We propose a generalized parametrized optimal filter (GPOF) for linear stochastic direct feed-through systems with correlated process and measurement disturbances. We consider a generic case in which any set of unknown parameters can simultaneously affect the stochastic process model and measurements. The GPOF allows unbiased estimates of states to be obtained in the presence of unknown inputs or parameters by appropriately choosing the gain matrix during the state update step. We additionally prove the stability and convergence properties of proposed GPOF for linear time invariant systems with correlated process and measurement noises. We also propose a parameter estimation approach which utilizes the biased innovations generated by GPOF. We then extend the results of GPOF to nonlinear stochastic direct feed-through systems with nonadditive correlated process and measurement noises. In particular we introduce an extended generalized parametrized optimal filter (EGPOF) for state and parameter estimation. The proposed method is applied to two simulation-based case studies. The results indicate that the proposed method can be a useful tool for state and parameter estimation of nonlinear systems with nonadditive correlated noises.