fix(symbol): F 废弃 a_{l,x} 下标导数简记

a_{l,x} ≜ ∂a_l(ξ)/∂x 的下标逗号当求导,违背 A 规则14
(一阶导数用分子布局 Jacobian ∂f/∂x^T、点号只表时间速率):
下标逗号既像"第 x 个分量"又像求导、且是逐标量而非 Jacobian,
正是规则14 要淘汰的写法。E/H 早已按规则14 重排,F 的 CP/IP
两处遗留此简记,现补齐一致。

删去 CP/IP 两处 a_{l,x} 定义式(无 label、下游无 eqref),保留
"对角度参数 x∈{α,β}"引子(后文 ∂ν_l/∂x 仍需通用 x);均值
Kronecker 导数 d_{l,p,α/β} 内的 a_{l,α}/a_{l,β} 直接写成显示式
∂a_l/∂α、∂a_l/∂β。
This commit is contained in:
2026-07-01 12:25:35 +08:00
parent 4f9f1b8847
commit 70c931b1fd
+6 -22
View File
@@ -78,15 +78,7 @@
\in\mathbb C^{M_\ell T\times 1}. \in\mathbb C^{M_\ell T\times 1}.
\end{equation} \end{equation}
对角度参数 $x\in\{\alpha,\beta\}$,记导向矢量导数为 对角度参数 $x\in\{\alpha,\beta\}$,由链式法则可得时间模板导数
%
\begin{equation}
\mathbf a_{\ell,x}
\triangleq
\frac{\partial \mathbf a_\ell(\boldsymbol\xi)}{\partial x}.
\end{equation}
%
由链式法则可得时间模板导数
% %
\begin{equation} \begin{equation}
\frac{\partial \mathbf q^{\mathrm{cp}}_{\ell,p}}{\partial x} \frac{\partial \mathbf q^{\mathrm{cp}}_{\ell,p}}{\partial x}
@@ -127,7 +119,7 @@
\triangleq \triangleq
\frac{\partial \mathbf g^{\mathrm{cp}}_{\ell,p}}{\partial \alpha} \frac{\partial \mathbf g^{\mathrm{cp}}_{\ell,p}}{\partial \alpha}
= =
\mathbf q^{\mathrm{cp}}_{\ell,p}\otimes \mathbf a_{\ell,\alpha} \mathbf q^{\mathrm{cp}}_{\ell,p}\otimes \frac{\partial\mathbf a_\ell}{\partial\alpha}
+ +
\frac{\partial \mathbf q^{\mathrm{cp}}_{\ell,p}}{\partial \alpha}\otimes \mathbf a_\ell, \frac{\partial \mathbf q^{\mathrm{cp}}_{\ell,p}}{\partial \alpha}\otimes \mathbf a_\ell,
\end{equation} \end{equation}
@@ -136,7 +128,7 @@
\triangleq \triangleq
\frac{\partial \mathbf g^{\mathrm{cp}}_{\ell,p}}{\partial \beta} \frac{\partial \mathbf g^{\mathrm{cp}}_{\ell,p}}{\partial \beta}
= =
\mathbf q^{\mathrm{cp}}_{\ell,p}\otimes \mathbf a_{\ell,\beta} \mathbf q^{\mathrm{cp}}_{\ell,p}\otimes \frac{\partial\mathbf a_\ell}{\partial\beta}
+ +
\frac{\partial \mathbf q^{\mathrm{cp}}_{\ell,p}}{\partial \beta}\otimes \mathbf a_\ell, \frac{\partial \mathbf q^{\mathrm{cp}}_{\ell,p}}{\partial \beta}\otimes \mathbf a_\ell,
\end{equation} \end{equation}
@@ -1170,15 +1162,7 @@ $\mathcal T_{\mathrm{sub}}=\{\tau_{p_1},\ldots,\tau_{p_Q}\}$,则
% %
这里的 $\vartheta_{\ell,p}$ 是第 $(\ell,p)$ 个观测块的独立未知初始相位;与\gls{cp} 模型相比,跨帧绝对相位连续性已经被这些块级相位参数吸收。 这里的 $\vartheta_{\ell,p}$ 是第 $(\ell,p)$ 个观测块的独立未知初始相位;与\gls{cp} 模型相比,跨帧绝对相位连续性已经被这些块级相位参数吸收。
对角度参数 $x\in\{\alpha,\beta\}$,记 对角度参数 $x\in\{\alpha,\beta\}$,由链式法则可得
%
\begin{equation}
\mathbf a_{\ell,x}
\triangleq
\frac{\partial \mathbf a_\ell(\boldsymbol\xi)}{\partial x}.
\end{equation}
%
由链式法则可得
% %
\begin{equation} \begin{equation}
\frac{\partial \mathbf q^{\mathrm{ip}}_{\ell,p}}{\partial x} \frac{\partial \mathbf q^{\mathrm{ip}}_{\ell,p}}{\partial x}
@@ -1235,7 +1219,7 @@ $\mathcal T_{\mathrm{sub}}=\{\tau_{p_1},\ldots,\tau_{p_Q}\}$,则
\triangleq \triangleq
\frac{\partial \mathbf g^{\mathrm{ip}}_{\ell,p}}{\partial \alpha} \frac{\partial \mathbf g^{\mathrm{ip}}_{\ell,p}}{\partial \alpha}
= =
\mathbf q^{\mathrm{ip}}_{\ell,p}\otimes \mathbf a_{\ell,\alpha} \mathbf q^{\mathrm{ip}}_{\ell,p}\otimes \frac{\partial\mathbf a_\ell}{\partial\alpha}
+ +
\frac{\partial \mathbf q^{\mathrm{ip}}_{\ell,p}}{\partial \alpha}\otimes \mathbf a_\ell, \frac{\partial \mathbf q^{\mathrm{ip}}_{\ell,p}}{\partial \alpha}\otimes \mathbf a_\ell,
\end{equation} \end{equation}
@@ -1244,7 +1228,7 @@ $\mathcal T_{\mathrm{sub}}=\{\tau_{p_1},\ldots,\tau_{p_Q}\}$,则
\triangleq \triangleq
\frac{\partial \mathbf g^{\mathrm{ip}}_{\ell,p}}{\partial \beta} \frac{\partial \mathbf g^{\mathrm{ip}}_{\ell,p}}{\partial \beta}
= =
\mathbf q^{\mathrm{ip}}_{\ell,p}\otimes \mathbf a_{\ell,\beta} \mathbf q^{\mathrm{ip}}_{\ell,p}\otimes \frac{\partial\mathbf a_\ell}{\partial\beta}
+ +
\frac{\partial \mathbf q^{\mathrm{ip}}_{\ell,p}}{\partial \beta}\otimes \mathbf a_\ell, \frac{\partial \mathbf q^{\mathrm{ip}}_{\ell,p}}{\partial \beta}\otimes \mathbf a_\ell,
\end{equation} \end{equation}