# ARMAX

AcronymDefinition
ARMAXAutoregressive Moving Average eXogenous
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The proposed Recursive Identification Algorithms Library (RIA) fall into category of simple libraries for SIMULINK environment and is designed for recursive estimation of the parameters of the linear dynamic models ARX, ARMAX and OE.
This method is used for parameter estimations of ARMAX model.
The Recursive Identification Algorithm Library is designed for recursive parameter estimation of linear dynamics model ARX, ARMAX, OE using recursive identification methods: Least Square Method (RLS), Recursive Leaky Incremental Estimation (RLIE), Damped Least Squares (DLS), Adaptive Control with Selective Memory (ACSM), Instrumental Variable Method (RIV), Extended Least Square Method (RELS), Prediction Error Method (RPEM) and Extended Instrumental Variable Method (ERIV).
which is an ARMAX model with certain parameter restrictions imposed.
As with the supply equation, some care needs to be taken in interpreting the estimates of an ARMAX model from just 35 observations, particularly when the equation, such as equation (6), is subject to parameter restrictions.
With just 35 observations available to estimate this restricted vector ARMAX system, it is doubtful whether the results would be particularly robust to even slight changes in the specification of the underlying equations.
In discrete-time description, the ARMAX model is identified in sampling time T = 5 as
Keywords: Recursive estimation, ARX models, ARMAX models, Recursive identification algorithms, forgetting factors.
ARMAX, OE) which better describe the reality than more simple ARX model or eventually other recursive parameter estimation methods have to be used (e.
In this article we deal with the following well-known recursive identification methods: Least Square Method (RLS), Instrumental Variable Method (RIV), Extended Instrumental Variable Method (ERIV) which are used for estimation of unknown parameters of ARX model, Extended Least Square (RELS) for parameter estimation of ARMAX model and Prediction Error Method (RPEM) for parameter estimation of ARMAX and OE model in order to improve self-tuning controller performance and reliability.
The initial parameter estimates for ARX, ARMAX, OE model were chosen to be zero.
In the case of the ARMAX model, g is a linear function and in the case of an ANN, the above equation corresponds to Eq 12 with n = 2, m = 1, and u and y replaced, respectively, by [T[prime].
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