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As opposed to the analytic approach used in the modern theory of optimal filtering, a synthetic approach is presented. The signal/sensor data, which are generated by either computer simulation or actual experiments, are synthesized into a filter by training a recurrent multilayer perceptron (RMLP) with at least one hidden layer of fully or partially interconnected neurons and with or without output feedbacks. The RMLP, after adequate training, is a recursive filter optimal for the given structure, with the lagged feedbacks carrying the optimal conditional statistics at each time point. Above all, it converges to the minimum variance filter as the number of hidden neurons increases. We call such an RMLP a neural filter. Simulation results show that the neural filters with only a few hidden neurons consistently outperform the extended Kalman filter and even the iterated extended Kalman filter for the simple nonlinear signal/sensor systems considered