A differential algebra based importance sampling method for impact probability computation on Earth resonant returns of Near Earth Objects

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

A low-order automatic domain splitting approach for nonlinear uncertainty mapping

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 rigorously 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 some imposed linearity constraints are non met. The algorithm is illustrated in the critical case of orbital uncertainty propagation, and it is coupled with a tailored merging algorithm 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 mixtures models to accurately describe the propagation of a probability density function. A detailed analysis of the proposed method is presented, and the impact of the different available degrees of freedom on the accuracy and performance of the method is studied

Impact probability computation of Near-Earth Objects using Monte Carlo Line Sampling and Subset Simulation

This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the initial uncertainty region in different ways, with the result of either providing a more accurate estimate of the impact probability or reducing the number of required samples during the simulation with respect to standard MC techniques. The two methods are first described and then applied to some test cases, providing evidence of the increased accuracy or the reduced computational burden with respect to a standard MC simulation. Finally, a sensitivity analysis is carried out to show how parameter setting affects the accuracy of the results and the numerical efficiency of the two methods

Performance assessment of the multibeam radar sensor birales for space surveillance and tracking

Near-Earth space has become progressively more crowded in active satellites, inactive spacecraft and debris. Consequently, an international effort is currently being devoted to improving the performance of the network of optical and radar sensors for space objects monitoring. Within this framework, the use of the novel bistatic radar sensor BIRALES is investigated in this work, which makes use of a multibeam receiver. The tailored orbit determination algorithm is described, which receives as input the data processed by the acquisition system, that digitally assembles measured radar echoes. The performances of the orbit determination process are assessed on a set of numerical simulations carried out on the NORAD catalogue, using a dedicated simulator of the sensor.peer-reviewe

Impact probability computation for NEO resonant returns through a polynomial representation of the Line of Variations

A differential algebra based representation and propagation of the Line of Variations for Near Earth Objects impact monitoring is presented in this paper. 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 subdomains are then projected onto the target plane to compute the impact probability by numerically integrating an associated one-dimensional probability density function. The proposed approach is applied to several 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, which features critical nonlinearities

Perturbed Initial Orbit Determination

An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool is capable of not only returning an highly accurate solution to the IOD problem, but also estimating a range of validity for the aforementioned solution in which the true orbit state should lie. Automatic domain splitting is then used on top of the IOD routines to ensure the local truncation error introduced by a polynomial representation of the state estimate remains below a predefined threshold to meet the specified requirements in accuracy. The algorithm is adapted to three types of ground based sensors, namely range radars, Doppler-only radars and optical telescopes by taking into account their different constraints in terms of available measurements and sensor noise. Its improved performance with respect to a Keplerian based IOD solution is finally demonstrated with large scale numerical simulations over a subset of tracked objects in low Earth orbit.Comment: submitted to Astrodynamic

Multifidelity Orbit Uncertainty Propagation using Taylor Polynomials

A new multifidelity method is developed for nonlinear orbit uncertainty propagation. This approach guarantees improved computational efficiency and limited accuracy losses compared with fully high-fidelity counterparts. The initial uncertainty is modeled as a weighted sum of Gaussian distributions whose number is adapted online to satisfy the required accuracy. As needed, univariate splitting libraries are used to split the mixture components along the direction of maximum nonlinearity. Differential Algebraic techniques are used to propagate these Gaussian kernels and compute a measure of nonlinearity required for the split decision and direction identification. Taylor expansions of the flow of the dynamics are computed using a low-fidelity dynamical model to maximize computational efficiency and corrected with selected high-fidelity samples to minimize accuracy losses. The effectiveness of the proposed method is demonstrated for different dynamical regimes combining SGP4 theory and numerical propagation as low- and high-fidelity models respectively

A Multifidelity Approach to Robust Orbit Determination

This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem and detect possible outliers in the processed measurements. The uncertainty on the initial estimate is propagated forward in time and progressively reduced by exploiting sensor data available in said propagation window. Differential algebra techniques and a novel automatic domain splitting algorithm for second-order Taylor expansions are used to efficiently propagate uncertainties over time. A multifidelity approach is employed to minimize the computational effort while retaining the accuracy of the propagated estimate. At each observation epoch, a polynomial map is obtained by projecting the propagated states onto the observable space. Domains that do no overlap with the actual measurement are pruned thus reducing the uncertainty to be further propagated. Measurement outliers are also detected in this step. The refined estimate and retained observations are then used to improve the robustness of batch orbit determination tools. The effectiveness of the algorithm is demonstrated for a geostationary transfer orbit object using synthetic and real observation data from the TAROT network.Comment: submitted to Acta Astronautic

C60@Lysozyme: Direct observation by nuclear magnetic resonance of a 1:1 fullerene protein adduct

Integrating carbon nanoparticles (CNPs) with proteins to form hybrid functional assemblies is an innovative research area with great promise for medical, nanotechnology, and materials science. The comprehension of CNP-protein interactions requires the still-missing identification and characterization of the 'binding pocket' for the CNPs. Here, using Lysozyme and C-60 as model systems and NMR chemical shift perturbation analysis, a protein-CNP binding pocket is identified unambiguously in solution and the effect of the binding, at the level of the single amino acid, is characterized by a variety of experimental and computational approaches. Lysozyme forms a stoichiometric 1:1 adduct with C-60 that is dispersed monomolecularly in water. Lysozyme maintains its tridimensional structure upon interaction with C-60 and only a few identified residues are perturbed. The C-60 recognition is highly specific and localized in a well-defined pocket