Use empheq to style your equation set, together with subequations to achieve your numbering objective:

\documentclass{article}
\usepackage{empheq,etoolbox}
% Update display of subequation numbering (Xy) > (X.y)
\patchcmd{\subequations}% <cmd>
{\theparentequation\alph{equation}}% <search>
{\theparentequation.\alph{equation}}% <replace>
{}{}% <success><failure>
\begin{document}
\begin{subequations}
\begin{empheq}[left=\empheqlbrace]{align}
x_k &= f_d(x_{k-1},u_{k-1},\theta) + q_{k-1} \\
y_k &= h(x_k,\theta,k) + r_k
\end{empheq}
\end{subequations}
\end{document}
The default numbering within subequations has the form (Xy). The etoolbox patch is applied in the preamble to change this to (X.y) for all subequations.
articleclass?; How to reference equations using letters and numbers – Werner Apr 25 '17 at 18:26