Nummerierung der Schritte eines Algorithmus

Nummerierung der Schritte eines Algorithmus

Angenommen, ich muss in einem Algorithmus innerhalb eines nummerierten Schritts Schritte hinzufügen und möchte, dass diese automatisch durch Buchstaben des Alphabets markiert werden.

Ich versuche es \begin{description} \end{description}, aber an einem bestimmten Punkt muss ich meinen Algorithmus aufteilen (langer Algorithmus), und die Verwendung einer Beschreibungsumgebung verursacht Probleme, wenn ich den Algorithmus aufteilen möchte. Kann mir jemand helfen?

\documentclass[a4paper,english,12pt,oneside]{book}
%\documentclass[11pt,draft]{article}
%\usepackage{fullpage}
%\usepackage[top=1in, bottom=1in, left=1in, %right=1in]{geometry}
%\usepackage[margin=1in, paperwidth=8.5in, paperheight=11in]{geometry}
\usepackage[left=2cm, right=2cm, top=2.5cm, bottom=2.5cm]{geometry}
%\usepackage[left=20mm]{geometry}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{graphicx}
\usepackage{refstyle}
\usepackage{subcaption}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{enumerate}
\usepackage{epstopdf}
\usepackage{breqn}
\usepackage{mathtools}
%--------------------------------------------------------------------------------------------------
%\usepackage{a4wide}
\usepackage{amsfonts}
\usepackage{amstext}
\usepackage{amsthm}
\usepackage{newlfont}
\usepackage{graphics}
\usepackage{tabularx}
\usepackage{geometry}
\usepackage{lscape}
\usepackage{multirow}
\usepackage{epsfig}
%----------------------------------------------------------------------------------------------------
\usepackage{algorithm}
\usepackage{algcompatible}
\usepackage{algorithmicx}
\usepackage{algpseudocode}
\usepackage{pifont}
%\usepackage[lite]{mtpro2}
%----------------------------------------------------------------------------------------------------
%------------------------------------------------------------------------------------------------------------------------------
\usepackage{color}
\definecolor{violet}{rgb}{0.7,0.2,0.8}
\definecolor{bluevert}{rgb}{0,0.9,1}
\definecolor{trustcolor}{rgb}{0.71,0.14,0.07}
\definecolor{PinkTriton}{rgb}{.708 ,.055 ,.275}
\definecolor{RedTriton}{rgb}{.491 ,.097 ,.066} % couleur rouge du triton
\definecolor{OrangeTriton}{rgb}{.953 ,.502 ,.04}
%------------------------------------------------------------------------------------------------------------------------------
\usepackage[colorlinks=true,linkcolor=blue, citecolor=blue]{hyperref}

% define new commandes-------------------------------------------------------------------
\def\blank{\medskip\hrule\medskip}

%-----------------------------------------------------------------------------------------
\begin{document}
%\algstore{myalg}
 %   \end{algorithmic}
 %   \end{algorithm}
 %   \begin{algorithm}                     
 %   \begin{algorithmic} [1]              
 %   \algrestore{myalg}
%-------------------------------------------------------------------------------------------------------
\begin{algorithm}
\caption{Square Root Cubature Kalman Filter SRCKF}

 \textbf{Time update}

\begin{algorithmic}[1]
  \State Factorize the state error covariance matrix 
    \begin{equation}
    P_{k-1|k-1} = S_{k-1|k-1}S_{k-1|k-1}^T
    \label{eq:Ref_3}
    \end{equation}  
  \State Evaluate the cubature points (i=1,2,...,$m = 2n_x$)
    \begin{equation}
    X_{i,k-1|k-1} = \hat{x}_{k-1|k-1} + S_{i,k-1|k-1}\zeta_i
    \label{eq:Ref_3}
    \end{equation}
  \State Evaluate the propagated cubature points through the process equation (i=1,2,...,$m = 2n_x$)
    \begin{equation}
    X_{i,k|k-1}^*=f(X_{i,k-1|k-1},u_{k-1})
    \label{eq:Ref_3}
    \end{equation} 
  \State Estimate the predicted state
    \begin{equation}
    \hat{x}_{k|k-1} = \frac{1}{m}\sum_{i=1}^m{X_{i,k|k-1}^*}Y
    \label{eq:Ref_3}
    \end{equation}
  \State Estimate the predicted error covariance
    \begin{equation}
    P_{k|k-1}=\frac{1}{m}\sum_{i=1}^m{X_{i,k|k-1}^*X_{i,k|k-1}^{*T}}-\hat{x}_{k|k-1}\hat{x}_{k|k-1}^T+Q_{k-1} 
    \label{eq:Ref_3}
    \end{equation} 
\end{algorithmic}

 \textbf{Measurement update}\\

\begin{algorithmic}[1]          
  \State Factorize the state error covariance matrix:
    \begin{equation}
    P_{k|k-1} = S_{k|k-1}S_{k|k-1}^T
    \label{eq:Ref_3}
    \end{equation}
  \State Evaluate the cubature point (i=1,2,...,m)
    \begin{equation}
    X_{i,k|k-1} = \hat{x}_{k|k-1} + S_{k|k-1}\zeta_i
    \label{eq:Ref_3}
    \end{equation}
  \State Evaluate the propagated cubature point through the measurement equation
    \begin{equation}
    Y_{i,k|k-1} = h(X_{i,k|k-1})
    \label{eq:Ref_3}
    \end{equation}
    \begin{description}
  \item[a.] Estimate the predicted measurement
    \begin{equation}
    \hat{y}_{k|k-1} = \frac{1}{m}\sum_{i=1}^m{Y_{i,k|k-1}}
    \label{eq:Ref_3}
    \end{equation}
  \item[b.] Estimate the innovation covariance matrix 
    \begin{equation}
    P_{yy,k|k-1} = \frac{1}{m}\sum_{i=1}^m{Y_{i,k|k-1}Y_{i,k|k-1}^T}-\hat{y}_{k|k-1}\hat{y}_{k|k-1}^T+R_k
    \label{eq:Ref_3}
    \end{equation}  
  \item[c.] Estimate the cross-covariance matrix
    \begin{equation}
P_{xy,k|k-1}=\frac{1}{m}\sum_{i=1}^m{X_{i,k|k-1}Y_{i,k|k-1}^T}-\hat{x}_{k|k-1}\hat{y}_{k|k-1}^T
    \label{eq:Ref_3}
    \end{equation}
% split long alg-----------------------------------------------------------------------------------
      \algstore{myalg}
  \end{algorithmic}
\end{algorithm}

\clearpage

\begin{algorithm}
  \ContinuedFloat
%  \caption{Square Root Cubature Kalman Filter SRCKF (continued)}
  \begin{algorithmic}
      \algrestore{myalg}
%--------------------------------------------------------------------------------------------------    
  \item[d.] Estimate the Kalman gain
    \begin{equation}
    K_k=P_{xy,k|k-1}(P_{yy,k|k-1})^{-1}
    \label{eq:Ref_4}
    \end{equation}
    \end{description}
  \State Estimate the Updated state
    \begin{equation}
    \hat{x}_{k|k}=\hat{x}_{k|k-1}+K_k(y_k-\hat{y}_{k|k-1})
    \label{eq:Ref_2}
    \end{equation}
  \State Estimate the corresponding error covariance
    \begin{equation}
    P_{k|k}=P_{k|k-1}-K_kP_{yy,k|k-1}K^T_k
    \label{eq:Ref_3}
    \end{equation} 
\end{algorithmic}
\end{algorithm}

\end{document}

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