diff options
| -rw-r--r-- | R/estpoly.R | 24 | ||||
| -rw-r--r-- | man/estARX.Rd | 22 |
2 files changed, 33 insertions, 13 deletions
diff --git a/R/estpoly.R b/R/estpoly.R index 68bfb67..d87e7d6 100644 --- a/R/estpoly.R +++ b/R/estpoly.R @@ -29,7 +29,17 @@ plot.estPoly <- function(model,newdata=NULL){ #' the input-output delay #' #' @details -#' ARX models are of the form \\ +#' SISO ARX models are of the form +#' \deqn{ +#' y[k] + a_1 y[k-1] + \ldots + a_{na} y[k-na] = b_{nk} u[k-nk] + +#' \ldots + b_{nk+nb} u[k-nk-nb] + e[k] +#' } +#' The function estimates the coefficients using linear least squares (with +#' no regularization). Future versions may include regularization +#' parameters as well +#' \\ +#' The data is expected to have no offsets or trends. They can be removed +#' using the \code{\link{detrend}} function. #' #' @return #' An object with classes \code{estARX} and \code{estPoly}, containing @@ -40,8 +50,8 @@ plot.estPoly <- function(model,newdata=NULL){ #' fitted coefficients \cr #' \code{vcov} \tab the covariance matrix of the fitted coefficients\cr #' \code{sigma} \tab the standard deviation of the innovations\cr -#' \code{df} the residual degrees of freedom\tab \cr -#' \code{fitted.values} \tab the predicted response +#' \code{df} \tab the residual degrees of freedom \cr +#' \code{fitted.values} \tab the predicted response \cr #' \code{residuals} \tab the residuals \cr #' \code{call} \tab the matched call \cr #' \code{time} \tab the time of the data used \cr @@ -49,10 +59,10 @@ plot.estPoly <- function(model,newdata=NULL){ #' #' #' @references -#' Arun K. Tangirala (2015), Principles of System Identification: Theory and -#' Practice, CRC Press, Boca Raton. Section 21.6.1 +#' Arun K. Tangirala (2015), \emph{Principles of System Identification: +#' Theory and Practice}, CRC Press, Boca Raton. Section 21.6.1 #' -#' Lennart Ljung (1999) System Identification: Theory for the User, +#' Lennart Ljung (1999), \emph{System Identification: Theory for the User}, #' 2nd Edition, Prentice Hall, New York. Section 10.1 #' #' @examples @@ -66,7 +76,7 @@ estARX <- function(data,order=c(0,1,0)){ y <- as.matrix(data$output) u <- as.matrix(data$input); N <- dim(y)[1] na <- order[1];nb <- order[2]; nk <- order[3] - nb1 <- nb+nk; n <- max(na,nb1); df <- N - na - nb -nk + nb1 <- nb+nk. ; n <- max(na,nb1); df <- N - na - nb -nk padZeros <- function(x,n) c(rep(0,n),x,rep(0,n)) yout <- apply(y,2,padZeros,n=n); diff --git a/man/estARX.Rd b/man/estARX.Rd index d4ff9b6..11858f8 100644 --- a/man/estARX.Rd +++ b/man/estARX.Rd @@ -22,8 +22,8 @@ the following elements: fitted coefficients \cr \code{vcov} \tab the covariance matrix of the fitted coefficients\cr \code{sigma} \tab the standard deviation of the innovations\cr - \code{df} the residual degrees of freedom\tab \cr - \code{fitted.values} \tab the predicted response + \code{df} \tab the residual degrees of freedom \cr + \code{fitted.values} \tab the predicted response \cr \code{residuals} \tab the residuals \cr \code{call} \tab the matched call \cr \code{time} \tab the time of the data used \cr @@ -33,7 +33,17 @@ the following elements: Fit an ARX model of the specified order given the input-output data } \details{ -ARX models are of the form \\ +SISO ARX models are of the form +\deqn{ + y[k] + a_1 y[k-1] + \ldots + a_{na} y[k-na] = b_{nk} u[k-nk] + + \ldots + b_{nk+nb} u[k-nk-nb] + e[k] +} +The function estimates the coefficients using linear least squares (with +no regularization). Future versions may include regularization +parameters as well +\\ +The data is expected to have no offsets or trends. They can be removed +using the \code{\link{detrend}} function. } \examples{ data(arxsim) @@ -42,10 +52,10 @@ summary(model) # obtain estimates and their covariances plot(model) # plot the predicted and actual responses } \references{ -Arun K. Tangirala (2015), Principles of System Identification: Theory and -Practice, CRC Press, Boca Raton. Section 21.6.1 +Arun K. Tangirala (2015), \emph{Principles of System Identification: +Theory and Practice}, CRC Press, Boca Raton. Section 21.6.1 -Lennart Ljung (1999) System Identification: Theory for the User, +Lennart Ljung (1999), \emph{System Identification: Theory for the User}, 2nd Edition, Prentice Hall, New York. Section 10.1 } |