ETD

• Differential Algebra
• Maneuver Detection
• Multiple Model Adaptive Estimation
• Nonlinear Dynamics
• Orbit Determination

Recent advancements in aerospace engineering highlight the critical need for sophisticated computa-
tional 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 de-
tection. 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 solu-
tions. 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 up-
dates, polynomial-based covariance computations, and model pruning for dynamic adaptability.
The innovative MMAE extension addresses orbits with unknown maneuvers by hypothesizing veloc-
ity impulses across multiple models. This Bayesian framework runs parallel filters, updating probabili-
ties 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 propa-
ii
gation. 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 perturba-
tions, enhanced safety in aerial vehicle navigation, robust hypersonic re-entry bounds, improved de-
bris 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 coor-
dinated operations, and extensions to interplanetary multi-body dynamics