Often when discrete linear models are developed, they are based on experimental system responses rather than on converting a continuous model to a discrete model. The estimation of parameters for discrete dynamic models is no different from linear regression (least squares) analysis.
The measured inputs and outputs are the independent variables, and the dependent variables are the outputs. For simplicity, consider the following model where two previous values of the input and output are used to predict the next value. This model has four parameters
For the system of N data points we can write the following ...