When you name a variable in your function figure, you can no longer access the function figure(). For example:
>> figure = 1;
>> figure(figure)
ans =
1
% no figure is created
That is likely your main problem.
It seems like warp just plots to the current axes. I would recommend working with handles. I think this could work:
positionData = data;
% Plot orbit in ECI reference
% Generation of a sphere
f = figure;
ax = axes(f, 'NextPlot', 'add');
Earth3D(ax)
plot3(ax, positionData(:, 1), positionData(:, 2), positionData(:, 3),'o-r');
% grid(ax, 'on'); axis(ax, 'equal');
xlabel(ax, 'X'); ylabel(ax, 'Y'); zlabel(ax, 'Z');
title(ax, 'Orbit ECI (inertial) (m)')
with your function defined like this:
function Earth3D(ax)
% Defines the Earth object and it's parameters as well as the plot size for the transformation.
[x,y,z] = sphere(1000);
xe=x.*6378.137;
ye=y.*6378.137;
ze=z.*6356.752;
[I,~] = imread('STK_map.jpg');
axes(ax) % make ax the current axes
warp(xe,ye,-ze,I);
% ax.YDir='normal'; %Defines y axis of the plot with + at the top.
axis(ax, 'equal');
%xlabel(ax, 'x'); ylabel(ax, 'y'); zlabel(ax, 'z');
