This paper presents a description of application of stochastic weights in a neuron, problem solved through the adaptive estimation achieved with dynamical combination between the identification and estimation; having an adaptive structure that updates the estimated parameters into the integrated filter. The weights are dynamically adjusted in the neuron based on stochastic gradient, affecting the neuronal performance allowing that its response converges to the reference signal. In addition, the error is applied in identification as an innovative gain adjusting the neuron in its inputs and consequently its dendrites signals that are applied into gradient filter adjusting the neuron weights in accordance with the desired signal requirement. Such that the gradient estimation is built based on the Black-box scheme with unknown internal weights. All simulations were developed using Matlab® software.
In this article, a stochastic algorithm is briefly presented based on the one of second moment applied to a stochastic process model of second order. The design initially consisted in formulating the state equation model and the stochastic outputs, in order to apply the second moment using the internal product of Martingale and the stochastic operators of the expectation, variance and covariance. The design results generated the formulas on: the covariances and the internal product variances to calculate the lumped estimation parameters, the error functional based on the mean quadratic error, the output variable as a function of the estimation parameters obtained. Furthermore, the recursive form was formulated in this design starting from the premise of the obtained results using the second stochastic moment. The main interest lays on the recursive form, because this is the one capable of being implemented in a digital system. In order to observe the precision and the convergence of the estimation parameters and the output variables, Matlab-based figures are shown.
This paper presents two stochastic filters considering autoregressive models of first and second order for parameter estimation and system identification. Each model is applied to a reference of the corresponding order and their recursive and non-recursive estimation results are compared; obtaining their error functional values to determine their performance. Due to the recursive methods give better approximation results, than the non-recursive ones, they are applied to describe the behaviour of the wind, which is a stochastic signal useful in the aerodynamic field, comparing the tracking results through off the functional error and the surroundings of the relative frequency histograms; including also a computational complexity graphic. To conclude, the second order filter has a better convergence performance at the expense of a higher computational cost, its pros and cons are mentioned. Nevertheless, choosing the filter order depends on its application.
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