发表机构
Iowa State University（爱荷华州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对轨道碎片模拟中立方体方法的边界盲目性问题，提出双立方体（DC）方法保持\(\mathcal{O}(N)\)复杂度并降低盲目率。还发现立方体公式高估问题，推导出幂律和高斯两种校正方法并验证，已应用于MOCAT - MC。
AI 中文摘要
立方体方法通过在每个快照中仅评估共享同一网格单元的对象对，将轨道碎片模拟中的合取筛选成本降低到\(\mathcal{O}(N)\)，但会将 epoch 时刻被单元格边界隔开的对象对的碰撞概率系统地设为零，即边界盲目性。本文介绍了双立方体（DC）方法，它仅通过使用箱索引查找的空间移位辅助网格来恢复穿越边界的合取，保持\(\mathcal{O}(N)\)复杂度。经8000个蒙特卡罗种子验证，DC将盲目率从\(\beta_{\mathrm{Cube}} = 9.70\%\)降至\(\beta_{\mathrm{DC}} = 4.21\%\)；同步实验证实残余误差源于时间，精确达到\(0.00\%\)。去除盲目性后发现立方体公式存在系统的成对高估，而盲目零概率赋值掩盖了这一点，压低了总体预测碰撞率。推导出并验证了两种独立校正：由直接模拟蒙特卡罗动力学理论类比激发的幂律校正将校准误差在\(k = 1\)时从\(12.9\%\)降至\(1.9\%\)，在\(k = 2\)时降至\(4.0\%\)，从两侧逼近完美校准；从对距离分布几何得出的无参数高斯校正实现了\(0.08\%\)的残余误差。两种校正均已在MOCAT - MC中实现。
英文摘要
The cube method reduces conjunction screening in orbital debris simulations to $\mathcal{O}(N)$ cost by evaluating only object pairs sharing the same grid cell at each snapshot, but systematically assigns zero collision probability to pairs separated by a cell boundary at that epoch, a failure known as boundary blindness. This paper introduces the Double Cube (DC) method, which recovers boundary-crossing conjunctions through a spatially shifted secondary grid using bin-index lookup alone, preserving $\mathcal{O}(N)$ complexity. In an isotropic convergence benchmark at $L = 50$ km, DC reduces the blindness rate from $β_{\mathrm{Cube}} = 7.09\%$ to $β_{\mathrm{DC}} = 0.55\%$, and a synchronized experiment separates the temporal component from the geometric one and leaves DC below $0.01\%$ against $0.80\%$ for the cube. Recovering these pairs changes which pairs are evaluated and leaves the probability formula untouched, so it does not improve calibration by itself, and both uncorrected methods remain substantially miscalibrated, with a reliability slope of $m = 1.1314$ for the cube and $m = 1.0996$ for DC. The formula applies the full cell volume to every evaluated pair irrespective of separation, which is the same bias characterized in the no-time-counter scheme of Direct Simulation Monte Carlo. Two corrections are derived from the geometry of the uniform cell alone: a power-law form referenced to the Robbins mean separation $\bar{d} = 0.6617L$ and a Gaussian form using both that mean and the analytically derived standard deviation $σ= 0.2494L$, with no quantity fitted to simulation output. The power-law correction moves the reliability slope to $0.9973$ at $k = 1$ and $0.9429$ at $k = 2$, and the Gaussian correction reaches $0.9806$ with an intercept of $0.975$, the only configuration within $3\%$ of unity on both. Both corrections have been implemented in MOCAT-MC.
Comments21 pages, 7 figures, Submitted and presented at the 2026 AAS/AIAA Astrodynamics Specialist Conference, Whistler, British Columbia, July 26-30
