This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second-order Taylor expansions and polynomial bounding techniques is first introduced to estimate the Jacobian variation of a nonlinear transformation. This index is then embedded into a low-order automatic domain splitting algorithm that accurately describes the mapping of an initial uncertainty set through a generic nonlinear transformation by splitting the domain whenever nonlinearities grow above a predefined threshold. The algorithm is illustrated in the critical case of orbital uncertainty propagation, and it is coupled with a tailored merging process that limits the growth of the domains in time by recombining them when nonlinearities decrease. The low-order automatic domain splitting algorithm is then combined with Gaussian mixture models to accurately describe the propagation of a probability density function.

A differential algebra based importance sampling method for uncertainty propagation and impact probability computation on the first resonant returns of Near Earth Objects is presented in this paper. Starting from the results of an orbit determination process, we use a differential algebra based automatic domain pruning to estimate resonances and automatically propagate in time the regions of the initial uncertainty set that include the resonant return of interest. The result is a list of polynomial state vectors, each mapping specific regions of the uncertainty set from the observation epoch to the resonant return. Then, we employ a Monte Carlo importance sampling technique on the generated subsets for impact probability computation. We assess the performance of the proposed approach on the case of asteroid (99942) Apophis. A sensitivity analysis on the main parameters of the technique is carried out, providing guidelines for their selection. We finally compare the results of the proposed method to standard and advanced orbital sampling techniques.

An initial orbit determination algorithm for surveillance Doppler-only radars with embedded quantification capabilities is presented. The method is based on a combination of Gauss' and Lambert's solvers formulated in the differential algebra framework, which provides the Taylor expansion of the state estimate with respect to the measurement uncertainties. This feature makes the approach particularly suited for handling data association problems. The first part of the paper describes the mathematical formulation of the method, while an extensive analysis of its performance and a comparison with a reference algorithm are carried out in the second part, using both simulated and real data. The proposed approach is shown to be accurate and robust and particularly suited for short-arc observations.

The population of space debris in near-Earth space is continuously growing and it represents a serious problem for active satellites and spacecraft. A performant ground-based and space-based network of sensors is necessary for space surveillance and consequently to prevent new collisions and monitoring atmospheric reentry of these objects. This paper illustrates the possible role of the Italian ground-based novel bi-static radar sensor, named BIRALET, for space monitoring and resident space objects tracking. The main characteristics of the receiver system, the Sardinia Radio Telescope with its P-band mono-beam receiver, are described in detail. Then, a preliminary analysis of the performance of the sensor is presented, and the results of numerical simulations are shown, providing a general overview on both observation capabilities and orbit determination accuracy achievable with the Sardinia Radio Telescope.