Nonlinear non-Gaussian state-space models are ubiquitous
in statistics, econometrics, information engineering and signal processing.
Particle methods, also known as Sequential Monte Carlo (SMC)
methods, provide reliable numerical approximations to the associated
state inference problems. However, in most applications, the state-space
model of interest also depends on unknown static parameters that need
to be estimated from the data. In this context, standard particle methods
fail and it is necessary to rely on more sophisticated algorithms.
The aim of this paper is to present a comprehensive review of particle
methods that have been proposed to perform static parameter estimation
in state-space models. We discuss the advantages and limitations
of these methods and illustrate their performance on simple models.