Uncertainty Quantification and State Estimation in the Evolution of Reachable Sets of Maneuvers for Space Mission Applications
Università di Pisa
Dipartimento di Ingegneria Civile e Industriale
Laurea Magistrale in Ingegneria Aerospaziale
Candidate: Lalit Deshmukh
Advisors: Prof. Gianpietro Di Rito (University of Pisa) & Prof. Simone Servadio (Iowa State University)
This repository contains the complete implementation and supporting materials for a novel computational framework that integrates Differential Algebra (DA) with Multiple Model Adaptive Estimation (MMAE) to perform robust orbit determination and maneuver detection in the presence of unknown impulsive velocity changes.
The framework addresses a critical challenge in modern space operations: accurately estimating spacecraft states and reachable sets when non-cooperative objects execute sudden, unannounced maneuvers. Traditional single-model filters fail under these conditions. By combining DA’s high-order polynomial uncertainty propagation with a Bayesian multi-model adaptive filter, the system achieves fast, deterministic uncertainty quantification and real-time maneuver identification—capabilities essential for space situational awareness, collision avoidance, and autonomous navigation.
The code is implemented in C++ and leverages the DACE library for differential-algebraic computations, an RK78 integrator for high-fidelity orbital propagation, and a bank of parallel extended Kalman filters for adaptive estimation.
- DA-based uncertainty propagation – Second-order Taylor expansions propagate nonlinear orbital dynamics and uncertainties analytically, achieving ~3× faster computation than Monte Carlo methods while maintaining comparable accuracy for moderate perturbations.
- MMAE for unknown maneuvers – A bank of 614 parallel models hypothesizes possible velocity impulses (0.1–0.3 km/s in a discretized spherical grid). Bayesian weight updates and pruning dynamically focus on the most probable maneuver scenarios.
- Real-time orbit determination filter – DA-enhanced EKF handles nonlinear measurements (range, azimuth, elevation) without linearization approximations.
- Monte Carlo validation suite – 100–1000 independent runs quantify statistical performance, error bounds, and 3σ confidence regions.
- Reachable-set visualization – 2D (XY) and 3D projections of post-maneuver uncertainty envelopes.
- Model success metrics – Automatic classification of detection performance (perfect match, partial match, opposite-direction, or failure) with overall success rate of ~91.1 %.
├── src/ │ ├── DA_Orbital_Perturbations/ # Chapter 3: DA vs. Monte Carlo comparison │ ├── DA_EKF_Orbit_Determination/ # Baseline DA-enhanced EKF filter │ ├── MMAE_Impulse_Estimation/ # Core multi-model adaptive filter (614 models) │ └── utils/ # RK78 integrator, measurement models, CSV output ├── results/ │ ├── figures/ # All plots from the thesis (3D reachable sets, error vs. time, model weights, etc.) │ ├── csv/ # Raw Monte Carlo statistics, model probabilities, 3σ bounds │ └── success_analysis/ # Automatic success-rate classification ├── docs/ │ ├── thesis_abstract.md │ └── methodology_notes.md ├── CMakeLists.txt ├── README.md └── LICENSE