Tesi etd-09152025-152001 |
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Tipo di tesi
Tesi di laurea magistrale
Autore
DESHMUKH, LALIT
URN
etd-09152025-152001
Titolo
Uncertainty quantification and state estimation in the evolution of reachable set of maneuvers for space mission applications.
Dipartimento
INGEGNERIA CIVILE E INDUSTRIALE
Corso di studi
INGEGNERIA AEROSPAZIALE
Relatori
relatore Prof. Di Rito, Gianpietro
correlatore Prof. Servadio, Simone
correlatore Prof. Servadio, Simone
Parole chiave
- Differential Algebra
- Maneuver Detection
- Multiple Model Adaptive Estimation
- Nonlinear Dynamics
- Orbit Determination
Data inizio appello
03/10/2025
Consultabilità
Non consultabile
Data di rilascio
03/10/2095
Riassunto
Recent advancements in aerospace engineering highlight the critical need for sophisticated computational methods to address uncertainties in orbital dynamics, particularly for spacecraft encountering unexpected maneuvers. This thesis presents a novel framework integrating Differential Algebra (DA) with Multiple Model Adaptive Estimation (MMAE) to enhance orbit determination and maneuver detection. By leveraging DA’s polynomial expansions for nonlinear uncertainty propagation and MMAE’s Bayesian adaptability for handling abrupt changes, this approach overcomes limitations of traditional methods, such as high computational demands and limited real-time applicability.
The literature review underscores DA’s efficacy in reachable set computation, utilizing polynomial approximations to model nonlinear dynamics governed by differential-algebraic equations. Compared to geometric or statistical sampling methods, DA offers a superior balance of complexity and accuracy, ideal for moderately scaled aerospace systems. Historically, reachable sets evolved from linear control theory to complex applications in unmanned aerial vehicles, spacecraft, and missiles. Challenges like high-dimensional computations and non-convex constraints suggest hybrid techniques as future solutions. In uncertainty propagation, DA outperforms linear filters by capturing higher-order nonlinear effects, evident in applications like spacecraft trajectory planning, aerial navigation under disturbances, hypersonic re-entry, and debris tracking for collision risk assessment.
The methodology employs DA to analyze orbital perturbations in gravitational models, comparing polynomial expansions to Monte Carlo simulations. DA is favored for its computational speed, achieving results approximately three times faster than Monte Carlo, which relies on resource-intensive random sampling. DA’s analytical polynomial evaluations provide deterministic insights and efficiency for real-time use while maintaining accuracy for small to moderate uncertainties. Monte Carlo, however, excels in probabilistic robustness for highly nonlinear or large-perturbation scenarios, justifying DA’s selection for scalable, efficient integration into adaptive frameworks. Implemented techniques include DA-based Taylor expansions for state propagation, extended Kalman filtering for uncertainty management, and MMAE with parallel models for maneuver hypothesis testing, incorporating Bayesian probability updates, polynomial-based covariance computations, and model pruning for dynamic adaptability.
The innovative MMAE extension addresses orbits with unknown maneuvers by hypothesizing velocity impulses across multiple models. This Bayesian framework runs parallel filters, updating probabilities based on measurement fits to yield optimal estimates. Unlike static methods limited to predefined scenarios, it incorporates interactive and variable structures, with DA ensuring efficient nonlinear propagation. Validation demonstrates high maneuver detection success and reliable uncertainty bounds, with DA significantly outperforming Monte Carlo in speed while achieving comparable accuracy in most cases.
The framework’s theoretical applications span spacecraft trajectory optimization under perturbations, enhanced safety in aerial vehicle navigation, robust hypersonic re-entry bounds, improved debris collision predictions, and strengthened space-based maneuver detection for situational awareness.
Compared to Monte Carlo, DA’s efficiency and analytical depth make it ideal for real-time adaptive estimation, though Monte Carlo’s probabilistic coverage suits complex, high-uncertainty scenarios.
In conclusion, the DA-MMAE framework advances aerospace estimation by merging precise analysis with adaptive detection. Future directions include dynamic model adjustments, machine learning-enhanced architectures, real-time optimizations, multi-sensor integration, distributed systems for coordinated operations, and extensions to interplanetary multi-body dynamics
The literature review underscores DA’s efficacy in reachable set computation, utilizing polynomial approximations to model nonlinear dynamics governed by differential-algebraic equations. Compared to geometric or statistical sampling methods, DA offers a superior balance of complexity and accuracy, ideal for moderately scaled aerospace systems. Historically, reachable sets evolved from linear control theory to complex applications in unmanned aerial vehicles, spacecraft, and missiles. Challenges like high-dimensional computations and non-convex constraints suggest hybrid techniques as future solutions. In uncertainty propagation, DA outperforms linear filters by capturing higher-order nonlinear effects, evident in applications like spacecraft trajectory planning, aerial navigation under disturbances, hypersonic re-entry, and debris tracking for collision risk assessment.
The methodology employs DA to analyze orbital perturbations in gravitational models, comparing polynomial expansions to Monte Carlo simulations. DA is favored for its computational speed, achieving results approximately three times faster than Monte Carlo, which relies on resource-intensive random sampling. DA’s analytical polynomial evaluations provide deterministic insights and efficiency for real-time use while maintaining accuracy for small to moderate uncertainties. Monte Carlo, however, excels in probabilistic robustness for highly nonlinear or large-perturbation scenarios, justifying DA’s selection for scalable, efficient integration into adaptive frameworks. Implemented techniques include DA-based Taylor expansions for state propagation, extended Kalman filtering for uncertainty management, and MMAE with parallel models for maneuver hypothesis testing, incorporating Bayesian probability updates, polynomial-based covariance computations, and model pruning for dynamic adaptability.
The innovative MMAE extension addresses orbits with unknown maneuvers by hypothesizing velocity impulses across multiple models. This Bayesian framework runs parallel filters, updating probabilities based on measurement fits to yield optimal estimates. Unlike static methods limited to predefined scenarios, it incorporates interactive and variable structures, with DA ensuring efficient nonlinear propagation. Validation demonstrates high maneuver detection success and reliable uncertainty bounds, with DA significantly outperforming Monte Carlo in speed while achieving comparable accuracy in most cases.
The framework’s theoretical applications span spacecraft trajectory optimization under perturbations, enhanced safety in aerial vehicle navigation, robust hypersonic re-entry bounds, improved debris collision predictions, and strengthened space-based maneuver detection for situational awareness.
Compared to Monte Carlo, DA’s efficiency and analytical depth make it ideal for real-time adaptive estimation, though Monte Carlo’s probabilistic coverage suits complex, high-uncertainty scenarios.
In conclusion, the DA-MMAE framework advances aerospace estimation by merging precise analysis with adaptive detection. Future directions include dynamic model adjustments, machine learning-enhanced architectures, real-time optimizations, multi-sensor integration, distributed systems for coordinated operations, and extensions to interplanetary multi-body dynamics
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