Maximum likelihood estimation for trajectories prediction

I am currently working on a project where I have to estimate the parameters of an equation in order to estimate next states.

More specifically, I have the state space:
RHXt= a10+a11* RHZ(t-1)+a12*RHY(t-1)+a13*LHX(t-1)+a(2t)*(RHX(t-1)-RHX(t-2)) + ε.

Where t is the next time period and t-1 and t-2 the previous ones. X,Y&Z are trajectory coordinates. ε and u(t) are gaussian disturbances.
I need to use maximum likelihood estimation in order to estimate (I guess the parameters a10, a11,a12,a13,a(2t) and δ1 in order to predict the next state RHX. I have read a lot about maximum likelihood estimation but I didn't manage to figure out how to implement it practically on my state space.

Since statistics in not my field at all, any suggestions or help would be very much appreciated as I am stuck.