Description Usage Arguments Value Note Author(s) References Examples
View source: R/stateEstimation.R
Estimates the filtered state and the log-likelihood for a linear Gaussian state space model of the form x_{t} = φ x_{t-1} + σ_v v_t and y_t = x_t + σ_e e_t , where v_t and e_t denote independent standard Gaussian random variables, i.e.N(0,1).
1 | kalmanFilter(y, theta, initialState, initialStateCovariance)
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y |
Observations from the model for t=1,...,T. |
theta |
The parameters θ=\{φ,σ_v,σ_e\} of the LGSS model. The parameter φ scales the current state in the state dynamics. The standard deviations of the state process noise and the observation process noise are denoted σ_v and σ_e, respectively. |
initialState |
The initial state. |
initialStateCovariance |
The initial covariance of the state. |
The function returns a list with the elements:
xHatFiltered: The estimate of the filtered state at time t=1,...,T.
logLikelihood: The estimate of the log-likelihood.
See Section 3 in the reference for more details.
Johan Dahlin uni@johandahlin.com
Dahlin, J. & Schon, T. B. "Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models." Journal of Statistical Software, Code Snippets, 88(2): 1–41, 2019.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | # Generates 500 observations from a linear state space model with
# (phi, sigma_e, sigma_v) = (0.5, 1.0, 0.1) and zero initial state.
theta <- c(0.5, 1.0, 0.1)
d <- generateData(theta, noObservations=500, initialState=0.0)
# Estimate the filtered state using Kalman filter
kfOutput <- kalmanFilter(d$y, theta,
initialState=0.0, initialStateCovariance=0.01)
# Plot the estimate and the true state
par(mfrow=c(3, 1))
plot(d$x, type="l", xlab="time", ylab="true state", bty="n",
col="#1B9E77")
plot(kfOutput$xHatFiltered, type="l", xlab="time",
ylab="Kalman filter estimate", bty="n", col="#D95F02")
plot(d$x-kfOutput$xHatFiltered, type="l", xlab="time",
ylab="difference", bty="n", col="#7570B3")
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