Multiple Target Tracking Based on Sets of Trajectories Garcia-Fernandez, Angel F.; Svensson, Lennart; Morelande, Mark R.
IEEE transactions on aerospace and electronic systems,
06/2020, Letnik:
56, Številka:
3
Journal Article
Recenzirano
Odprti dostop
We propose a solution of the multiple target tracking (MTT) problem based on sets of trajectories and the random finite set framework. A full Bayesian approach to MTT should characterize the ...distribution of the trajectories given the measurements, as it contains all information about the trajectories. We attain this by considering multiobject density functions in which objects are trajectories. For the standard tracking models, we also describe a conjugate family of multitrajectory density functions.
The problem considered in this paper is detection and estimation of multiple radiation sources using a time series of radiation counts from a collection of sensors. A Bayesian framework is adopted. ...Source detection is approached as a model selection problem in which competing models are compared using partial Bayes factors. Given the number of sources, the posterior mean is the minimum mean square error estimator of the source parameters. Exact calculation of the partial Bayes factors and the posterior mean is not possible due to the presence of intractable integrals. Importance sampling using progressive correction is proposed as a computationally efficient method for approximating these integrals. Previously proposed algorithms have been restricted to one or two sources. A simulation analysis shows that the proposed methods can detect and accurately estimate the parameters of four sources with reasonable computational expense.
This paper considers the multi-target tracking (MTT) problem through the use of dynamic programming based track-before-detect (DP-TBD) methods. The usual solution of this problem is to adopt a ...multi-target state, which is the concatenation of individual target states, then search the estimate in the expanded multi-target state space. However, this solution involves a high-dimensional joint maximization which is computationally intractable for most realistic problems. Additionally, the dimension of the multi-target state has to be determined before implementing the DP search. This is problematic when the number of targets is unknown. We make two contributions towards addressing these problems. Firstly, by factorizing the joint posterior density using the structure of MTT, an efficient DP-TBD algorithm is developed to approximately solve the joint maximization in a fast but accurate manner. Secondly, we propose a novel detection procedure such that the dimension of the multi-target state no longer needs be to pre-determined before the DP search. Our analysis indicates that the proposed algorithm could achieve a computational complexity which is almost linear to the number of processed frames and independent of the number of targets. Simulation results show that this algorithm can accurately estimate the number of targets and reliably track multiple targets even when targets are in proximity.
This paper considers the problem of simultaneously detecting and tracking multiple targets. The problem can be formulated in a Bayesian framework and solved, in principle, by computation of the joint ...multitarget probability density (JMPD). In practice, exact computation of the JMPD is impossible, and the predominant challenge is to arrive at a computationally tractable approximation. A particle filtering scheme is developed for this purpose in which each particle is a hypothesis on the number of targets present and the states of those targets. The importance density for the particle filter is designed in such a way that the measurements can guide sampling of both the target number and the target states. Simulation results, with measurements generated from real target trajectories, demonstrate the ability of the proposed procedure to simultaneously detect and track ten targets with a reasonable sample size
Particle filter (PF) based multi-target tracking (MTT) methods suffer from the curse of dimensionality. Existing strategies to combat this assume posterior independence between target states, in ...order to then sample targets independently, or to perform joint sampling of closely spaced targets only. When many targets are in proximity, these strategies either perform poorly or are too computationally expensive. We make two contributions towards addressing these limitations. Firstly, we advocate an alternative view of the use of posterior independence which emphasizes the statistical effect of assuming posterior independence on the Monte Carlo (MC) approximation of posterior density. Our analysis suggests that assuming posterior independence can provide a better MC approximation of the prior distribution at the next time, and therefore the posterior at the next time, without regard for how sampling is performed. Secondly, we present a computationally efficient, measurement directed, joint sampling method to cope with the target coupling and measurement ambiguity when targets are near each other. Consequently, we develop a PF which employs posterior independence while sampling targets jointly. This PF is applicable to both the traditional thresholded and track-before-detect style pixelized models. Simulation results for a challenging tracking scenario show that the proposed PF substantially outperforms existing approaches.
Kalman filter, particle filter, IMM, PDA, ITS, random sets... The number of useful object-tracking methods is exploding. But how are they related? How do they help track everything from aircraft, ...missiles and extra-terrestrial objects to people and lymphocyte cells? How can they be adapted to novel applications? Fundamentals of Object Tracking tells you how. Starting with the generic object-tracking problem, it outlines the generic Bayesian solution. It then shows systematically how to formulate the major tracking problems – maneuvering, multiobject, clutter, out-of-sequence sensors – within this Bayesian framework and how to derive the standard tracking solutions. This structured approach makes very complex object-tracking algorithms accessible to the growing number of users working on real-world tracking problems and supports them in designing their own tracking filters under their unique application constraints. The book concludes with a chapter on issues critical to successful implementation of tracking algorithms, such as track initialization and merging.
A theoretical analysis is presented of the correction step of the Kalman filter (KF) and its various approximations for the case of a nonlinear measurement equation with additive Gaussian noise. The ...KF is based on a Gaussian approximation to the joint density of the state and the measurement. The analysis metric is the Kullback-Leibler divergence of this approximation from the true joint density. The purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the KF and its variants in nonlinear scenarios. This is illustrated using a numerical example.
This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, ...sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples.
Parametric estimation of phase-modulated signals (PMS) in additive white Gaussian noise is considered. The prohibitive computational expense of maximum likelihood estimation for this problem has led ...to the development of many suboptimal estimators which are relatively inaccurate and cannot operate at low signal-to-noise ratios (SNRs). In this paper, a novel technique based on a probabilistic unwrapping of the phase of the observations is developed. The method is capable of more accurate estimation and operates effectively at much lower SNRs than existing algorithms. This is demonstrated in Monte Carlo simulations.
Truncated Unscented Kalman Filtering Garcia-Fernandez, A. F.; Morelande, M. R.; Grajal, J.
IEEE transactions on signal processing,
07/2012, Letnik:
60, Številka:
7
Journal Article
Recenzirano
We devise a filtering algorithm to approximate the first two moments of the posterior probability density function (PDF). The novelties of the algorithm are in the update step. If the likelihood has ...a bounded support, we can use a modified prior distribution that meets Bayes' rule exactly. Applying a Kalman filter (KF) to the modified prior distribution, referred to as truncated Kalman filter (TKF), can vastly improve the performance of the conventional Kalman filter, particularly when the measurements are informative relative to the prior. The application of the TKF to practical problems in which the measurement noise PDF has unbounded support is achieved by imposing several approximating assumptions which are valid only when the measurements are informative. This implies that we adaptively choose between an approximation to the KF or the TKF according to the information provided by the measurement. The resulting algorithm based on the unscented transformation is referred to as truncated unscented KF.
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