It sounds like you’re doing online updating; you want to run your filter on incoming streaming data, one point at a time. Is that right? If so, the statespace module won’t help.
Do you also want to update the parameter priors whenever new data comes in, or do you only want to update the hidden states?
- Is it possible to sample posterior given multivariate gaussian prior for 4 variables, while respecting above constraints?
No, because by definition this is not a multivariate normal after the constraints are applied. You will need to either use a different distribution or do some kind of transformation (as you bring up in the edit)