fitting cosine curve

Using a more stable nonlinear modeling tool will also help, but key is to get
the periodicity right.

y=c(16.82, 16.72, 16.63, 16.47, 16.84, 16.25, 16.15, 16.83, 17.41, 17.67,
17.62, 17.81, 17.91, 17.85, 17.70, 17.67, 17.45, 17.58, 16.99, 17.10)
t=c(7,  37,  58,  79,  96, 110, 114, 127, 146, 156, 161, 169, 176, 182,
190, 197, 209, 218, 232, 240)

lidata <- data.frame(y=y, t=t)

#I use the method to fit a curve, but it is different from the real curve,
#which can be seen in the figure.
linFit  <- lm(y ~ cos(t))
library(nlsr)
#fullFit <- nls(y ~ A*cos(omega*t+C) + B,
#start=list(A=coef(linFit)[1],B=coef(linFit)[2],C=0,omega=.4))
#omega cannot be set to 1, don't know why.
fullFit <- nlxb(y ~ A*cos(omega*t+C) + B, data=lidata,
  start=list(A=coef(linFit)[1],B=coef(linFit)[2],C=0,omega=.04), trace=TRUE)
co <- coef(fullFit)
fit <- function(x, a, b, c, d) {a*cos(b*x+c)+d}
plot(x=t, y=y)
curve(fit(x, a=co['A'], b=co['omega'], c=co['C'],d=co['B']), add=TRUE
,lwd=2, col="steelblue")
jstart <- list(A=20, B=100, C=0, omega=0.01)
jfit <- nlxb(y ~ A*cos(omega*t+C) + B, data=lidata,
         start=jstart, trace=TRUE)
co <- coef(jfit)
fit <- function(x, a, b, c, d) {a*cos(b*x+c)+d}
plot(x=t, y=y)
curve(fit(x, a=co['A'], b=co['omega'], c=co['C'],d=co['B']), add=TRUE
       ,lwd=2, col="steelblue")

JN

fitting cosine curve

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