function [thetaHat,rul]=NLS_Battery(theta0)
clear global; global DegraUnit ...
TimeUnit time y thres ParamName thetaTrue signiLevel ns ny np
%=== PROBLEM DEFINITION 1 (Required Variables) ==============
WorkName='Battery_NLS';
DegraUnit='C/1 Capacity';
TimeUnit='Cycles';
time=[0:5:200]';
y=[1.00 0.99 0.99 0.94 0.95 0.94 0.91 0.91 0.87 0.86]';
thres=0.7;
ParamName=['b'; 's'];
thetaTrue=[0.003; 0.02];
signiLevel=5;
ns=5e3;
%============================================================
% % % PROGNOSIS using NLS
ny=length(y);
np=size(ParamName,1);             %% Deterministic Estimation
Optio=optimset('algorithm',{'levenberg-marquardt',0.01});
[thetaH,~,resid,~,~,~,J]=lsqnonlin(@FUNC,theta0,[],[],Optio);
sse=resid'*resid;                    %% Distribution of Theta
dof=ny-np+1;
sigmaH=sqrt(sse/dof);
W=eye(ny)*1/sigmaH^2; thetaCov=inv(J'*W*J);
sigTheta=sqrt(diag(thetaCov));
mvt=mvtrnd(thetaCov,dof,ns)';
thetaHat=repmat(thetaH,1,ns)+mvt.*repmat(sigTheta,1,ns);
thetaHat(np,:)=sigmaH*ones(1,ns);   %% Final Sampling Results
for k=1:length(time(ny:end));       %% Degradation Prediction
 zHat(k,:)=MODEL(thetaHat,time(ny-1+k));
 degraPredi(k,:)=zHat(k,:)+trnd(dof,1,ns)*sigmaH;
end;
% % % POST-PROCESSING
degraTrue=[];                             %% True Degradation
if ~isempty(thetaTrue); degraTrue=MODEL(thetaTrue,time); end
rul=POST(thetaHat,degraPredi,degraTrue); %% RUL & Result Disp
Name=[WorkName ' at ' num2str(time(ny)) '.mat']; save(Name);
end
function objec=FUNC(theta)
 global time y ny
 z=MODEL(theta,time(1:ny));
 objec=(y-z);
end
function z=MODEL(theta,t)
 global ParamName np
 for j=1:np-1; eval([ParamName(j,:) '=theta(j,:);']); end
 %===== PROBLEM DEFINITION 2 (model equation) ===============
 z=exp(-b.*t);
 %===========================================================
end