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543
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.
Analytic Momentbased Gaussian Process Filtering
"... We propose an analytic momentbased filter for nonlinear stochastic dynamic systems modeled by Gaussian processes. Exact expressions for the expected value and the covariance matrix are provided for both the prediction step and the filter step, where an additional Gaussian assumption is exploited in ..."
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Cited by 36 (13 self)
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We propose an analytic momentbased filter for nonlinear stochastic dynamic systems modeled by Gaussian processes. Exact expressions for the expected value and the covariance matrix are provided for both the prediction step and the filter step, where an additional Gaussian assumption is exploited in the latter case. Our filter does not require further approximations. In particular, it avoids finitesample approximations. We compare the filter to a variety of Gaussian filters, that is, the EKF, the UKF, and the recent GPUKF proposed by Ko et al. (2007). 1.
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 36 (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 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 34 (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
Visual Odometry based on Stereo Image Sequences with RANSACbased Outlier Rejection Scheme
"... Abstract — A common prerequisite for many visionbased driver assistance systems is the knowledge of the vehicle’s own movement. In this paper we propose a novel approach for estimating the egomotion of the vehicle from a sequence of stereo images. Our method is directly based on the trifocal geomet ..."
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Cited by 34 (1 self)
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Abstract — A common prerequisite for many visionbased driver assistance systems is the knowledge of the vehicle’s own movement. In this paper we propose a novel approach for estimating the egomotion of the vehicle from a sequence of stereo images. Our method is directly based on the trifocal geometry between image triples, thus no time expensive recovery of the 3dimensional scene structure is needed. The only assumption we make is a known camera geometry, where the calibration may also vary over time. We employ an Iterated Sigma Point Kalman Filter in combination with a RANSACbased outlier rejection scheme which yields robust frametoframe motion estimation even in dynamic environments. A highaccuracy inertial navigation system is used to evaluate our results on challenging realworld video sequences. Experiments show that our approach is clearly superior compared to other filtering techniques in terms of both, accuracy and runtime. I.
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 32 (4 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.
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 basic convergence result for particle filtering
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2007
"... The basic nonlinear ltering problem for dynamical systems is considered. Approximating the optimal lter estimate by particle lter methods has become perhaps the most common and useful method in recent years. Many variants of particle lters have been suggested, and there is an extensive literature o ..."
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Cited by 29 (8 self)
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The basic nonlinear ltering problem for dynamical systems is considered. Approximating the optimal lter estimate by particle lter methods has become perhaps the most common and useful method in recent years. Many variants of particle lters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still, a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to in nity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result.
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 25 (18 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.
Integrated task and motion planning in belief space
"... We describe an integrated strategy for planning, perception, stateestimation and action in complex mobile manipulation domains based on planning in the belief space of probability distributions over states using hierarchical goal regression (preimage backchaining). We develop a vocabulary of logi ..."
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Cited by 23 (0 self)
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We describe an integrated strategy for planning, perception, stateestimation and action in complex mobile manipulation domains based on planning in the belief space of probability distributions over states using hierarchical goal regression (preimage backchaining). We develop a vocabulary of logical expressions that describe sets of belief states, which are goals and subgoals in the planning process. We show that a relatively small set of symbolic operators can give rise to taskoriented perception in support of the manipulation goals. An implementation of this method is demonstrated in simulation and on a real PR2 robot, showing robust, flexible solution of mobile manipulation problems with multiple objects and substantial uncertainty. 1