Bayesian estimation and the Kalman filter

Barker, Allen L.; Brown, Donald E.; Martin, Worthy N.

doi:10.1016/0898-1221(95)00156-s

Cited by 72 publications

(56 citation statements)

References 5 publications

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“…The Kalman filter was initially proposed in (Kalman 1960) and, although originally not formulated as such, it has been later shown to belong to the more general class of Bayesian estimators (Barker et al 1994). It was also proved to be optimal in case of linear systems with Gaussian noises, for which the posterior in (4) becomes the following:…”

Section: Ekf Implementationmentioning

confidence: 99%

Computationally efficient solutions for tracking people with a mobile robot: an experimental evaluation of Bayesian filters

Bellotto

2009

Auton Robot

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Modern service robots will soon become an essential part of modern society. As they have to move and act in human environments, it is essential for them to be provided with a fast and reliable tracking system that localizes people in the neighbourhood. It is therefore important to select the most appropriate filter to estimate the position of these persons. This paper presents three efficient implementations of multisensor-human tracking based on different Bayesian estimators: Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Sampling Importance Resampling (SIR) particle filter. The system implemented on a mobile robot is explained, introducing the methods used to detect and estimate the position of multiple people. Then, the solutions based on the three filters are discussed in detail. Several real experiments are conducted to evaluate their performance, which is compared in terms of accuracy, robustness and execution time of the estimation. The results show that a solution based on the UKF can perform as good as particle filters and can be often a better choice when computational efficiency is a key issue.

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Section: Ekf Implementationmentioning

confidence: 99%

Computationally efficient solutions for tracking people with a mobile robot: an experimental evaluation of Bayesian filters

Bellotto

2009

Auton Robot

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“…For instance, Hong and Slotine [4] and Riley and Atkeson [7] model the trajectories of a flying ball as a parabola, and subsequently recursively estimate the ball's trajectory through least squares optimization. Frese et al [6], Bauml et al [10] and Park et al [9] also assume a parabolic form for the ball trajectories which they use in conjunction with an Extended Kalman filter [17] for on-line re-estimation. Ribnick et al [18] and Herrejon et al [19] estimate 3D trajectories directly from monocular image sequences based on the ballistic ball movement equation.…”

Section: Robotic Catchingmentioning

confidence: 99%

“…It can then be used in conjunction with the Extended Kalman Filter (EKF) [17] to ensure a robust noise filter when re-estimating the object's motion in flight. For the EKF, the augmented estimate f AUG of the system dynamics (estimated using either of the six estimation techniques described earlier on) and measurement model are given by:…”

Section: Dealing With Noisementioning

confidence: 99%

Estimating the non-linear dynamics of free-flying objects

Kim

Billard

2012

Robotics and Autonomous Systems

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a b s t r a c tThis paper develops a model-free method to estimate the dynamics of free-flying objects. We take a realistic perspective to the problem and investigate tracking accurately and very rapidly the trajectory and orientation of an object so as to catch it in flight. We consider the dynamics of complex objects where the grasping point is not located at the center of mass.To achieve this, a density estimate of the translational and rotational velocity is built based on the trajectories of various examples. We contrast the performance of six non-linear regression methods (Support Vector Regression (SVR) with Radial Basis Function (RBF) kernel, SVR with polynomial kernel, Gaussian Mixture Regression (GMR), Echo State Network (ESN), Genetic Programming (GP) and Locally Weighted Projection Regression (LWPR)) in terms of precision of recall, computational cost and sensitivity to choice of hyper-parameters. We validate the approach for real-time motion tracking of 5 daily life objects with complex dynamics (a ball, a fully-filled bottle, a half-filled bottle, a hammer and a pingpong racket). To enable real-time tracking, the estimated model of the object's dynamics is coupled with an Extended Kalman Filter for robustness against noisy sensing.

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“…Until recently, the Bayesian approach to perception has been largely static; however, Bayesian techniques can be used to model both learning [49] and time-variant processes [24,5]. (Myth 4: Bayes lacks dynamics.)…”

Section: Pattern Inference Theories Of Visionmentioning

confidence: 99%