Nonlinear Bootstrap Particle Filter (Univariate Non-Linear State Space Model)
pfNonlinBS function provides a simple example for
RcppSMC. It is a simple “bootstrap” particle filter which employs
multinomial resampling after each iteration applied to the ubiquitous "nonlinear
state space model" following Gordon, Salmond and Smith (1993).
simNonlin function simulates data from the associated model.
A vector variable containing the sequence of observations.
An integer specifying the number of particles.
A boolean variable describing whether a plot should illustrate the (posterior mean) estimated path along with one and two standard deviation intervals.
The length of data sequence to simulate.
pfNonlinbs function provides a simple example for
RcppSMC. It is based on a simple nonlinear state space model in
which the state evolution and observation equations are:
x(n) = 0.5 x(n-1) + 25 x(n-1) / (1+x(n-1)^2) + 8 cos(1.2(n-1))+ e(n) and
y(n) = x(n)^2 / 20 + f(n)
where e(n) and f(n) are mutually-independent normal random
variables of variances 10.0 and 1.0, respectively. A boostrap proposal
(i.e. sampling from the state equation) is used, together with multinomial
resampling after each iteration.
simNonlin function simulates from the same model.
pfNonlinBS function returns two vectors, the first containing the posterior
filtering means; the second the posterior filtering standard deviations.
simNonlin function returns a list containing the state and data sequences.
Adam M. Johansen and Dirk Eddelbuettel
N. J. Gordon, S. J. Salmond, and A. F. M. Smith. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings-F, 140(2):107-113, April 1993.
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