Kalman Filter of Dynamic Hierarchical Model

Abstract

In a specific way, the dynamic hierarchical model has been presented alongside with the derivation of the final formula of the Kalman filter. The filtering coefficient used along with the equations necessary for the filtering process has also been determined. Most of the related works were studied which gave rise to the problem statement of filtering problems placed under the case of st = . Most of the basic concepts of the dynamic hierarchical linear model were also displayed based on some previous works. A mathematical formula was also formulated and derived to calculate the dynamic hierarchical Kalman filter model, which results in a repetitive measure to estimate the model parameters. The proposed derived formula reduces the error associated with the model and achieves a successful optimal estimation of the parameters. This proves that the Kalman coefficient is the best filtering for any normal probability distribution and provides the least variance among the estimates. This study also provides an illustrative example of the model with the filtering process concerned. It was further illustrated that the findings can be used in practical applications, which reveals the fields that can be investigated in this area.