josh
60dabc6334
承 A.2-5(B5):把 sec4 的 G_ℓ 投影联合 ML(O(K^3))改写为对 延时-Doppler 网格字典的行稀疏(MMV)恢复 Y_ℓ^T=Q_ℓX_ℓ+N, 活跃用户=非零行、行值=空间信道 ĥ、行网格点=(τ̂,ν̂),与 sec4 充分统计量口径一致。附录 I 三节:I.1 字典化测量模型 (网格+行稀疏+离格细化)、I.2 AMP 不动点(线性+Onsager+行 去噪/软阈值)、I.3 SBL 不动点(后验+证据最大化超参更新); 末注 state-evolution 挂界+互相干条件为后续(B5 c)。sec4 加 "低复杂度路径"过渡小节指向附录 I。口径=网格粗+细化(Josh 定)。paper-agnostic:只述经典 AMP/SBL 方法,不提 AI/展开/ 学参数(留 §2B 给 AI 仓)。主文件 input 接入附录 I。
205 lines
7.6 KiB
TeX
205 lines
7.6 KiB
TeX
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\newacronym{mcrb}{MCRB}{Misspecified Cramér–Rao Bound}
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\newacronym{kl}{KL}{Kullback–Leibler}
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\newacronym{mse}{MSE}{Mean Square Error}
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\newacronym{music}{MUSIC}{MUtiple SIgnal Classification}
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\newacronym{pdf}{PDF}{Probability Density Function}
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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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\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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\renewcommand*{\bibfont}{\footnotesize}
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\printbibliography
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\end{document}
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