## The Unscented Kalman Filter for nonlinear estimation (2000)

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Citations: | 79 - 4 self |

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@INPROCEEDINGS{Wan00theunscented,

author = {Eric A. Wan and Rudolph Van Der Merwe},

title = {The Unscented Kalman Filter for nonlinear estimation},

booktitle = {},

year = {2000},

pages = {153--158}

}

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### Abstract

The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system, estimating parameters for nonlinear system identification (e.g., learning the weights of a neural network), and dual estimation (e.g., the Expectation Maximization (EM) algorithm) where both states and parameters are estimated simultaneously. This paper points out the flaws in using the EKF, and introduces an improvement, the Unscented Kalman Filter (UKF), proposed by Julier and Uhlman [5]. A central and vital operation performed in the Kalman Filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF, the state distribution is approximated

### Citations

8520 | Maximum likelihood from incomplete data
- Dempster, Laird, et al.
- 1967
(Show Context)
Citation Context ...Equation 7). As expressed earlier, a number of algorithmic approaches exist for this problem. We present results for the Dual UKF and Joint UKF. Development of a Unscented Smoother for an EM approach =-=[2]-=- was presented in [13]. As in the prior state-estimation example, we utilize a noisy time-series application modeled with neural networks for illustration of the approaches. In the the dual extended K... |

5073 | Neural Networks for Pattern Recognition - Bishop - 1995 |

3878 | Neural Network: A Comprehensive Foundation - Haykin - 1994 |

1283 |
Adaptive Filter Theory
- Haykin
- 2001
(Show Context)
Citation Context ...pplied directly as an efficient "second-order" technique for learning the parameters. In the linear case, the relationship between the Kalman Filter (KF) and Recursive Least Squares (RLS) is=-= given in [3]-=-. The use of the EKF for training neural networks has been developed by Singhal and Wu [9] and Puskorious and Feldkamp [8]. Dual Estimation A special case of machine learning arises when the input x k... |

463 | Uhlmann, “A new extension of the Kalman filter to nonlinear systems
- Julier, K
- 1997
(Show Context)
Citation Context ...h states and parameters are estimated simultaneously. This paper points out the flaws in using the EKF, and introduces an improvement, the Unscented Kalman Filter (UKF), proposed by Julier and Uhlman =-=[5]-=-. A central and vital operation performed in the Kalman Filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF, the state distribution is approximated by... |

282 | Unscented filtering and nonlinear estimation - Julier, Uhlmann - 2004 |

242 | Oscillation and chaos in physiological control systems, Science 197 - Mackey, Glass - 1977 |

160 | The Unscented Particle Filter - Merwe, Freitas, et al. - 2000 |

149 | A new approach for filtering nonlinear systems - Julier, Uhlmann, et al. - 1995 |

129 | Aircraft Control and Simulation - 16Stevens, Lewis - 2004 |

93 | Gaussian filters for nonlinear filtering problems - Ito, Xiong - 2000 |

86 | The scaled unscented transformation
- Julier
(Show Context)
Citation Context ...s for all nonlinearities. For non-Gaussian inputs, approximations are accurate to at least the second-order, with the accuracy of third and higher order moments determined by the choice of ands(See [=-=4]-=- for a detailed discussion of the UT). A simple example is shown in Figure 1 for a 2-dimensional system: the left plot shows the true mean and covariance propagation using Monte-Carlo sampling; the ce... |

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65 |
Training multilayer perceptrons with the extended Kalman algorithm
- Singhal, Wu
- 1989
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Citation Context ...he linear case, the relationship between the Kalman Filter (KF) and Recursive Least Squares (RLS) is given in [3]. The use of the EKF for training neural networks has been developed by Singhal and Wu =-=[9]-=- and Puskorious and Feldkamp [8]. Dual Estimation A special case of machine learning arises when the input x k is unobserved, and requires coupling both state-estimation and parameter estimation. For ... |

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Decoupled extended Kalman filter training of feedforward layered networks
- Puskorius, Feldkamp
- 1991
(Show Context)
Citation Context ... between the Kalman Filter (KF) and Recursive Least Squares (RLS) is given in [3]. The use of the EKF for training neural networks has been developed by Singhal and Wu [9] and Puskorious and Feldkamp =-=[8]-=-. Dual Estimation A special case of machine learning arises when the input x k is unobserved, and requires coupling both state-estimation and parameter estimation. For these dual estimation problems, ... |

48 |
Optimal estimation
- Lewis
- 1986
(Show Context)
Citation Context .... The EKF and its Flaws Consider the basic state-space estimation framework as in Equations 1 and 2. Given the noisy observation y k , a recursive estimation for x k can be expressed in the form (see =-=[6-=-]), ^ xk = (prediction of xk ) +Kk [yk (prediction of yk )] (8) This recursion provides the optimal minimum mean-squared error (MMSE) estimate for x k assuming the prior estimate ^ x k 1 and current ... |

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27 | Strapdown inertial navigation integration algorithm design - SAVAGE - 1998 |

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- Wan, Merwe, et al.
- 1999
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Citation Context ...KF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. Our preliminary results were presented in =-=[13]-=-. In this paper, the algorithms are further developed and illustrated with a number of additional examples. This work was sponsored by the NSF under grant grant IRI-9712346 1. Introduction The EKF has... |

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A state-space approach to adaptive nonlinear filtering using recurrent neural networks
- Matthews
- 1990
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Citation Context ...ght-estimation are done with the UKF. Note that the state-transition is linear in the weight filter, so the nonlinearity is restricted to the measurement equation. In the joint extended Kalman filter =-=[7]-=-, the signal-state and weight vectors are concatenated into a single, joint state vector: [x T k w T k ] T . Estimation is done recursively by writing the state-space equations for the joint state as:... |

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- Wan, Nelson
- 1997
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Citation Context ...d in [13]. As in the prior state-estimation example, we utilize a noisy time-series application modeled with neural networks for illustration of the approaches. In the the dual extended Kalman filter =-=[11]-=-, a separate state-space representation is used for the signal and the weights. The state-space representation for the state x k is the same as in Equation 20. In the context of a time-series, the sta... |

11 | A multisine approach for trajectory optimization based on information gain - Mihaylova, Schutter, et al. - 2003 |

10 | Sequential Monte Carlo methods for optimisation of neural network models
- Freitas, Niranjan, et al.
- 1998
(Show Context)
Citation Context ... i=0 W (m) i Y i (17) Py 2L X i=0 W (c) i fY i yg fY i yg T (18) Note that this method differs substantially from general "sampling " methods (e.g., Monte-Carlo methods such as particle f=-=ilters [1]-=-) which require orders of magnitude more sample points in an attempt to propagate an accurate (possibly nonGaussian) distribution of the state. The deceptively simple approach taken with the UT result... |

10 | 2002), Parametric contour tracking using unscented Kalman filter, paper presented at - Chen, Huang, et al. |

9 | State estimation for distributed systems with sensing delay - Alexander - 1991 |

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8 | Nonlinear regulation and nonlinear H-infinity control via the state-dependent Riccati equation technique: Part2, Examples - Cloutier, D’Souza, et al. - 1996 |

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