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\begin{document}
\begin{equation*}
\begin{aligned}
  P(k+1) &= A^T P(k) A^T + R_v - A P(k)C^T(R_w + C P C^T)^{-1} C P^T(k) A^T \\
  P(0) &= P_0 \\
  L &= A^T P(k) C^T (R_w + C P C^T)^{-1}
\end{aligned}
\end{equation*}
\end{document}