Split-KalmanNet: A Robust Model-Based Deep Learning Approach for State Estimation

Estimation of the state of a discrete-time state-space model from noisy measurements is a crucial aspect of signal processing. The extended Kalman filter (EKF) is widely used as a low-complexity solution based on a state evolution and measurement model of the state-space model. However, obtaining precise information about these models can be difficult in practice, and model mismatch greatly reduces state estimation accuracy. In this paper, we introduce Split-KalmanNet, a robust EKF algorithm that utilizes the power of deep learning for state estimation. Split-KalmanNet is inspired by the recent KalmanNet and calculates the Kalman gain using the Jacobian matrix of a measurement function and two recurrent neural networks (RNNs) with a split structure. The RNNs independently learn the covariance matrices of the prior state estimate and the innovation from data. The proposed split structure in calculating the Kalman gain allows for compensation of both state and measurement model mismatch effects. Numerical simulations show that Split-KalmanNet outperforms traditional EKF and the state-of-the-art KalmanNet algorithm in various scenarios of model mismatch.