Selecting the type of an algorithm is strongly related to your data set which you use. However, do not forget that normalization could improve the performance.
What's your specific problem, is it about a classification problem ! or regression (prediction), because the parameters of an ANN algorithm are dependents on the problem type itself. so if you estimate for exemple the state or covariance, i think that means a non-linear relationship because EKF is the nonlinear version of KF, so a simple back propagation NN is enough, and how you can said that the NN has a poor performance on testing results !
you can calculate error manually in each epoch, but this take a time and the most important think in ANN training is the adjusted weights when training is terminated, so why you calculate error in each epoch !, also, when you attend the least RMSE or any other performance you take your adjusted weights and analyze your NN model if he give a logical results or not, you can also make a parametric study to show the feasibility of your NN.
Neural network with 2 hidden layers / cost function / back propagation implemented in Matlab / vectorized implementation, i.e. much faster than standard implementations with loops