Models and algorithms for tracking of maneuvering objects using variable rate particle filters

Standard algorithms in tracking and other state-space models assume identical and synchronous sampling rates for the state and measurement processes. However, real trajectories of objects are typically characterized by prolonged smooth sections, with sharp, but infrequent, changes. Thus, a more parsimonious representation of a target trajectory may be obtained by direct modeling of maneuver times in the state process, independently from the observation times. This is achieved by assuming the state arrival times to follow a random process, typically specified as Markovian, so that state points may be allocated along the trajectory according to the degree of variation observed. The resulting variable dimension state inference problem is solved by developing an efficient variable rate particle filtering algorithm to recursively update the posterior distribution of the state sequence as new data becomes available. The methodology is quite general and can be applied across many models where dynamic model uncertainty occurs on-line. Specific models are proposed for the dynamics of a moving object under internal forcing, expressed in terms of the intrinsic dynamics of the object. The performance of the algorithms with these dynamical models is demonstrated on several challenging maneuvering target tracking problems in clutter. © 2006 IEEE.

The role of the catalytic particle in the growth of carbon nanotubes by plasma enhanced chemical vapor deposition

Vertically aligned carbon nanotubes were synthesized by plasma enhanced chemical vapor deposition using nickel as a metal catalyst. High resolution transmission electron microscopy analysis of the particle found at the tip of the tubes reveals the presence of a metastable carbide Ni3C. Since the carbide is found to decompose upon annealing at 600 degreesC, we suggest that Ni3C is formed after the growth is stopped due to the rapid cooling of the Ni-C interstitial solid solution. A detailed description of the tip growth mechanism is given, that accounts for the composite structure of the tube walls. The shape and size of the catalytic particle determine the concentration gradient that drives the diffusion of C atoms across and though the metal. (C) 2004 American Institute of Physics.

Resistance of cast polyurethane elastomers to solid particle erosion

The rates of erosive wear have been measured for a series of eight polyester-based one-component castable polyurethane elastomers, with widely varying mechanical properties. Erosion tests were conducted with airborne silica sand, 120μm in particle size, at an impact velocity of 50 ms-1 and impact angles of 30° and 90°. For these materials, which all showed similar values of rebound resilience, the erosion rate increased with increasing hardness, tensile modulus and tensile strength. These findings are at variance with those expected for wear by abrasion, perhaps because of differences in the strain rate or strain levels imposed on the elastomer during erosion and abrasion.

Comparative study of the slurry erosion and free-fall particle erosion of aluminum

A study has been performed of the erosion of aluminium by silica sand particles at a velocity of 4.5 m s-1, both air-borne and in the form of a water-borne slurry. Measurements made under similar experimental conditions show that slurry erosion proceeds at a rate several times that of air-borne erosion, the ratio of the two rates depending strongly on the angle of impact. Sand particles become embedded into the metal surface during air-borne particle erosion, forming a composite layer of metal and silica, and provide the major cause of the difference in wear rate. The embedded particles giving rise to surface hardening and a significant reduction in the erosion rate. Embedment of erodent particles was not observed during slurry erosion. Lubrication of the impacting interfaces by water appears to have minimal effect on the wear of aluminium by slurry erosion.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.