Editorial 2241

In most problems of sequential signal processing, measured or received data are processed in real time. Typically, the data are modeled by state-space models with linear or nonlinear unknowns and noise sources that are assumed either Gaussian or non-Gaussian. When the models describing the data are linear and the noise is Gaussian, the optimal solution is the renowned Kalman filter. For models that deviate from linearity and Gaussianity, many different methods exist, of which the best known perhaps is the extended Kalman filter. About a decade ago, Gordon et al. published an article on nonlinear and non-Gaussian state estimation that captured much attention of the signal processing community [1]. The article introduced a method for sequential signal processing based onMonte Carlo sampling and showed that the method may have profound potential. Not surprisingly, it has incited a great deal of research, which has contributed to making sequential signal processing by Monte Carlo methods one of the most prominent developments in statistical signal processing in the recent years. The underlying idea of the method is the approximation of posterior densities by discrete randommeasures. Themeasures are composed of samples from the states of the unknowns and of weights associated with the samples. The samples are usually referred to as particles, and the process of updating the random measures with the arrival of new data as particle filtering. One may view particle filtering as exploration of the space of unknowns with random grids whose nodes are the particles. With the acquisition of new data, the random grids evolve and their nodes are assigned weights to approximate optimally the desired densities. The assignment of new weights is carried out recursively and is based on Bayesian importance sampling theory. The beginnings of particle filtering can be traced back to the late 1940s and early 1950s, which were followed in the last fifty years with sporadic outbreaks of intense activity [2]. Although its implementation is computationally intensive, the widespread availability of fast computers and the amenability of the particle filtering methods for parallel implementation make them very attractive for solving difficult signal processing problems. The papers of the special issue may be arranged into four groups, that is, papers on (1) general theory, (2) applications of particle filtering to target tracking, (3) applications of particle filtering to communications, and (4) applications of particle filtering to speech andmusic processing. In this issue, we do not have tutorials on particle filtering, and instead, we refer the reader to some recent references [3, 4, 5, 6].