The extended Kalman filter, when employed in the GPS receiver as the navigation state estimator, provides optimal solutions if the noise statistics for the measurement and system are completely known. In practice, the noise varies with time, which results in performance degradation. The covariance matching method is a conventional adaptive approach for estimation of noise covariance matrices. The technique attempts to make the actual filter residuals consistent with their theoretical covariance. However, this innovation-based adaptive estimation shows very noisy results if the window size is small. To resolve the problem, a multilayered neural network is trained to identify the measurement noise covariance matrix, in which the back-propagation algorithm is employed to iteratively adjust the link weights using the steepest descent technique. Numerical simulations show that based on the proposed approach the adaptation performance is substantially enhanced and the positioning accuracy is substantially improved.