ekf_smoother: Extended Kalman Smoothing

In bssm: Bayesian Inference of Non-Linear and Non-Gaussian State Space Models

Extended Kalman Smoothing

Description

Function ekf_smoother runs the (iterated) extended Kalman smoother for the given non-linear Gaussian model of class ssm_nlg, and returns the smoothed estimates of the states and the corresponding variances. Function ekf_fast_smoother computes only smoothed estimates of the states.

Usage

ekf_smoother(model, iekf_iter = 0)

ekf_fast_smoother(model, iekf_iter = 0)

Arguments

model	Model of class ssm_nlg.
iekf_iter	Non-negative integer. The default zero corresponds to normal EKF, whereas iekf_iter > 0 corresponds to iterated EKF with iekf_iter iterations.

Value

List containing the log-likelihood, smoothed state estimates alphahat, and the corresponding variances Vt and Ptt.

Examples

 # Takes a while on CRAN
set.seed(1)
mu <- -0.2
rho <- 0.7
sigma_y <- 0.1
sigma_x <- 1
x <- numeric(50)
x[1] <- rnorm(1, mu, sigma_x / sqrt(1 - rho^2))
for(i in 2:length(x)) {
  x[i] <- rnorm(1, mu * (1 - rho) + rho * x[i - 1], sigma_x)
}
y <- rnorm(length(x), exp(x), sigma_y)

pntrs <- cpp_example_model("nlg_ar_exp")

model_nlg <- ssm_nlg(y = y, a1 = pntrs$a1, P1 = pntrs$P1, 
  Z = pntrs$Z_fn, H = pntrs$H_fn, T = pntrs$T_fn, R = pntrs$R_fn, 
  Z_gn = pntrs$Z_gn, T_gn = pntrs$T_gn,
  theta = c(mu= mu, rho = rho, 
    log_sigma_x = log(sigma_x), log_sigma_y = log(sigma_y)), 
  log_prior_pdf = pntrs$log_prior_pdf,
  n_states = 1, n_etas = 1, state_names = "state")

out_ekf <- ekf_smoother(model_nlg, iekf_iter = 0)
out_iekf <- ekf_smoother(model_nlg, iekf_iter = 1)
ts.plot(cbind(x, out_ekf$alphahat, out_iekf$alphahat), col = 1:3)

bssm documentation built on Nov. 2, 2023, 6:25 p.m.