function df = ekf_df_dx(X,params)
% X: state vector
% params: a cell containing all parameters:
% W: process noise vector
% nk: a vector indicating the number of Gaussian Kernels used for modeling
% each independent component
% fs:sampling frequency
L=size(X,1); % number of states in the state vector X
W= params{1};
nk= params{2};
fs= params{3};
Lind = length(nk); % number of independent components used for MECG cancellation
w=W(1); % average heart-rate in rads
df= eye(L); % Note that L=Lind+1
ptr=1; % pointer to the current parameter extracted from the W vector
for i=1:Lind
kernelParam = reshape(W(ptr+1:ptr+nk(i)*3),3,[]); % kernel parameters for the current independent component
df(i+1,1)= feval(@df_dtheta, X, kernelParam, w, fs);
ptr=ptr+nk(i)*3;
end
end
function y = df_dtheta(X, kp, w, fs)
% X: state vector
% kp: kernel parameters
% w: average heart-rate in rads
% fs: sampling frequency
dt= 1/fs;
alpha= kp(1,:);
theta= kp(2,:);
b=kp(3,:);
dtheta= rem(X(1) - theta,2*pi);
y= -dt*sum( w*alpha./(b.^2).*(1 - dtheta.^2./b.^2).*exp(-dtheta.^2./(2*b.^2)) );
end