摘要
天基光学监视系统利用天基平台搭载的光学传感器对空间目标进行探测、预警、跟踪、编目，具有探测范围广、作用距离远、不受地理位置限制等优点，成为各大国在空间领域的发展重点。天基观测条件下的空间目标跟踪定轨技术以及天基网络路由技术是天基光学监视系统信息处理和信息传输的关键技术。本文针对天基观测低轨多目标跟踪方法、高轨目标短弧定轨方法以及天基低轨通信网络的路由算法展开研究，主要工作包括：
1.基于随机有限集理论的天基观测低轨多目标跟踪方法研究
针对低轨多目标的天基像平面跟踪问题，给出了混合高斯势概率假设密度(Gaussian Mixture Cardinalized Probability Hypothesis Density, GM-CPHD)滤波方法。该方法利用GM-CPHD滤波估计像平面上的目标数量和目标状态，采用最小权匹配方法生成目标在像平面上的运动轨迹。仿真结果表明，GM-CPHD滤波方法相对GM-PHD滤波对目标数量的估计精度有显著提高，能够较为准确的生成目标的轨迹。
提出了基于多伯努利平滑的低轨多目标天基像平面跟踪方法，用来提高基于滤波的跟踪方法的性能。多伯努利平滑采用多伯努利近似方法实现多目标平滑状态概率密度的反向递推计算，利用序贯蒙特卡洛方法解决多重积分的计算问题。仿真结果表明，与滤波相比，多伯努利平滑对目标数量和目标状态的估计精度都有显著提高。
针对天基观测低轨多目标的三维跟踪问题，提出了多模型CPHD滤波。该滤波建立了低轨目标的多个运动模型，将目标的运动状态与运动模式组合成增广状态，利用CPHD滤波递推目标数量的后验分布和增广状态的后验PHD，同时得到目标数量和目标三维状态的估计。仿真结果表明，多模型CPHD滤波的跟踪性能优于单模型CPHD滤波和多模型PHD滤波。
针对天基观测低轨多目标跟踪的传感器系统误差自校准问题，提出了扩展CPHD滤波。该滤波将传感器系统误差添加到目标运动状态中构成扩展状态，利用CPHD滤波递推目标数量的后验分布和扩展状态的后验PHD，同时得到目标数量、目标状态和传感器系统误差的估计。仿真结果表明，扩展CPHD滤波能够实时估计校正系统误差，跟踪性能相对标准CPHD滤波有显著提高。
2.低轨单星观测条件下的高轨目标短弧定轨方法研究
给出了利用两个相邻短弧段的测角数据确定目标轨道的两种方法。第一种方法利用二体轨道能量约束构造容许域，对第一个短弧段的容许域进行三角剖分采样，通过分析这些采样点与第二个短弧段的差异，优先选取多个采样点轨道作为初轨，分别对各初轨进行轨道改进。仿真结果表明，该方法能成功解算最小二乘轨道。第二种方法由两个短弧段的测角数据建立二体轨道能量角动量守恒方程，采用变量替换法求解守恒方程获得空间目标的多个轨道，通过方差分析从中选择最合适的轨道作为初轨，对该初轨进行轨道改进。仿真结果表明，此方法在无空间目标轨道任何先验信息的条件下能够实现初轨计算，轨道改进的收敛性较好，能够成功收敛于最小二乘解。
3.天基低轨通信网络的路由算法研究
提出了多约束最优路由算法。该算法建立了以传输时延、跳数和可用带宽为约束条件以优化链路切换率、时延、带宽利用率为目标的多约束最优路由模型，采用缩小可行解搜索空间的方法减少求解多约束最优路径的计算量。仿真结果表明，路由算法的复杂度和切换性能优于同类算法，适合于星上在线路由计算。
By using optical sensors on orbiting platforms, the space-based optical surveillancesystem has the capabilities of detecting, warning, tracking and cataloging space targets.The world’ powerful nations focus on developing space-based optical surveillancesystem in the field of aerospace, since this system has some attractive advantages suchas wide detection area, far surveillance distance, not suffering from geographicconstraints, and so on. The tracking and orbit determination technologies for spacetarget, and the routing technology for space-based network conditioned on space-basedobservation play key roles in the information processing and transmission of thespace-based optical surveillance system. This paper investigates the low-Earth-orbit(LEO) multi-target tracking and the short-arc orbit determination of high-Earth-orbit(HEO) target using space-based observations, and the routing algorithm of space-basedLEO network. The main contributions of this paper are as follows:
1. Random finite set theory based LEO multi-target tracking using space-basedobservations
For tracking of LEO multi-target on space-based focal plane, a method of Gaussianmixture cardinalized probability hypothesis density (GM-CPHD) filter is given. Thismethod estimates the number and the target states on the focal plane by usingGM-CPHD filter, and then generates target tracks on the focal plane by using themethod of minimum weighted matching. Simulation results show that the GM-CPHDfilter method outperforms the GM-PHD filter for the estimation accuracy of targetnumber, and that the target tracks can be generated almost exactly.
A multi-Bernoulli smoother for tracking of LEO multi-target on space-based focalplane is proposed. The smoother is desired to improve the performance of trackingmethod based on the filter. For the multi-Bernoulli smoother, the backward recursion ofthe smoothed multi-target probability density is derived by using the method ofmulti-Bernoulli approximation, and the computational problem of multiple integrals issolved by using sequential Monte Carlo method. Simulation results show that thesmoother can dramatically improve the estimation accuracy of target number and targetstates over the filter.
For3D tracking of LEO multi-target using space-based observations, a multiplemodel CPHD filter is proposed. This filter constructs multiple motion models for LEOtarget. The augmented state is established by combining the target state with the targetmotion mode. Both the posterior cardinality distribution of targets and the posteriorPHD of the augmented state are propagated by using CPHD filter. The target numberand the target3D states are jointly estimated. Simulation results show that the multiplemodel CPHD filter outperforms the single model CPHD filter and the multiple model PHD filter.
For the self-calibration of systematical error of sensors in space-based LEOmulti-target tracking problem, an extended CPHD filter is proposed. This filterestablishes extended state by appending the sensor biases to the target state. Both theposterior cardinality distribution of targets and the posterior PHD of the extended stateare propagated by using CPHD filter. The number and the states of the targets and thesensor biases are jointly estimated. Simulation results show that the extended CPHDfilter successfully achieves real-time estimation and alignment of the systematical error,and outperforms the standard CPHD filter.
2. Short-arc orbit determination method for HEO target conditioned on LEO singlesatellite observation
We give two methods of orbit determination using two adjacent short-arcs ofangular measurements. The first method constructs admissible region by using theenergy constraint of two-body orbit. The admissible region of the first arc is sampled bytriangulation. Comparing these samples with the second arc, several proper orbits ofthese samples are determined as initial orbits. These initial orbits are all used for orbitimprovement. Simulation results show that this method can successfully achieve theleast square solution. The second method establishes energy and angular-momentumconservation equations of two-body orbit using two short arcs of angular measurements.Multiple solutions of these equations are obtained via variable transformation. Theoptimal solution is selected by covariance analysis, and is used for computing the initialorbit. This initial orbit is used for orbit improvement. Simulation results show that thismethod can derive initial orbit without any prior information about the orbit of spacetarget. The orbit improvement can successfully achieve the least square solution,indicating the excellent convergence behavior.
3. Routing algorithm of space-based LEO network
A multi-constrained optimal routing algorithm is proposed. This algorithmestablishes the multi-constrained optimal path (MCOP) model, whose constraints aredelay, hop-count and available bandwidth and objective is to optimize the performanceof handover, delay and bandwidth utilization. The computational amount of findingMCOP is reduced by decreasing the searching field of feasible solutions. Simulationresults show that the routing algorithm is superior to other current algorithms in theaspects of computing complexity and handover performance, indicating the adaptabilityfor on-line routing.
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