bssm (version 2.0.2)

ukf: Unscented Kalman Filtering

Description

Function ukf runs the unscented Kalman filter for the given non-linear Gaussian model of class ssm_nlg, and returns the filtered estimates and one-step-ahead predictions of the states \(\alpha_t\) given the data up to time \(t\).

Usage

ukf(model, alpha = 0.001, beta = 2, kappa = 0)

Value

List containing the log-likelihood, one-step-ahead predictions at and filtered estimates att of states, and the corresponding variances Pt and Ptt.

Arguments

model

Model of class ssm_nlg.

alpha

Positive tuning parameter of the UKF. Default is 0.001. Smaller the value, closer the sigma point are to the mean of the state.

beta

Non-negative tuning parameter of the UKF. The default value is 2, which is optimal for Gaussian states.

kappa

Non-negative tuning parameter of the UKF, which also affects the spread of sigma points. Default value is 0.

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(50, 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_iekf <- ekf(model_nlg, iekf_iter = 5)
out_ukf <- ukf(model_nlg, alpha = 0.01, beta = 2, kappa = 1)
ts.plot(cbind(x, out_iekf$att, out_ukf$att), col = 1:3)