开栏卷首——目标跟踪

先试试segmentfault好不好用哈哈哈哈
后期慢慢改

我来试试公式 看看md的渲染咋样

高斯乘积定理: $\quad$ 给定 $\mathbf{x}_{1}, \mathbf{\mu}_{1} \in \mathbb{R}^{d_{1}}, \mathbf{H} \in \mathbb{R}^{d_{2} \times d_{1}}, \mathbf{x}_{2} \in \mathbb{R}^{d_{2}}$ 和正定矩阵$\mathbf{P}_{1}, \mathbf{P}_{2}$

$$ N\left(\mathbf{x}_{2} ; \mathbf{H} \mathbf{x}_{1}, \mathbf{P}_{2}\right) N\left(\mathbf{x}_{1} ; \mathbf{\mu}_{1}, \mathbf{P}_{1}\right)=N\left(\mathbf{x}_{2} ; \mathbf{H} \mathbf{\mu}_{1}, \mathbf{P}_{3}\right) N\left(\mathbf{x}_{1} ; \mathbf{\mu}, \mathbf{P}\right) $$

其中

$$ \begin{array}{c} \mathbf{P}_{3}=\mathbf{H} \mathbf{P}_{1} \mathbf{H}^{\mathrm{T}}+\mathbf{P}_{2} \\ \mathbf{\mu}=\mathbf{\mu}_{1}+\mathbf{K}\left(\mathbf{x}_{2}-\mathbf{H} \mathbf{\mu}_{1}\right) \\ \mathbf{P}=\mathbf{P}_{1}+\mathbf{K} \mathbf{H} \mathbf{P}_{1} \\ \mathbf{K}=\mathbf{P}_{1} \mathbf{H}^{\mathrm{T}} \mathbf{P}_{3}^{-1} \end{array} $$

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