#' \code{Helske5.model} is a wrapper for estimating speed and location with Kalman filtering \code{SSMcustom}.
#'
#' @usage uses \code{Helske3.model} code.
#' @param tdf1df2 speed and location data, data.frame
# #' @examples
# #' Helske5.model(tdf1df2)
#' @export
Helske5.model <- function(tdf1df2) {
df <- tdf1df2[,c(2,3,5,6)]
start <- 0
end <- 40
u <- round(53*5280/3600,0)
usd <- round(5280/3600*5,1)
data <- ts(df, start, end, frequency = 8)
browser()
ar <- arima(data[,1],order = c(1,1,0))
print(ar)
acf(diff(data[,1]))
model <- SSModel(data[,1] ~
SSMtrend(degree = 3, index = 1, Q = list(matrix(NA,1,1), matrix(0,1,1),
matrix(NA,1,1), matrix(0,1,1),
matrix(NA,1,1), matrix(0,1,1)
)),
H = matrix(NA),
distribution = "gaussian",
data = data,
tol = .Machine$double.eps^0.5
)
check_model <- function(model) (model["H"] > 0 &
model["Q", etas = "level"] > 0 &
model["Q", etas = "custom1"] > 0
)
fit <- fitSSM(model,
check_fn = check_model,
inits = rep(u/10,3),
method = "BFGS")
out <- KFS(fit$model)
print(out$P[,,end])
browser()
par(mfrow = c(1,2), pty = "s")
print("Q and R")
print(fit$optim.out[[1]])
print("fit$optim.out")
print(out)
print(head(data))
stand = rep(u,321)
Out <- ts(data.frame(stand, obs = data[,1], smooth = out$muhat, prd = out$att[,1]),
start, end, frequency = 8)
ts.plot(window(Out, start = c(0,1), end = c(40,0)),
col = c("gold", gray(0.5), "black", "blue"),
ylim = c(0,150),
ylab = "u(t), feet per second", lty = c(1,3,1,1), lwd = c(6,2,2,2)
)
title(main = expression(dot(x)[t]))
legend("bottomright",
legend = c("Gold Standard", "Observed", "One-step ahead predictions", "Smoothed estimates" ),
lty = c(1,3,1,1),
lwd = c(6,2,2,2),
col = c("gold", gray(0.5), "blue","black"),
bty = "n")
legend("topleft",c(
expression(""),
bquote(bar(u) == .(u)),
bquote(sigma[w] == .(usd))),
bty = "n"
)
p1 <- as.numeric(out$P[1,,][1,])
p2 <- as.numeric(out$P[1,,][2,])
p3 <- as.numeric(out$P[1,,][3,])
tseq <- seq(start, end, 0.125)
plot(tseq, p1[-1], typ = "l", lwd = 2, ylim = c(0,max(c(p1,p2,p3))), xlab = "Time", ylab = "P")
lines(tseq,p2[-1], lwd = 2)
title(main = "Covariance")
### Notes
# 1. u = 50 = speed
# 2. Q = 0 Here, the goal is to reach u = 50
# 3. tracks well for all usd
# 4. Covariance quickly reach steady state
# 5. Use default updatefn.
browser()
}
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