In view of the insufficient accuracy of the orbital state prediction method based on the physical model in the space surveillance environment, and the insufficient reliability of the error compensation model based on machine learning, as well as the demand for uncertainty modeling in the SSA application, we reformulate the orbital state prediction error estimation problem as a probability prediction problem, and propose a method of using a gradient boosting machine to model the orbital state prediction error distribution. In order to quantify the uncertainty in the state error estimation, the parameters of the conditional distribution of the orbital state error is treated as targets for the gradient boosting algorithm. Since the probability distribution function corresponding to the parameter is located in the Riemann space, the natural gradient based on the Fisher information matrix is used instead of the standard gradient, and the formula of the natural gradient is deduced. As a result, conditional distribution of state prediction error can be calculated. Experiments show that compared with the state prediction method that only uses the physical dynamics, the root mean square error of each component of the orbital state is reduced by at least about 60%. At the same time, compared with other commonly used uncertainty estimation methods, the proposed method can achieve a better negative log likehood. Therefore, the method can effectively estimate the distribution of state prediction errors, and improve the reliability of using machine learning methods for space situational awareness tasks.