Recent developments have demonstrated that particle filtering is an emerging and powerful methodology, using Monte Carlo methods, for sequential signal processing with a wide range of applications in science and engineering. It has captured the attention of many researchers in various communities, including those of signal processing, statistics and econometrics. Based on the concept of sequential importance sampling and the use of Bayesian theory, particle filtering is particularly useful in dealing with difficult nonlinear and non-Gaussian problems. The underlying principle of the methodology is the approximation of relevant distributions with random measures composed of particles (samples from the space of the unknowns) and their associated weights. First, we present a brief review of particle filtering theory; and then we show how it can be used for resolving many problems in wireless communications. We demonstrate its application to blind equalization, blind detection over flat fading channels, multiuser detection, and estimation and detection of space-time codes in fading channels.

Two decades ago, with the publication, we witnessed the rebirth of particle filtering (PF) as a methodology for sequential signal processing. Since then, PF has become very popular because of its ability to process observations represented by nonlinear state-space models where the noises of the model can be non-Gaussian. This methodology has been adopted in various fields, including finance, geophysical systems, wireless communications, control, navigation and tracking, and robotics. The popularity of PF has also spurred the publication of several review articles. In this article, the state of the art of resampling methods was reviewed. The methods were classified and their properties were compared in the framework of the proposed classifications. The emphasis in the article was on the classification and qualitative descriptions of the algorithms. The intention was to provide guidelines to practitioners and researchers.

Sequential Bayesian estimation for nonlinear dynamic state-space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations. This paper introduces a new filter called the Gaussian particle filter. It is based on the particle filtering concept, and it approximates the posterior distributions by single Gaussians, similar to Gaussian filters like the extended Kalman filter and its variants. It is shown that under the Gaussianity assumption, the Gaussian particle filter is asymptotically optimal in the number of particles and, hence, has much-improved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Simulation results are presented to demonstrate the versatility and improved performance of the Gaussian particle filter over conventional Gaussian filters and the lower complexity than known particle filters.

In the last decade, the research on and the technology for outdoor tracking have seen an explosion of advances. It is expected that in the near future, we will witness similar trends for indoor scenarios where people spend more than 70% of their lives. The rationale for this is that there is a need for reliable and high-definition real-time tracking systems that have the ability to operate in indoor environments, thus complementing those based on satellite technologies, such as the Global Positioning System (GPS). The indoor environments are very challenging, and as a result, a large variety of technologies have been proposed for coping with them, but no legacy solution has emerged. This paper presents a survey on indoor wireless tracking of mobile nodes from a signal processing perspective. It can be argued that the indoor tracking problem is more challenging than the problem on indoor localization. The reason is simple: From a set of measurements, one has to estimate not one location but a series of correlated locations of a mobile node. The paper illustrates the theory, the main tools, and the most promising technologies for indoor tracking. New directions of research are also discussed.

We use the Gaussian particle filter to build several types of Gaussian sum particle filters. These filters approximate the filtering and predictive distributions by weighted Gaussian mixtures and are basically banks of Gaussian particle filters. Then, we extend the use of Gaussian particle filters and Gaussian sum particle filters to dynamic state space (DSS) models with non-Gaussian noise. With non-Gaussian noise approximated by Gaussian mixtures, the non-Gaussian noise models are approximated by banks of Gaussian noise models, and Gaussian mixture filters are developed using algorithms developed for Gaussian noise DSS models. As a result, problems involving heavy-tailed densities can be conveniently addressed. Simulations are presented to exhibit the application of the framework developed herein, and the performance of the algorithms is examined.

The identification of neural stem and progenitor cells (NPCs) by in vivo brain imaging could have important implications for diagnostic, prognostic, and therapeutic purposes. We describe a metabolic biomarker for the detection and quantification of NPCs in the human brain in vivo. We used proton nuclear magnetic resonance spectroscopy to identify and characterize a biomarker in which NPCs are enriched and demonstrated its use as a reference for monitoring neurogenesis. To detect low concentrations of NPCs in vivo, we developed a signal processing method that enabled the use of magnetic resonance spectroscopy for the analysis of the NPC biomarker in both the rodent brain and the hippocampus of live humans. Our findings thus open the possibility of investigating the role of NPCs and neurogenesis in a wide variety of human brain disorders.