S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In Proceedings of AeroSense: The 11 th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, Session: Multi Sensor Fusion and Resource Management II, Orlando, FL, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....(We will return to this topic in Section 6.2. When the functions f k and h k are nonlinear, by linearization the Extended Kalman Filter (EKF) 5, p. 106] is obtained, the posterior density being still modeled as Gaussian. A recent alternative to the EKF is the Unscented Kalman Filter (UKF) [42] which uses a set of discretely sampled points to parameterize the mean and covariance of the posterior density. When the state space is discrete and consists of a finite number of states, Hidden Markov Models (HMM) filters [60] can be applied for tracking. The most general class of filters is ....

S. Julier and J. Uhlmann, "A New Extension of the Kalman Filter to Nonlinear Systems," Proc. SPIE, vol. 3068, pp. 182-193, 1997.

....to the nonlinear functions, can be complex causing implementation difficulties. Second, these linearizations can lead to filter instability if the timestep intervals are not sufficiently small[6] To address these limitations, Julier and Uhlmann developed the unscented Kalman filter (UKF)[7]. The UKF operates on the premise that it is easier to approximate a Gaussian distribution than it is to approximate an arbitrary nonlinear function. Instead of linearizing using Jacobian matrices, the UKF using a deterministic sampling approach to capture the mean and covariance estimates with a ....

....using Jacobian matrices, the UKF uses a deterministic sampling approach to capture the mean and covariance estimates with a minimal set of sample points[9] As with the EKF, we present an algorithmic description of the UKF omitting some theoretical considerations. More details can be found in [7][6] 18] 1 (we use the same state vector as in equation 2, we compute a collection of sigma points, stored in the columns of the L (2L 1) sigma point k 1 where L is the dimension of the state vector. In our case, L = 7 so k 1 is a 7 15 matrix. The columns of k 1 are computed by (X ....

Julier, Simon J. and Jeffery K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In The Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing,Simulation and Controls, Multi Sensor Fusion, Tracking and Resource Management II, SPIE, 1997.

....functions, along with a filter, to estimate the state of the world. Most implementations of the stochastic map use an extended Kalman filter [20] 8] 10] 3] The EKF will be used for illustration in this paper, but is not the only filter which could be used. For instance, an unscented filter [11] or sequential Monte Carlo algorithms [7] 21] could be chosen instead. For alternative approaches to CML that do not use a featurebased representation, see Thrun [21] Choset and Nagatani [5] and Kuipers [14] The basic stochastic mapping algorithm is summarized as follows [20] 8] A. ....

S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In The Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Orlando, Florida. SPIE, 1997. Multi Sensor Fusion, Tracking and Resource Management II.

.... general particle filters [6] and Markov Chain Monte Carlo techniques for neural networks [4] It is similar to the arc reversal technique proposed for particle filters applied to Bayes networks [10] and it is similar to recent work by van der Merwe [24] who uses an unscented filtering step [9] for generating proposal distributions that accommodate the measurement. While this modification is conceptually simple, it has important ramifications. A key contribution of this paper is a convergence proof for linear SLAM problems using a single particle. The resulting algorithm requires ....

S. J. Julier and J. K. Uhlmann. A new extension of the Kalman filter to nonlinear systems. Proc. AeroSense, 1997.

....stand alone estimators as well as in SMC SPKF hybrids (see Section 5) 4 Experimental Results: SPKF applied to state, parameter and dual estimation 4. 1 State Estimation The UKF was originally designed for state estimation applied to nonlinear control applications requiring full state feedback [16, 18, 19]. We provide a new application example corresponding to noisy time series estimation with neural networks. For further examples, see [45] Noisy time series estimation: In this example, a SPKF (UKF) is used to estimate an underlying clean time series corrupted by additive Gaussian white noise. ....

S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In Proc. of AeroSense: The 11th Int. Syrup. on Aerospace/Defence Sensing, Simulation and Controls'., 1997.

....(We will return to this topic in Section 6.2. When the functions = and ) are nonlinear, by linearization the Extended Kalman Filter (EKF) 5, p.106] is obtained, the posterior density being still modeled as Gaussian. A recent alternative to the EKF is the Unscented Kalman Filter (UKF) [42] which uses a set of discretely sampled points to parameterize the mean and covariance of the posterior density. When the state space is discrete and consists of a finite number of states, Hidden Markov Models (HMM) filters [60] can be applied for tracking. The most general class of filters is ....

S. Julier and J. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proc. SPIE, volume 3068, 1997, pp. 182--193.

.... The key areas of research, in our opinion, are i) to develop a recursive implementation of our proposed batch method, perhaps contrasting the results from an Extended Kalman Filter, which is known to be sensitive to initial conditions and the Unscented Filter proposed by Jullier and Uhlmann [131]. We view the unscented filter as a key component of computer vision systems utilising recursion; it is not plagued by the effects of nonlinearities as with the EKF, and it is computationally tractable, unlike particle filters. Another key area of research is ii) a functional definition of camera ....

S.J. Jullier and J.K. Uhlmann. A new extension of the kalman filter to nonlinear systems. In Proc. of AeroSense: The 11th International Symposium on Aeroapace /Defence Sensing, Simulation and Controls, Orlando, Florida, 1997.

....is added to the dis tance. Finally the polar coordinates are transformed into world coordinates taking the observing robot s pose estimate into account. In order to estimate the position and the covariance 2) of an opponent robot, we will use a technique called the un scented transformation [13]. This transformation allows the efficient propagation of uncertainties without creating the necessity to derive the partial derivatives of the propagation functions. Julier and Uhlmann also proved that the unscented transformation provides more realistic uncertainty estimations than a standard ....

S. Julier and J. Uhlmann, "A new extension of the kalman filter to nonlinear systems," The 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls., 1997.

....precision 3 rule for every value of u 6= 0, different choices of u do lead to different approximations. Small values of u lead to more local approximations which are based on the behavior of f near the mean of the Gaussian and are less affected by the higher order terms of f . Julier and Uhlmann [JU97] suggest to choose u = 3, but in general different values of u can lead to better or worse approximations depending on the function f . For precision 5, we will look for a rule of the form: N (x; 0; I) f(x)dx w 0 f[0] w 1 f [ Sigmau] w 2 f [ Sigmau; Sigmau] 6.8) Note that we get 1 ....

.... Sigmau] If we divide the third equation by the second we obtain u = 3 and the other values follow immediately. We get u = 3, w 0 = 1 Gamma7d , w 1 = 4 Gammad 36 . The technique of exact monomial rules provides a new and useful perspective on the Unscented Filter (UF) JU97] which was suggested as an alternative to EKF for tracking non linear dynamic systems. The UF can be extremely accurate, even in cases where the EKF leads to a poor approximation [JU97] We point out that the Unscented Filter is exactly our precision 3 rule from Equation 6.7, and the superior ....

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S. Julier and J. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, 1997.

....for O(d ) implementations. A common approximation in non linear nonGaussian systems is to linearize the actuation and measurements models. If the linearization is obtained via a firstorder Taylor series expansion, the result is known as extended Kalman filter, or EKF [32] Unscented filters [21] obtain often a better linear model through (non random) sampling. However, all these techniques are confined to cases where the Gaussian linear assumption is a suitable approximation. Particle filters address the more general case of (nearly) unconstrained Markov chains. The basic idea is to ....

S. J. Julier and J. K. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In ADSSC-97.

.... algorithms based on the multi hypothesis Kalman filter [1,2] represent beliefs using mixtures of Gaussians [9,34,60,61] To calculate the covariance matrices of the individual Gaussian mixture components, the Kalman filtering approach linearizes the motion model and the perceptual model (see [35] for a recent non linear extension of Kalman filters) It also assumes that errors in sensor measurements and robot motion are Gaussian. For most robot sensors, measurement noise is not Gaussian. Therefore, Kalman filtering algorithms usually do not use raw sensor data for localization. Instead, ....

S.J. Julier, J.K. Uhlmann, A new extension of the kalman filter to nonlinear systems, in: Proc. AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, 1997.

....system as a set of fixed point equations. For the inference task, we provide some new insights into the problem of tracking nonlinear systems. This task is commonly performed using the Extended Kalman Filter (EKF) Bar Shalom et al. 2001] or the simpler and more accurate Unscented Filter (UF) [Julier and Uhlmann, 1997] . We view the problem as a numerical integration problem and demonstrate that the UF is an instance of a numerical integration technique. More importantly, our approach naturally leads to important generalizations of the UF: We show how to take advantage of the structure of the DBN and present a ....

....Some nonlinear functions may not be differentiable (e.g. the max function) preventing the use of an EKF. Even if the function is differentiable, computing the derivatives may be hard if the function is represented as a black box rather than in some analytical form. The Unscented Filter (UF) [Julier and Uhlmann, 1997] provides an alternative approach to tracking nonlinear behavior. As with the EKF, the UF assumes that X = f(X ) and X N ( Sigma) The UF works by deterministically choosing 2d 1 points x 0 ; x 2d , where x 0 = and the other points are symmetric around (the actual points depend on ....

[Article contains additional citation context not shown here]

S. Julier and J. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, 1997.

....detection is performed on the basis of blob analysis. The position of an object is estimated on the basis of a pinhole camera model. Due to rotations and radial distortions of the lenses this model is highly non linear. The uncertainty estimation process is based on the unscented transformation [7]. This allows the use of non linear measurement equations, the incorporation of parameters describing the measurement uncertainty of the sensor at hand as well as an efficient way of propagating the uncertainty of the observing robots pose. A detailed description of the feature extraction ....

S. Julier and J. Uhlmann. A new extension of the kalman filter to nonlinear systems. The 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls., 1997.

....random variable x with mean Yc and covariance C we would like to estimate the mean y and the covariance Cy of an m dimensional vector random variable y. Both variables are related to each other by a non linear transformation y g(x) The unscented transformation is defined as follows [8]: 1. Compute the set Z of 2n points from the rows or columns of the matrices nv nCxx. This set is zero mean with covariance Cx. The matrix square root can efficiently be calculated by the Cholesky decomposition. 2. Compute a set of points X with the same covariance, but with mean Yc, by ....

....radius is added to the distance. Finally the polar coordinates are transformed into world coordinates taking the observing robot s pose (I) into account. In order to estimate the position ) and the covariance C of an opponent robot, we will use a technique similar to the unscented transformation [8] (see Fig. Figure : Propagation es. First an intermediate mean and covariance C describing jointly the observing robot s pose and the observed robot is set up: c = row, col, width] 0 3 0 0 C= 0 040 0 0 0 3 (i) q , row, col and width are assumed to be uncorrelated with a variance of a ....

S. Julier and J. Uhlmann. A new extension of the kalman filter to nonlinear systems. The 11th Int. Syrup. on Aerospace/Defence Sensing, Simulation and Controls., 1997.

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S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In Proceedings of AeroSense: The 11 th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, Session: Multi Sensor Fusion and Resource Management II, Orlando, FL, 1997.

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S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In Proceedings of AeroSense: The 11 th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, Session: Multi Sensor Fusion and Resource Management II, Orlando, FL, 1997.

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S. Julier and J. Uhlmann. A new extension of the kalman filter to nonlinear systems. In Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, 1997.

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S. Julier and J. Uhlmann. A new extension of the kalman filter to nonlinear systems. In SPIE AeroSense Symposium, 1997.

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S. J. Julier and J. K. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proceedings of AeroSense: The 11th International Symposium on Aerospace / Defence Sensing, Simulation and Controls, vol. Multi Sensor Fusion, Tracking and Resource Management II, 1997.

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S.J. Julier and J. K. Uhlmann, A New Extension of the Kalman Filter to Nonlinear Systems, In Proc. of AeroSense: The 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls, 1997

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S. Julier and J. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, 1997.

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S. J. Julier and J. K. Uhlmann. A new extension of the kalman filter to nonlinear systems. Int. Symp. Aerospace/Defense Sensing, Simulation and Controls, 1997.

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S. Julier and J. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, 1997.

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S. J. Julier and J. K. Uhlmann, "A new extension of the kalman filter to nonlinear systems," in The Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, (Orlando, Florida), 1997.

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S. J. Julier and J. K. Uhlmann, "A new extension of the kalman filter to nonlinear systems," SPIE AeroSense Symposium, April 1997.

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S. Julier and J. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proceedings SPIE, volume 3068, 1997, pp. 182--193.

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Julier, S.J. and Uhlmann, J.K., "A new extension of the Kalman filter to nonlinear systems", Proceedings of AeroSense, Orlando, 1997.

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S. J. Julier and J. K. Uhlmann, "A new extension of the kalman filter to nonlinear systems," in Proc. SPIE, 1997, vol. 3068, pp. 182--193.

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S. J. Julier and J. K. Uhlmann. "A New Extension of the Kalman Filter to Nonlinear Systems." Proc. of AeroSense: The 11th Int. Symp. On Aerospace/Defence Sensing, Simulation and Controls, SPIE

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S. J. Julier and J. K. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, Orlando, FL, 1997.

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S. J. JULIER AND J. K. UHLMANN, A new extension of the Kalman filter to nonlinear systems. In I. Kadar, ed., Proceedings of the 11th SPIE International Symposium on Aerospace/Defense Sensing, Simulation, and Controls, pp. 182-- 193, International Society for Optical Engineering, Orlando, April 1997.

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S. Julier and J. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, 1997.

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S. Julier and J. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, 1997.

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S. J. Julier and J. K. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In Aerosense: The 11 th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Orlando, Florida, 1997.

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S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In Proc. of AeroSense: The 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls., 1997.

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S. J. Julier and J. K. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proc. AeroSense, Orlando, FL, 1997.

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S. J. Julier and J. K. Uhlmann. A new extension of the Kalman filter to nonlinear systems. In In Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, 1997.

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S. Julier and J. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. In Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, 1997.

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S. Julier and J. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proc. SPIE, volume 3068, 1997, pp. 182--193.

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