This chapter introduces an attitude determination framework designed for satellite missions characterized by limited on-orbit data and uncertain measurements. Unlike traditional probabilistic approaches that require extensive statistical sampling, the methodology adopted here utilizes non-probabilistic interval analysis techniques to model system uncertainties as unknown-but-bounded (UBB) parameters. A key contribution discussed is the development of a narrow bound theory, which employs interval dimension-wise analysis (IDWA) rooted in polynomial chaos expansions. This approach effectively mitigates the overestimation issues often associated with conventional interval perturbation methods, ensuring more precise bound estimation for the attitude determination system. The classical Wahba problem is reformulated into a multi-objective optimization context, aiming to simultaneously minimize the nominal loss function and its uncertainty radius. To solve this complex problem, the strength Pareto evolutionary algorithm based on reference direction (SPEA/R) is utilized, balancing convergence and diversity in the solution set. Numerical simulations confirm that this interval-based strategy achieves high attitude estimation accuracy and computational efficiency, offering a resilient alternative for spacecraft attitude operating in data-sparse environments.