josh
73fcd77cce
补界谱系门限档(计划 §7.3 阈值/§7.4 ZZB):新附录 J。 J.1 误指定 Barankin:检验点 + 似然比 Gram 捕获大误差,远 模糊检验点(错延时-Doppler 格/几何近简并)使界跳起=阈值; 误指定化承 F5(数据含真 δ、似然比用假设同步、参考=伪真 值)。J.2 ZZB(Bellini-Tartara+填谷):P_min=Q(½√D²)、D²= 去相关度跨星可加;高 SNR 退 CRB,模糊方向 P_min→½ 留地板。 ★少用户基本极限:最危模糊=位置-时间戳同轴(承 F6),D² 对 用户求和、共享 δ 须解释全用户 → K≤3 欠定、地板不随 SNR 降(几何/可辨识基本极限,非估计器);多用户超定抬 D²。 sec7 加指针;主文件 input 接入。paper-agnostic(不提 失效边界/route/figure 等 paper 框架)。
207 lines
7.7 KiB
TeX
207 lines
7.7 KiB
TeX
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\newacronym{mcrb}{MCRB}{Misspecified Cramér–Rao Bound}
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\newacronym{mml}{MML}{Misspecified Maximum Likelihood}
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\newacronym{kl}{KL}{Kullback–Leibler}
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\newacronym{mse}{MSE}{Mean Square Error}
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\newacronym{rmse}{RMSE}{Root-Mean Square Error}
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\title{DoA 与 Doppler 估计}
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\author{Josh Gao}
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\date{\today}
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\linespread{1.5}
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\allowdisplaybreaks[4]
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\setlength{\abovedisplayskip}{0pt}
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\begin{document}
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\maketitle
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\begin{abstract}
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使用通信信号估计来波方向与 Doppler 参数，是通信感知一体化和低轨卫星协作感知中的基础问题。
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本文以学习笔记的方式记录这一问题的递进路径：每节只沿一个维度推进模型，其余维度保持最简形态。
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正文从多快拍单阵列确定信号 \gls{doa} 估计出发，依次引入 Doppler、多星几何，并以多用户与星间时间戳误差两节给出后续方向所需的模型接口与初步分析；随后转入多帧连续相位结构，最后以从全局方向到用户三维位置的输出参数化收尾，为多星协作定位等拓展方向提供模型接口。
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正文仅写到集中似然的最终形式与 \gls{efim} 的 Schur complement 表达式，详细矩阵代入与逐步化简见附录。
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附录按``是否共享推导框架''组织：单阵列三种 \gls{crb} 合并为\appref{sec:singleArrayCrb}，多星静态模型为\appref{sec:A6_multiArrayStatDetDoaDopplerCrb}，时间戳误差 \gls{fim} 分析为\appref{sec:timestampErrCrb}，多帧动态模型的连续/独立相位对比为\appref{sec:multiFrameCrb}，用户三维位置 \gls{crb} 为\appref{sec:userPositionCrb}。
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\end{abstract}
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\input{parts/preface.tex}
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\input{parts/sec1_singleArrayDoa.tex}
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\input{parts/sec2_singleArrayDoaDoppler.tex}
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\input{parts/sec3_multiSatSingleUser.tex}
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\input{parts/sec4_multiSatMultiUser.tex}
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\input{parts/sec5_multiFrameCp.tex}
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\input{parts/sec6_userPositioning.tex}
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\input{parts/sec7_timestampError.tex}
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% \input{parts/sec8_beamforming.tex} % 预留，本次不展开
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\appendix
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\newpage
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\input{parts/A-symbolIndex.tex}
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\newpage
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\input{parts/B-mathBackground.tex}
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\newpage
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\input{parts/C-classicalDoa.tex}
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\newpage
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\input{parts/D-singleArrayCrb.tex}
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\newpage
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\input{parts/E-multiSatStaticCrb.tex}
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\newpage
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\input{parts/F-multiFrameCrb.tex}
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\newpage
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\input{parts/G-userPositionCrb.tex}
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\newpage
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\input{parts/H-timestampErrCrb.tex}
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\newpage
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\input{parts/I-dictSeparationAmp.tex}
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\newpage
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\input{parts/J-thresholdBounds.tex}
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\newpage
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\renewcommand*{\bibfont}{\footnotesize}
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\printbibliography
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\end{document}
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