Marco Guerriero

Shooting two birds with two bullets: How to find Minimum Mean OSPA estimates

Most area-defense formulations follow from the assumption that threats must first be identified and then neutralized. This is reasonable, but inherent to it is a process of labeling: threat A must be identified and then threat B, and then action must be taken. This manuscript begins from the assumption that such labeling (A & B) is irrelevant. The problem naturally devolves to one of Random Finite Set (RFS) estimation: we show that by eschewing any concern of target label we relax the estimation procedure, and it is perhaps not surprising that by such a removal of constraint (of labeling) performance (in terms of localization) is enhanced. A suitable measure for the estimation of unla-beled objects is the Mean OSPA (MOSPA). We derive a general algorithm which provided the optimal estimator which minimize the MOSPA. We call such an estimator a Minimum MOSPA (MMOSPA) estimator.

Set JPDA Filter for Multitarget Tracking

In this article, we show that when targets are closely spaced, traditional tracking algorithms can be adjusted to perform better under a performance measure that disregards identity. More specifically, we propose an adjusted version of the joint probabilistic data association (JPDA) filter, which we call set JPDA (SJPDA). Through examples and theory we motivate the new approach, and show its possibilities. To decrease the computational requirements, we further show that the SJPDA filter can be formulated as a continuous optimization problem which is fairly easy to handle. Optimal approximations are also discussed, and an algorithm, Kullback-Leibler SJPDA (KLSJPDA), which provides optimal Gaussian approximations in the Kullback-Leibler sense is derived. Finally, we evaluate the SJPDA filter on two scenarios with closely spaced targets, and compare the performance in terms of the mean optimal subpattern assignment (MOSPA) measure with the JPDA filter, and also with the Gaussian-mixture cardinalized probability hypothesis density (GM-CPHD) filter. The results show that the SJPDA filter performs substantially better than the JPDA filter, and almost as well as the more complex GM-CPHD filter.

Bayesian Data Fusion for Distributed Target Detection in Sensor Networks

In this correspondence, we study different approaches for Bayesian data fusion for distributed target detection in sensor networks. Due to communication and bandwidth constraints, we assume that each sensor can only transmit a local decision to the fusion center (FC), which is in charge to take the final decision about the presence of a target. The optimal Bayesian test statistic at the FC is derived in the case where both the number and locations of the sensors are known. On the other hand, if both the number and the locations of the sensors are unknown, the optimal Bayesian test statistic is computed based on the same observations that the Scan Statistic test utilizes. The performances of the different approaches are compared through simulation.

Distributed Target Detection in Sensor Networks Using Scan Statistics

We introduce a sequential procedure to detect a target with distributed sensors in a two dimensional region. The detection is carried out in a mobile fusion center which successively counts the number of binary decisions reported by local sensors lying inside its moving field of view. This is a two-dimensional scan statistic-an emerging tool from the statistics field that has been applied to a variety of anomaly detection problems such as of epidemics or computer intrusion, but that seems to be unfamiliar to the signal processing community. We show that an optimal size of the field of view exists. We compare the sequential two-dimensional scan statistic test and two other tests. Results for system level detection are presented.

Stochastic Resonance in Sequential Detectors

Stochastic resonance (SR) is a nonlinear phenomenon known in physics that has attracted recent interest in the signal-processing literature, and specifically in the context of detection. We investigate the SR effect arising in sequential detectors for shift-in-mean binary hypothesis testing and characterize the optimal resonance as the solution of specific optimization problems. One particular (and at first glance perhaps counterintuitive) finding is that certain sequential detection procedures can be made more efficient by randomly adding or subtracting a suitable constant value to the data at the input of the detector.

An approximate Minimum MOSPA estimator

Optimizing over a variant of the Mean Optimal Subpattern Assignment (MOSPA) metric is equivalent to optimizing over the track accuracy statistic often used in target tracking benchmarks. Past work has shown how obtaining a Minimum MOSPA (MMOSPA) estimate for target locations from a Probability Density Function (PDF) outperforms more traditional methods (e.g. maximum likelihood (ML) or Minimum Mean Squared Error (MMSE) estimates) with regard to track accuracy metrics. In this paper, we derive an approximation to the MMOSPA estimator in the two-target case, which is generally very complicated, based on minimizing a Bhattacharyya-like bound. It has a particularly nice form for Gaussian mixtures. We thence compare the new estimator to that obtained from using the MMSE and the optimal MMOSPA estimators.

Selective Measurement Transmission in Distributed Estimation With Data Association

In distributed multisensor estimation/tracking the problem of fusion is complicated by that of data association (i.e., with false alarms and missed detections): not only is it of concern to provide an estimation-efficient sensor level quantization of the “target-originated” measurement, but it is also unclear which among each sensors measurements this might be, if any at all. The former issue has been studied previously; in this paper we address only the latter concern. At first we assume that each sensor is tasked to communicate exactly one of its observations to a Fusion Center (FC) for a global estimate, and we work in one dimension. Via order statistics we show that, surprisingly, the nearest neighbor (NN) is not always the most appropriate measurement to share. We also expand our bandwidth to allow for transmission of multiple measurements, for example the nearest and third-nearest: it turns out that a single-measurement transmission is more bandwidth efficient than multiple. The analysis and results are further extended to two dimensions, but the moral-that sharing of the NNs is not always a good idea-remains.

Some aspects of DOA estimation using a network of blind sensors

Recently, the DOA (direction of arrival) estimation of an acoustic wavefront has been considered in a setting where the inference task is performed by a wireless sensor network (WSN) made of isotropic (hence individually useless) sensors. The WSN was designed according to the SENMA (SEnsor Network with Mobile Agents) architecture with a mobile agent (MA) that successively queries the sensors lying inside its field of view. In this paper the ideal assumption previously made that the visibility of individual sensors is governed by deterministic laws is relaxed; this yields, interestingly, simpler analytical formulas. Both fast/simple and optimal DOA-estimation schemes are proposed, and an optimization of the MAs observation management is also carried out, with the surprising finding that the MA ought to orient itself at an oblique angle to the expected DOA, rather than directly toward it. The extension to multiple sources is also considered; intriguingly, per-source DOA accuracy is higher when there is more than one source. In all cases, performance is investigated by simulation and compared, when appropriate, with asymptotic bounds; these latter are usually met after a moderate number of MA dwells.

Analysis of Scan and Batch Processing Approaches to Static Fusion in Sensor Networks

Multi-sensor tracking holds the potential for improving the surveillance performance achieved through single-sensor tracking. This potential has been demonstrated in many domains: at NURC, in the context of multi-static undersea surveillance. Nonetheless, the issue remains of how best to process data in large sensor networks. This issue is taken up in this paper. We are interested to compare multi-sensor scan-based tracking with a two-stage approach: static fusion followed by scan-based tracking. This paper focuses on some candidate methodologies for static fusion. The methods developed in this paper fall into two categories. The scan-based approach leverages the Gaussian mixture probabilistic hypothesis density (GM-PHD) filter; the batch approaches are based on scan statistics, and on the multi-hypothesis PDA (MHPDA). Preliminary simulation-based performance analysis suggests that the MHPDA approach to static fusion is the most robust in dealing with closely spaced targets and small sensor networks. Leveraging the results presented here, follow-on work will address the determination of an optimal fusion and tracking architecture. In particular, we will test scan-based tracking based on the NURC distributed multi-hypothesis tracker (DMHT), with MHPDA processing followed by scan-based tracking (with the DMHT). We anticipate that, for large sensor networks, the latter approach will outperform the former.

A Repeated Significance Test With Applications To Sequential Detection In Sensor Networks

In this paper we introduce a randomly truncated sequential hypothesis test. Using the framework of a repeated significance test (RST), we study a sequential test with truncation time based on a random stopping time. Using the functional central limit theorem (FCLT) for a sequence of statistics, we derive a general result that can be employed in developing a repeated significance test with random sample size. We present effective methods for evaluating accurate approximations for the probability of type I error and the power function. Numerical results are presented to evaluate the accuracy of these approximations. We apply the proposed test to a decentralized sequential detection problem in sensor networks (SNs) with communication constraints. Finally, a sequential detection problem with measurements at random times is investigated.