kalman - How to find optimal noise covariance matrices Q & R

I am trying to use the discrete Kalman filter for forecasting and I wonder what is commonly considered as the optimal way of determining the measurement noise covariance constants (Q and R) for a given time series? Do you recommend some approaches based on your research/experience?

Answer

I recently blogged about this very topic.

Essentially, there are 3 ways to estimate Q & R.

1. approximate
   
   
   
   • calculate variate estimate of error in a controlled environment
   
   
   • if z doesn't change, calculate variance estimate of z
   
   
   • if z does change, calculate variance of regression estimate of z
   
   
   
   
   


2. guess
   
   
   
   • use some constant multiplied by the identity matrix
   
   
   • higher the constant, higher the noise
   
   
   
   


3. MLE
   
   
   
   
   • pykalman's em
   
   
   • unfortunately, non-convex problem => local optima
   
   
   
   

Check out the rest of my post here