基于条件马尔可夫模型的移动目标制导弹道数学建模
Mathematical Modeling of Guidance Trajectory with a Moving Destination Using Conditionally Markov Modeling
摘要：
目的地定向的移动对象（例如，从起点机场到目的地机场的飞机）的轨迹具有三个主要分量：起点、目的地和在它们之间的运动。我们把这种到达目的地的轨迹称为\textit{destination-directed trajectory (DDT)}。一类条件马尔可夫（CM）序列（称为CM $_\text{L}$）具有以下主要成分：两个端点的联合密度和类马尔可夫演化律。CM $_\text{L}$动态模型可以描述DDT的演变，但不能描述被引导物体追逐移动引导的演变。被引导对象的轨迹被称为\textit{guided trajectory (GT)}。受CM $_\text{L}$模型的启发，本文提出了一种带移动导轨的GT模型。所提出的模型减少到CM $_\text{L}$模型，如果指南是不移动的。我们还研究了基于该模型的滤波和轨迹预测。仿真结果。
英文摘要：
A trajectory of a destination-directed moving object (e.g. an aircraft from an origin airport to a destination airport) has three main components: an origin, a destination, and motion in between. We call such a trajectory that end up at the destination \textit{destination-directed trajectory (DDT)}. A class of conditionally Markov (CM) sequences (called CM$_\text{L}$) has the following main components: a joint density of two endpoints and a Markov-like evolution law. A CM$_\text{L}$ dynamic model can describe the evolution of a DDT but not of a guided object chasing a moving guide. The trajectory of a guided object is called a \textit{guided trajectory (GT)}. Inspired by a CM$_\text{L}$ model, this paper proposes a model for a GT with a moving guide. The proposed model reduces to a CM$_\text{L}$ model if the guide is not moving. We also study filtering and trajectory prediction based on the proposed model. Simulation results are presented.
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