How do I call for the posterior (refined) state estimates from a Kalman Filter simulation in R using the DSE package?
I have added an example below. Assume that I have created a simple random walk state space with the error being a standard normal distribution. The model is created using the SS function, with initialised state and covariance estimates of zero. The theoretical model form is thus: X(t) = X(t-1) + e(t)~N(0,1) for state evolution Y(t) = X(t) + w(t)~N(0,1)
We now implement this in R by following the instructions on page 6 and 7 of the "Kalman Filtering in R" article in the Journal of Statistical Software. First we create the state space model using the SS() function and store it in the variable called kalman.filter:
kalman.filter=dse::SS(F = matrix(1,1,1),
Q = matrix(1,1,1),
H = matrix(1,1,1),
R = matrix(1,1,1),
z0 = matrix(0,1,1),
P0 = matrix(0,1,1)
)
Then we simulate a 100 observations from the model form using simulate() and put them in a variable called simulate.kalman.filter:
simulate.kalman.filter=simulate(kalman.filter, start = 1, freq = 1, sampleT = 100)
Then we run the kalman filter against the measurements using l() and store it under the variable called test:
test=l(kalman.filter, simulate.kalman.filter)
From the outputs, which ones are my filtered estimates?