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41
Unscented Filtering and Nonlinear Estimation
 PROCEEDINGS OF THE IEEE
, 2004
"... The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the ..."
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Cited by 555 (3 self)
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The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.
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.
Kalman Filters for nonlinear systems: a comparison of performance
, 2001
"... The Kalman Filter is a wellknown recursive state estimator for linear systems. In practice the algorithm is often used for nonlinear systems by linearizing the system's process and measurement functions. Different Kalman Filter variants linearize the functions in different ways. This paper exp ..."
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Cited by 61 (4 self)
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The Kalman Filter is a wellknown recursive state estimator for linear systems. In practice the algorithm is often used for nonlinear systems by linearizing the system's process and measurement functions. Different Kalman Filter variants linearize the functions in different ways. This paper explains how the best known Kalman Filter variants  i.e. the Extended Kalman Filter (EKF), Iterated Extended Kalman Filter (IEKF), the Central Difference Filter (CDF), the first order Divided Difference Filter (DD1) and the Unscented Kalman Filter (UKF)  (i) linearize the process and measurement functions; (ii) take the linearization errors into account; and (iii) how the quality of the state estimates depends on the previous two choices. Besides some
Decentralized sigmapoint information filters for target tracking in collaborative sensor networks
 IEEE Trans. Signal Process
, 2005
"... Abstract—Tracking a target in a cluttered environment is a representative application of sensor networks and a benchmark for collaborative signal processing algorithms. This paper presents a strictly decentralized approach to Bayesian filtering that is well fit for innetwork signal processing. By c ..."
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Cited by 15 (0 self)
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Abstract—Tracking a target in a cluttered environment is a representative application of sensor networks and a benchmark for collaborative signal processing algorithms. This paper presents a strictly decentralized approach to Bayesian filtering that is well fit for innetwork signal processing. By combining the sigmapoint filter methodology and the information filter framework, a class of algorithms denoted as sigmapoint information filters is developed. These techniques exhibit the robustness and accuracy of the sigmapoint filters for nonlinear dynamic inference while being as easily decentralized as the information filters. Furthermore, the computational cost of this approach is equivalent to a local Kalman filter running in each active node while the communication burden can be made linearly growing in the number of sensors involved. The proposed algorithms are then adapted to the specific problem of target tracking with data association ambiguity. Making use of a local probabilistic data association, we formulate a decentralized tracking scheme that significantly outperforms the existing schemes with similar computational and communication complexity. Index Terms—Decentralized filtering, information filter, sensor networks, sigmapoint Kalman filter, target tracking.
A survey of maneuvering target tracking: approximation techniques for nonlinear filtering
 in Proc. 2004 SPIE Conf. Signal and Data Processing of Small Targets
, 2004
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Statistically Linearized Recursive Least Squares
 IN PROCEEDINGS OF THE IEEE INTERNATIONAL WORKSHOP ON MACHINE LEARNING FOR SIGNAL PROCESSING (MLSP 2010), KITTILÄ (FINLAND), AUGUSTSEPTEMBER
, 2010
"... This article proposes a new interpretation of the sigmapoint kalman filter (SPKF) for parameter estimation as being a statistically linearized recursive leastsquares algorithm. This gives new insight on the SPKF for parameter estimation and particularly this provides an alternative proof for a resu ..."
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Cited by 7 (6 self)
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This article proposes a new interpretation of the sigmapoint kalman filter (SPKF) for parameter estimation as being a statistically linearized recursive leastsquares algorithm. This gives new insight on the SPKF for parameter estimation and particularly this provides an alternative proof for a result of Van der Merwe. On the other hand, it legitimates the use of statistical linearization and suggests many ways to use it for parameter estimation, not necessarily in a leastsquares sens.
Nonlinearity in sensor fusion: Divergence issues
 in EKF, modified truncated SOF, and UKF,” in Proc. AIAA Guidance, Navigation, and Control Conf
, 2007
"... Relative navigation is a challenging technological component of many planned NASA and ESA missions. It typically uses recursive filters to fuse measurements (e.g., range and angle) from sensors with contrasting accuracies to estimate the vehicle state vectors in real time. The tendency of Extended K ..."
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Cited by 7 (0 self)
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Relative navigation is a challenging technological component of many planned NASA and ESA missions. It typically uses recursive filters to fuse measurements (e.g., range and angle) from sensors with contrasting accuracies to estimate the vehicle state vectors in real time. The tendency of Extended Kalman filter to diverge under these conditions is well documented in the literature. As such, we have investigated the application of the modified truncated SecondOrder Filter (mtSOF) and the Unscented Kalman filter (UKF) to those mission scenarios using numerical simulations of a representative experimental configuration: estimation of a static position in space using distance and angle measurements. These simulation results showed that the mtSOF and UKF may also converge to an incorrect state estimate. A detailed study establishes the divergence process of the mtSOF and UKF, and designs new strategies that improve the accuracy of these filters. I.
CDGPSBased Relative Navigation for Multiple Spacecraft
 MASSACHUSETTS INSTITUTE OF TECHNOLOGY, DEPT
, 2004
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On the Complexity and Consistency of UKFbased SLAM
"... Abstract — This paper addresses two key limitations of the unscented Kalman filter (UKF) when applied to the simultaneous localization and mapping (SLAM) problem: the cubic, in the number of states, computational complexity, and the inconsistency of the state estimates. In particular, we introduce a ..."
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Cited by 3 (2 self)
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Abstract — This paper addresses two key limitations of the unscented Kalman filter (UKF) when applied to the simultaneous localization and mapping (SLAM) problem: the cubic, in the number of states, computational complexity, and the inconsistency of the state estimates. In particular, we introduce a new sampling strategy that minimizes the linearization error and whose computational complexity is constant (i.e., independent of the size of the state vector). As a result, the overall computational complexity of UKFbased SLAM becomes of the same order as that of the extended Kalman filter (EKF) when applied to SLAM. Furthermore, we investigate the observability properties of the linearregressionbased model employed by the UKF, and propose a new algorithm, termed the ObservabilityConstrained (OC)UKF, that improves the consistency of the state estimates. The superior performance of the OCUKF compared to the standard UKF and its robustness to large linearization errors are validated by extensive simulations. I.
Unscented Kalman Filters for Multiple Target Tracking with Symmetric Measurement Equations
, 2005
"... The symmetric measurement equation approach to multiple target tracking is revisited using unscented Kalman and particle filters. The characteristics and performance of these filters are compared to the original symmetric measurement equation implementation relying upon an extended Kalman filter. Co ..."
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The symmetric measurement equation approach to multiple target tracking is revisited using unscented Kalman and particle filters. The characteristics and performance of these filters are compared to the original symmetric measurement equation implementation relying upon an extended Kalman filter. Counterintuitive results are presented and explained for two sets of symmetric measurement equations, including a previously unknown limitation of the unscented Kalman filter. The point is made that the performance of the SME approach is dependent on the interaction of the set of SME equations and the filter used. Furthermore, an SME/unscented Kalman filter pairing is shown to have improved performance versus previous approaches while possessing simpler implementation and equivalent computational complexity. Finally, Taylor series expansions are used to analyze the properties of the SME approach in conjunction with the Kalman filters.