Synthesis of feed-forward artificial neural networks approximating a maximum likelihood estimator
This report reveals an approach for synthesizing maximum likelihood parameter estimators using feedforward artificial neural network (ANN) of multilayer perceptron architecture. There are two learning approach for the neural network which output approximates vector parameter estimator based on maximum likelihood. The first one is conventional minimization of the squared errors between ANN output and solution obtained by numerical optimization technique. The second approach is based on maximization of the target function evaluated by substituting the measured data and the parameter vector estimated by the ANN. A brief theoretical foundation of the proposed approach is presented in the assumption that the model of observation is known as well as the values of its vector of parameters. For a practical example, the implementation of direction-of-arrival (DOA) estimator for the active ring antenna array is shown. The comparative analysis between proposed ANN and optimal numerical solution, regarding Cramer-Rao Lower Bound, shows that there is no significant dependency of the accuracy of estimation on actual parameter value. The carried out simulation shows that the standard deviation of estimator increases no more than 10 per cent while the consumed computer time decreases no less than 12 times.