I am using a particle filter to estimate the parameters($\Phi_{n\times1}$) of a non-linear model. Say my input (observations) is $t=1:k$, I will have a vector of length $k$ for each of the parameter estimates. Thus, at the end of the particle filter, I will end up with a parameter estimate matrix ($\Theta$) of $k\times n$ size, where the $k$ rows are the estimates at each time a new observation is made with the $k^{th}$ observation as my final estimate.
My question:
Does it make sense to find the correlation coefficient matrix ($C_{n \times n}$) of this parameter estimate matrix $\Theta$? If so, what will this represent?
--AM
edit:
The non-linear model is a physiological signal model with 4 states and 7 unknown parameters. These 7 parameters are treated as state variables, thus yielding a 11 state vector which needs to be estimated. This is done in a particle filter framework.
Yes, the final estimates are the only ones of interest but I came across a report where the correlation of the estimates of the particles in the filtering timeline (as I mentioned above) was measured. Seeing how the estimates evolve tells a great deal about the filtering process. So I am interesting in knowing what (if any) does the correlation matrix of this evolution tell.