Black-Box Expectation-Maximization Algorithm for Estimating Latent States of High-Speed Vehicles

Tracking an object under a noisy environment is difficult especially when there exist unknown parameters that affect the object’s behavior. In the case of a high-speed ballistic vehicle, the trajectory of the ballistic vehicle is affected by the change of atmospheric conditions as well as the various parameters of the object itself. To filter these latent factors of the dynamics model, this paper proposes a black-box Expectation-Maximization algorithm to estimate the latent parameters for enhancing the accuracy of the trajectory tracking. The Expectation step calculates the likelihood of the observation by the Extended Kalman Smoothing that reflects the forward-backward probability combination. The Maximization step optimizes the unknown parameters to maximize the likelihood by the Bayesian optimization with Gaussian process. Our simulation experiment results show that the error of tracking position of the ballistic vehicle reduced when there exist much noise in the observations, and some important parameters are unknown.