The simNonlin function simulates data from the models used
in link{pfNonlinBS} and link{nonLinPMMH}.
simNonlin(len = 50, var_init = 10, var_evol = 10, var_obs = 1,
cosSeqOffset = -1)The length of data sequence to simulate.
The variance of the noise for the initial state.
The variance of the noise for the state evolution .
The variance of the observation noise.
This is related to the indexing in the cosine function in the evoluation equation. A value of -1 can be used to follow the specification of Gordon, Salmond and Smith (1993) and 0 can be used to follow Andrieu, Doucet and Holenstein (2010).
The simNonlin function returns a list containing the state and data sequences.
The simNonlin function simulates from
a simple nonlinear state space model with
state evolution and observation equations:
\(x(n) = 0.5 x(n-1) + 25 x(n-1) / (1+x(n-1)^2) + 8 cos(1.2(n+cosSeqOffset))+ e(n)\) and
\(y(n) = x(n)^2 / 20 + f(n)\)
where \(e(n)\) and \(f(n)\) are mutually-independent normal random variables of variances var_evol and var_obs, respectively, and \(x(0) ~ N(0,var_init)\).
Different variations of this model can be found in Gordon, Salmond and Smith (1993) and Andrieu, Doucet and Holenstein (2010). A cosSeqOffset of -1 is consistent with the former and 0 is consistent with the latter.
C. Andrieu, A. Doucet, and R. Holenstein. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(3):269-342, 2010.
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.
pfNonlinBS for a simple bootrap particle filter
applied to this model and nonLinPMMH for particle
marginal Metropolis Hastings applied to estimating the standard
deviation of the state evolution and observation noise.