Neural network synthesis of an optimal linear stochastic system according to the criterion of minimum mean square error

The paper is devoted to the new synthesis method for linear optimal stochastic systems according to the criterion of minimum mean square error (MSE) *and neural network technology. It is supposed that one-dimensional input signal is the sum of known signal and additive Gaussian noise. Noise is independent of signal parameters. At output, it is necessary to perform corresponding input transformation. The paper describes architecture of three-layer wavelet neural network (WNN) with one reserved layer. The activation function of reserved layer is described using orthonormal wavelet basis with compact carrier. For WNN functioning, a tutoring algorithm based on the method of quick descend is used. The MSE optimal operator is constructed. The MSE estimate is presented in the form of linear combination of basis wavelet functions. An illustrative example is given. The basic results are formulated and discussed.