Tài liệu Kalman Filtering and Neural Networks - Chapter 6: LEARNING NONLINEAR DYNAMICAL SYSTEMS USING THE EXPECTATION– MAXIMIZATION ALGORITHM doc

... Second, they can be characterized by175 Kalman Filtering and Neural Networks, Edited by Simon HaykinISBN 0-4 7 1-3 699 8-5 # 2001 John Wiley & Sons, Inc. Kalman Filtering and Neural Networks, ... smooth-ing (EKS), which infers the hidden state distribution during the E-step of our algorithm. The nonlinear model is linearized about the current state esti-mate at each time, and then Kalman ... for nonlinear dynamical systems and also as a basis for on-line learning algorithms for feedforward neural networks [15] and radial basis function networks [16, 17]. For moredetails, see Chapter...

Tài liệu Kalman Filtering and Neural Networks - Chapter 1: KALMAN FILTERS doc

... paper by Kalman [1] for the 1 Kalman Filtering and Neural Networks, Edited by Simon HaykinISBN 0-4 7 1-3 699 8-5 # 2001 John Wiley & Sons, Inc. Kalman Filtering and Neural Networks, Edited by Simon ... Inc.ISBNs: 0-4 7 1-3 699 8-5 (Hardback); 0-4 7 1-2 215 4-6 (Electronic)With these two theorems at hand, the derivation of the Kalman filterfollows.1.3 KALMAN FILTERSuppose that a measurement on a linear dynamical ... thatE½wkyTi¼0:1.3 KALMAN FILTER5Given the linearized state-space model of Eqs. (1.58) and (1.59), wemay then proceed and apply the Kalman filter theory of Section 1.3 toderive the extended Kalman filter....

Tài liệu Kalman Filtering and Neural Networks - Chapter 4: CHAOTIC DYNAMICS pdf

... 6-4 R-2R-1 5,000 25,000 1 0.69 1.04Ikeda 6-6 R-5R-1 5,000 25,000 1 0.354 1.51Lorenz 3-8 R-7R-1 5,000 25,000 40 0.040 2.09NH3laser 9-1 0R-8R-1 1,000 9,000 1a0.147 2.01Sea clutter 6-8 R-7R-1 ... Inc. Kalman Filtering and Neural Networks, Edited by Simon HaykinCopyright # 2001 John Wiley & Sons, Inc.ISBNs: 0-4 7 1-3 699 8-5 (Hardback); 0-4 7 1-2 215 4-6 (Electronic)Figure 4.2 Results for the ... networkconﬁguration of 3-8 R-7R-1, consisting of 216 weights including the biases, was trained with the EKF algorithm, and the convergence of the training MSE is shown in Figure 4.10.Open-Loop Evaluation The results...

Tài liệu Kalman Filtering and Neural Networks - Chapter 5: DUAL EXTENDED KALMAN FILTER METHODS docx

... observations.123 Kalman Filtering and Neural Networks, Edited by Simon HaykinISBN 0-4 7 1-3 699 8-5 # 2001 John Wiley & Sons, Inc. Kalman Filtering and Neural Networks, Edited by Simon HaykinCopyright ... 514–519.[16] Z. Ghahramani and S.T. Roweis, ‘‘ Learning nonlinear dynamical systems using an EM algorithm, ’’ in Advances in Neural Information Processing Systems 11: Proceedings of the 1998 Conference. ... neural networks using sequential-update forms of the extended Kalman ﬁlter,’’ Informal Report LA-UR-9 5-4 22, Los AlamosNational Laboratory, January 1995.[33] A.H. Sayed and T. Kailath, ‘‘A state-space...

Tài liệu Kalman Filtering and Neural Networks - Chapter VII: THE UNSCENTED KALMAN FILTER pdf

... patternfell within the assigned region and 0:8 otherwise. Figure 7.10 illustrates the classification task, learning curves for the UKF and EKF, and the finalclassification regions. For the learning curve, ... smoother performance. In this case, the network models aretrained on the clean time series, and then tested on the noisy data using the standard extended Kalman smoother with linearized backward modelˆxTime ... wk. The EKF can then be applied directly as an efficient‘‘second-order’’ technique for learning the parameters. The use of the EKFfor training neural networks has been developed by Singhal and...

Tài liệu Kalman Filtering and Neural Networks P2 doc

... Pik and the weight vectors wikare independent of the chosen number of streams.On the other hand, we noted above the increase in size for the derivativematrices Hik: l, as well as of the Kalman ... diagonal value of 100 and 1,000 for weights corresponding to nonlinear and linear nodes,respectively. Then, the user of these methods must set values for the learning rate and process-noise term according ... consistent with previously observed data. On the other hand,derivative calculations and the extended Kalman recursion for nonlinear networks utilizeﬁrst-order approximations, so that weight updates...

Tài liệu Kalman Filtering and Neural Networks P3 doc

... in the complexity of the learning task. However, since the number of weights in the network islimited and remains the same as in the other experiments, the networkcannot simply memorize the ... order. Then, during testing, the order of the sequences wasvaried and the network was asked to predict the correct shape and locationof the next image in the sequence. The complexity of the problem ... so that the network would not learn the order ofpresentation of the sequences. The network was therefore expected tolearn the motions associated with each of the three shapes, and not the order...

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