function theta = SequentialLSExample2 (Nmax, sigma2)

a = -6; b = -0.6; c = 0.004;

theta_prev = zeros(3,1);
cov_prev = sigma2*eye(3);

for n=1:Nmax
    x(n) = a + b*n + c*n.^2 + sqrt(sigma2)*randn();
    ht = [1 n n^2];
    K = (cov_prev*ht')/(sigma2+ht*cov_prev*ht');
    % we assume all data points have the same variance
    theta = theta_prev + K*(x(n)-ht*theta_prev);
    cov_prev = (eye(3)-K*ht)*cov_prev
    theta_prev = theta;
    figure(1);clf;hold on;
    plot(x,'*-');
    xfit = theta(1) + theta(2)*(1:Nmax) + theta(3)*(1:Nmax).^2;
    plot(xfit,'ro-');
    axis([0 Nmax -100 100]);
    pause(0.1);
end;