CRLB for the Event Triggered Area Target Tracking System With Intermittent Observations
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摘要: 面目标跟踪系统状态估计问题中，附加的强非线性面目标扩展测量会增加系统的通信量和估计中心的计算量.为此，基于工程应用，提出一种不完全量测下的事件触发机制来控制面目标测量传输.从理论上推导了事件触发机制下面目标跟踪系统的理想（枚举）克拉美罗下界（Cramer-Rao lower bound，CRLB）和统计意义下的CRLB，该统计意义CRLB为理想CRLB的下界，计算复杂度远小于理想CRLB，便于工程应用.典型测试航路下的仿真结果表明：不完全量测下，面目标跟踪系统CRLB明显小于传统质点目标跟踪系统CRLB；同时，利用所提事件触发机制，可在大幅减少面目标跟踪系统通信量的同时保证系统的最优估计性能.
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关键词:
- 不完全量测 /
- 面目标 /
- 事件触发机制 /
- Cramer-Rao下界
Abstract: In area target tracking systems, communication cost and computational burden are increased by additional nonlinear extended area target measurements. Hence, based on practical engineering, an event triggered transmission mechanism with intermittent observations is proposed. We theoretically derive the ideal (enumeration) Cramer-Rao lower bound (CRLB) and the statistical CRLB of the event triggered area target tracking system. The proposed statistical CRLB, which can be readily implemented in practical applications, is a lower bound of the ideal CRLB. Finally, simulation experiments in typical test routes demonstrate that, with intermittent observations, the CRLB of the area target tracking system is significantly smaller than that of the traditional particle target tracking system. Moreover, by using the proposed event triggered transmission mechanism, the communication cost can be significantly reduced while the optimal estimation performance is slightly affected.1) 本文责任编委 潘泉 -
图 2 CRLB与面目标扩展测量通道探测概率$\lambda_{{\rm{e}}}$的关系
Fig. 2 The relationship between the CRLB and the detection probability $\lambda_{{\rm{e}}}$ of extended area target measurements
图 3 双探测通道触发频度$\alpha_i$ $(i={\rm p}, {\rm e})$与触发阈值$\delta$的关系
Fig. 3 The relationship between the triggered frequency $\alpha_i$ $(i={\rm p}, {\rm e})$ and the triggered threshold $\delta$
图 4 不同触发频度下面目标跟踪系统CRLB
Fig. 4 The CRLB of the area target tracking system with different triggered frequencies
图 5 CRLB与面目标扩展测量通道探测概率$\lambda_{{\rm{e}}}$的关系
Fig. 5 The relationship between the CRLB and the detection probability $\lambda_{{\rm{e}}}$ of extended area target measurements
图 6 双探测通道触发频度$\alpha_i$ $(i={\rm p}, {\rm e})$与触发阈值$\delta$的关系
Fig. 6 The relationship between the triggered frequency $\alpha_i$ $(i={\rm p}, {\rm e})$ and the triggered threshold $\delta$
图 7 不同触发频度下面目标跟踪系统CRLB
Fig. 7 The CRLB of the area target tracking system with different triggered frequencies
图 8 CRLB与面目标扩展测量通道探测概率$\lambda_{{\rm{e}}}$的关系
Fig. 8 The relationship between the CRLB and the detection probability $\lambda_{{\rm{e}}}$ of extended area target measurements
图 9 双探测通道触发频度$\alpha_i$ $(i={\rm p}, {\rm e})$与触发阈值$\delta$的关系
Fig. 9 The relationship between the triggered frequency $\alpha_i$ $(i={\rm p}, {\rm e})$ and the triggered threshold $\delta$
图 10 不同触发频度下面目标跟踪系统CRLB
Fig. 10 The CRLB of the area target tracking system with different triggered frequencies
图 11 CRLB与面目标扩展测量通道探测概率$\lambda_{{\rm{e}}}$的关系
Fig. 11 The relationship between the CRLB and the detection probability $\lambda_{{\rm{e}}}$ of extended area target measurements
图 12 双探测通道触发频度$\alpha_i(i={\rm p}, {\rm e})$与触发阈值$\delta$的关系
Fig. 12 The relationship between the triggered frequency $\alpha_i(i={\rm p}, {\rm e})$ and the triggered threshold $\delta$
图 13 不同触发频度下面目标跟踪系统CRLB
Fig. 13 The CRLB of the area target tracking system with different triggered frequencies
表 1 面目标跟踪系统测量信息核心数据发送协议
Table 1 The core data transmission protocol of the area target tracking system
数据 距离 方位角 顺向距离 横向距离 字长 2字节 2字节 2字节 2字节 
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表 2 不同触发频度下基于事件触发机制的面目标跟踪系统平均CRLB
Table 2 Comparison of average CRLBs of the event triggered area target tracking system with different triggered probabilities
平均$\mathrm{CRLB}$ $\alpha_{{\rm{p}}}=1.0$ $\alpha_{{\rm{p}}}=0.8$ $\alpha_{{\rm{p}}}=0.6$ $\alpha_{{\rm{e}}}=1.0$ $\alpha_{{\rm{e}}}=0.6$ $\alpha_{{\rm{e}}}=0.4$ 位置/$\mathrm{(m)}~({\rm{CV}})$ 18.38 18.92 19.84 速度/$\mathrm{(m/s)}~({\rm{CV}})$ 2.59 2.68 2.80 位置/$\mathrm{(m)}~({\rm{CA}})$ 19.78 20.51 21.71 速度/$\mathrm{(m/s)}~({\rm{CA}})$ 3.02 3.21 3.48 位置/$\mathrm{(m)}~(\mathrm{CT})$ 13.94 14.03 14.31 速度/$\mathrm{(m/s)}~(\mathrm{CT})$ 1.75 1.78 1.81 位置/$\mathrm{(m)}~(\mathrm{Singer})$ 19.17 19.71 20.72 速度/$\mathrm{(m/s)}~(\mathrm{Singer})$ 2.62 2.74 2.94
下载: 导出CSV
表 3 不同探测概率下基于事件触发机制的面目标跟踪系统平均CRLB
Table 3 Comparison of average CRLBs of the event triggered area target tracking system with different detection probabilities
平均$\mathrm{CRLB}$ $\lambda_{{\rm{p}}}=0.6$ $\lambda_{{\rm{p}}}=0.7$ $\lambda_{{\rm{p}}}=0.8$ $\lambda_{{\rm{e}}}=0.7$ $\lambda_{{\rm{e}}}=0.8$ $\lambda_{{\rm{e}}}=0.9$ 位置/$\mathrm{(m)}~({\rm{CV}})$ 22.12 20.87 19.81 速度/$\mathrm{(m/s)}~({\rm{CV}})$ 2.88 2.81 2.75 位置/$\mathrm{(m)}~({\rm{CA}})$ 24.07 22.59 21.39 速度/$\mathrm{(m/s)}~({\rm{CA}})$ 3.63 3.47 3.35 位置/$\mathrm{(m)}~(\mathrm{CT})$ 16.02 15.21 14.54 速度/$\mathrm{(m/s)}~(\mathrm{CT})$ 1.86 1.83 1.80 位置/$\mathrm{(m)}~(\mathrm{Singer})$ 22.53 21.24 20.17 速度/$\mathrm{(m/s)}~(\mathrm{Singer})$ 2.92 2.81 2.72
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