# How does maximum likelihood estimation from the Kalman filter work?

My understanding is

Step 1: You would run through the Kalman filter equations

with initial parameter values.

Step 2: After you run through the Kalman filter equations,

you will have innovations obtained with initial parameter values i.e., $$\zeta_{t \mid t-1} = z_{t}-G\omega _{t\mid t-1}-HY_{t}$$ for t = 1,.....,T,

where $$\zeta_{t \mid t-1}$$ is the innovation.

You would use those innovations with parameter values treated unknown and compute the MLEs of parameters.

Step 3: You will check whether your initial parameter values and MLEs of parameter values satisfy

the convergence criterion (i.e., log likelihood criteria and estimates of parameters criteria).

If they don't satisfy, you would use the obtained MLEs of parameters to

run through the Kalman filter equations again.

Step 4: Repeat step 2, 3, until convergence occurs.

Is this the general idea?

I just want the general idea so that I can talk about it for 5-10 minutes.

If this is not the general idea, please correct me.

Also, if possible, I would like the answer to be not too mathematical.

Plain english would be the best. Any helps are appreciated.