Format an algorithm without using algorithm environment

• To get multi-level indentation, I would suggest to use the enumitem package: Define a new type of list (say level) that has no item symbol, and thus only provides an indentation that can be nested.
• To get user-defined references, you need to define a counter (say algo) and call \refstepcounter at the point where you want your reference to point to.

I combined these two things (together with horizontal lines) in a definition of a new environment àlgorithm:

\documentclass{article}
\usepackage{hyperref}
\usepackage{enumitem}

\newlist{level}{itemize}{4}
\setlist[level]{label={},noitemsep,topsep=0pt}
\newcounter{algo}
\renewcommand{\thealgo}{\arabic{algo}.}
\newenvironment{algorithm}[1]{%
    \refstepcounter{algo}%
    \paragraph{Algorithm \thealgo}#1%
    \vspace{2pt}\hrule\vspace{5pt}%
    \begin{level}
}{%
    \end{level}%
    \vspace{5pt}\hrule\vspace{\baselineskip}%
}

\begin{document}

We summarize the PF-EKF in Algorithm~\ref{algo:ekf}

\begin{algorithm}{Particle filter with EKF proposal}\label{algo:ekf}
    \item \textbf{Initialize:}
    \item Draw the particles by using $\{x_0^f\}_{i=1}^M\!\sim\!p(x_0)$
    \item \textbf{for} k=1 to N \textbf{do}
    \begin{level}
        \item \textbf{Prediction Step:}
        \item Draw the particles by using the Equation 52
        \item \textbf{Measurement Step:}
        \item Update the weight by using the Equation 56
        \item \textbf{Resample Step}
    \end{level}
    \item end for
\end{algorithm}

\end{document}