%%% Section 1.2
%%% Noisy Depth Sensors

clear
close all
% Az = Y
A = 1;
z = -3;
sigma = 0.02;


%%% estimate z 1000 times

A = ones(4,1);
zm = z+sigma*randn(4,1000);

zest = inv(A'*A)*A'*zm;

vest = std(zest)
v1 = std(zm(1,:))





[n,x] = hist(zest,40);
[n2,x2] = hist(zm(1,:),40);

figure(1)
bar(x2,n2,'hist')
hold on; 
h=bar(x,n,'hist'); 
hold off
set(h,'facecolor','y')
legend('Single Measurement','LLSE')
text(-3.06, 70, ['STD = 0.02 meters'])
text(-3.06, 60, ['LLSE = ',num2str(round(10000*std(zest))/10000),'meters'])