Black-box expectation–maximization algorithm for estimating latent states of high-speed vehicles

Tracking an object in a noisy environment is difficult, especially when unknown parameters affect the object’s behavior. In the case of a high-speed ballistic object, its trajectory is affected by changes in atmospheric conditions as well as 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 and enhance the accuracy of object tracking. The expectation step involves calculating the likelihood of observations through extended Kalman smoothing, which reflects the forward–backward probability combination. The maximization step involves optimizing the unknown parameter, which is the object mass, to maximize the likelihood through Bayesian optimization with Gaussian process regressions. Our simulation experiments show that our algorithm reduces the error of tracking a ballistic object’s position given noisy observations with unknown parameters.