Artificial Neural Networks Implementing Maximum Likelihood Estimator for Passive Radars
This paper introduces the maximum likelihood estimator (MLE) based on artificial neural network (ANN) for a fast computation of the bearing that indicates the direction to the source of the electromagnetic wave received by a passive radar system equipped with an array antenna. Authors propose the cascade scheme for ANN training phase where the network is fed with the pair-wise delays of received stationary or cyclostationary signals and the output of the network goes to the input of the target function being maximized together with the same data. The designed ANN topology has the modified output layer consisting of the custom neuron that implements argument function of a complex number rather than linear or sigmoid-like ones used in the conventional multilayer perceptron topologies. The simulation carried out for the ring array antenna shows that a single estimation obtained via ANN MLE takes 12 times less computational time comparing to the MLE implemented via the numerical optimization technique. The degradation of accuracy measured as the increase of mean-squared error does not exceed 10% of the potential value for the particular signal-to-noise ratio (SNR) and that difference has no tendency to decrease for higher SNR. The estimation error appeared to be independent from the true value in the wide range of bearings.