Assume that $W(t)$ is a one-parameter stochastic process given by $W(t) := X_1^2(t) + X_2^2(t)$ where $X_i(t)$ are independent copies of a stationary gaussian process with known covariance function. This is a special case of a chi-square process ($\chi^2$-process) for which interesting known facts can be found on the web. Yet
What method(s) can be used to compute predictions for $W(t)$?
If moreover each $X_i(t)$ has a state-space representation, can a specific filtering algorithm be designed for $W(t)$?
