For the state estimation problem of linear systems with unknown but bounded noise, a particle swarm optimization based orthometric hyperparallel space filtering is proposed. Firstly, we construct the orthometric hyperparallel space by the vertices of the hyperparallel space, that wraps the feasible set of the system state. Then, the real-state search space for the particle swarm iteration optimization method is studied. Subsequently, we construct a fitness function using the system's observations to judge the performance of particles, by driving particles to move within the orthometric hyperparallel space, to make the particles distribute around the real state. The irregular high-likelihood region of the particle swarm with the smallest outer orthometric hyperparallel space is given to solve the upper and lower bounds of the orthometric hyperparallel space by linear programming, and a compact envelope of the system state is obtained. Finally, the effectiveness and practicality of the proposed algorithm are verified by a constructed lithium-ion battery operating state analysis platform.