Neural Net Gains Estimation Based on an Equivalent Model

A model of an Equivalent Artificial Neural Net (EANN) describes the gains set, viewed as parameters in a layer, and this consideration is a reproducible process, applicable to a neuron in a neural net (NN). The EANN helps to estimate the NN gains or parameters, so we propose two methods to determine them. The first considers a fuzzy inference combined with the traditional Kalman filter, obtaining the equivalent model and estimating in a fuzzy sense the gains matrix A and the proper gain K into the traditional filter identification. The second develops a direct estimation in state space, describing an EANN using the expected value and the recursive description of the gains estimation. Finally, a comparison of both descriptions is performed; highlighting the analytical method describes the neural net coefficients in a direct form, whereas the other technique requires selecting into the Knowledge Base (KB) the factors based on the functional error and the reference signal built with the past information of the system

Neural fuzzy digital filtering: multivariate identifier filters involving multiple inputs and multiple outputs (mimo)

Multivariate identifier filters (multiple inputs and multiple outputs - MIMO) are adaptive digital systems having a loop in accordance with an objective function to adjust matrix parameter convergence to observable reference system dynamics. One way of complying with this condition is to use fuzzy logic inference mechanisms which interpret and select the best matrix parameter from a knowledge base. Such selection mechanisms with neural networks can provide a response from the best operational level for each change in state (Shannon, 1948). This paper considers the MIMO digital filter model using neuro fuzzy digital filtering to find an adaptive  parameter matrix which is integrated into the Kalman filter by the transition matrix. The filter uses the neural network as back-propagation into the fuzzy mechanism to do this, interpreting its variables and its respective levels and selecting the best values for automatically adjusting transition matrix values. The Matlab simulation describes the neural fuzzy digital filter giving an approximation of exponential convergence seen in functional error.Los filtros identificadores multivariables (MIMO) son sistemas digitales adaptivos que cuentan con retroalimentación para que, de acuerdo a una función objetivo, ajusten su matriz de parámetros con la que se aproximan a la di-námica observable del sistema de referencia. Una forma de que un identificador cumpla con esas condiciones, es la de la lógica difusa por medio de sus mecanismos de in-ferencia que interpretan y seleccionan en una base de co-nocimiento la mejor matriz de parámetros. Estos mecanismos de selección mediante las redes neuronales permiten encontrar la respuesta con el mejor nivel de operación para cada cambio de estado (Shannon, 1948). En este artículo se considera en el modelo MIMO del filtrado digital, el proceso neuronal difuso para la estimación matricial de parámetros adaptiva, que se integra en el filtro de Kalman a través de la matriz de transición. Para ello se utilizó la red neuronal del tipo retropropagación en el mecanismo difuso, interpretando sus variables y sus respectivos niveles, seleccionando los mejores valores para ajustar automáticamente los valores de la matriz de transición. La simulación en Matlab presenta al filtrado digital neuronal difuso dando el seguimiento, observándose un funcional de error decreciente exponencialmente