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:

$$x=[2+5*randn(100)]$$
$$y=[0.5+2*randn(100)]$$

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.