Investigation On Kernel Adaptive Filter With Feedback Structure

Recently, plenty of kernel adaptive filtering methods have been proposed for practical applications, including time series prediction, channel equalization, pattern classification, noise removal and echo cancelation, etc. The structure of the system and the method of adaptive learning rate are two powerful keys in improving the convergence speed and estimation accuracy. In this thesis, we study the way of designing kernel adaptive filters from the two aspects mentioned above.First, a recurrent kernel online learning algorithm with a processed feedback is proposed. The delayed output is processed by a well-designed nonlinear piecewise function, which strengthens or weakens the feedback in response to different situation.Second, metalearning, which studies how learning system itself can become more efficient by using past experience, is a method of great importance in the field of machine learning. Our algorithm includes an adaptive learning rate which evolves from kernel incremental meta-learning algorithm(KIMEL), main idea of which is to treat the prediction error as a function of learning rate so that gradient descent method can be used to update the learning rate.Experimental results show that the proposed kernel adaptive filtering algorithm,namely the incremental meta-learning with processed feedback, outperforms both the kernel adaptive filter with multiple feedback and the kernel algorithm with single feedback in terms of convergence speed and estimation accuracy.