基于Tobit回归模型的偏差多速率系统估计问题研究

Multi-sensor measurements of distant early warning systems have the feature of multi-rate sampling. Meanwhile, complex environments and incessant disturbances lead to sensor biases and data censoring. Traditional multi-rate estimation methods cannot be applied to systems with random parameters, while existing bias and censoring estimation methods transform bias and censoring phenomena into random parameters. The limited dependent variable structure of the Tobit regression model has the distinctive advantage of avoiding converting bias and censoring phenomena into random parameters. Hence, it is of great necessities to conduct the research on the estimation problem of multi-rate systems with biases based on the Tobit regression model. Firstly, modeling errors caused by biases are represented by unknown disturbances, and the disturbance free low-dimension equivalent system is constructed. The multi-rate Tobit observer is then designed, and uncertainties due to censoring are modeled as unknown inputs to the estimation error system. Then, the detectability, observability and stability of the estimation error system is analyzed, and the internal relation among the multi-rate sampling, bias, censoring probability and estimation performance is found. Finally, the realization of the proposed multi-rate Tobit target tracking method is achieved under backgrounds of distant early warning and target tracking. This item would be helpful in enriching and extending existing results, and further improving theories of the modeling and estimation of complex systems and multi-source information fusion.

远程预警系统的多传感器量测具有多种速率采样特点，且复杂多变的探测环境和层出不穷的干扰欺骗造成传感器偏差和数据删失。传统的多速率估计不适用于随机参数，而现有的偏差和删失估计将偏差和删失转化为随机参数处理。Tobit回归模型特有的因变量受限结构能避免偏差和删失的随机参数问题。因此，很有必要开展基于Tobit回归模型的偏差多速率系统估计研究。首先，将偏差引起的建模误差表征为未知扰动，利用多源冗余信息的相关与对消构造与扰动无关的降维系统，设计多速率Tobit观测器，将删失引起的不确定性表征为估计误差系统输入扰动，进而设计多速率Tobit估计器。然后，分析误差系统可测性、能观性和稳定性，揭示多速率、偏差、删失概率和估计性能内在联系。最后，结合远程预警目标跟踪应用背景，研究多速率Tobit目标跟踪方法的有效实现。本项目将大大丰富、拓展现有研究成果，进一步完善复杂系统建模估计与多源信息融合理论体系。

开展基于Tobit回归模型的多速率估计器的建模、鲁棒估计器设计、稳定性分析及其在预警雷达数据处理应用研究，主要进展如下：针对预警装备交接与协同探测中的多速率特性，设计量测删失下的多速率线性最小方差观测器；针对多速率系统中出现的系统偏差问题，设计了基于慢速率传感器量测的快速偏差诊断机制，实现对多速率系统的快速系统偏差辨识与估计；针对预测方差期望最优意义下多速率数据融合问题，发现其存在关键删失概率阈值，并讨论阈值的上下限的解析和数值求解问题；针对预警探测中协同探测与目标跟踪，提出一种基于通信协议的分布式多传感器删失数据融合算法；针对远程预警中目标状态和电离层高度参数联合估计问题，提出快速状态更新和间歇式参数演变的多速率估计模型。发表和录用SCI期刊文章8篇，其中JCR一、二区5篇。

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