Parameter Estimation in a Chaotic Supply Chain System Using Extended Kalman Filter

Demand, inventory, and production continuously influence one another in supply chains. Sudden demand changes, inaccurate records, production disruptions, and external factors can create irregular fluctuations. Although demand or sales data are often available, inventory and production information may be incomplete or delayed. This study applies the Extended Kalman Filter (EKF) to jointly estimate inventory, production quantity, and three model parameters using demand as the only measured variable. Its main contribution is a recursive structure that updates the state and parameter estimates with each new measurement. The method is tested on a three-variable supply chain model exhibiting chaotic behavior. Performance is assessed through numerical errors, convergence, time series, phase portraits, and bifurcation diagrams. Robustness to different initial estimates, sensitivity to process- and measurement-noise covariance settings, and performance under chaotic, semi-chaotic, and ordered regimes are also examined. Parameter errors range from 1.5% to 2.4%, while normalized errors for demand, inventory, and production remain below 3%. A larger assumed measurement-noise covariance slows convergence. Under the selected conditions, the closest agreement occurs in the chaotic regime, but this is not interpreted as a general superiority of the EKF. With real-data validation, the framework could support estimation of missing or delayed information, short-term monitoring, early warning, and decision support.