ARMAX identification via hereditary algorithm

In this note, we limit ourselves to the most commonly models used, say the output error model and auto regressive moving average with exogenous input. In both cases, we treat the case multiple-input-single-output. Our aim is to give the parameters of the model under lattice form, in reference to its numerical robustness allowing to deal with great state space dimension (>20). This calculation is achieved considering time varying predictor of the output based on the predictor derived at the previous step. It leads to an hereditary algorithm introduced in previous works.