How to draw such a figure?

Question

I am trying to draw figure shown below, how do I proceed to get Idon't know

Here is my MWE which I tried so far
documentclass[tikz,border=2pt]{standalone}
usepackage{cmap}
PassOptionsToPackage{hyphens}{url}
usepackage[pdftex, unicode=true, plainpages=true, pdfpagelabels=true]{hyperref}
usepackage{mathtext}
usepackage[T2A]{fontenc}
%usepackage{pscyr}
usepackage[utf8]{inputenc}
usepackage[english,russian]{babel}
DeclareSymbolFont{T2Aletters}{T2A}{cmr}{m}{it}
usepackage{amsmath}
usepackage{amssymb}
usepackage{fixltx2e}
usetikzlibrary{calc, trees, positioning, backgrounds, arrows, shapes, shapes.multipart, shadows, matrix, decorations.pathreplacing, decorations.pathmorphing, decorations.text, fit, patterns, arrows.meta,decorations.markings}
begin{document}
    begin{tikzpicture}[scale=0.7, every node/.style={transform shape}, >=stealth', on grid, node distance=5.2em, thick,
    objq/.style={rectangle, draw, minimum height=3em, minimum width=4em, align=center},
    objt/.style={rectangle, align=center}]
    node[rectangle, draw, minimum height=12em, minimum width=30em, align=center](obju){};
    node[objq](objq2) at ([shift=({0em,3em})]obju.center){$q[t-1]$};
    node[objq, left=8em of objq2](objq1){$q[t-2]$};
    node[objq, right=8em of objq2](objq3){$q[t]$};
    node[objt, left=5em of objq1](objt1){bfseriesldots};
    node[objt, right=5em of objq3](objt2){bfseriesldots};
    %
    node[objt, left=4em of obju.west](x){$x[t]$};
    node[objt, above=4em of obju.north](u){$u[t]$};
    node[objt, right=4em of obju.east](y){$y[t]$};
    %
    draw [->] (objt1) -- (objq1);
    draw [->] (objq1) -- (objq2);
    draw [->] (objq2) -- (objq3);
    draw [->] (objq3) -- (objt2);
    %
    draw [->] (x) -- (obju);
    draw [->] (u) -- (obju);
    draw [->] (obju) -- (y);
    end{tikzpicture}
end{document}

Thank you in advance.

Ignasi · Accepted Answer

You can use a pic made with a tree and a fit node with double copy shadow and place where you need it.
documentclass[tikz,border=5mm]{standalone}
usetikzlibrary{trees, positioning, backgrounds, arrows, shadows, fit}

tikzset{
    tree/.pic={%
    begin{scope}[level distance=5mm,
        every node/.style={circle, inner sep=0pt, minimum size=1mm, draw},
        level distance=5mm,
        sibling distance=4mm]
        node (a) {}
            child {node (b1) {}}
            child {node (b2) {} child {node (c1) {}} child{node (c2) {}}}
            child {node (b3) {}};
    end{scope}
   begin{scope}[on background layer]   
    node[fit={(a) (b1) (b3) (c1)}, double copy shadow, draw, fill=white] {};
    end{scope}}
}

begin{document}
    begin{tikzpicture}[scale=0.7, every node/.style={transform shape}, >=stealth', on grid, node distance=5.2em, thick,
    objq/.style={rectangle, draw, minimum height=3em, minimum width=4em, align=center},
    objt/.style={rectangle, align=center}]
    node[rectangle, draw, minimum height=12em, minimum width=30em, align=center](obju){};
    node[objq](objq2) at ([shift=({0em,3em})]obju.center){$q[t-1]$};
    node[objq, left=8em of objq2](objq1){$q[t-2]$};
    node[objq, right=8em of objq2](objq3){$q[t]$};
    foreach i in {objq1, objq2, objq3}
     pic at ([yshift=-7mm]i.south) {tree};

node[objt, left=5em of objq1](objt1){bfseriesldots};
    node[objt, right=5em of objq3](objt2){bfseriesldots};
    %
    node[objt, left=4em of obju.west](x){$x[t]$};
    node[objt, above=4em of obju.north](u){$u[t]$};
    node[objt, right=4em of obju.east](y){$y[t]$};

pic at ([shift={(4mm,-6mm)}]x.south east) {tree};
     pic at ([shift={(-5mm,-6mm)}]y.south west) {tree};
     pic at ([shift={(6mm,-1mm)}]u.south east) {tree};
    %
    draw [->] (objt1) -- (objq1);
    draw [->] (objq1) -- (objq2);
    draw [->] (objq2) -- (objq3);
    draw [->] (objq3) -- (objt2);
    %
    draw [->] (x) -- (obju);
    draw [->] (u) -- (obju);
    draw [->] (obju) -- (y);
    end{tikzpicture}
    
end{document}

How to draw such a figure?

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