Efficient Reachable Domain Search-Tracking for Cislunar Non-Cooperative Targets via Designed Quadrature

Abstract

To address the triple challenges of data sparsity, highly nonlinear dynamics, and maneuver uncertainty in tracking non-cooperative targets in cislunar space, we propose a collaborative framework combining Particle Filter (PF) and Unscented Kalman Filter (UKF). This framework optimizes search efficiency through a two-phase strategy: in the search phase, PF constructs the target reachable domain and leverages undetected information to dynamically shrink the search scope; upon target detection, the framework switches to UKF for high-precision and low-overhead tracking. To overcome the computational bottleneck in high-dimensional reachable domain integration, we integrate a non-product-type Designed Quadrature (DQ) method—one that generates minimal quadrature point sets to replace traditional Monte Carlo sampling by matching the moment conditions of mixed distributions via Gauss–Newton optimization. Distinct from existing single-filter or reachability modeling approaches, the key novelties of this work lie in a two-phase PF-UKF switching framework tailored to the unique cislunar environment resolving the trade-off between search capability and computational efficiency and integration of the non-product DQ method to break the dimensionality curse in high-dimensional reachable domain computation ensuring both moment-matching accuracy and real-time performance. This work holds potential to support space domain awareness and cislunar mission safety: reliable tracking of non-cooperative targets is a key prerequisite for avoiding collisions, safeguarding space assets, and enabling effective space defense, and the proposed framework provides a feasible technical path for this goal through simulation validation. Simulations demonstrate that on a three-dimensional Distant Retrograde Orbit (DRO) observation platform, successful recapture of cislunar transfer orbit targets can be achieved. Under fifth-order accuracy conditions, the system exhibits a position error of $3.745\times {10}^{-1}\mathrm{km}$ and a velocity tracking error of $9.703\times {10}^{-3}\mathrm{m}/\mathrm{s}$ for target search-and-tracking tasks, with a system response time of 1.8343 h. Compared with the traditional PF + numerical integration method, our proposed PF-UKF framework achieves an 86.7% reduction in time cost and a 24.1% reduction in position error.