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219
Kalman Temporal Differences
 Journal of Artificial Intelligence Research (JAIR
, 2010
"... Because reinforcement learning suffers from a lack of scalability, online value (and Q) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman Temporal Differences (KTD) framework, that exhibits the foll ..."
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Cited by 17 (15 self)
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Because reinforcement learning suffers from a lack of scalability, online value (and Q) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman Temporal Differences (KTD) framework, that exhibits the following features: sampleefficiency, nonlinear approximation, nonstationarity handling and uncertainty management. A first KTDbased algorithm is provided for deterministic Markov Decision Processes (MDP) which produces biased estimates in the case of stochastic transitions. Than the eXtended KTD framework (XKTD), solving stochastic MDP, is described. Convergence is analyzed for special cases for both deterministic and stochastic transitions. Related algorithms are experimented on classical benchmarks. They compare favorably to the state of the art while exhibiting the announced features. 1.
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 17 (7 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.
Kalman filtering with state constraints: a survey of linear and nonlinear algorithms’. http://academic. csuohio.edu/simond/ConstrKF, accessed
, 2010
"... Abstract: The Kalman filter is the minimumvariance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is nonGaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed ..."
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Cited by 16 (0 self)
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Abstract: The Kalman filter is the minimumvariance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is nonGaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results. 1
Unscented SLAM for LargeScale Outdoor Environments
, 2005
"... This paper presents an experimentally validated alternative to the classical extended Kalman filter approach to the solution of the probabilistic statespace Simultaneous Localization and Mapping (SLAM) problem. Several authors have recently reported the divergence of this classical approach due to ..."
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Cited by 16 (4 self)
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This paper presents an experimentally validated alternative to the classical extended Kalman filter approach to the solution of the probabilistic statespace Simultaneous Localization and Mapping (SLAM) problem. Several authors have recently reported the divergence of this classical approach due to the linearization of the inherent nonlinear nature of the SLAM problem. Hence, the approach described in this work aims to avoid the analytical linearization based on Taylorseries expansion of both the model and measurement equations by using the unscented filter. An innovationbased consistency checking validates the feasibility and applicability of the unscented SLAM approach to a real largescale outdoor exploration mission.
ClosedForm Prediction of Nonlinear Dynamic Systems by Means of Gaussian Mixture Approximation of the Transition Density
 in IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems
"... Abstract — Recursive prediction of the state of a nonlinear stochastic dynamic system cannot be efficiently performed in general, since the complexity of the probability density function characterizing the system state increases with every prediction step. Thus, representing the density in an exact ..."
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Cited by 15 (13 self)
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Abstract — Recursive prediction of the state of a nonlinear stochastic dynamic system cannot be efficiently performed in general, since the complexity of the probability density function characterizing the system state increases with every prediction step. Thus, representing the density in an exact closedform manner is too complex or even impossible. So, an appropriate approximation of the density is required. Instead of directly approximating the predicted density, we propose the approximation of the transition density by means of Gaussian mixtures. We treat the approximation task as an optimization problem that is solved offline via progressive processing to bypass initialization problems and to achieve high quality approximations. Once having calculated the transition density approximation offline, prediction can be performed efficiently resulting in a closedform density representation with constant complexity. I.
Analytic implementations of the cardinalized probability hypothesis density filter
 IEEE Trans. SP
, 2007
"... Abstract — The probability hypothesis density (PHD) recursion propagates the posterior intensity of the random finite set of targets in time. The cardinalized PHD (CPHD) recursion is a generalization of the PHD recursion, which jointly propagates the posterior intensity and the posterior cardinality ..."
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Cited by 15 (2 self)
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Abstract — The probability hypothesis density (PHD) recursion propagates the posterior intensity of the random finite set of targets in time. The cardinalized PHD (CPHD) recursion is a generalization of the PHD recursion, which jointly propagates the posterior intensity and the posterior cardinality distribution. In general, the CPHD recursion is computationally intractable. This paper proposes a closedform solution to the CPHD recursion under linear Gaussian assumptions on the target dynamics and birth process. Based on this solution, an effective multitarget tracking algorithm is developed. Extensions of the proposed closed form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques. The proposed CPHD implementations not only sidestep the need to perform data association found in traditional methods, but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard PHD filter. Our implementations only have a cubic complexity, but simulations suggest favourable performance compared to the standard JPDA filter which has a nonpolynomial complexity. Index Terms — Multitarget tracking, Random finite sets, Multitarget Bayesian filtering, Probability hypothesis density
Unscented RauchTungStriebel Smoother
"... This article considers the application of the unscented transform to optimal smoothing of nonlinear state space models. In this article, a new RauchTungStriebel type form of the fixedinterval unscented Kalman smoother is derived. The new smoother differs from the previously proposed twofilter f ..."
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Cited by 15 (3 self)
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This article considers the application of the unscented transform to optimal smoothing of nonlinear state space models. In this article, a new RauchTungStriebel type form of the fixedinterval unscented Kalman smoother is derived. The new smoother differs from the previously proposed twofilter formulation based unscented Kalman smoother in the sense that it is not based on running two independent filters forward and backward in time. Instead, a separate backward smoothing pass is used, which recursively computes corrections to the forward filtering result. The smoother equations are derived as approximations to the formal Bayesian optimal smoothing equations. The performance of the new smoother is demonstrated with a simulation.
Kalman Temporal Differences: the deterministic case
 In IEEE International Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL 2009
, 2009
"... Abstract — This paper deals with value function and Qfunction approximation in deterministic Markovian decision processes. A general statistical framework based on the Kalman filtering paradigm is introduced. Its principle is to adopt a parametric representation of the value function, to model the ..."
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Cited by 14 (12 self)
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Abstract — This paper deals with value function and Qfunction approximation in deterministic Markovian decision processes. A general statistical framework based on the Kalman filtering paradigm is introduced. Its principle is to adopt a parametric representation of the value function, to model the associated parameter vector as a random variable and to minimize the meansquared error of the parameters conditioned on past observed transitions. From this general framework, which will be called Kalman Temporal Differences (KTD), and using an approximation scheme called the unscented transform, a family of algorithms is derived, namely KTDV, KTDSARSA and KTDQ, which aim respectively at estimating the value function of a given policy, the Qfunction of a given policy and the optimal Qfunction. The proposed approach holds for linear and nonlinear parameterization. This framework is discussed and potential advantages and shortcomings are highlighted.
MultisensorBased Human Detection and Tracking for Mobile Service Robots
"... Abstract—One of fundamental issues for service robots is human–robot interaction. In order to perform such a task and provide the desired services, these robots need to detect and track people in the surroundings. In this paper, we propose a solution for human tracking with a mobile robot that imple ..."
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Cited by 12 (3 self)
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Abstract—One of fundamental issues for service robots is human–robot interaction. In order to perform such a task and provide the desired services, these robots need to detect and track people in the surroundings. In this paper, we propose a solution for human tracking with a mobile robot that implements multisensor data fusion techniques. The system utilizes a new algorithm for laserbased leg detection using the onboard laser range finder (LRF). The approach is based on the recognition of typical leg patterns extracted from laser scans, which are shown to also be very discriminative in cluttered environments. These patterns can be used to localize both static and walking persons, even when the robot moves. Furthermore, faces are detected using the robot’s camera, and the information is fused to the legs ’ position using a sequential implementation of unscented Kalman filter. The proposed solution is feasible for service robots with a similar device configuration and has been successfully implemented on two different mobile platforms. Several experiments illustrate the effectiveness of our approach, showing that robust human tracking can be performed within complex indoor environments. Index Terms—Leg detection, people tracking, sensor fusion, service robotics, unscented Kalman filter (UKF). I.
EXTENDED VTS FOR NOISEROBUST SPEECH RECOGNITION
"... Model compensation is a standard way of improving speech recognisers’ robustness to noise. Currently popular schemes are based on vector Taylor series (VTS) compensation. They often use the continuous time approximation to compensate dynamic parameters. In this paper, the accuracy of dynamic paramet ..."
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Cited by 12 (10 self)
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Model compensation is a standard way of improving speech recognisers’ robustness to noise. Currently popular schemes are based on vector Taylor series (VTS) compensation. They often use the continuous time approximation to compensate dynamic parameters. In this paper, the accuracy of dynamic parameter compensation is improved by representing the dynamic features as a linear transformation of a window of static features. A modified version of VTS compensation is applied to the distribution of the window of static features and, importantly, their correlations. These compensated distributions are then transformed to standard static and dynamic distributions. The proposed scheme outperformed the standard VTS scheme by about 10 % relative. Index Terms — Speech recognition, acoustic noise, robustness 1.