Simulated time series data of a damped linear oscillator
A dataset simulated using a damped linear oscillator model in continuous time with 1 observed indicator for identifying two latent factors (position and velocity). The variables are as follows:
data(Oscillator)
A data frame with 1000 rows and 5 variables
id. ID of the systems (1 to 1 because this is a single person)
y1. Noisy observed position
times. Time index (1000 time points) spaced at one unit intervals
x1. True latent position
x2. True latent velocity
# The following was used to generate the data
#--------------------------------------
# Data Generation
## Not run:
require(mvtnorm)
require(Matrix)
xdim <- 2
udim <- 1
ydim <- 1
tdim <- 1000
set.seed(315)
tA <- matrix(c(0, -.3, 1, -.7), xdim, xdim)
tB <- matrix(c(0), xdim, udim)
tC <- matrix(c(1, 0), ydim, xdim)
tD <- matrix(c(0), ydim, udim)
tQ <- matrix(c(0), xdim, xdim); diag(tQ) <- c(0, 2.2)
tR <- matrix(c(0), ydim, ydim); diag(tR) <- c(1.5)
x0 <- matrix(c(0, 1), xdim, 1)
P0 <- diag(c(1), xdim)
tdx <- matrix(0, xdim, tdim+1)
tx <- matrix(0, xdim, tdim+1)
tu <- matrix(0, udim, tdim)
ty <- matrix(0, ydim, tdim)
tT <- matrix(0:tdim, nrow=1, ncol=tdim+1)
tI <- diag(1, nrow=xdim)
tx[,1] <- x0
for(i in 2:(tdim+1)){
q <- t(rmvnorm(1, rep(0, xdim), tQ))
tdx[,i] <- tA %*% tx[,i-1] + tB %*% tu[,i-1] + q
expA <- as.matrix(expm(tA * (tT[,i]-tT[,i-1])))
intA <- solve(tA) %*% (expA - tI)
tx[,i] <- expA %*% tx[, i-1] + intA %*% tB %*% tu[,i-1] + intA %*% q
ty[,i-1] <- tC %*% tx[,i] + tD %*% tu[,i-1] + t(rmvnorm(1, rep(0, ydim), tR))
}
rownames(ty) <- paste('y', 1:ydim, sep='')
rownames(tx) <- paste('x', 1:xdim, sep='')
simdata <- cbind(id=rep(1, tdim), t(ty), times=tT[,-1], t(tx)[-1,])
write.table(simdata, file='Oscillator.txt', row.names=FALSE, col.names=TRUE)
plot(tx[1,], type='l')
plot(tT[,-1], ty[1,], type='l')
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.