States and parameters estimation for biomass substrate hypothetical system

To overcome the problem of uncertainty in the environmental models, we are focused on the difficulty of, the cost related with, getting the measurements, of dual state and/or parameter estimates. This paper, presents an Iterated Square-Root Central Difference Kalman Particle Filter (ISRCDKF-PF) extension which is suggested for the estimation of the joint state and parameters in environmental systems. Amongst the different Byesian techniques, are compared and calculated for the estimation performance, called the conventional of the Square-Root Central Difference Kalman Filter (SRCDKF), the Iterated Square-Root Central Difference Kalman Filter (ISRCDKF), the Particle Filter (PF), the Square-Root Central Difference Kalman Particle Filter (SRCDK-PF) and the Iterated Square-Root Central Difference Kalman Particle Filter (ISRCDKF-PF). The proposed approach consists of a PF based on ISRCDKF to exceed the standard Particle Filter by delivering more accuracy state and parameter estimations. The proposal distribution incorporates the latest observation in system state transition density, so it may well match the a posteriori density. The estimation performance of the proposed Bayesian methods, namely the Square-Root Central Difference Kalman Filter (SRCDKF), the Iterated Square-Root Central Difference Kalman Filter (ISRCDKF), the Particle Filter (PF), the Square-Root Central Difference Kalman Particle Filter (SRCDKF-PF) and the Iterated Square-Root Central Difference Kalman Particle Filter (ISRCDKF-PF) are compared by measuring the Root Mean Square Error (RMSE) and respect to the noise-free data. The results reveal that the ISRCDKF-PF extension provides a significant improvement and a better estimation accuracy than the SRCDKF, ISRCDKF, PF and SRCDKF-PF techniques.