This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits-namely the orbit set-that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus allowing for a compact analytical description of the orbit set. The automatic domain splitting tool controls the truncation error of the polynomial approximation by patching the uncertainty domain with different polynomial expansions, effectively creating a mesh. The algorithm is tested for different observing strategies to understand the working boundaries, thus defining the region for which the admissible region is necessary to extract meaningful information from observations and highlight where the new method can achieve a smaller uncertainty region, effectively showing that for some observing strategies it is possible to extract more information from a tracklet than the attributable. Consequently, the method enables comparison of orbit sets avoiding sampling when looking for correlation of different observations. Linear regression is also implemented to improve the uncertainty estimation and study the influence of the confidence level on the orbit set size. This is shown both for simulated and real observations obtained from the TFRM observatory.

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A differential algebra based representation of the Line of Variations for Near Earth Objects impact monitoring is presented in this paper. In this framework, the Line of Variations is described at the initial epoch by a high-order polynomial that is propagated forward in time. An Automatic Domain Splitting algorithm is embedded in the numerical integrator, in such a way that when the polynomials truncation error becomes too large, the line is split as many times as necessary to meet accuracy requirements. The Line of Variations is propagated forward in time until an intersection with a properly defined target plane occurs for all the generated subdomains. The projection of the subdomains onto the target plane allows to compute the impact probability by numerically integrating an associated one-dimensional probability density function. The proposed approach is applied to different test-cases to assess the performance of the method for the different possible shapes of the initial confidence region. Starting from a case of direct encounter, the technique is tested up to the case of a resonant return, in which the nonlinearities of the problem represent a critical aspect.