josh
0e25a23b2d
按 agent_instruction.md 阶段 1 重排附录： - 01-assumptions → A-symbolIndex（迁入附录区，符号索引） - A1 → B（数学基础）、A2 → C（经典 DoA 方法） - A3+A5+A4 合并为 D-singleArrayCrb，子节顺序 D.1 确定 DoA → D.2 确定 DoA-Doppler → D.3 随机 DoA（对照） - A6 → E（多星静态 CRB，暂不扩展多用户） - A7+A8 合并为 G-multiFrameCrb，子节 G.1 CP / G.2 IP 合并依据：D 三者共享 FIM+Schur 推导框架；G 中 CP 与 IP 是对比关系，合并便于量化跨帧相位连续性的信息量。 合并后内部 \subsection 降一级为 \subsubsection，原 \subsubsection 降一级为 \paragraph*；原 \section 行去除，原 \label 保留在新 \subsection 上以维持交叉引用。主文件 \input 列表同步更新。
174 lines
6.0 KiB
TeX
174 lines
6.0 KiB
TeX
\documentclass[11pt,a4paper]{article}
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% packages
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\usepackage{xeCJK}
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\usepackage{geometry} % 用于设置上下左右页边距
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\geometry{
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left=1.9cm,
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right=1.9cm,
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top=2.54cm,
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bottom=2.54cm
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}
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\usepackage{indentfirst}
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\setlength{\parindent}{2em}
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\usepackage{amsmath,amssymb,amsfonts,bm}
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\usepackage{array}
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\usepackage{longtable}
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\numberwithin{equation}{section}
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\DeclareMathOperator*{\argmax}{arg\,max}
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\DeclareMathOperator*{\argmin}{arg\,min}
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\DeclareMathOperator*{\diag}{diag}
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\DeclareMathOperator*{\maximize}{maximize}
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\DeclareMathOperator*{\minimize}{minimize}
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\DeclareMathOperator{\tr}{tr}
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\DeclareMathOperator{\vect}{vec}
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\newcommand{\Tran}{\mathsf{T}}
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\newcommand{\Herm}{\mathsf{H}}
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\newcommand{\diff}{\mathop{}\!\mathrm{d}}
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\usepackage{arydshln}
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\usepackage[
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hidelinks,
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bookmarksopen = true,
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bookmarksnumbered,
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hypertexnames = false,
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colorlinks = true,
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allcolors = blue
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]{hyperref}
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\usepackage{bookmark}
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\usepackage[
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backend=biber,
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style=ieee,
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maxcitenames=1,
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mincitenames=1,
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url=false,
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doi=false,
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isbn=false]{biblatex}
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% \addbibresource{IEEEabrv.bib}
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\addbibresource{ref.bib}
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\usepackage[inline]{enumitem}
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\setlist[itemize]{leftmargin=*,itemsep=0pt, topsep=0pt, parsep=0pt, partopsep=0pt}
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\setlist[enumerate]{leftmargin=*,itemsep=0pt, topsep=0pt, parsep=0pt, partopsep=0pt}
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\usepackage[most]{tcolorbox}
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\newenvironment{mdquote}{
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\begin{tcolorbox}[
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colback=gray!12,
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colframe=gray!40,
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boxrule=0pt,
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left=6pt,
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right=6pt,
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top=6pt,
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bottom=6pt,
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arc=2pt,
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breakable,
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before skip=4pt,
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after skip=4pt
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]
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\setlength{\parindent}{2em}
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}{
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\end{tcolorbox}
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}
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\usepackage{caption}
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\captionsetup[figure]{font=small}
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\usepackage{titlesec}
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\titlespacing*{\section}{0pt}{*0}{*0} % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
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\titlespacing*{\subsection}{0pt}{*0}{*0} % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
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\titlespacing*{\subsubsection}{0pt}{*0}{*0} % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
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\usepackage[acronym]{glossaries}
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\makeglossaries%
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\glsdisablehyper%
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\setacronymstyle{short-long}
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\newacronym{cml}{CML}{Conditional Maximum Likelihood，条件最大似然}
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\newacronym{crb}{CRB}{Cramér–Rao Bound，克拉美罗界}
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\newacronym{crlb}{CRLB}{Cramér–Rao Lower Bound，克拉美罗下界}
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\newacronym{cdml}{CDML}{Concentrated Deterministic Maximum Likelihood，集中确定最大似然}
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\newacronym{cpi}{CPI}{Coherent Processing Interval，相干处理间隔}
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\newacronym{csml}{CSML}{Concentrated Stochastic Maximum Likelihood，集中随机最大似然}
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\newacronym{dml}{DML}{Deterministic Maximum Likelihood，确定最大似然}
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\newacronym{doa}{DoA}{Direction-of-Arrival，波达方向}
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\newacronym{ecef}{ECEF}{Earth-centered, Earth-fixed，地心地固}
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\newacronym{eci}{ECI}{Earth-centered Inertial，地心惯性}
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\newacronym{esprit}{ESPRIT}{Estimation of Signal Parameters via Rotational Invariant Techniques，旋转不变信号参数估计法}
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\newacronym{fdoa}{FDOA}{Frequency Difference of Arrival，到达频率差}
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\newacronym{fim}{FIM}{Fisher Information Matrix，费舍尔信息矩阵}
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\newacronym{leo}{LEO}{Low Earth Orbir，低地球轨道}
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\newacronym{mle}{MLE}{Maximum Likelihood Estimation，最大似然估计}
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\newacronym{mse}{MSE}{Mean Square Error，均方误差}
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\newacronym{music}{MUSIC}{MUtiple SIgnal Classification，多重信号分类}
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\newacronym{pdf}{PDF}{Probability Density Function，概率密度函数}
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\newacronym{rmse}{RMSE}{Root-Mean Square Error，均方根误差}
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\newacronym{sml}{SML}{Stochastic Maximum Likelihood，随机最大似然}
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\newacronym{tdoa}{TDOA}{Time Difference of Arrival，到达时间差}
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\newacronym{ula}{ULA}{Uniform Linear Array，均匀线性阵列}
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\newacronym{uml}{UML}{Unconditional Maximum Likelihood，无条件最大似然}
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\newacronym{upa}{UPA}{Uniform Planar Array，均匀平面阵列}
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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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\setlength{\belowdisplayskip}{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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本文以一份可持续扩展的推导笔记为目标，先在单阵列确定信号与随机信号模型下整理经典 \gls{doa} 估计、DoA--Doppler 联合估计及其 \gls{crb}，再将模型推进到单用户多星协作场景。
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多星主线采用统一的全局方向参数 $\boldsymbol\xi=[\alpha,\beta]^\Tran$ 与参考星链路归一化 Doppler 参数 $\nu_{\mathrm{ref}}$，先建立静态 DoA--Doppler 基线模型，再引入多帧索引、Doppler rate $\dot\nu_{\mathrm{ref}}$ 和跨帧连续相位结构，进一步比较 relaxed 连续相位模型与独立相位基线模型的信息差异。
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在此基础上，本文还给出 DoA--Doppler--delay 扩展和相应附录推导，使单阵列基础、多星主线、对比模型与 \gls{crb} 分析在同一符号体系下衔接。
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\end{abstract}
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\input{parts/00-roadmap.tex}
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\input{parts/02-modeling.tex}
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\input{parts/detDoaEst.tex}
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\input{parts/stoDoaEst.tex}
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\input{parts/detDoaDopplerEst.tex}
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% \input{parts/stoDoaDopplerEst.tex}
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\input{parts/multiArrayStoDoaEst.tex}
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\input{parts/multiArrayStatDetDoaDopplerEst.tex}
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\input{parts/multiArrayDynDetDoaDopplerEst.tex}
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\input{parts/multiArrayDetDoaDopplerDelayEst.tex}
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% \input{parts/98-future work.tex}
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% \input{parts/99-literature.tex}
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\appendix
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\renewcommand{\thesection}{附录~\Alph{section}}
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\renewcommand{\thesubsection}{\Alph{section}.\arabic{subsection}}
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\renewcommand{\thesubsubsection}{\Alph{section}.\arabic{subsection}.\arabic{subsubsection}}
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\renewcommand{\theequation}{\Alph{section}.\arabic{equation}}
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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/G-multiFrameCrb.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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