A new method for the nonlinear transformation of means and covariances in filters and estimators

Julier, Simon; Uhlmann, Jeffrey; Durrant‐Whyte, Hugh

doi:10.1109/9.847726

Cited by 3,165 publications

(1,834 citation statements)

References 15 publications

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“…Therefore, the degree of accuracy of the EKF relies on the validity of the linear approximation and is not suitable for highly non-Gaussian conditional probability density functions, since it only updates the first two moments (mean and covariance) [13]. In addition, the calculation of the Jacobian matrix, used to linearize the nonlinear function in an EKF algorithm, can be complex causing implementation difficulties [14], [15]. In order to overcome these limitations, the Unscented Kalman Filter (UKF) has been proposed by Julier and Uhlmann [14], [15].…”

Section: Kalman Filtermentioning

confidence: 99%

“…In addition, the calculation of the Jacobian matrix, used to linearize the nonlinear function in an EKF algorithm, can be complex causing implementation difficulties [14], [15]. In order to overcome these limitations, the Unscented Kalman Filter (UKF) has been proposed by Julier and Uhlmann [14], [15]. Based on EKF and UKF, adaptive Kalman filters have been developed to achieve much better estimation performance for non linear systems by adjusting the noise covariance matrices during estimation [16].…”

Section: Kalman Filtermentioning

confidence: 99%

See 1 more Smart Citation

Performance Comparison of the Kalman Filter Variants for Dynamic Mobile Localization in Urban Area Using Cellular Network

Bouzera¹,

Mezhoud²,

Khireddine³

et al. 2015

IJCTE

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Section: Kalman Filtermentioning

confidence: 99%

Section: Kalman Filtermentioning

confidence: 99%

Performance Comparison of the Kalman Filter Variants for Dynamic Mobile Localization in Urban Area Using Cellular Network

Bouzera¹,

Mezhoud²,

Khireddine³

et al. 2015

IJCTE

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“…One approach to reduce the effect of nonlinearities is to apply iteratively the filter (IEKF) as indicated by Zhang [220]. Another solution is to use the Unscented Kalman Filter (UKF), an extension to the EKF that takes into account the nonlinear transformation of means and covariances [105,107,203]. Numerical instability may occur even with the Joseph form of the error covariance matrix.…”

Section: C6 Bibliographical Notesmentioning

confidence: 99%

“…They argue that the divergence of the algorithm is due to the nonlinearities of the model used. Their contribution suggests that robust statistics and nonlinear approaches to KF, such as the Unscented KF [105], should be explored as means to more robust solutions to CML.…”

Section: Divergencementioning

confidence: 99%

Environment Learning for Indoor Mobile Robots

Andrade‐Cetto¹

2006

Springer Tracts in Advanced Robotics

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This thesis focuses on the various aspects of autonomous environment learning for indoor service robots. Particularly, on landmark extraction from sensor data, autonomous map building, and robot localization.To univocally identify landmarks from sensor data, we study several landmark representations, and the mathematical foundation necessary to extract the features that build them from images and laser range data. The features extracted from just one sensor may not suffice in the invariant characterization of landmarks and objects, pushing for the combination of information from multiple sources. We present a new algorithm that fuses complementary information from two low level vision modules into coherent object models that can be tracked and learned in a mobile robotics context. Illumination conditions and occlusions are the most prominent artifacts that hinder data association in computer vision. By using photogrammetric and geometric constraints we restrict the search for landmark matches in successive images, and by locking our interest in one or a set of landmarks in the scene, we track those landmarks along successive frames, reducing considerably the data association problem. We concentrate on those tools from the geometry of multiple views that are relevant to the computation of initial landmark location estimates for coarse motion recovery; a desirable characteristic when odometry is not available or is highly unreliable.Once landmarks are accurately extracted and identified, the second part of the problem is to use these observations for the localization of the robot, as well as the refinement of the landmark location estimates. We consider robot motion and sensor observations as stochastic processes, and treat the problem from an estimation theoretic point of view, dealing with noise by using probabilistic methods.The main drawback we encounter is that current estimation techniques have been devised for static environments, and that they lack robustness in more realistic situations. To aid in those situations in which landmark observations might not be consistent in time, we propose a new set of temporal landmark quality functions, and show how iii by incorporating these functions in the data association tests, the overall estimationtheoretic approach to map building and localization is improved. The basic idea consists on using the history of data association mismatches for the computation of the likelihood of future data association, together with the spatial compatibility tests already available.Special attention is paid in that the removal of spurious landmarks from the map does not violate the basic convergence properties of the localization and map building algorithms already described in the literature; namely, asymptotic convergence and full correlation.The thesis also gives an in depth analysis of the fully correlated model to localization and map building from a control systems theory point of view. Considering the fact that the Kalman filter is nothing else but an optimal observer,...

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“…First, if they are linear (or mildly nonlinear) functions, the celebrated Kalman filter (or its extended or unscented variants) dominates the class of possible solutions. [5][6][7] Second, if f k is linear or nonlinear and h k severely nonlinear but known and computationally tractable, the particle filters estimating x k and ξ k via a Monte Carlo sampling from the state space prevail, eg, the work of Cappé et al 8 Moreover, the model structure allows marginalized (Rao-Blackwellized) particle filtering (MPF): ξ k is sampled, whereas x k is estimated via a Kalman filter. 9,10 The marginalization reduces the number of necessary particles and leads to a lower estimator variance.…”

Section: Introductionmentioning

confidence: 99%

Marginalized approximate filtering of state‐space models

Dedecius

2017

Adaptive Control & Signal

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SummaryThe marginalized particle filtering (MPF) is a powerful technique reducing the number of particles necessary to effectively estimate hidden states of state-space models. This paper alleviates the assumption of a fully known and computationally tractable observation model. Exploiting the recent developments in the theory of approximate Bayesian computation (ABC) filtration, an ABC counterpart of MPF is proposed, applicable when the observation model is too complex to be evaluated analytically or even numerically, but it is still possible to sample from it by plugging in the state. The novelty is 2-fold. First, ABC methods have not been used in marginalized filtering yet. Second, a new multivariate robust method for evaluation of particle weights is proposed. The goal of this paper is to demonstrate the idea on the background of the MPF with a particular accent on exposition.

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A new method for the nonlinear transformation of means and covariances in filters and estimators

Cited by 3,165 publications

References 15 publications

Performance Comparison of the Kalman Filter Variants for Dynamic Mobile Localization in Urban Area Using Cellular Network

Performance Comparison of the Kalman Filter Variants for Dynamic Mobile Localization in Urban Area Using Cellular Network

Environment Learning for Indoor Mobile Robots

Marginalized approximate filtering of state‐space models

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