content(symbol): 正文 DoA 统一用 \gls{doa}
正文(含附录、符号索引)散文中 108 处裸 "DoA" 改用 \gls{doa},与既有
\gls{crb}/\gls{fim}/\gls{efim} 用法一致。section/subsection 标题、\title、
\newacronym 短形式保留裸 "DoA"——\gls 进标题需 \texorpdfstring 且有首次
展开落入标题之虞。因无 \printglossary 且 \glsdisablehyper,渲染输出不变,
仅源码统一;\gls{doa} 首次展开仍在摘要。
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@@ -103,7 +103,7 @@ In practical implementation, the sample covariance matrix is used, leading to
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}.
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\label{eq:mvdr_sample_spectrum}
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\end{equation}
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The DoA estimates are then obtained by locating the $K$ dominant peaks of the MVDR spatial spectrum, namely,
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The \gls{doa} estimates are then obtained by locating the $K$ dominant peaks of the MVDR spatial spectrum, namely,
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\begin{equation}
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\hat{\theta}_k
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=
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@@ -216,7 +216,7 @@ P_{\mathrm{MUSIC}}(\theta)
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\mathbf{a}(\theta)}.
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\label{eq:music_spectrum}
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\end{equation}
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The DoA estimates are then obtained by locating the $K$ dominant peaks of the pseudospectrum, i.e.,
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The \gls{doa} estimates are then obtained by locating the $K$ dominant peaks of the pseudospectrum, i.e.,
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\begin{equation}
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\hat{\theta}_k
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=
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@@ -226,7 +226,7 @@ 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 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 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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@@ -385,7 +385,7 @@ Let $\hat{\kappa}_k$ denote the $k$th eigenvalue of $\widehat{\bm{\Psi}}$. Then
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\qquad k = 1,\dots,K,
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\label{eq:esprit_mu_estimate}
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\end{equation}
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where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the DoA estimate is obtained from
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where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the \gls{doa} estimate is obtained from
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\begin{equation}
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\hat{\theta}_k
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=
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@@ -396,7 +396,7 @@ 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 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 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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\subsection{Spatio-Temporal MUSIC Algorithm\texorpdfstring{~\cite{waxSpatioTemporalSpectralAnalysis1984}}{}}
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@@ -415,7 +415,7 @@ Consider a narrowband far-field source model observed by an $M$-element array ov
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\qquad \ell = 1,\dots,L,
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\label{eq:st_music_block_model}
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\end{equation}
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where $\zeta_{k,\ell} \in \mathbb{C}$ is the complex gain of the $k$th source in the $\ell$th block, $\mathbf{a}(\theta_k) \in \mathbb{C}^{M \times 1}$ is the spatial steering vector associated with the direction of arrival (DoA) $\theta_k$, $\mathbf q_k(\nu_k) \in \mathbb{C}^{T \times 1}$ is the temporal steering vector associated with the normalized angular Doppler $\nu_k$, and $\mathbf{N}_{\ell}$ is the additive noise matrix. For a uniform linear array (ULA), the spatial steering vector is given by
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where $\zeta_{k,\ell} \in \mathbb{C}$ is the complex gain of the $k$th source in the $\ell$th block, $\mathbf{a}(\theta_k) \in \mathbb{C}^{M \times 1}$ is the spatial steering vector associated with the direction of arrival (\gls{doa}) $\theta_k$, $\mathbf q_k(\nu_k) \in \mathbb{C}^{T \times 1}$ is the temporal steering vector associated with the normalized angular Doppler $\nu_k$, and $\mathbf{N}_{\ell}$ is the additive noise matrix. For a uniform linear array (ULA), the spatial steering vector is given by
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\begin{equation}
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\mathbf{a}(\theta_k)
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=
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@@ -523,7 +523,7 @@ P_{\mathrm{ST\text{-}MUSIC}}(\theta,\nu)
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\mathbf b_{\mathrm{st}}(\theta,\nu)}.
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\label{eq:st_music_spectrum}
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\end{equation}
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The joint estimates of DoA and Doppler are then obtained by searching for the $K$ dominant peaks of \eqref{eq:st_music_spectrum}, namely,
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The joint estimates of \gls{doa} and Doppler are then obtained by searching for the $K$ dominant peaks of \eqref{eq:st_music_spectrum}, namely,
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\begin{equation}
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(\hat{\theta}_k,\hat{\nu}_k)
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=
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@@ -812,7 +812,7 @@ where $(\cdot)^{\dagger}$ denotes the Moore--Penrose pseudoinverse. Let $\hat{\k
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\qquad k=1,\dots,K,
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\label{eq:st_esprit_mu_nu_estimation}
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\end{equation}
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where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the DoA estimate and, if needed, the corresponding physical Doppler conversion are given by
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where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the \gls{doa} estimate and, if needed, the corresponding physical Doppler conversion are given by
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\begin{equation}
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\hat{\theta}_k
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=
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@@ -827,6 +827,6 @@ 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 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 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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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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