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function [pbest]=rc1fit1(p0,data)
% p0 in the sequence of r0,r1,c1
ydata= data(:,3) %  voltage
pbest=nlinfit(data,ydata,@rc1_v,p0) % use nlinfit() to fit
plot(data(:,1),data(:,3),'o',data(:,1),rc1_v(pbest,data)) % plot
xlabel('s')
ylabel('v')
legend('experiment','fit')
end

function ycal = rc1_v(p0,data)
% the function returns terminal voltage (ycal) at time 't'
load('sococveve') % soc_ocv relation
soc=sococveve(:,1) % needs to specify for other cells
ocv=sococveve(:,2) % needs to specify for other cells
dt=diff(data(:,1))
i=data(:,2)
capa=5 % need to be modified accordingly
r0=p0(1)
r1=p0(2)
c1=p0(3)

% this function assume r1 and c1 and r0 constant

     ocv(1)=data(1,3) % when t=0
     soc(1)=interp1(ocv,soc,ocv(1))% return soc(1) at t=0
     ycal(1)=ocv(1)     % when t=0
     ir1(1)=0         % when t=0, instantaneous current through paralleled r1 is 0
     
for ii=1:length(data(:,1))-1
     ir1(ii+1)=exp(-dt(ii)/(r1*c1))*ir1(ii)+(1-exp(-dt(ii)/(r1*c1)))*i(ii) % dominant function
     soc(ii+1)=interp1(ocv,soc,ocv(ii))+dt(ii)*i(ii+1)/3600/capa
     ocv(ii+1)=interp1(soc,ocv,soc(ii+1))
     ycal(ii+1)=ocv(ii+1)+ r0*i(ii+1)+ r1*ir1(ii+1)
end
ycal=ycal'
end
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