A Comparison Between Kalman-MLE and KalmanNet for State Estimation with Unknown Noise Parameters

This paper presents a comparison between the recently proposed KalmanNet for dynamic state estimation with unknown measurement and dynamic noise covariance matrices, and a classic approach to solve this problem. Given known transition and measurement functions and a training data set that consists of sequences of ground truth states and the associated measurements, KalmanNet learns the parameters of a network that aims to compute the Kalman gain. The classic approach we consider is to estimate the noise covariance matrices via maximum likelihood estimation (MLE) during training. Then, a Kalman filter with the estimated covariance matrices is used during testing (Kalman-MLE). The benefits of Kalman-MLE versus KalmanNet are shown via experiments in two linear-Gaussian systems, and a non-linear system.