State estimator design using Jordan based long short-term memory networks

State estimation refers to estimating the state of a dynamical system given an imperfect model, noisy measurements, and some or no information about the initial state. The calculation of optimal estimators for nonlinear systems is challenging. Many approaches using neural networks have been proposed in the literature, but the training time remains a drawback. We focus on improving training time by extending the recurrent connections motivated by Jordan recurrent neural networks (JRNs) to Elman-long short-term memory networks (ELSTMs). The results are compared to the corresponding ELSTM and the Kalman filter (KF) for linear systems and the extended Kalman filter (EKF) for nonlinear systems. The results suggest that the Jordan-based long short-term memory networks (JLSTMs) require less training to achieve performance similar to ELSTMs. We also observe that the use of long short-term memory networks can improve estimation error and also computation time as compared to Kalman-based methods.