rarx {sysid}

Estimate parameters of ARX recursively

Description

Estimates the parameters of a single-output ARX model of the specified order from data using the recursive weighted least-squares algorithm.

Usage

rarx(x, order = c(1, 1, 1), lambda = 0.95)

Arguments

x

an object of class idframe

order

Specification of the orders: the three integer components (na,nb,nk) are the order of polynolnomial A, (order of polynomial B + 1) and the input-output delay

lambda

Forgetting factor(Default=0.95)

Value

A list containing the following objects

theta

Estimated parameters of the model. The k^{th} row contains the parameters associated with the k^{th} sample. Each row in theta has the following format:
theta[i,:]=[a1,a2,...,ana,b1,...bnb]

yhat

Predicted value of the output, according to the current model - parameters based on all past data

References

Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Section 25.1.3

Lennart Ljung (1999), System Identification: Theory for the User, 2nd Edition, Prentice Hall, New York. Section 11.2

Examples

Gp1 <- idpoly(c(1,-0.9,0.2),2,ioDelay=2,noiseVar = 0.1)
Gp2 <- idpoly(c(1,-1.2,0.35),2.5,ioDelay=2,noiseVar = 0.1)
uk = idinput(2044,'prbs',c(0,1/4)); N = length(uk);
N1 = round(0.35*N); N2 = round(0.4*N); N3 = N-N1-N2;
yk1 <- sim(Gp1,uk[1:N1],addNoise = TRUE)
yk2 <- sim(Gp2,uk[N1+1:N2],addNoise = TRUE)
yk3 <- sim(Gp1,uk[N1+N2+1:N3],addNoise = TRUE)
yk <- c(yk1,yk2,yk3)
z <- idframe(yk,uk,1)
g(theta,yhat) %=% rarx(z,c(2,1,2))