1,720,996 research outputs found
Advances in Particle Flow Filters with Taylor Expansion Series
Full text linkParticle Flow Filters perform the measurement update by moving particles to a different location rather than modifying the particles' weight based on the likelihood. Their movement (flow) is dictated by a drift term, which continuously pushes the particle toward the posterior distribution, and a diffusion term, which guarantees the spread of particles. This work presents a novel derivation of these terms based on high-order polynomial expansions, where the common techniques based on linearization reduce to a simpler version of the new methodology. Thanks to differential algebra, the high-order particle flow is derived directly onto the polynomials representation of the distribution, embedded with differentiation and evaluation. The resulting technique proposes two new particle flow filters, whose difference relies on the selection of the expansion center for the Taylor polynomial evaluation. Numerical applications show the improvement gained by the inclusion of high-order terms, especially when comparing performance with the Gromov flow and the "exact" flow.This is a preprint from Servadio, Simone. "Advances in Particle Flow Filters with Taylor Expansion Series." arXiv preprint arXiv:2505.01597 (2025). doi: https://doi.org/10.48550/arXiv.2505.01597
Quadratic Extended and Unscented Kalman Filter Updates
Full text linkCommon filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively, but remain linear estimators, meaning that the state estimate is a linear function of the measurement. This paper proposes a quadratic approximation of the optimal estimator, creating the Quadratic Extended and Quadratic Unscented Kalman Filter. These retain the structure of their linear counterpart, but include information from the measurement square to obtain a more accurate estimate. Numerical results show the benefits in accuracy of the new technique, which can be generalized to upgrade other linear estimators to their quadratic versions.This is a preprint from Servadio, Simone, and Chiran Cherian. "Quadratic Extended and Unscented Kalman Filter Updates." arXiv preprint arXiv:2506.06256 (2025).
doi: https://doi.org/10.48550/arXiv.2506.06256
Dynamical Update Maps for Particle Flow with Differential Algebra
Full text linkParticle Flow Filters estimate the "a posteriori" probability density function (PDF) by moving an ensemble of particles according to the likelihood. Particles are propagated under the system dynamics until a measurement becomes available when each particle undergoes an additional stochastic differential equation in a pseudo-time that updates the distribution following a homotopy transformation. This flow of particles can be represented as a recursive update step of the filter. In this work, we leverage the Differential Algebra (DA) representation of the solution flow of dynamics to improve the computational burden of particle flow filters. Thanks to this approximation, both the prediction and the update differential equations are solved in the DA framework, creating two sets of polynomial maps: the first propagates particles forward in time while the second updates particles, achieving the flow. The final result is a new particle flow filter that rapidly propagates and updates PDFs using mathematics based on deviation vectors. Numerical applications show the benefits of the proposed technique, especially in reducing computational time, so that small systems such as CubeSats can run the filter for attitude determination.This is a preprint from Servadio, Simone. "Dynamical Update Maps for Particle Flow with Differential Algebra." arXiv preprint arXiv:2505.01598 (2025).
doi: https://doi.org/10.48550/arXiv.2505.01598
Analytical Uncertainty Propagation and Maximum A Posteriori Filtering with the Koopman Operato
Full text linkThis paper proposes a method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the system, where the dynamics have been projected on a well-defined set of basis functions. The prediction technique is derived following both the analytical (Galerkin) and numerical (EDMD) derivation of the KO, and a least square reduction algorithm assures the recursivity of the proposed methodology. Furthermore, a complete filtering algorithm is proposed, where the predicted uncertainties are updated analytically using the likelihood function, following Bayes’ formulation. Estimates are provided after optimization according to the Maximum A Posteriori formulation, where a backtracking Newton solver identifies the global most likely posterior state.This is a manuscript of an article published as Servadio, Simone, Giovanni Lavezzi, Christian Hofmann, Di Wu, and Richard Linares. "Analytical Uncertainty Propagation and Maximum A Posteriori Filtering with the Koopman Operator." IEEE Transactions on Aerospace and Electronic Systems (2025). doi: https://doi.org/10.1109/TAES.2025.3566685
Threat Level Estimation From Possible Break-Up Events In LEO
Full text linkThe NASA Standard Break-Up Model models collisions and explosions in space, which identifies the future distribution of debris. Given a possible break-up event, this work analyses the threat posed by the generated debris in the orbit of an asset spacecraft. Using the Koopman Operator solution of the J2 perturbed two-body dynamics, the family of all possible orbits that cross the asset's pathway is identified and parameterized according to their velocity. The threat level assessment of a collision onto the asset is estimated considering the intersection between the velocities of the break-up model and the Koopman transfer solutions.This is a manuscript of the article Published as Servadio, Simone, Daniel Jang, and Richard Linares. "Threat Level Estimation From Possible Break-Up Events In LEO." In AIAA SCITECH 2024 Forum, p. 1065. 2024. doi: https://doi.org/10.2514/6.2024-1065
Propagation of Uncertainty with the Koopman Operator
Full text linkThis paper proposes a new method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the system, where the dynamics have been projected on a well-defined set of basis functions. The prediction technique is derived following both the analytical (Galerkin) and numerical (EDMD) derivation of the KO, and a least square reduction algorithm assures the recursivity of the proposed methodology.This is a preprint from Servadio, Simone, Giovanni Lavezzi, Christian Hofmann, Di Wu, and Richard Linares. "Propagation of Uncertainty with the Koopman Operator." arXiv preprint arXiv:2407.20170 (2024).
doi: https://doi.org/10.48550/arXiv.2407.20170
Nonlinear Prediction in Marker-Based Spacecraft Pose Estimation with Polynomial Transition Maps
Full text linkSpacecraft relative state estimation is of paramount importance in the problem of rendezvous with an uncooperative target; indeed, an accurate prediction of its relative position and attitude is crucial for safe proximity operations, especially considering autonomous guidance, navigation, and control. Therefore, a key point for the success of these missions is the development of efficient algorithms capable of limiting the computational burden without any reduction in performance. This paper addresses the issue proposing and analyzing nonlinear filters based on differential algebra. High-order numerical extended Kalman filter and unscented Kalman filter are developed in the differential algebra framework, and their performance is assessed and compared in terms of accuracy, robustness, and computational time, highlighting advantages and drawbacks. The European Space Agency e.deorbit mission, involving Envisat, is considered as the reference case, and the analysis is carried out through numerous numerical simulations, taking into account different measurement acquisition frequencies and levels of uncertainties
Koopman-Operator Control Optimization for Relative Motion in Space
Full text linkA high-order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy-optimal inverse control methodology. The operator theory can reformulate a nonlinear dynamic system of finite dimension into a linear system with an infinite number of dimensions. As a result, the state of any nonlinear dynamics is represented as a linear combination of high-order orthogonal polynomials, which creates the state transition polynomial map of the solution. Because the optimal control technique can be reduced to a two-point boundary value problem, the Koopman map is used to connect the state and control variables in time, such that optimal values are obtained through map inversion and polynomial evaluation. The new technique is applied to rendezvous applications in space, where the relative motion between two satellites is modeled with a high-order polynomial series expansion of the Lagrangian of the system, such that the Clohessy–Wiltshire equations represent the reduction of the high-order model to a linear truncation. The proposed numerical applications are analyzed to show the robustness and limitations of the novel technique.This is a manuscript of an article published as Servadio, Simone, Roberto Armellin, and Richard Linares. "Koopman-operator control optimization for relative motion in space." Journal of Guidance, Control, and Dynamics 46, no. 11 (2023): 2121-2132. doi: https://doi.org/10.2514/1.G007217.The authors want to acknowledge the support of this work by the Air Force’s Office of Scientific Research under Contract Number FA9550-22-1-0092
Effects of Orbit Raising and Deorbiting in Source-Sink Evolutionary Models
Full text linkThe sustainability of the low-Earth-orbit (LEO) environment is threatened by the growing number of anthropogenic space objects planned to be launched in the coming years. This paper investigates the evolution of objects residing in LEO through the MIT Orbital Capacity Assessment Tool (MOCAT), an evolutionary multishell, multispecies source-sink model. The proposed novelty considers the flow of objects crossing multiple shells during orbit raising and deorbiting maneuvers, modeled through the secular variation of the semimajor axis under a low-thrust continuous applied control. To this aim, a higher-fidelity MOCAT version, including active satellites, derelicts, debris, and rocket bodies, has been developed and used. The results demonstrate that incorporating orbit transfer fluxes into the model results in a higher number of collisions, which leads to a greater quantity of debris and poses a greater threat to the safety of LEO
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