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iSAM: Incremental Smoothing and Mapping
, 2008
"... We present incremental smoothing and mapping (iSAM), a novel approach to the simultaneous localization and mapping problem that is based on fast incremental matrix factorization. iSAM provides an efficient and exact solution by updating a QR factorization of the naturally sparse smoothing informatio ..."
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Cited by 153 (35 self)
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We present incremental smoothing and mapping (iSAM), a novel approach to the simultaneous localization and mapping problem that is based on fast incremental matrix factorization. iSAM provides an efficient and exact solution by updating a QR factorization of the naturally sparse smoothing information matrix, therefore recalculating only the matrix entries that actually change. iSAM is efficient even for robot trajectories with many loops as it avoids unnecessary fillin in the factor matrix by periodic variable reordering. Also, to enable data association in realtime, we provide efficient algorithms to access the estimation uncertainties of interest based on the factored information matrix. We systematically evaluate the different components of iSAM as well as the overall algorithm using various simulated and realworld datasets for both landmark and poseonly settings.
The Unscented Kalman Filter for nonlinear estimation
, 2000
"... The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system, estimating parameters for nonlinear system identification (e.g., learning the weights of a ne ..."
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Cited by 152 (4 self)
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The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system, estimating parameters for nonlinear system identification (e.g., learning the weights of a neural network), and dual estimation (e.g., the Expectation Maximization (EM) algorithm) where both states and parameters are estimated simultaneously. This paper points out the flaws in using the EKF, and introduces an improvement, the Unscented Kalman Filter (UKF), proposed by Julier and Uhlman [5]. A central and vital operation performed in the Kalman Filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF, the state distribution is approximated
SigmaPoint Kalman Filters for Probabilistic Inference in Dynamic StateSpace Models
 In Proceedings of the Workshop on Advances in Machine Learning
, 2003
"... Probabilistic inference is the problem of estimating the hidden states of a system in an optimal and consistent fashion given a set of noisy or incomplete observations. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the post ..."
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Cited by 78 (5 self)
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Probabilistic inference is the problem of estimating the hidden states of a system in an optimal and consistent fashion given a set of noisy or incomplete observations. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive online.
On Unscented Kalman Filtering for State Estimation of ContinuousTime Nonlinear Systems
, 2007
"... This article considers the application of the unscented Kalman filter (UKF) to continuoustime filtering problems, where both the state and measurement processes are modeled as stochastic differential equations. The mean and covariance differential equations which result in the continuoustime lim ..."
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Cited by 37 (8 self)
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This article considers the application of the unscented Kalman filter (UKF) to continuoustime filtering problems, where both the state and measurement processes are modeled as stochastic differential equations. The mean and covariance differential equations which result in the continuoustime limit of the UKF are derived. The continuousdiscrete unscented Kalman filter is derived as a special case of the continuoustime filter, when the continuoustime prediction equations are combined with the update step of the discretetime unscented Kalman filter. The filter equations are also transformed into sigmapoint differential equations, which can be interpreted as matrix square root versions of the filter equations.
SigmaPoint Kalman Filters For Integrated Navigation
, 2004
"... Core to integrated navigation systems is the concept of fusing noisy observations from GPS, Inertial Measurement Units (IMU), and other available sensors. The current industry standard and most widely used algorithm for this purpose is the extended Kalman filter (EKF) [6]. The EKF combines the senso ..."
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Cited by 30 (1 self)
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Core to integrated navigation systems is the concept of fusing noisy observations from GPS, Inertial Measurement Units (IMU), and other available sensors. The current industry standard and most widely used algorithm for this purpose is the extended Kalman filter (EKF) [6]. The EKF combines the sensor measurements with predictions coming from a model of vehicle motion (either dynamic or kinematic), in order to generate an estimate of the current navigational state (position, velocity, and attitude). This paper points out the inherent shortcomings in using the EKF and presents, as an alternative, a family of improved derivativeless nonlinear Kalman filters called sigmapoint Kalman filters (SPKF). We demonstrate the improved state estimation performance of the SPKF by applying it to the problem of loosely coupled GPS/INS integration. A novel method to account for latency in the GPS updates is also developed for the SPKF (such latency compensation is typically inaccurate or not practical with the EKF). A UAV (rotorcraft) test platform is used to demonstrate the results. Performance metrics indicate an approximate 30% error reduction in both attitude and position estimates relative to the baseline EKF implementation.
A square root unscented Kalman filter for visual monoSLAM
 in Proc. of the IEEE International Conference on Robotics and Automation
, 2008
"... Abstract — This paper introduces a Square Root Unscented Kalman Filter (SRUKF) solution to the problem of performing visual Simultaneous Localization and Mapping (SLAM) using a single camera. Several authors have proposed the conventional UKF for SLAM to improve the handling of nonlinearities compa ..."
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Cited by 14 (1 self)
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Abstract — This paper introduces a Square Root Unscented Kalman Filter (SRUKF) solution to the problem of performing visual Simultaneous Localization and Mapping (SLAM) using a single camera. Several authors have proposed the conventional UKF for SLAM to improve the handling of nonlinearities compared with the more widely used EKF, but at the expense increasing computational complexity from O(N 2) to O(N 3) in the map size, making it unattractive for videorate application. Van der Merwe and Wan’s general SRUKF delivers identical results to a general UKF along with computational savings, but remains O(N 3) overall. This paper shows how the SRUKF for the SLAM problem can be reposed with O(N 2) complexity, matching that of the EKF. The paper also shows how the method of inverse depth feature initialization developed by Montiel et al. for the EKF can be reformulated to work with the SRUKF. Experimental results confirm that the SRUKF and the UKF produce identical estimates, and that the SRUKF is more consistent than the EKF. Although the complexity is the same, the SRUKF remains more expensive to compute. I.
Using the Unscented Kalman Filter in MonoSLAM with Inverse Depth Parametrization for Autonomous Airship Control
"... Abstract — In this paper, we present an approach for aiding control of an autonomous airship by the means of SLAM. We show how the Unscented Kalman Filter can be applied in a SLAM context with monocular vision. The recently published Inverse Depth Parametrization is used for undelayed singlehypothe ..."
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Cited by 8 (0 self)
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Abstract — In this paper, we present an approach for aiding control of an autonomous airship by the means of SLAM. We show how the Unscented Kalman Filter can be applied in a SLAM context with monocular vision. The recently published Inverse Depth Parametrization is used for undelayed singlehypothesis landmark initialization and modelling. The novelty of the presented approach lies in the combination of UKF, Inverse Depth Parametrization and bearingonly SLAM and its application for autonomous airship control and UAV control in general.
Ultraswarm: A further step towards a flock of miniature helicopters
 IN PROCEEDINGS OF THE SAB WORKSHOP ON SWARM ROBOTICS
, 2006
"... We describe further progress towards the development of a MAV (micro aerial vehicle) designed as an enabling tool to investigate aerial flocking. Our research focuses on the use of low cost off the shelf vehicles and sensors to enable fast prototyping and to reduce development costs. Details on the ..."
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Cited by 7 (0 self)
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We describe further progress towards the development of a MAV (micro aerial vehicle) designed as an enabling tool to investigate aerial flocking. Our research focuses on the use of low cost off the shelf vehicles and sensors to enable fast prototyping and to reduce development costs. Details on the design of the embedded electronics and the modification of the chosen toy helicopter are presented, and the technique used for state estimation is described. The fusion of inertial data through an unscented Kalman filter is used to estimate the helicopter’s state, and this forms the main input to the control system. Since no detailed dynamic model of the helicopter in use is available, a method is proposed for automated system identification, and for subsequent controller design based on artificial evolution. Preliminary results obtained with a dynamic simulator of a helicopter are reported, along with some encouraging results for tackling the problem of flocking.
Dynamic Probabilistic CCA for Analysis of Affective Behavior and Fusion of Continuous Annotations
"... Abstract—Fusing multiple continuous expert annotations is a crucial problem in machine learning and computer vision, particularly when dealing with uncertain and subjective tasks related to affective behavior. Inspired by the concept of inferring shared and individual latent spaces in Probabilistic ..."
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Cited by 6 (3 self)
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Abstract—Fusing multiple continuous expert annotations is a crucial problem in machine learning and computer vision, particularly when dealing with uncertain and subjective tasks related to affective behavior. Inspired by the concept of inferring shared and individual latent spaces in Probabilistic Canonical Correlation Analysis (PCCA), we propose a novel, generative model that discovers temporal dependencies on the shared/individual spaces (Dynamic Probabilistic CCA, DPCCA). In order to accommodate for temporal lags, which are prominent amongst continuous annotations, we further introduce a latent warping process, leading to the DPCCA with Time Warpings (DPCTW) model. Finally, we propose two supervised variants of DPCCA/DPCTW which incorporate inputs (i.e. visual or audio features), both in a generative (SGDPCCA) and discriminative manner (SDDPCCA). We show that the resulting family of models (i) can be used as a unifying framework for solving the problems of temporal alignment and fusion of multiple annotations in time, (ii) can automatically rank and filter annotations based on latent posteriors or other model statistics, and (iii) that by incorporating dynamics, modeling annotationspecific biases, noise estimation, time warping and supervision, DPCTW outperforms stateoftheart methods for both the aggregation of multiple, yet imperfect expert annotations as well as the alignment of affective behavior. Index Terms—Fusion of continuous annotations, component analysis, temporal alignment, dimensional emotion, affect analysis 1
A Serial Approach to Handling HighDimensional Measurements in the SigmaPoint Kalman Filter
"... Abstract—Pose estimation is a critical skill in mobile robotics and is often accomplished using onboard sensors and a Kalman filter estimation technique. For systems to run online, computational efficiency of the filter design is crucial, especially when faced with limited computing resources. In th ..."
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Cited by 5 (0 self)
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Abstract—Pose estimation is a critical skill in mobile robotics and is often accomplished using onboard sensors and a Kalman filter estimation technique. For systems to run online, computational efficiency of the filter design is crucial, especially when faced with limited computing resources. In this paper, we present a novel approach to serially process highdimensional measurements in the SigmaPoint Kalman Filter (SPKF), in order to achieve a low computational cost that is linear is the measurement dimension. Although the concept of serially processing measurements has been around for quite some time in the context of the Extended Kalman Filter (EKF), few have considered this approach with the SPKF. At first glance, it may be tempting to apply the SPKF update step serially. However, we prove that without redrawing sigma points, this ‘naive ’ approach cannot guarantee the positivedefiniteness of the state covariance matrix (not the case for the EKF). We then introduce a novel method for the SigmaPoint Kalman Filter to process highdimensional, uncorrelated measurements serially that is algebraically equivalent to processing the measurements in parallel, but still achieves a computational cost linear in the measurement dimension. I.