Mạng thần kinh thường xuyên cho dự đoán P2

FundamentalsAdaptive systems are at the very core of modern digital signal processing. There are many reasons for this, foremost amongst these is that adaptive filtering, prediction or identification do not require explicit a priori statistical knowledge of the input data. Adaptive systems are employed in numerous areas such as biomedicine, communications, control, radar, sonar and video processing (Haykin 1996a).
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Mạng thần kinh thường xuyên cho dự đoán P2 Recurrent Neural Networks for Prediction Authored by Danilo P. Mandic, Jonathon A. Chambers Copyright c 2001 John Wiley & Sons Ltd ISBNs: 0-471-49517-4 (Hardback); 0-470-84535-X (Electronic)2Fundamentals2.1 PerspectiveAdaptive systems are at the very core of modern digital signal processing. There aremany reasons for this, foremost amongst these is that adaptive filtering, prediction oridentification do not require explicit a priori statistical knowledge of the input data.Adaptive systems are employed in numerous areas such as biomedicine, communica-tions, control, radar, sonar and video processing (Haykin 1996a).2.1.1 Chapter SummaryIn this chapter the fundamentals of adaptive systems are introduced. Emphasis isfirst placed upon the various structures available for adaptive signal processing, andincludes the predictor structure which is the focus of this book. Basic learning algo-rithms and concepts are next detailed in the context of linear and nonlinear structurefilters and networks. Finally, the issue of modularity is discussed.2.2 Adaptive SystemsAdaptability, in essence, is the ability to react in sympathy with disturbances to theenvironment. A system that exhibits adaptability is said to be adaptive. Biologicalsystems are adaptive systems; animals, for example, can adapt to changes in theirenvironment through a learning process (Haykin 1999a). A generic adaptive system employed in engineering is shown in Figure 2.1. It consistsof • a set of adjustable parameters (weights) within some filter structure; • an error calculation block (the difference between the desired response and the output of the filter structure); • a control (learning) algorithm for the adaptation of the weights. The type of learning represented in Figure 2.1 is so-called supervised learning,since the learning is directed by the desired response of the system. Here, the goal10 ADAPTIVE SYSTEMS Comparator _ Filter + Structure Σ Desired Input Signal Response Control Algorithm Error Figure 2.1 Block diagram of an adaptive systemis to adjust iteratively the free parameters (weights) of the adaptive system so as tominimise a prescribed cost function in some predetermined sense. 1 The filter structurewithin the adaptive system may be linear, such as a finite impulse response (FIR) orinfinite impulse response (IIR) filter, or nonlinear, such as a Volterra filter or a neuralnetwork.2.2.1 Configurations of Adaptive Systems Used in Signal ProcessingFour typical configurations of adaptive systems used in engineering are shown inFigure 2.2 (Jenkins et al. 1996). The notions of an adaptive filter and adaptive systemare used here interchangeably. For the system identification configuration shown in Figure 2.2(a), both the adap-tive filter and the unknown system are fed with the same input signal x(k). The errorsignal e(k) is formed at the output as e(k) = d(k) − y(k), and the parameters of theadaptive system are adjusted using this error information. An attractive point of thisconfiguration is that the desired response signal d(k), also known as a teaching ortraining signal, is readily available from the unknown system (plant). Applications ofthis scheme are in acoustic and electrical echo cancellation, control and regulation ofreal-time industrial and other processes (plants). The knowledge about the system isstored in the set of converged weights of the adaptive system. If the dynamics of theplant are not time-varying, it is possible to identify the parameters (weights) of theplant to an arbitrary accuracy. If we desire to form a system which inter-relates noise components in the inputand desired response signals, the noise cancelling configuration can be implemented(Figure 2.2(b)). The only requirement is that the noise in the primary input and thereference noise are correlated. This configuration subtracts an estimate of the noisefrom the received signal. Applications of this configuration include noise cancellation 1 The aim is to minimise some function of the error e. If E[e2 ] is minimised, we consider minimummean squared error (MSE) adaptation, the statistical expectation operator, E[ · ], is du ...