One-Step Ahead Prediction of the Wiener-Hammerstein Benchmark with - PowerPoint PPT Presentation

One-Step Ahead Prediction of the Wiener-Hammerstein Benchmark with Process Noise using Kernel Adaptive Learning Rishi Relan Dieter Verbecke Koen Tiels Department ELEC 12.05.2017

Idea of this workshop: Nonlinear System 2

Idea of this workshop: Different methods 3

Overview 4

Benchmark 5

Physical Electronic Circuit 6

Linear Adaptive Filters • Widrow and Hoff (1960): LMS filter • Kalman (1960): Kalman filter 7

Two Simple Adaptive Filters 8

Nonlinear Adaptive Filter 9

Kernel Methods 10

Putting it formally 11

Kernel Regression 12

The Standard Online Algorithm 13

The main Questions? 14

The Bayesian Viewpoint 15

Further Extensions 1) Steven Van Vaerenbergh, Miguel Lázaro-Gredilla and Ignacio Santamaría, "Kernel Recursive Least-Squares Tracker for Time-Varying Regression," IEEE Transactions on Neural Networks and Learning Systems, Vol. 23, No. 8, pp. 1313-1326, Aug 2012. 2) F. Perez-Cruz, S. Van Vaerenbergh, J. J. Murillo-Fuentes, M. Lazaro-Gredilla and I. Santamaria, "Gaussian Processes for Nonlinear Signal Processing: An Overview of Recent Advances," in IEEE Signal Processing Magazine, vol. 30, no. 4, pp. 40-50, July 2013. 16

Observations 17

Observations 18

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Conclusions 20

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