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Convex Analysisの二,三の進展について

Network localization and navigation (NLN) is a promising paradigm, in which mobile nodes exploit spatiotemporal cooperation, to provide reliable location information for a diverse range of wireless applications. This paper presents a theoretical foundation of NLN, including a mathematical formulation for NLN, an introduction of equivalent Fisher information analysis, and determination of the fundamental limits of localization accuracy. Key ingredients such as spatiotemporal cooperation, array signal processing, and map exploitation are then studied. We also develop a geometric interpretation to provide insights into the essence of NLN for network design. Finally, the paper highlights the connection between the theoretical foundation and algorithm development for NLN, guiding the design and operation of practical localization systems.

A Theoretical Foundation of Network Localization and Navigation

Situation-aware technologies enabled by multitarget tracking will lead to new services and applications in fields such as autonomous driving, indoor localization, robotic networks, and crowd counting In this tutorial paper, we advocate a recently proposed paradigm for scalable multitarget tracking that is based on message passing or, more concretely, the loopy sum–product algorithm This approach has advantages regarding estimation accuracy, computational complexity, and implementation flexibility Most importantly, it provides a highly effective, efficient, and scalable solution to the probabilistic data association problem, a major challenge in multitarget tracking This fact makes it attractive for emerging applications requiring real-time operation on resource-limited devices In addition, the message passing approach is intuitively appealing and suited to nonlinear and non-Gaussian models We present message-passing-based multitarget tracking methods for single-sensor and multiple-sensor scenarios, and for a known and unknown number of targets The presented methods can cope with clutter, missed detections, and an unknown association between targets and measurements We also discuss the integration of message-passing-based probabilistic data association into existing multitarget tracking methods The superior performance, low complexity, and attractive scaling properties of the presented methods are verified numerically In addition to simulated data, we use measured data captured by two radar stations with overlapping fields-of-view observing a large number of targets simultaneously

Message Passing Algorithms for Scalable Multitarget Tracking

Recent developments in random finite sets (RFSs) have yielded a variety of tracking methods that avoid data association. This paper derives a form of the full Bayes RFS filter and observes that data association is implicitly present, in a data structure similar to multiple hypothesis tracking (MHT). Subsequently, algorithms are obtained by approximating the distribution of associations. Two algorithms result: one nearly identical to joint integrated probabilistic data association (JIPDA), and another related to the multiple target multi-Bernoulli (MeMBer) filter. Both improve performance in challenging environments.

Marginal multi-bernoulli filters: RFS derivation of MHT, JIPDA, and association-based member

We propose an algorithm for tracking an unknown number of targets based on measurements provided by multiple sensors. Our algorithm achieves low computational complexity and excellent scalability by running belief propagation on a suitably devised factor graph. A redundant formulation of data association uncertainty and the use of “augmented target states” including binary target indicators make it possible to exploit statistical independencies for a drastic reduction of complexity. An increase in the number of targets, sensors, or measurements leads to additional variable nodes in the factor graph but not to higher dimensions of the messages. As a consequence, the complexity of our method scales only quadratically in the number of targets, linearly in the number of sensors, and linearly in the number of measurements per sensor. The performance of the method compares well with that of previously proposed methods, including methods with a less favorable scaling behavior. In particular, our method can outperform multisensor versions of the probability hypothesis density (PHD) filter, the cardinalized PHD filter, and the multi-Bernoulli filter.

A Scalable Algorithm for Tracking an Unknown Number of Targets Using Multiple Sensors

Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate inference method, belief propagation (BP), to obtain estimates of marginal association probabilities. We prove that BP is guaranteed to converge, and bound the number of iterations necessary. Experiments reveal a favourable comparison to prior methods in terms of accuracy and computational complexity.

Approximate evaluation of marginal association probabilities with belief propagation

Data association is the problem of determining the correspondence between targets and measurements. In this paper, we present a graphical model approach to data association and apply an approximate inference method, loopy belief propagation, to obtain the marginal association weights (e.g., for JPDA). In general, loopy belief propagation is not guaranteed to converge, and when convergence is obtained the result is not guaranteed to be the correct answer. We investigate the convergence properties of a loopy belief propagation algorithm for data association, proving that it converges, and demonstrating its practical efficiency. A greatly simplified implementation is provided, which exploits the structure in the factors to reduce the cost per iteration from O(m2n2) to O(mn) operations where n is the number of targets and m is the number of measurements. Combined with the previously published results on the accuracy of the approximation, the convergence results reveal loopy belief propagation as a highly attractive method for approximate calculation of joint association weights.

Convergence of loopy belief propagation for data association

Data association, the reasoning over correspondence between targets and measurements, is a problem of fundamental importance in target tracking. Recently, belief propagation (BP) has emerged as a promising method for estimating the marginal probabilities of measurement to target association, providing fast, accurate estimates. The excellent performance of BP in the particular formulation used may be attributed to the convexity of the underlying free energy, which it implicitly optimizes. This paper studies multiple scan data association problems, i.e., problems that reason over correspondence between targets and several sets of measurements, which may correspond to different sensors or different time steps. We find that the multiple scan extension of the single scan BP formulation is nonconvex and demonstrate the undesirable behavior that can result. A convex free energy is constructed using the recently proposed fractional free energy (FFE). A convergent, BP-like algorithm is provided for the single scan FFE, and employed in optimizing the multiple scan free energy using primal-dual coordinate ascent. Finally, based on a variational interpretation of joint probabilistic data association (JPDA), we develop a sequential variant of the algorithm that is similar to JPDA, but retains consistency constraints from prior scans. The performance of the proposed methods is demonstrated on a bearings only target localization problem.

Roslyn A. Lau

Papers

Message Passing Algorithms for Scalable Multitarget Tracking

Approximate evaluation of marginal association probabilities with belief propagation

Convergence of loopy belief propagation for data association

Multiple Scan Data Association by Convex Variational Inference

Approximate evaluation of marginal association probabilities with belief propagation