On Kalman Filtering and Observability in Nonlinear Sequential Relative Orbit Estimation

Butcher, Eric A.; Wang, Jingwei; Lovell, T. Alan

doi:10.2514/1.g002702

Cited by 30 publications

(11 citation statements)

References 22 publications

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“…Cooperation based research has focused on developing consensus-based algorithms for both maintenance and reconfiguration problems [35,36]. Navigation research has focused on determining relative positions of the spacecraft in the swarm [37,38]. Another line of research is the development of hardware platforms to realize and test swarm architectures.…”

Section: Related Workmentioning

confidence: 99%

Attitude Control of Spacecraft Swarms for Visual Mapping of Planetary Bodies

Nallapu

Thangavelautham

2019

2019 IEEE Aerospace Conference

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Planetary bodies such as asteroids, comets, and planetary moons are high-value science targets as they hold important information about the formation and evolution of our solar system. However, due to their low-gravity, variable sizes and shapes, dedicated orbiting spacecraft missions around these target bodies is difficult. Therefore, many planetary bodies are observed during flyby encounters, and consequently, the mapping coverage of the target body is limited. In this work, we propose the use of a spacecraft swarm to provide complete surface maps of a planetary body during a close encounter flyby. With the advancement of low-cost spacecraft technology, such a swarm can be realized by using multiple miniature spacecraft. The design of a swarm mission is a complex multi-disciplinary problem. To get started, we propose the Integrated Design Engineering & Automation of Swarms (IDEAS) software. In this work, we will introduce the development of the Automated Swarm Designer module of the software. The Automated Swarm Designer module will use evolutionary algorithms to optimize the design of swarms. The designed swarm will use 2 attitude control strategies to map the surface of a target body, namely: Nadir Pointing (NP), and Field of View Sweeping (FoV Sweeping). In the former strategy, the spacecraft are commanded to passively observe the sub-satellite point on the target body whenever the target is in the field of view of the individual spacecraft. This strategy is used when the observing instrument on board the spacecraft is large enough to capture the target from the desired encounter distance. In case the instrument is not large enough, then the spacecraft will have to maneuver their field of view to improve the coverage. The Field of View Sweeping strategy describes one such maneuver to improve coverage. In this strategy, the spacecraft in the swarm are commanded to sweep their fields of view about their principal axis normal to the swarm plane.The current work addresses different aspects of the swarm design problem. First, the coverage problem is addressed, and the parameters: instrument size, and target flyby distance are determined. Following this, the modeling of the swarm is described, where the individual spacecraft are arranged to define a circular plane around the target body during the encounter. Then the encounter trajectories of the spacecraft swarm are modeled. Here a Newton-Raphson iterative scheme using the state transition matrix of the dynamics is proposed for the entire swarm, which finds the trajectories between the desired starting points and destination points of the spacecraft within a specified flyby duration. Following this, the two proposed attitude control strategies are then described as they occur on these flyby trajectories. Then the design of these swarms is presented using as 2 optimization problems. The proposed strategies are used to develop a numerical simulator which will serve as the Automated Swarm Designer module of IDEAS for visual mapping missions. Finally, the simulator d...

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Section: Related Workmentioning

confidence: 99%

Attitude Control of Spacecraft Swarms for Visual Mapping of Planetary Bodies

Nallapu

Thangavelautham

2019

2019 IEEE Aerospace Conference

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“…rendezvous and docking) [13]. In [14] and in [15] the authors have shown that considering the full nonlinear dynamics of the spacecraft will results in improved state estimation in otherwise weakly observable or unobservable linear models. Hence, we consider linearized spacecraft relative motion equations and apply our hybrid Kalman filter to estimate the state from aperiodic position measurements.…”

Section: Introductionmentioning

confidence: 99%

Robust Hybrid Kalman Filter for a Class of Nonlinear Systems

Malladi

Sanfelice

Butcher

2018

2018 Annual American Control Conference (ACC)

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Motivated by real-world applications with intermittent sensor data, an extended Kalman filter is formulated as a hybrid system and constructive conditions on its parameters guaranteeing an asymptotic stability property are provided. The dynamical properties of the estimation error are first characterized infinitesimally so to yield bounds on the rate of convergence and overshoot that depend on the parameters. By recasting the problem as the stabilization of a compact set, robustness properties of the proposed algorithm in the presence of disturbances in the system dynamics as well as measurement noise in the output are established. The proposed strategy is applied to spacecraft relative motion control with position-only measurements.

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“…The size of this nonlinear observability matrix clearly depends on the number of states and measurements in the system, so the computation of the higher-order derivatives can become quite intensive. As such, Butcher and Wang [101] highlight that a sufficient (but not necessary) condition for observability can be obtained by only constructing the Ąrst N rows of O(x), or by constructing only a subsequent number of rows necessary to show that the truncated version of O(x) is full rank. Further numerical metrics for quantifying observability, including the gramian, the observability index, and the estimation condition number, are also summarized by Butcher and WangŠs paper, but for the work conducted for this thesis, the construction of the observability matrix was necessary to identify which states require measuring.…”

Section: Observability Analysismentioning

confidence: 99%

Section: The Measurement Correction Phasementioning

confidence: 99%

“…Given the nonlinear framework of the spacecraft formation Ćying dynamics used in the research proposed here, this appendix will accordingly focus on the observability criteria for nonlinear systems. For the time-varying nonlinear system described by a state vector x ∈ R n and an output vector y(t) ∈ R p , the system is said to be locally observable over the interval t ∈ [0, T ] if the mapping from the intial state x 0 to the output y(t) is one-toone [101]. Stated differently, local observability implies that the initial state x 0 can be reconstructed from the knowledge contained in the outputs over the given time interval.…”

Section: Appendix Amentioning

confidence: 99%

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Adaptive Extended Kalman Filtering Strategies for Autonomous Relative Navigation of Formation Flying Spacecraft

Fraser¹

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This research addresses the relative navigation problem for spacecraft formation Ćying missions in near-Earth orbit. Technological and economic inĆuences have expedited the miniaturization of spacecraft systems, popularizing the notion of satellite teamwork due to the potential reductions in overall costs and complexity. It is now feasible to use a coordinated group of close-proximity satellites, known as a formation, to autonomously perform rendezvous, on-orbit servicing and science-based missions for a fraction of the resources a large-scale satellite would require. Despite the growing interest in formation Ćying spacecraft however, only a limited number of applications have been Ćight validated as a result of the difficulties associated with accurately determining the relative motion of the spacecraft within a formation. To enhance the capabilities of onboard autonomous guidance, navigation and control systems, this thesis presents the development of two adaptive extended Kalman Ąlter navigation algorithms for spacecraft formation Ćying. The proposed adaptive Ąlters are capable of updating the internal noise characteristics of the Kalman Ąlter in real time, and are viable in all orbit scenarios, including highly elliptical orbits in the presence of perturbations. The Ąrst Kalman Ąlter approach uses maximum likelihood estimation techniques to derive analytical adaptations laws for the Ąlter, which are then improved through the novel inclusion of an intrinsic smoothing routine. The second approach uses an embedded fuzzy logic system based on a covariancematching analysis of the Ąlter residuals, where the fuzzy system has been speciĄcally designed for the spacecraft navigation problem at hand. Numerical simulations of three spacecraft formations are used to demonstrate that the proposed adaptive navigation algorithms are appreciably more robust to Ąlter initialization errors, dynamics modelling deĄciencies, and measurement noise than the standard Kalman Ąlter. iii To Dr. Steve Ulrich, formally my supervisor, but more importantly my mentor, my professor, and my friend; your steadfast support and leadership have made my studies in Ottawa immensely fulĄlling. Thank you for providing this opportunity to continually learn from your expertise, and for instilling conĄdence and direction throughout the span of our collaboration. The dedication you have shown to me, and all of the members of our research group, is remarkable. It has been an honor to work with you, and a whole lot of fun too. To the professors who have guided me along this journey, including Bruce Burlton, Tarik Kaya, Alex Ellery, Victor Aitken, Howard Schwartz, and many others from Carleton University. The knowledge and wisdom you have shared has been invaluable to my growth as an engineer. And from the days at Dalhousie University, my thanks in particular to Professors Darrel Doman, Jeff Dahn, Timothy Little, and Guy Kember. You managed to imbue a fascination with space elevators, the laws of nature, the rules of mathematics, and the process of learning,...

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On Kalman Filtering and Observability in Nonlinear Sequential Relative Orbit Estimation

Cited by 30 publications

References 22 publications

Attitude Control of Spacecraft Swarms for Visual Mapping of Planetary Bodies

Attitude Control of Spacecraft Swarms for Visual Mapping of Planetary Bodies

Robust Hybrid Kalman Filter for a Class of Nonlinear Systems

Adaptive Extended Kalman Filtering Strategies for Autonomous Relative Navigation of Formation Flying Spacecraft

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