I have three differential equations in the form of:
$$\frac{dx}{dt}=ax+y+z$$
$$\frac{dy}{dt}=x+by+z$$
$$\frac{dz}{dt}=x+y+cz$$
I have measured data:
$$x=[2+5randn(100)]$$
$$y=[0.5+2randn(100)]$$
I do not have data for $$z$$
The initial parameters are $$a,b,c=3,4,5$$
How do I optimize this parameter only knowing the measured value of 2 states only? Thanks in advance.