A multi-target robust observation method for satellite constellations based on hypergraph algebraic connectivity and observation precision theory is proposed to address the challenges posed by the surge in space targets and system failures. First, a precision metric framework is constructed based on nonlinear batch least squares estimation theory, deriving the theoretical precision covariance through cumulative observation matrices to provide a theoretical foundation for tracking accuracy evaluation. Second, multi-satellite collaborative observation is modeled as an edge-dependent vertex-weighted hypergraph, enhancing system robustness by maximizing algebraic connectivity. A constrained simulated annealing (CSA) algorithm is designed, employing a precision-guided perturbation strategy to efficiently solve the optimization problem. Simulation experiments are conducted using 24 Walker constellation satellites tracking 50 targets, comparing the proposed method with greedy algorithm, CBBA, and CSA-bipartite Graph methods across three scenarios: baseline, maneuvering, and failure. Results demonstrate that the CSA-hypergraph method achieves 0.089 km steady-state precision in the baseline scenario, representing a 41.4% improvement over traditional methods; in maneuvering scenarios, detection delay is reduced by 34.3% and re-achievement time is decreased by 47.4%; with a 30% satellite failure rate, performance degradation is only 9.8%, significantly outperforming other methods.