Performance evaluation of UKF-based nonlinear filtering

Particle filtering (PF) is a new class of algorithms to solve the nonlinear filtering problem. These PFs are very general and easy to code. The main issue with PF is the large computational complexity. In particular, for typical low dimensional tracking problems, the PF requires 2 to 6 orders of magnitude more computer throughput than the extended Kalman filter, to achieve the same accuracy. It has been asserted that the PF avoids the curse of dimensionality, but there is no formula or theorem that bounds or, approximates the computational complexity of the PF as a function of dimension (d). In this paper, we derive a simple back-of-the-envelope formula that explains why a carefully designed PF should mitigate the curse of dimensionality for certain filtering problems, but the PF does not avoid the curse of dimensionality in general. We also show experimental results which c o n f i i our simple formula. We consider this a triumph of theory. This new theory hinges on the fact that the volume of the d dimensional unit sphere is an amazingly small fraction of the volume of the d dimensional unit cube, for large d.

Curse of dimensionality and particle filters

This paper proposes a numerical-integration perspective on the Gaussian filters. A Gaussian filter is approximation of the Bayesian inference with the Gaussian posterior probability density assumption being valid. There exists a variation of Gaussian filters in the literature that derived themselves from very different backgrounds. From the numerical-integration viewpoint, various versions of Gaussian filters are only distinctive from each other in their specific treatments of approximating the multiple statistical integrations. A common base is provided for the first time to analyze and compare Gaussian filters with respect to accuracy, efficiency and stability factor. This study is expected to facilitate the selection of appropriate Gaussian filters in practice and to help design more efficient filters by employing better numerical integration methods

A Numerical-Integration Perspective on Gaussian Filters

We review methods for kinematic tracking of the human body in video. The review is part of a projected book that is intended to cross-fertilize ideas about motion representation between the animation and computer vision communities. The review confines itself to the earlier stages of motion, focusing on tracking and motion synthesis; future material will cover activity representation and motion generation.

http://www.nowpublishers.com/article/DownloadSummary/CGV-005

Computational Studies of Human Motion

This paper is the second part in a series that provides a comprehensive survey of maneuvering target tracking without addressing the so-called measurement-origin uncertainty. It surveys motion models of ballistic targets used for target tracking. Models for all three phases (i.e., boost, coast, and reentry) of motion are covered.

Survey of Maneuvering Target Tracking. Part II: Motion Models of Ballistic and Space Targets

This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.

Tracking a ballistic target: comparison of several nonlinear filters

Tracking of a ballistic re-entry object from radar observations is a highly complex problem in nonlinear filtering. The paper adopts a one-dimensional vertical motion model with unknown ballistic coefficient, derives and analyses the posterior Cramer-Rao lower bounds (CRLBs) for this problem, and compares the error performance of three nonlinear filters against the theoretical CRLBs. The considered nonlinear filters include the extended Kalman filter, the unscented Kalman filter and the bootstrap (particle) filter. Taking into account the computational and statistical performance, the unscented Kalman filter is found to be the preferred choice for this application.

Performance bounds and comparison of nonlinear filters for tracking a ballistic object on re-entry

This paper studies the problem of tracking a re-entry ballistic object by means of radar measurements. Practical applications are in the fields of surveillance for defense and for safety against the re-entry of old satellites. In particular, the investigation determines the estimation accuracy of the impact point of a ballistic target by processing radar measurements during the re-entry phase of the target. In practice, the radar measurements are available only for a limited part of the re-entry trajectory; while it is of interest to estimate the target landing point and its accuracy. This problem is tackled via non linear filtering technique and by resorting to the theory of Cramer-Rao lower bound (CRLB) recently developed for such filters.

Estimation accuracy of a landing point of a ballistic target

A comparative study of the Benes filtering problem

Tracking of a ballistic reentry object from radar observations is a highly complex problem in nonlinear filtering. We derive the Cramer-Rao lower bounds (CRLBs) for the variance of the estimation error for this problem. Subsequently we compare several nonlinear filtering techniques to the derived CRLBs. The considered nonlinear filters include the extended Kalman filter, the unscented Kalman filter and the bootstrap (particle) filter. Considering the computational and statistical performance, the unscented Kalman filter is found to be the preferred choice for this application.

D. Benvenuti

Papers

Tracking a ballistic target: comparison of several nonlinear filters

Performance bounds and comparison of nonlinear filters for tracking a ballistic object on re-entry

Estimation accuracy of a landing point of a ballistic target

A comparative study of the Benes filtering problem

Tracking a ballistic object on reentry: performance bounds and comparison of nonlinear filters