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目前,纯方位跟踪(BOT)的可观测性分析仍然是重要的学术研究课题。与以前的连续时间分析研究不同,我们的研究依赖于离散时间分析。而且还允许我们直接而有效地使用简单的线性代数公式系。使用直接方法,可观测性分析实际上简化为子空间范围的基本研究。虽然这种方法在概念上是相当直接的,但随着源相遇情况复杂性的增加,它会变得越来越复杂。对于复杂情况,由于直接使用多重线性代数方法,对偶方法可能体现某些基本优点。因此得出关于机动源的BOT可观测性的新结果。继而可将可观测性分析扩展到源速度变化的未知时刻。 尽管可观测性分析使我们能更充分地了解BOT问题的代数结构,但观测者机动的最优化实际上是一个控制问题。基本代数研究证明这种控制问题的相关成本函数是费歇尔信息矩阵(FIM)的行列式。因此大部分工作集中在对这个成本泛函的分析上。使用多重线性代数给出了这个泛函的一般近似。这些近似结果表明最感兴趣的事仅涉及到直接可估计参数,即源方位变化率。用这些近似,可导出最优化观测者轨迹的一般框架,这允许我们近似最优控制序列。值得强调的是我们的方法不需要有关源轨迹参数的知识且对机动源仍然有效。
At present, the analysis of observability of BOT is still an important subject of academic research. Unlike previous continuous-time analysis studies, our research relies on discrete-time analysis. But also allows us to use simple linear algebraic formulas directly and effectively. Using the direct method, observability analysis actually simplifies the basic research into the subspace range. Although this approach is conceptually fairly straightforward, it can become more and more complicated as the complexity of the source encounters increases. For complex cases, the dual approach may have some basic advantages due to the direct use of multiple linear algebra methods. This leads to new results on BOT observability of maneuver sources. The observability analysis can then be extended to an unknown moment of source velocity change. Although observability analysis allows us to have a fuller understanding of the algebraic structure of BOT problems, the optimization of observer maneuver is actually a matter of control. The basic algebraic studies show that the related cost function for this control problem is the determinant of the Fischer Information Matrix (FIM). Therefore, most of the work focused on the analysis of the cost function. The general approximation of this functional is given using multiple linear algebra. These approximate results show that the most interesting things only involve the directly estimable parameters, namely the source azimuth rate of change. Using these approximations, a general framework for optimizing the trajectory of the observer can be derived, which allows us to approximate the optimal control sequence. It is worth stressing that our method does not require knowledge of source trajectory parameters and is still valid for maneuvering sources.