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 Gaussian mixture MCMC particle algorithm for dynamic cluster tracking

We present a novel filtering algorithm for tracking multiple clusters of coordinated objects. Based on a Markov chain Monte Carlo (MCMC) mechanism, the new algorithm propagates a discrete approximation of the underlying filtering density. A dynamic Gaussian mixture model is utilized for representing the time-varying clustering structure. This involves point process formulations of typical behavioral moves such as birth and death of clusters as well as merging and splitting. For handling complex, possibly large scale scenarios, the sampling efficiency of the basic MCMC scheme is enhanced via the use of a Metropolis within Gibbs particle refinement step. As the proposed methodology essentially involves random set representations, a new type of estimator, termed the probability hypothesis density surface (PHDS), is derived for computing point estimates. It is further proved that this estimator is optimal in the sense of the mean relative entropy. Finally, the algorithm's performance is assessed and demonstrated in both synthetic and realistic tracking scenarios. © 2012 Elsevier Ltd. All rights reserved.

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.

Video tracking using dual-treewavelet polar matching and particle filtering

In this paper, we describe a video tracking application using the dual-tree polar matching algorithm. The models are specified in a probabilistic setting, and a particle ilter is used to perform the sequential inference. Computer simulations demonstrate the ability of the algorithm to track a simulated video moving target in an urban environment with complete and partial occlusions. © The Institution of Engineering and Technology.

A backward-simulation based Rao-Blackwellized particle smoother for conditionally linear Gaussian models

In this article, we develop a new Rao-Blackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forward-filtering backward-simulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space of the non-Gaussian state component while treating the linear part analytically. Unlike the previously proposed backward-simulation based Rao-Blackwellized smoothing approaches, it does not require sampling of the Gaussian state component and is also able to overcome certain normalization problems of two-filter smoother based approaches. The performance of the algorithm is illustrated in a simulated application. © 2012 IFAC.

Interactive multi-objective particle swarm optimisation using decision space interaction

The most common approach to decision making in multi-objective optimisation with metaheuristics is a posteriori preference articulation. Increased model complexity and a gradual increase of optimisation problems with three or more objectives have revived an interest in progressively interactive decision making, where a human decision maker interacts with the algorithm at regular intervals. This paper presents an interactive approach to multi-objective particle swarm optimisation (MOPSO) using a novel technique to preference articulation based on decision space interaction and visual preference articulation. The approach is tested on a 2D aerofoil design case study and comparisons are drawn to non-interactive MOPSO. © 2013 IEEE.