3 research outputs found
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
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
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