One of the most common misconceptions made about the Kalman filter when applied to linear systems is that it requires an assumption that all error and noise processes are Gaussian. This misconception has frequently led to the Kalman filter being dismissed in favor of complicated and/or purely heuristic approaches that are supposedly ``more general'' in that they can be applied to problems involving non-Gaussian noise. The fact is that the Kalman filter provides rigorous and optimal performance guarantees that do not rely on any distribution assumptions beyond mean and error covariance information. These guarantees even apply to use of the Kalman update formula when applied with nonlinear models, as long as its other required assumptions are satisfied. Here we discuss misconceptions about its generality that are often found and reinforced in the literature, especially outside the traditional fields of estimation and control.

This work considers the control of a spacecraft in indefinite near-rectilinear halo orbit about the Earth-Moon L2. For indefinite station-keeping, it is important to minimize fuel consumption, while allowing for occasional transfer to a new orbit. The control scheme therefore consists of two components: the first component is the tracking of the nominal NRHO and the second component is an orbit correction maneuver between NRHO trajectories. The nominal NRHO is computed using a multiple-shooting technique that takes into account all forces on the spacecraft whose magnitude is larger than the dominant disturbance forces caused by navigational error. The tracking component is a linear-quadratic regulation scheme that rejects disturbances caused by orbit determination error, using a Lyapunov sublevel set that models the state covariance generated using sequential Kalman filter. The orbit correction maneuver is computed to minimize fuel costs. AAS/AIAA Space Flight Mechanics Meeting This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2020 201 Broadway, Cambridge, Massachusetts 02139 Control Strategy for Long-Term Station-Keeping on Near-Rectilinear Halo Orbits∗ Vivek Muralidharan† Purdue University, West Lafayette, IN 47907 Avishai Weiss‡ and Uroš Kalabić§ Mitsubishi Electric Research Laboratories, Cambridge, MA 02139 This work considers the control of a spacecraft in indefinite near-rectilinear halo orbit about the Earth-Moon L2. For indefinite station-keeping, it is important to minimize fuel consumption, while allowing for occasional transfer to a new orbit. The control scheme therefore consists of two components: the first component is the tracking of the nominal NRHO and the second component is an orbit correction maneuver between NRHO trajectories. The nominal NRHO is computed using a multiple-shooting technique that takes into account all forces on the spacecraft whosemagnitude is larger than the dominant disturbance forces caused by navigational error. The tracking component is a linear-quadratic regulation scheme that rejects disturbances caused by orbit determination error, using a Lyapunov sublevel set that models the state covariance generated using sequential Kalman filter. The orbit correction maneuver is computed to minimize fuel costs. Nomenclature Ak,Bk = system matrices ãji = acceleration of body i with respect to j ãiJ2 = J2 perturbing acceleration due to body i ãSRP = acceleration due to solar radiation pressure Cr = coefficient of reflectivity ∆v = maneuver vector, or change in instantaneous velocity states δxk = vector of state deviation at time step k δyk = measurement residue vector at time step k k = measurement noise Hk = measurement matrix at time step k K = gain matrix μi = gravitational parameter of body i P,Q,R = weighting matrices on cost functional P = covariance of state estimation error Q = covariance of process noise R = covariance of measurement noise R = range Û R = range rate ρ = system mass ratio r̄, v̄ = position and velocity substates S = positive definite matrix that represent acceptable bounds on uncertainty T = propagation time tk = k-th time step τ = epoch time ∗This work was supported by Mitsubishi Electric Research Laboratories. †Graduate Student, School of Aeronautics and Astronautics, muralidv@purdue.edu

Ultraviolet and infrared sensors at high quantum efficiency on-board a small satellite (UVSQ-SAT) is a CubeSat dedicated to the observation of the Earth and the Sun. This satellite has been in orbit since January 2021. It measures the Earth's outgoing shortwave and longwave radiations. The satellite does not have an active pointing system. To improve the accuracy of the Earth's radiative measurements and to resolve spatio-temporal fluctuations as much as possible, it is necessary to have a good knowledge of the attitude of the UVSQ-SAT CubeSat. The attitude determination of small satellites remains a challenge, and UVSQ-SAT represents a real and unique example to date for testing and validating different methods to improve the in-orbit attitude determination of a CubeSat. This paper presents the flight results of the UVSQ-SAT's attitude determination. The Tri-Axial Attitude Determination (TRIAD) method was used, which represents one of the simplest solutions to the spacecraft attitude determination problem. Another method based on the Multiplicative Extended Kalman Filter (MEKF) was used to improve the results obtained with the TRIAD method. In sunlight, the CubeSat attitude is determined at an accuracy better than 3° (at one σ) for both methods. During eclipses, the accuracy of the TRIAD method is 14°, while it reaches 10° (at one σ) for the recursive MEKF method. Many future satellites could benefit from these studies in order to validate methods and configurations before launch.

This study focuses on the transfer alignment issue between a master spacecraft and a slave spacecraft for the scenario in which the slave spacecraft is mounted on the master satellite before release and should be ready to depart and perform its space mission independently. The challenge of the transfer alignment is to estimate the attitude and calibration parameters of the gyroscope unit (GU) on the slave spacecraft based on the attitude determination system (ADS) of the master spacecraft. To improve the accuracy and rapidity of the transfer alignment, a novel attitude plus angular rate matching scheme is presented using fused sensor information on the master spacecraft. Accordingly, a fifteen-dimensional state-space model is derived to estimate the spacecraft attitude, the GU bias, scale factor error and misalignment simultaneously. A Q-learning Kalman filter (QKF) is designed to fine tune the process noise covariance matrix related to the calibration parameters, which benefits the state estimation performance. The simulation results show that the presented attitude plus angular rate matching scheme performs better than the traditional attitude matching scheme, and the QKF outperforms the standard Kalman filter (KF) and the adaptive Kalman filter (AKF).

To reduce the collision risk to civil airliners caused by suborbital vehicle disintegration events, this paper uses a covariance propagation algorithm to model the debris landing point of suborbital disintegration accidents and gives a collision probability analysis method for civil airliners encountering debris during the cruise. Collision warning is performed for airborne risk targets to improve the emergency response capability of the ATC surveillance system to hazardous situations. The algorithm models the three-dimensional spatial motion target localization problem as a Gauss-Markov process, quantifying the location of debris landing points in the vicinity of nominal trajectories. By predicting the aircraft trajectory, the calculation of the inter-target collision probability is converted into an integration problem of a two-dimensional normally distributed probability density function in a circular domain. Compared with the traditional Monte Carlo method, the calculation speed of debris drop points is improved, which can meet the requirements of civil aviation for real-time response to unexpected situations.

Orbit determination for non-cooperative low Earth orbit (LEO) objects undergoing continuous low-thrust maneuvers remains a significant challenge, particularly for large satellite constellations like Starlink. This paper presents a method that integrates the unscented transformation into a batch filtering framework with an optimized rho-minimum sigma points sampling strategy. The proposed approach uses a reduced dynamics model that considers Earth's non-spherical gravity and models the combined effects of low-thrust and atmospheric drag as an equivalent along-track acceleration. Numerical simulations under different measurement noise levels, initial state uncertainties, and across multiple satellites confirm the method's reliable convergence and favorable accuracy, even in the absence of prior knowledge of the along-track acceleration. The method consistently converges within 10 iterations and achieves 24 h position predictions with root mean square errors of less than 3 km under realistic noise conditions. Additional validation using a higher-fidelity model that explicitly accounts for atmospheric drag demonstrates improved accuracy and robustness. The proposed method can provide accurate orbit knowledge for space situational awareness associated with continuously maneuvering Starlink satellites.

version of the Kalman filtering (KF) algorithm and in which the covariance matrices are not calculated from the dynamical equations but are pre-determined Data assimilation refers to a large group of methods that update information from numerical computer models with information from observations. Data assimilation is used to update model states, model trajectories over time, model parameters, and combinations thereof. What distinguishes data assimilation from other estimation methods is that the computer model is a dynamical model, i.e. the model d In 1922, Lewis Fry Richardson published the first attempt at forecasting the weather numerically. Using a hydrostatic variation of Bjerknes's primitive equations, Richardson produced by hand a 6-hour forecast for the state of the atmosphere over two points in central Europe, taking at least six weeks to do so. His forecast calculated that the change in surface pressure would be 145 millibars (4.3 inHg), an unrealistic value incorrect by two orders of magnitude. The large error was caused by an imbalance in the pressure and wind velocity fields used as the initial conditions in his analysis, indicating the need for a data assimilation scheme. Originally "subjective analysis" had been used in which numerical weather prediction (NWP) forecasts had been adjusted by meteorologists using their operational expertise. Then "objective analysis" (e.g. Cressman algorithm) was introduced for automated data assimilation. These objective methods used…

[ES] En las misiones reales a pesar de contar con instrumentos y sensores de gran precisión y del avance de la tecnología es posible que sea necesario considerar una cierta incertidumbre o alguna limitación en alguno de los parámetros orbitales. Este trabajo se dispone a estudiar la optimización de las misiones espaciales teniendo en cuenta estas restricciones mediante la programación de un algoritmo convexo. Para implementar el algoritmo se estudiará el caso de una transferencia orbital de la Tierra a Marte.

Determining the orbits of space debris.

On-Orbit Servicing (OOS) robots are transforming space exploration by enabling vital maintenance and repair of spacecraft directly in space. However, achieving precise and safe manipulation in microgravity necessitates overcoming significant challenges. This survey delves into four crucial areas essential for successful OOS manipulation: object state estimation, motion planning, and feedback control. Techniques from traditional vision to advanced X-ray and neural network methods are explored for object state estimation. Strategies for fuel-optimized trajectories, docking maneuvers, and collision avoidance are examined in motion planning. The survey also explores control methods for various scenarios, including cooperative manipulation and handling uncertainties, in feedback control. Additionally, this survey examines how Machine learning techniques can further propel OOS robots towards more complex and delicate tasks in space.