, updating, downdating, RaoBlackwellized, particle filter, multitarget tracking, merged measurements, linear least squares, laser range scanner.
Exploiting locality by nested dissection for square root smoothing and mapping
 In Robotics: Science and Systems (RSS
, 2006
"... The problem of creating a map given only the erroneous odometry and feature measurements and locating the own position in this environment is known in the literature as the Simultaneous Localization and Mapping (SLAM) problem. In this paper we investigate how a Nested Dissection Ordering scheme can ..."
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Cited by 16 (8 self)
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The problem of creating a map given only the erroneous odometry and feature measurements and locating the own position in this environment is known in the literature as the Simultaneous Localization and Mapping (SLAM) problem. In this paper we investigate how a Nested Dissection Ordering scheme can improve the the performance of a recently proposed Square Root Information Smoothing (SRIS) approach. As the SRIS does perform smoothing rather than filtering the SLAM problem becomes the Smoothing and Mapping problem (SAM). The computational complexity of the SRIS solution is dominated by the cost of transforming a matrix of all measurements into a square root form through factorization. The factorization of a fully dense measurement matrix has a cubic complexity in the worst case. We show that the computational complexity for the factorization of typical measurement matrices occurring in the SAM problem can be bound tighter under reasonable assumptions. Our work is motivated both from a numerical / linear algebra standpoint as well as by submaps used in EKF solutions to SLAM.
Probabilistic Structure Matching for Visual SLAM with a MultiCamera Rig
"... We propose to use a multicamera rig for simultaneous localization and mapping (SLAM), providing flexibility in sensor placement on mobile robot platforms while exploiting the stronger localization constraints provided by omnidirectional sensors. In this context, we present a novel probabilistic ap ..."
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Cited by 4 (0 self)
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We propose to use a multicamera rig for simultaneous localization and mapping (SLAM), providing flexibility in sensor placement on mobile robot platforms while exploiting the stronger localization constraints provided by omnidirectional sensors. In this context, we present a novel probabilistic approach to data association, that takes into account that features can also move between cameras under robot motion. Our approach circumvents the combinatorial data association problem by using an incremental expectation maximization algorithm. In the expectation step we determine a distribution over correspondences by sampling. In the maximization step, we find optimal parameters of a density over the robot motion and environment structure. By summarizing the sampling results in socalled virtual measurements, the resulting optimization simplifies to the equivalent optimization problem for known correspondences. We present results for simulated data, as well as for data obtained by a mobile robot equipped with a multicamera rig. Key words: localization, mapping, mobile robot, multicamera rig, omnidirectional, SFM
Graph Projection Block Splitting for Distributed Optimization
, 2012
"... This paper describes a general purpose method for solving convex optimization problems in a distributed computing environment. In particular, if the problem data includes a large linear operator or matrix A, the method allows for handling each subblock of A on a separate machine. The approach works ..."
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Cited by 3 (0 self)
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This paper describes a general purpose method for solving convex optimization problems in a distributed computing environment. In particular, if the problem data includes a large linear operator or matrix A, the method allows for handling each subblock of A on a separate machine. The approach works as follows. First, we define a canonical problem form called graph form, in which we have two sets of variables x and y related by a linear operator A, such that the objective function is separable across these two sets of variables. Many problems are easily expressed in graph form, including cone programs and a wide variety of regularized loss minimization problems from statistics, like logistic regression, the support vector machine, and the lasso. Next, we describe graph projection splitting, a form of DouglasRachford splitting or the alternating direction method of multipliers, to solve graph form problems serially. Finally, we derive a distributed block splitting algorithm based on graph projection splitting. In a statistical or machine learning context, this allows for training models exactly with a huge number of both training examples and features, such that each processor handles only a subset of both. To the best of our knowledge, this is the only general purpose method with this property. We present several numerical experiments in both the serial and distributed settings. 1
An Interior Point Approach to Quadratic and Parametric Quadratic Optimization
, 2004
"... In this thesis sensitivity analysis for quadratic optimization problems is studied. In sensitivity analysis, which is often referred to as parametric optimization or parametric programming, a perturbation parameter is introduced into the optimization problem, which means that the coefficients in ..."
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Cited by 2 (1 self)
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In this thesis sensitivity analysis for quadratic optimization problems is studied. In sensitivity analysis, which is often referred to as parametric optimization or parametric programming, a perturbation parameter is introduced into the optimization problem, which means that the coefficients in the objective function of the problem and in the righthandside of the constraints are perturbed. First, we describe quadratic programming problems and their parametric versions. Second, the theory for finding solutions of the parametric problems is developed. We also present an algorithm for solving such problems. In the implementation part, the implementation of the quadratic optimization solver is made. For that purpose, we extend the linear interior point package McIPM to solve quadratic problems. The quadratic solver is tested on the problems from the Maros and Mészáros test set. Finally, we implement the algorithm for parametric quadratic optimization. It utilizes the quadratic solver to solve auxiliary problems. We present numerical results produced by our parametric optimization package.
Rigid Partitioning Techniques for Efficiently Generating Three Dimensional Reconstructions from Images
, 2004
"... ..."
unknown title
"... Abstract — Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filterbased solutions to the problem. In particular, we look at approaches that factoriz ..."
Abstract
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Abstract — Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filterbased solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement matrix into square root form. Such techniques have several significant advantages over the EKF: they are faster yet exact, they can be used in either batch or incremental mode, are better equipped to deal with nonlinear process and measurement models, and yield the entire robot trajectory, at lower cost. In addition, in an indirect but dramatic way, column ordering heuristics automatically exploit the locality inherent in the geographic nature of the SLAM problem. In this paper we present the theory underlying these methods, an interpretation of factorization in terms of the graphical model associated with the SLAM problem, and simulation results that underscore the potential of these methods for use in practice. I.
Dellaert: MCMC Data Association and Sparse Factorization Updating for Real Time Multitarget Tracking with Merged and Multiple Measurements
 IEEE Trans. on PAMI
, 2006
"... In several multitarget tracking applications a target may return more than one measurement per target, and interacting targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially applied to radar tracking, do not adequately addres ..."
Abstract
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In several multitarget tracking applications a target may return more than one measurement per target, and interacting targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially applied to radar tracking, do not adequately address these types of measurements. Here, we introduce a probabilistic model for interacting targets that addresses both types of measurements simultaneously. We provide an algorithm for approximate inference in this model using a Markov chain Monte Carlo (MCMC) based auxiliary variable particle filter. We RaoBlackwellize the Markov chain to eliminate sampling over the continuous state space of the targets. A major contribution of this work is the use of sparse least squares updating and downdating techniques, which significantly reduce the computational cost per iteration of the Markov chain. Also, when combined with a simple heuristic, they enable the algorithm to correctly focus computation on interacting targets. We include experimental results on a challenging simulation sequence. We test the accuracy of the algorithm using two sensor modalities, video and laser range data. We also show the algorithm exhibits real time performance on a conventional PC.