\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} \makeglossaries% \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{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 Orbir,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。 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。 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。 \end{abstract} \input{parts/00-roadmap.tex} \input{parts/02-modeling.tex} \input{parts/detDoaEst.tex} \input{parts/stoDoaEst.tex} \input{parts/detDoaDopplerEst.tex} % \input{parts/stoDoaDopplerEst.tex} \input{parts/multiArrayStoDoaEst.tex} \input{parts/multiArrayStatDetDoaDopplerEst.tex} \input{parts/multiArrayDynDetDoaDopplerEst.tex} \input{parts/multiArrayDetDoaDopplerDelayEst.tex} % \input{parts/98-future work.tex} % \input{parts/99-literature.tex} \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/G-multiFrameCrb.tex} % \newpage % \renewcommand*{\bibfont}{\footnotesize} % \printbibliography\ \end{document}