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

State estimation of a dynamical system refers to estimating the state of a system given an imperfect model, noisy measurements and some or no information about the initial state. While Kalman filtering is optimal for estimation of linear systems with Gaussian noises, calculation of optimal estimators for nonlinear systems is challenging. We focus on establishing a pathway to optimal estimation of high-order systems by using recurrent connections motivated by Jordan recurrent neural networks(JRNs). The results are compared to the corresponding Elman structure based long short-term memory network(ELSTM) and the KF for linear and EKF for nonlinear systems. The results suggest that for nonlinear systems, the use of long short-term memory networks can improve estimation error and also computation time. Also, the Jordan based long short-term memory networks(JLSTMs) require less training to achieve performance similar to ELSTMs.