content(symbol): 正文缩写裸短形式统一为 \gls
正文已定义缩写（EFIM/CRB/FIM/MUSIC/ESPRIT/MLE/ULA/UPA）的裸短形式共
128 处改用 \gls{key}。排除：section 标题、数学模式记号与下标（如
\mathrm{CDML}、\mathrm{UPA}）、\caption 题注、"全称（缩写）"并列释义，
以及 \ref/\eqref/\label/\cite 标签键（键内 _EFIM 等会被误伤）。
diff 为 1:1 替换，两遍编译无 undefined references。
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\section{常用 DoA 估计方法}
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\label{sec:doa_methods}
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本附录汇总 MVDR、MUSIC、ESPRIT 及其空时扩展形式，主要用于补充算法背景；综合性的子空间方法回顾可参见~\cite{krimTwoDecadesArray1996,vantreesOptimumArrayProcessing2002}。这里的算法记号服务于经典单阵列或空时阵列模型，不改变正文多星主线中 $\boldsymbol\xi$、$\nu_{\mathrm{ref}}$ 和 $\dot\nu_{\mathrm{ref}}$ 的参数分组。
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本附录汇总 MVDR、\gls{music}、\gls{esprit} 及其空时扩展形式，主要用于补充算法背景；综合性的子空间方法回顾可参见~\cite{krimTwoDecadesArray1996,vantreesOptimumArrayProcessing2002}。这里的算法记号服务于经典单阵列或空时阵列模型，不改变正文多星主线中 $\boldsymbol\xi$、$\nu_{\mathrm{ref}}$ 和 $\dot\nu_{\mathrm{ref}}$ 的参数分组。
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本附录的空间导向矢量已与正文统一采用 $e^{-j(\cdot)}$ 相位约定；但空时方法中的时间导向矢量 $\mathbf q_k(\nu_k)$ 取无导频加权的纯 Fourier 形式 $[1,e^{j\nu_k},\ldots,e^{j(T-1)\nu_k}]^\Tran$（经典子空间法不假设已知导频），与正文第~\ref{sec:det_doa_doppler_est} 节含已知导频 $s_k(t)$ 的同名 $\mathbf q_k$ 含义不同，仅在本附录局部使用。
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\subsection{MVDR Algorithm\texorpdfstring{~\cite{caponHighResolutionFrequencyWavenumberSpectrum1969}}{}}
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@@ -239,7 +239,7 @@ Under ideal conditions, the steering vectors associated with the true source dir
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\label{eq:music_orthogonality}
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\end{equation}
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%
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Based on this orthogonality property, the MUSIC pseudospectrum is constructed as
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Based on this orthogonality property, the \gls{music} pseudospectrum is constructed as
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%
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\begin{equation}
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P_{\mathrm{MUSIC}}(\theta)
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@@ -262,7 +262,7 @@ P_{\mathrm{MUSIC}}(\theta),
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\label{eq:music_estimation}
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\end{equation}
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The MUSIC algorithm achieves high-resolution \gls{doa} estimation by exploiting the orthogonality between the array steering vectors and the noise subspace, and has been widely used in subspace-based array signal processing.
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The \gls{music} algorithm achieves high-resolution \gls{doa} estimation by exploiting the orthogonality between the array steering vectors and the noise subspace, and has been widely used in subspace-based array signal processing.
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\subsection{ESPRIT Algorithm\texorpdfstring{~\cite{royESPRITEstimationSignalParameters1989}}{}}
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@@ -308,7 +308,7 @@ where
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%
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with $d$ denoting the inter-element spacing and $\lambda_{\mathrm{c}}$ the carrier wavelength.
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The ESPRIT algorithm exploits the translational invariance structure of the array. To this end, two maximally overlapped subarrays are constructed from the original ULA. Define the selection matrices
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The \gls{esprit} algorithm exploits the translational invariance structure of the array. To this end, two maximally overlapped subarrays are constructed from the original \gls{ula}. Define the selection matrices
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%
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\begin{equation}
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\mathbf{J}_1
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@@ -336,7 +336,7 @@ Then the corresponding subarray manifold matrices are
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\label{eq:esprit_subarray_manifolds}
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\end{equation}
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%
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Due to the shift invariance of the ULA, $\mathbf{A}_1$ and $\mathbf{A}_2$ satisfy
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Due to the shift invariance of the \gls{ula}, $\mathbf{A}_1$ and $\mathbf{A}_2$ satisfy
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%
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\begin{equation}
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\mathbf{A}_2
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@@ -465,7 +465,7 @@ where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the
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\label{eq:esprit_theta_estimate}
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\end{equation}
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Compared with MUSIC, the ESPRIT algorithm avoids explicit spectral search and directly retrieves the \gls{doa} parameters from the rotational invariance structure of the signal subspace, thereby offering lower computational complexity while maintaining high estimation accuracy.
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Compared with \gls{music}, the \gls{esprit} algorithm avoids explicit spectral search and directly retrieves the \gls{doa} parameters from the rotational invariance structure of the signal subspace, thereby offering lower computational complexity while maintaining high estimation accuracy.
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\subsection{Spatio-Temporal MUSIC Algorithm\texorpdfstring{~\cite{waxSpatioTemporalSpectralAnalysis1984}}{}}
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@@ -602,7 +602,7 @@ where $\mathbf{U}_s \in \mathbb{C}^{MT \times K}$ and $\mathbf{U}_n \in \mathbb{
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\label{eq:orthogonality_condition}
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\end{equation}
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%
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Based on this orthogonality property, the spatio-temporal MUSIC pseudospectrum is constructed as
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Based on this orthogonality property, the spatio-temporal \gls{music} pseudospectrum is constructed as
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%
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\begin{equation}
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P_{\mathrm{ST\text{-}MUSIC}}(\theta,\nu)
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@@ -625,7 +625,7 @@ P_{\mathrm{ST\text{-}MUSIC}}(\theta,\nu),
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\label{eq:st_music_estimation}
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\end{equation}
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Compared with conventional MUSIC, the spatio-temporal MUSIC algorithm exploits both the spatial array manifold and the temporal Doppler structure, thereby enabling joint angle-Doppler estimation in a unified subspace framework.
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Compared with conventional \gls{music}, the spatio-temporal \gls{music} algorithm exploits both the spatial array manifold and the temporal Doppler structure, thereby enabling joint angle-Doppler estimation in a unified subspace framework.
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\subsection{Spatio-Temporal ESPRIT Algorithm\texorpdfstring{~\cite{royESPRITEstimationSignalParameters1989,waxSpatioTemporalSpectralAnalysis1984}}{}}
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@@ -753,7 +753,7 @@ where $\mathbf{U}_s\in\mathbb{C}^{MT\times K}$ denotes the estimated signal subs
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\label{eq:st_esprit_subspace_relation}
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\end{equation}
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The spatio-temporal ESPRIT algorithm exploits the shift invariance structure in both the spatial and temporal dimensions. First, define the spatial selection matrices
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The spatio-temporal \gls{esprit} algorithm exploits the shift invariance structure in both the spatial and temporal dimensions. First, define the spatial selection matrices
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%
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\begin{equation}
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\mathbf{J}_{s,1}
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@@ -966,6 +966,6 @@ where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the
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\label{eq:st_esprit_theta_fd_estimation}
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\end{equation}
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Compared with spatio-temporal MUSIC, the spatio-temporal ESPRIT algorithm avoids two-dimensional spectral search and directly retrieves the \gls{doa} and Doppler parameters from the rotational invariance structure of the spatio-temporal signal subspace, thereby achieving lower computational complexity.
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Compared with spatio-temporal \gls{music}, the spatio-temporal \gls{esprit} algorithm avoids two-dimensional spectral search and directly retrieves the \gls{doa} and Doppler parameters from the rotational invariance structure of the spatio-temporal signal subspace, thereby achieving lower computational complexity.
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这些经典方法提供了谱搜索和子空间估计的算法背景，但本文多星主线的重点仍是似然建模、参考星参数化和 Fisher 信息分析。因此，附录中的方法可作为实现参考，而不是当前符号体系的定义来源。
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