基于GARCH波动性的新型机动目标跟踪方法
A Novel Maneuvering Target Tracking Approach by Stochastic Volatility GARCH Model
AI总结：
本文提出一种基于GARCH波动性的新型单模型机动目标跟踪方法，通过随机微分方程（SDE）建模目标的马尔可夫跳跃加速度，利用贝叶斯滤波器同时估计原始状态和随机波动性（SV），并通过仿真验证了该方法在目标跟踪性能上的改进。
摘要：
在本文中，我们介绍了一种基于GARCH波动性的新型单模型机动目标跟踪方法，该方法基于随机微分方程（SDE）。传统输入估计（IE）技术假设加速度水平恒定，无法涵盖所有可能的加速度本质。相比之下，多模型（MM）算法虽然弥补了IE的一些不足，但对转移概率矩阵敏感。本文提出了一种创新模型，通过使用新的加速度动态建模方法和贝叶斯滤波器来克服这些缺点。我们利用SDE通过GARCH过程作为SDE波动性来建模机动目标的马尔可夫跳跃加速度。在所提出的方案中，通过bootstrap粒子滤波器（PF）同时估计原始状态和随机波动性（SV）。我们引入bootstrap重采样以获得GARCH密度的统计特性。由于GARCH分布的厚尾性质，bootstrap PF在状态方程中可能出现的大误差情况下更为有效。我们通过分析证明，考虑GARCH加速度模型可以提高目标跟踪性能。最后，通过仿真研究验证了所提出策略（PF-AR-GARCH）的有效性和能力。
英文摘要：
In this paper, we introduce a new single model maneuvering target tracking approach using stochastic differential equation (SDE) based on GARCH volatility. The traditional input estimation (IE) techniques assume constant acceleration level which do not cover all the possible acceleration quintessence. In contrast, the multiple model (MM) algorithms that take care of some IE's shortcomings, are sensitive to the transition probability matrices. In this paper, an innovative model is proposed to overcome these drawbacks by using a new generalized dynamic modeling of acceleration and a Bayesian filter. We utilize SDE to model Markovian jump acceleration of a maneuvering target through GARCH process as the SDE volatility. In the proposed scheme, the original state and stochastic volatility (SV) are estimated simultaneously by a bootstrap particle filter (PF). We introduce the bootstrap resampling to obtain the statistical properties of a GARCH density. Due to the heavy-tailed nature of the GARCH distribution, the bootstrap PF is more effective in the presence of large errors that can occur in the state equation. We show analytically that the target tracking performance is improved by considering GARCH acceleration model. Finally, the effectiveness and capabilities of our proposed strategy (PF-AR-GARCH) are demonstrated and validated through simulation studies.
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