Maximum likelihood estimation for trajectories estimation

Questions
1

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)+a12RHY(t-1)+a13LHX(t-1)+a(2t)(RHX(t-1)-RHX(t-2)) + ?.
&
a(2t)=?1a(2t-1)+u(t).

Where t is the next time period and t-1 and t-2 the previous ones. X,Y&Z are trajectory coordinates. ? 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 ?1 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.

2

Isn’t it a VARMA process? Parameters can by obtained through ML (among several stimaton methods).

Claude

3

I was suggested to work with either Maximum likelihood estimation method or Kalman filtering which are kind of similar to my knowledge. My problem is that I haven’t managed yet to find how to estimate the parameters in my equeation.

4

Look at the documentation for KalmanEstimator. Specifically, look at the block diagram in the details section and conform your model to the diagram to get the correct inputs to the KalmanEstimator function.

Regards,

Neil