josh
37ec3c0c61
沿"输出参数化"维度把主参数从全局方向 ξ 升到三维位置 p： 正文新增第 7 节，主参数 η_pos=[p, ν_ref]，逐星视线 u_ℓ(p)=Ω_ℓ^T (p-s_ℓ)/‖p-s_ℓ‖ 诱导各星本地角与差分 Doppler， 阵列平面波模型与参考星 Doppler 不变（用户运动/载频仍折叠进 ν_ref），并给出远场退化为全局方向模型的命题、L≥2 可辨识性 与 GDOP 几何各向异性。 附录 H 给出位置 CRB：复用附录 E 的联合堆叠/复增益 Schur 补/ EFIM 投影—Gram，仅重写主参数 Jacobian——∂u_ℓ/∂p= (I-u u^T)/‖r_ℓ‖ 的秩 2 投影显式给出"径向不可观、靠多星视差 补满秩"的结构，远场极限下退化为二维方向 CRB。 方法定位为 DPD，引 wei/li/hao/xv（均已发表）；wei 条目补入 ref.bib。前言与摘要同步补入该节与附录。
176 lines
6.3 KiB
TeX
176 lines
6.3 KiB
TeX
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\usepackage[acronym]{glossaries}
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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{efim}{EFIM}{equivalent Fisher information matrix，有效费舍尔信息矩阵}
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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 Orbit，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；随后回到第一篇论文的多帧连续相位结构，最后以从全局方向到用户三维位置的输出参数化收尾，给出第二篇论文多星定位所需的模型接口。
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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。
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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\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}，用户三维位置 \gls{crb} 为\ref{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_timestampError.tex}
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\input{parts/sec6_multiFrameCp.tex}
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\input{parts/sec7_userPositioning.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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\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/F-timestampErrCrb.tex}
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\newpage
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\input{parts/G-multiFrameCrb.tex}
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\newpage
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\input{parts/H-userPositionCrb.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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