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主要内容：

健康状态 SOH采用平均加权最小二乘法（AWTLS）进行估计，并对比了加权最小二乘 （WLS）、总最小二乘法（TLS）以及加权总最小二乘法（WTLS）算法。

充电状态SOC采用扩展卡尔曼滤波算法进行估计。

部分代码：

binsize = 2*maxI/precisionI;        % resolution of current sensor
rn1 = ones(n,1);                    % init std. dev. for each measurement
sx = socnoise*rn1;                  % scale Gaussian std. dev.
if theCase == 1,                    % the typical case 
  rn2 = rn1;                        % same scale on y(i) as x(i) noise
  sy = binsize*sqrt(m/12)/3600*rn2; % std. dev. for y(i)
else                                % this case will be discussed for BEV case 2
  mu = log(mode)+sigma^2;   
  m = 3600*lognrnd(mu,sigma,n,1);   
  sy = binsize*sqrt(m/12)/3600;     % std.dev. for y(i)
end

x = x + sx.*randn(n,1);             % measured x(i) data, including noise
y = y + sy.*randn(n,1);             % measured y(i) data, including noise

% Execute the algorithms for BEV case 2
[QhatBEV3,SigmaQBEV3] = xLSalgos(x,y,sx.^2,sy.^2,gamma,Qnom,sy(1)^2);

% Plot estimates of capacity for BEV case 2
hold on; Qhat = QhatBEV3; SigmaQ = SigmaQBEV3;
plot(Qhat(:,1),'b','linewidth',2);       % WLS
plot(Qhat(:,2),'m','linewidth',2);       % WTLS
plot(Qhat(:,3),'r','linewidth',2);       % TLS
plot(Qhat(:,4),'c','linewidth',2);       % AWTLS
plot(1:length(x),Q,'k--','linewidth',1);   % Plot true capacity

ylim([88 103]);
xlabel('Algorithm update index');
ylabel('Capacity estimate (Ah)');
title(sprintf('%s: Capacity estimates',plotTitle));
legend('WLS','WTLS','TLS','AWTLS','location','northeast');

% Compute RMS estimation error for all methods
errWLS   = Q - QhatBEV3(:,1); rmsErrWLS = sqrt(mean(errWLS.^2))
errWTLS  = Q - QhatBEV3(:,2); rmsErrWTLS = sqrt(mean(errWTLS.^2))
errTLS   = Q - QhatBEV3(:,3); rmsErrTLS = sqrt(mean(errTLS.^2))
errAWTLS = Q - QhatBEV3(:,4); rmsErrAWTLS = sqrt(mean(errAWTLS.^2))

健康状态 SOH运行结果：

充电状态SOC估计结果：