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?
I recently blogged about this very topic.
Essentially, there are 3 ways to estimate Q & R.
- 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
- use some constant multiplied by the identity matrix
- higher the constant, higher the noise
- pykalman's em
- unfortunately, non-convex problem => local optima
Check out the rest of my post here