A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low-dimensional. This is of utmost importance for highperformance real-time applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter based algorithms. Here the use of non-linear models and non-Gaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map, and a car's horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable to satellite navigation (as GPS), but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

The task of acoustic source tracking plays an important role in many practical speech acquisition systems. This research presents an extensive study of sequential Monte Carlo methods applied to the source localisation problem, based on the signals received at an array of microphones. A general framework for acoustic source localisation using particle filtering is proposed, and four di#erent algorithms that fit within this framework are subsequently developed. To assess the performance of these new methods, statistical simulations are carried out using both synthetic and real-life samples of audio data. The simulation results demonstrate the superiority of an approach based on sequential estimation. The resulting particle filters are shown to drastically outperform traditional acoustic source localisation methods. Further

A hierarchical statistical model is made up generically of a data model, a process model, and occasionally a prior model for all the unknown parameters. The process model, known as the state equations in the filtering literature, is where most of the scientist's physical/chemical/biological knowledge about the problem is used. In the case of a dynamically changing configuration of objects moving through a spatial domain of interest, that knowledge is summarized through equations of motion with random perturbations. In this paper, our interest is in dynamically filtering noisy observations on these objects, where the state equations are nonlinear. Two recent methods of filtering, the Unscented Particle filter (UPF) and the Unscented Kalman filter, are presented and compared to the better known Extended Kalman filter. Other sources of nonlinearity arise when we wish to estimate nonlinear functions of the objects positions; it is here where the UPF shows its superiority, since optimal estimates and associated variances are straightforward to obtain.

... In this article, we propose a Monte Carlo method for linkage analysis based on sequential imputation. Unlike exact methods, sequential imputation can handle large pedigrees with a moderate number of loci in its current implementation. This Monte Carlo method is an application of importance sampling, in which we sequentially impute ordered genotypes locus by locus, and then impute inheritance vectors conditioned on these genotypes. The resulting inheritance vectors, together with the importance sampling weights, are used to derive a consistent estimator of any linkage statistic of interest. The linkage statistic can be parametric or nonparametric; we focus on nonparametric linkage statistics. We demonstrate that accurate estimates can be achieved within a reasonable computing time. A simulation study illustrates the potential gain in power using our method for multilocus linkage analysis with large pedigrees. We simulated data at six markers under three models. We analyzed them using both sequential imputation and GENEHUNTER. GENEHUNTER had to drop between 38--54% of pedigree members, whereas our method was able to use all pedigree members. The power gains of using all pedigree members were substantial under 2 of the 3 models. We implemented sequential imputation for multilocus linkage analysis in a user-friendly software package called SIMPLE.

Positioning in wireless networks is today mainly used for yellow page services, but its importance will grow when emergency call services become mandatory and with the advent of more advanced location based services and mobile gaming. It is also plausible that future resource management algorithms may rely on position estimation and prediction. We will in this survey paper discuss and illustrate possibilities and fundamental limitations associated with mobile positioning. 1.