josh
cdd0ac9171
preface 5 处、abstract 4 处硬编码"附录 A/B/C/D/E/F/G"，
没有用交叉引用。\thesection 已经把 \ref{sec:xxx} 渲染为
"附录 X"，改用 \ref{} 后：
- 视觉输出不变
- PDF 中变为可点击锚链接
- 后续若调整附录顺序，引用自动跟随
173 lines
6.1 KiB
TeX
173 lines
6.1 KiB
TeX
\documentclass[11pt,a4paper]{article}
|
||
|
||
% packages
|
||
\usepackage{xeCJK}
|
||
\usepackage{geometry} % 用于设置上下左右页边距
|
||
\geometry{
|
||
left=1.9cm,
|
||
right=1.9cm,
|
||
top=2.54cm,
|
||
bottom=2.54cm
|
||
}
|
||
|
||
\usepackage{indentfirst}
|
||
\setlength{\parindent}{2em}
|
||
|
||
\usepackage{amsmath,amssymb,amsfonts,bm}
|
||
\usepackage{array}
|
||
\usepackage{longtable}
|
||
\numberwithin{equation}{section}
|
||
\DeclareMathOperator*{\argmax}{arg\,max}
|
||
\DeclareMathOperator*{\argmin}{arg\,min}
|
||
\DeclareMathOperator*{\diag}{diag}
|
||
\DeclareMathOperator*{\maximize}{maximize}
|
||
\DeclareMathOperator*{\minimize}{minimize}
|
||
\DeclareMathOperator{\tr}{tr}
|
||
\DeclareMathOperator{\vect}{vec}
|
||
\newcommand{\Tran}{\mathsf{T}}
|
||
\newcommand{\Herm}{\mathsf{H}}
|
||
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
|
||
|
||
\usepackage{arydshln}
|
||
|
||
\usepackage[
|
||
hidelinks,
|
||
bookmarksopen = true,
|
||
bookmarksnumbered,
|
||
hypertexnames = false,
|
||
colorlinks = true,
|
||
allcolors = blue
|
||
]{hyperref}
|
||
|
||
\usepackage{bookmark}
|
||
|
||
\usepackage[
|
||
backend=biber,
|
||
style=ieee,
|
||
maxcitenames=1,
|
||
mincitenames=1,
|
||
url=false,
|
||
doi=false,
|
||
isbn=false]{biblatex}
|
||
% \addbibresource{IEEEabrv.bib}
|
||
\addbibresource{ref.bib}
|
||
|
||
\usepackage[inline]{enumitem}
|
||
\setlist[itemize]{leftmargin=*,itemsep=0pt, topsep=0pt, parsep=0pt, partopsep=0pt}
|
||
\setlist[enumerate]{leftmargin=*,itemsep=0pt, topsep=0pt, parsep=0pt, partopsep=0pt}
|
||
|
||
\usepackage[most]{tcolorbox}
|
||
|
||
\newenvironment{mdquote}{
|
||
\begin{tcolorbox}[
|
||
colback=gray!12,
|
||
colframe=gray!40,
|
||
boxrule=0pt,
|
||
left=6pt,
|
||
right=6pt,
|
||
top=6pt,
|
||
bottom=6pt,
|
||
arc=2pt,
|
||
breakable,
|
||
before skip=4pt,
|
||
after skip=4pt
|
||
]
|
||
\setlength{\parindent}{2em}
|
||
}{
|
||
\end{tcolorbox}
|
||
}
|
||
|
||
\usepackage{caption}
|
||
\captionsetup[figure]{font=small}
|
||
|
||
\usepackage{titlesec}
|
||
\titlespacing*{\section}{0pt}{*0}{*0} % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
|
||
\titlespacing*{\subsection}{0pt}{*0}{*0} % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
|
||
\titlespacing*{\subsubsection}{0pt}{*0}{*0} % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
|
||
|
||
\usepackage[acronym]{glossaries}
|
||
\glsdisablehyper%
|
||
\setacronymstyle{short-long}
|
||
\newacronym{cml}{CML}{Conditional Maximum Likelihood，条件最大似然}
|
||
\newacronym{crb}{CRB}{Cramér–Rao Bound，克拉美罗界}
|
||
\newacronym{crlb}{CRLB}{Cramér–Rao Lower Bound，克拉美罗下界}
|
||
\newacronym{cdml}{CDML}{Concentrated Deterministic Maximum Likelihood，集中确定最大似然}
|
||
\newacronym{cpi}{CPI}{Coherent Processing Interval，相干处理间隔}
|
||
\newacronym{csml}{CSML}{Concentrated Stochastic Maximum Likelihood，集中随机最大似然}
|
||
\newacronym{dml}{DML}{Deterministic Maximum Likelihood，确定最大似然}
|
||
\newacronym{doa}{DoA}{Direction-of-Arrival，波达方向}
|
||
\newacronym{ecef}{ECEF}{Earth-centered, Earth-fixed，地心地固}
|
||
\newacronym{eci}{ECI}{Earth-centered Inertial，地心惯性}
|
||
\newacronym{efim}{EFIM}{equivalent Fisher information matrix，有效费舍尔信息矩阵}
|
||
\newacronym{esprit}{ESPRIT}{Estimation of Signal Parameters via Rotational Invariant Techniques，旋转不变信号参数估计法}
|
||
\newacronym{fdoa}{FDOA}{Frequency Difference of Arrival，到达频率差}
|
||
\newacronym{fim}{FIM}{Fisher Information Matrix，费舍尔信息矩阵}
|
||
\newacronym{leo}{LEO}{Low Earth Orbit，低地球轨道}
|
||
\newacronym{mle}{MLE}{Maximum Likelihood Estimation，最大似然估计}
|
||
\newacronym{mse}{MSE}{Mean Square Error，均方误差}
|
||
\newacronym{music}{MUSIC}{MUtiple SIgnal Classification，多重信号分类}
|
||
\newacronym{pdf}{PDF}{Probability Density Function，概率密度函数}
|
||
\newacronym{rmse}{RMSE}{Root-Mean Square Error，均方根误差}
|
||
\newacronym{sml}{SML}{Stochastic Maximum Likelihood，随机最大似然}
|
||
\newacronym{tdoa}{TDOA}{Time Difference of Arrival，到达时间差}
|
||
\newacronym{ula}{ULA}{Uniform Linear Array，均匀线性阵列}
|
||
\newacronym{uml}{UML}{Unconditional Maximum Likelihood，无条件最大似然}
|
||
\newacronym{upa}{UPA}{Uniform Planar Array，均匀平面阵列}
|
||
|
||
\title{DoA 与 Doppler 估计}
|
||
\author{Josh Gao}
|
||
\date{\today}
|
||
|
||
\linespread{1.5}
|
||
\allowdisplaybreaks[4]
|
||
\setlength{\abovedisplayskip}{0pt}
|
||
\setlength{\belowdisplayskip}{0pt}
|
||
|
||
\begin{document}
|
||
|
||
\maketitle
|
||
|
||
\begin{abstract}
|
||
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。
|
||
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。
|
||
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；最后回到第一篇论文的多帧连续相位结构。
|
||
正文仅写到集中似然的最终形式与有效 \gls{fim} 的 Schur complement 表达式，详细矩阵代入与逐步化简均迁移至附录。
|
||
附录按"是否共享推导框架"组织：单阵列三种 \gls{crb} 合并为\ref{sec:singleArrayCrb}，多星静态模型为\ref{sec:A6_multiArrayStatDetDoaDopplerCrb}，时间戳误差 \gls{fim} 分析为\ref{sec:timestampErrCrb}，多帧动态模型的连续/独立相位对比为\ref{sec:multiFrameCrb}。
|
||
\end{abstract}
|
||
|
||
\input{parts/preface.tex}
|
||
\input{parts/sec1_singleArrayDoa.tex}
|
||
\input{parts/sec2_singleArrayDoaDoppler.tex}
|
||
\input{parts/sec3_multiSatSingleUser.tex}
|
||
\input{parts/sec4_multiSatMultiUser.tex}
|
||
\input{parts/sec5_timestampError.tex}
|
||
\input{parts/sec6_multiFrameCp.tex}
|
||
% \input{parts/sec7_beamforming.tex} % 预留，本次不展开
|
||
|
||
\appendix
|
||
\renewcommand{\thesection}{附录~\Alph{section}}
|
||
\renewcommand{\thesubsection}{\Alph{section}.\arabic{subsection}}
|
||
\renewcommand{\thesubsubsection}{\Alph{section}.\arabic{subsection}.\arabic{subsubsection}}
|
||
\renewcommand{\theequation}{\Alph{section}.\arabic{equation}}
|
||
|
||
\newpage
|
||
\input{parts/A-symbolIndex.tex}
|
||
\newpage
|
||
\input{parts/B-mathBackground.tex}
|
||
\newpage
|
||
\input{parts/C-classicalDoa.tex}
|
||
\newpage
|
||
\input{parts/D-singleArrayCrb.tex}
|
||
\newpage
|
||
\input{parts/E-multiSatStaticCrb.tex}
|
||
\newpage
|
||
\input{parts/F-timestampErrCrb.tex}
|
||
\newpage
|
||
\input{parts/G-multiFrameCrb.tex}
|
||
|
||
\newpage
|
||
\renewcommand*{\bibfont}{\footnotesize}
|
||
\printbibliography
|
||
|
||
\end{document}
|