Recursive Least Square is a popular method used to identify model parameters using a given set of data. This process could be carried out either on-line when each time a new data point becomes available or off-line using past known data. A continuous-time state-space model is z-transformed into a sampled-data transfer function before being converted to an Auto Regression Moving Average model in the backward shift operator with a random stochastic disturbance process included. In this study, Recursive Least Square Estimation is used to identify a plant representation to model the economic growth in the Southeastern United States. A 6th-order algorithm is developed with a parameter estimator and a Kalman filter to predict future economic growth based on some known past growths. Economic growth is estimated from information on new orders, production, employment, supplier delivery time and finished inventory.
To estimate the unknown least square parameters that will minimize the J-loss function, a weighing factor is included in the performance index in order to weight new data more heavily than older data. A positive-definite diagonal matrix is used to measure the estimation error of the parameter estimates.