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fix: 大括号包分式改 \left\right、D_ell^pos 与 H_ell 矩阵条目改 \frac

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eq:H_dnudp 的 \Big[…\frac…\Big] → \left[…\right]；eq:H_dadp 行向量斜杠→\frac 且 \big[→\left[；eq:H4_Hl 的 bmatrix 条目斜杠→\frac。A 规则14 注脚更正：仅行内紧排矩阵条目用斜杠，行间矩阵照常 \frac。
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josh
2026-06-22 14:16:55 +08:00
parent 7b6497e2b4
commit b84214b7a4
2 changed files with 8 additions and 8 deletions
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parts/G-userPositionCrb.tex
+7 -7
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@@ -31,8 +31,8 @@ Doppler 部分，由 $\nu_\ell=\nu_{\mathrm{ref}}+\Delta\nu_\ell(\mathbf p)$ 与
\frac{\partial\nu_\ell}{\partial\mathbf p}
=\frac{\partial\Delta\nu_\ell}{\partial\mathbf p}
=\frac{2\pi T_{\mathrm s}}{\lambda_{\mathrm c}}
\Big[\mathbf v_\ell^\Tran\frac{\partial\mathbf u_\ell}{\partial\mathbf p}
-\mathbf v_{\ell_{\mathrm{ref}}}^\Tran\frac{\partial\mathbf u_{\ell_{\mathrm{ref}}}}{\partial\mathbf p}\Big]\in\mathbb R^{1\times3},
\left[\mathbf v_\ell^\Tran\frac{\partial\mathbf u_\ell}{\partial\mathbf p}
-\mathbf v_{\ell_{\mathrm{ref}}}^\Tran\frac{\partial\mathbf u_{\ell_{\mathrm{ref}}}}{\partial\mathbf p}\right]\in\mathbb R^{1\times3},
\qquad
\frac{\partial\nu_\ell}{\partial\nu_{\mathrm{ref}}}=1,
\label{eq:H_dnudp}
@@ -46,9 +46,9 @@ Doppler 部分，由 $\nu_\ell=\nu_{\mathrm{ref}}+\Delta\nu_\ell(\mathbf p)$ 与
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\begin{equation}
\mathbf D_\ell^{\mathrm{pos}}
=\big[\,
\partial\mathbf g_\ell/\partial p_x,\ \partial\mathbf g_\ell/\partial p_y,\ \partial\mathbf g_\ell/\partial p_z,\ \partial\mathbf g_\ell/\partial\nu_{\mathrm{ref}}
\,\big]\in\mathbb C^{M_\ell T\times4},
=\left[\,
\frac{\partial\mathbf g_\ell}{\partial p_x},\ \frac{\partial\mathbf g_\ell}{\partial p_y},\ \frac{\partial\mathbf g_\ell}{\partial p_z},\ \frac{\partial\mathbf g_\ell}{\partial\nu_{\mathrm{ref}}}
\,\right]\in\mathbb C^{M_\ell T\times4},
\end{equation}
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其中位置列 $\dfrac{\partial\mathbf g_\ell}{\partial p_i}=\mathbf q_\ell\otimes\left(\dfrac{\partial\mathbf a_\ell}{\partial p_i}\right)+\left(\dfrac{\partial\mathbf q_\ell}{\partial p_i}\right)\otimes\mathbf a_\ell$、Doppler 列 $\dfrac{\partial\mathbf g_\ell}{\partial\nu_{\mathrm{ref}}}=\left(\dfrac{\partial\mathbf q_\ell}{\partial\nu_\ell}\right)\otimes\mathbf a_\ell$，$\dfrac{\partial\mathbf a_\ell}{\partial p_i}$ 取 \eqref{eq:H_dadp} 的第 $i$ 列。消去复增益后的 \gls{efim} 与 \eqref{eq:A6_Ieff_final} 同形：
@@ -95,8 +95,8 @@ Doppler 部分，由 $\nu_\ell=\nu_{\mathrm{ref}}+\Delta\nu_\ell(\mathbf p)$ 与
\mathbf H_\ell
=\frac{\partial\boldsymbol\xi_\ell^{\mathrm{loc}}}{\partial\mathbf p}
=\begin{bmatrix}
\partial\alpha_\ell^{\mathrm{loc}}/\partial\mathbf p\\
\partial\beta_\ell^{\mathrm{loc}}/\partial\mathbf p
\frac{\partial\alpha_\ell^{\mathrm{loc}}}{\partial\mathbf p}\\
\frac{\partial\beta_\ell^{\mathrm{loc}}}{\partial\mathbf p}
\end{bmatrix}\in\mathbb R^{2\times3},
\end{equation}
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