Journal papers by Peter Willett
In this letter we propose the Rao test as a simpler alternative to the generalized likelihood rat... more In this letter we propose the Rao test as a simpler alternative to the generalized likelihood ratio test (GLRT) for multisensor fusion. We consider sensors observing an unknown deterministic parameter with symmetric and unimodal noise. A decision fusion center (DFC) receives quantized sensor observations through error-prone binary symmetric channels and makes a global decision. We analyze the optimal quantizer thresholds and we study the performance of the Rao test in comparison to the GLRT. Also, a theoretical comparison is made and asymptotic performance is derived in a scenario with homogeneous sensors. All the results are confirmed through simulations.
Papers by Peter Willett
Proceedings of SPIE, May 2, 2017
IEEE Transactions on Signal Processing, May 1, 2016
IEEE Transactions on Aerospace and Electronic Systems, Oct 1, 2015
The IMM estimator outperforms fixed model filters, e.g. the Kalman filter, in scenarios where the... more The IMM estimator outperforms fixed model filters, e.g. the Kalman filter, in scenarios where the targets have periods of disparate behavior. Key to the good performance and low complexity is the mode mixing. Here we propose a systematic approach to mode mixing when the modes have states of different dimensions. The proposed approach is general and encompasses previously suggested solutions. Different mixing approaches are compared, and the proposed methodology is shown to perform very well.
arXiv (Cornell University), Jan 16, 2023
We study the performance of machine learning binary classification techniques in terms of error p... more We study the performance of machine learning binary classification techniques in terms of error probabilities. The statistical test is based on the Data-Driven Decision Function (D3F), learned in the training phase, i.e., what is thresholded before the final binary decision is made. Based on large deviations theory, we show that under appropriate conditions the classification error probabilities vanish exponentially, as ∼ exp (-n I + o(n)), where I is the error rate and n is the number of observations available for testing. We also propose two different approximations for the error probability curves, one based on a refined asymptotic formula (often referred to as exact asymptotics), and another one based on the central limit theorem. The theoretical findings are finally tested using the popular MNIST dataset.
arXiv (Cornell University), Feb 3, 2023
The explosions on September 26th, 2022, which damaged the gas pipelines of Nord Stream 1 and Nord... more The explosions on September 26th, 2022, which damaged the gas pipelines of Nord Stream 1 and Nord Stream 2, have highlighted the need and urgency of improving the resilience of Underwater Critical Infrastructures (UCIs). Comprising gas pipelines and power and communication cables, these connect countries worldwide and are critical for the global economy and stability. An attack targeting multiple of such infrastructures simultaneously could potentially cause significant damage and greatly affect various aspects of daily life. Due to the increasing number and continuous deployment of UCIs, existing underwater surveillance solutions, such as Autonomous Underwater Vehicles (AUVs) or Remotely Operated Vehicles (ROVs), are not adequate enough to ensure thorough monitoring. We show that the combination of information from both underwater and above-water surveillance sensors enables achieving Seabed-to-Space Situational Awareness (S3A), mainly thanks to Artificial Intelligence (AI) and Information Fusion (IF) methodologies. These are designed to process immense volumes of information, fused from a variety of sources and generated from monitoring a very large number of assets on a daily basis. The learned knowledge can be used to anticipate future behaviors, identify threats, and determine critical situations concerning UCIs. To illustrate the capabilities and importance of S3A, we consider three events that occurred in the second half of 2022: the aforementioned Nord Stream explosions, the cutoff of the underwater communication cable SHEFA-2 connecting the Shetland Islands and the UK mainland, and the suspicious activity of a large vessel in the Adriatic Sea. Specifically, we provide analyses of the available data, from Automatic Identification System (AIS) and satellite data, integrated with possible contextual information, e.g., bathymetry, Patterns Of Life (POLs), weather conditions, and human intelligence (HUMINT).
IEEE Aerospace and Electronic Systems Magazine, 2017
everal months hence I bent your ears about "citation stacking," this being a practice both seemin... more everal months hence I bent your ears about "citation stacking," this being a practice both seemingly weird in itself and apparently odd for me to get exercised about. It refers to the various means to encourage bibliographic references to a specific journal (or group of journals or body of work) with the aim of inflating the "numbers." For a researcher, these numbers are the citation count or h-index: a researcher with h=24, say, has authored 24 works each cited 24 or more times. And for a publication, the number is the impact factor (IF), the average number of times each published article is cited over a rolling period, usually two years. Both numbers are often (yes, too often) a proxy for quality. Bigger is better. I'm not sure how a researcher could manipulate his/her own citation count in a meaningful way: remember that for senior researchers these counts are quite high (see Google Scholar) and an extra few would have little import. And anyway, I don't know what would happen if such behavior was caught; but I'm forever in awe of my academic colleagues' creativity. On the other hand, publications are monitored ("indexed") regularly and professionally -in our field by Clarivate Analytics. Bibliometric manipulation can be observed indirectly by inexplicable improvements in key indices, most notably impact factor. If wrongdoing is confirmed, a publication can be suspended. A suspended journal has no impact factor. Even past-published articles in a suspended journal become suspect. If you've ever looked at a researcher's h-index to see if you really need to pay attention, or if you've ever decided where to submit your article based on impact … you're not alone, and actually, I'll admit, I've done it too. And I'm aware that many of my international colleagues are judged by where they publish more than what: a good and highly-cited article in a journal with a low IF may do less for a career than a mediocre one that scrapes into a journal with a high IF and then gets justly ignored. There is an excellent presentation by Gianluca Setti whose message -here distilled to far too few words -is that if you really need "numbers" please use several together, and not just (say) impact factor. And … please understand how they are calculated. I will give you more information from Dr. Setti in a future editorial. Let's go on to nicer matters. And a much nicer matter is Maria Sabrina Greco. Sabrina, my boss at Systems Magazine, is the incoming AESS VP of Publications. Sabrina will replace current VP of Publications Dale Blair in January 2018. Dale, whose term is ending, has done a wonderful job as VP Pubs these last three years, dealing with all sorts of matters that you all are thankfully shielded from, and facilitating promising publication initiatives like early-posting and enhanced archiving. I'm excited to work with Sabrina in the future. She has a lot to live up to in Dale, but I think she'll do it. This month we have (as usual) articles that make me proud. Leppinen (from Aalto) explores the benefits promised and issues posed by basing spacecraft information systems on Linux. As he notes: "Platform-independent, Linux-targeted software could even be developed and used across various missions" -but if so, there are concerns that must be addressed. Next, a large team from Wichita State discusses morphing aircraft that enable "a single aircraft to perform multiple missions during a single flight by executing its shape change feature." The article focuses on measurement of structural deformation, which of course is key when the deformation must stay controlled and stable. Fertig and Baden from GTRI and Guerci from ISL offer their expertise on the role of knowledge-aided processing in multipath-exploitation radar. MER is an exciting and emerging technology that facilitates surveillance in traditionally (mostly) denied venues such as downtown / urban. The results are intriguing, and show that "[c]ontrary to the view that multipath is a problem, it is evident that the proper exploitation of multipath enables localization and tracking superior to that obtained in the absence of multipath." Our last regular article is from a team based at the French-German Research Institute of Saint-Louis. It introduces the idea of the gun-launched micro air vehicle (GLMAV). The "GL" is key, since the ability of hovering MAVs to observe is of little use if their slow progress to the site of interest risks the site being … no longer of interest. The article focuses on the electronics, and especially the vision system -these must be effective but also robust due to the means of delivery. The issue ends with a Student Highlight and an AESS Historical Interview. The Student Highlight is a neat application of earth-mover's distance as a means to register objects prior to image-based tracking. EMD, an emerging metric from the image-processing community, offers a focused methodology to register and match scenes as observation perspectives and target appearances change. Following the Student Highlight is an interview with Professor Hugh Griffiths. This historical Interview is the Magazine's sixth. Lorenzo Lo Monte interviews Hugh about his career and inspirations and shares with us all he learns. Hugh's career is impressive, full of achievements, discoveries, awards, and honors. He regularly contributes historical articles to our magazine and as you will see when you read the interview, history and radar continue to fascinate him. Although he acknowledges that radar is a mature technology, he reminds us that all you have to do is look around at the conferences and journals on radar to see that there are "plenty of new things happening" and always something new to learn. I hope you enjoy this issue, and I look forward to our next meeting.
IEEE Aerospace and Electronic Systems Magazine, 2019
'll begin with some (extremely!) happy AESS news: It was recently announced that Hugh Griffiths h... more 'll begin with some (extremely!) happy AESS news: It was recently announced that Hugh Griffiths has been appointed by the Queen of England as an "Officer in the Order of the British Empire" (OBE) for "Services to Engineering." I don't know that many details yet, and I'll share them with you when I do (it's quite new news); but I'm sure most of you know Dr. Griffiths well through his service to AESS (he was AESS President 2012 and 2013), his excellent AESS publications (for one example amongst many, see his "Radar Detection and Tracking of German V-2 Rocket Launches in WW2" in this publication, March 2013) and his enormous footprint in the radar research community. But I need also to share unhappy news, that of the passing of Dave Dobson. Dave left us on August 19, 2017 -not recently, and I am sorry we have not previously written of it. To many of us involved in our AES Society, Dave Dobson and AESS Publications were for many years synonymous. If one steps back through old issues of the Transactions and Magazine one can see references to him throughout. The first I saw was news in the February 1964 IEEE Transactions on Aerospace, which reported, regarding the minutes of the Professional Technical Group on AeroSpace contemplating a merger with another PTG, that "considerable discussion" occurred. It listed Dave's name as one of a short list of the meeting's attendees. I note this with a smile on my face because I know that Dave was sometimes opinionated, frequently irascible, often playful, generally right -and always involved. I was hugely saddened to hear, a few years ago, that Dave was not well; and very unhappy to hear that he had passed from us. But it is hard for me to write about him without that smile. Dave was extremely serious about the success and quality of AESS Publications. But he had, I think, a sense of lighthearted joy about what he did, and those of us who worked with him had fun being part of that. When I took over from Dale Blair as chief editor for the AES Transactions, Dale advised me that all I needed to do was "talk to Dave" to get things done. I did; and these talks usually had me laughing and looking forward to when he would get around to discussing, as he always did, "those […] in Piscataway," referring to the good-natured Thirty Years' War between him and IEEE Operations. I don't think I can compare anyone to Dave in terms of giving of himself so completely, selflessly and over such a period of time for the betterment of his profession. We at AESS have been blessed that Dave has made this gift to us. I strongly recommend taking a look at Dale Blair's interview with Dave (Bill Walsh helped) in the June 2015 issue of this magazine, from which a picture above has been extracted. Even better, go to center.aess.ieee.org and click on "Membership" to see a video of the interview. It makes me smile to hear his voice again. In this month's issue we have four nice articles. First, from Finland, we have a report on the Aalto-1 small satellite, with special attention to the reusable Linux software. We have from universities in Barcelona and Boston, along with the European Space Agency, a report on the vital synchronization issues in deep-space communications. A team from TU Munich and the LSE Space company (near Munich) explain space-based coordination -and especially of satellite communications -of search and rescue operations. Finally, since data security is of increasing importance, authors from Queens U in Belfast, (Northern Ireland) and from Radionavigation in Cork (Ireland), discuss measures to combat spoofing in GNSS systems, especially the associated costs of such. -Peter Willett
Proceedings of SPIE, May 17, 2016
Multiple target tracking (MTT) is a challenging task that aims to estimate the number of targets ... more Multiple target tracking (MTT) is a challenging task that aims to estimate the number of targets and their states in the presence of process noise, measurement noise and data association uncertainty. This paper considers a special MTT problem characterized by additional complexity. In this problem, multiple targets are launched simultaneously in nearby locations at the same speed with slightly different directions. As the distances between the initial locations of these targets are smaller than the resolution of the sensor, this results in merged measurements, i.e., unresolved tracks at the very beginning. To deal with this problem, the recently proposed Multi-Bernoulli (MB) filter is applied. Using a model for the merged measurements, simulation results with 2-D Cartesian measurements in an optical sensor's focal plane in the presence of clutter show that the initially unresolved tracks become resolved with MB filtering a few time steps after the measurements become resolved. Thus, the MB filter is capable of keeping track of the number of targets and their corresponding states when they are initially unresolved.
arXiv (Cornell University), Jul 6, 2015
This paper presents a model for tracking of extended targets, where each target is represented by... more This paper presents a model for tracking of extended targets, where each target is represented by a given number of elliptic subobjects. A gamma Gaussian inverse Wishart implementation is derived, and necessary approximations are suggested to alleviate the data association complexity. A simulation study shows the merits of the model compared to previous work on the topic.
arXiv (Cornell University), Aug 11, 2023
Joint probabilistic data association (JPDA) filter methods and multiple hypothesis tracking (MHT)... more Joint probabilistic data association (JPDA) filter methods and multiple hypothesis tracking (MHT) methods are widely used for multitarget tracking (MTT). However, they are known to exhibit undesirable behavior in tracking scenarios with targets in close proximity: JPDA filter methods suffer from the track coalescence effect, i.e., the estimated tracks of targets in close proximity tend to merge and can become indistinguishable, and MHT methods suffer from an opposite effect known as track repulsion. In this paper, we review the JPDA filter and MHT methods and discuss the track coalescence and track repulsion effects. We also consider a more recent methodology for MTT that is based on the belief propagation (BP) algorithm, and we argue that BP-based MTT exhibits significantly reduced track coalescence and no track repulsion. Our theoretical arguments are confirmed by numerical results.
arXiv (Cornell University), Aug 14, 2023
Multi-platform radar networks (MPRNs) are an emerging sensing technology due to their ability to ... more Multi-platform radar networks (MPRNs) are an emerging sensing technology due to their ability to provide improved surveillance capabilities over plain monostatic and bistatic systems. The design of advanced detection, localization, and tracking algorithms for efficient fusion of information obtained through multiple receivers has attracted much attention. However, considerable challenges remain. This article provides an overview on recent unconstrained and constrained localization techniques as well as multitarget tracking (MTT) algorithms tailored to MPRNs. In particular, two data-processing methods are illustrated and explored in detail, one aimed at accomplishing localization tasks the other tracking functions. As to the former, assuming a MPRN with one transmitter and multiple receivers, the angular and range constrained estimator (ARCE) algorithm capitalizes on the knowledge of the transmitter antenna beamwidth. As to the latter, the scalable sum-product algorithm (SPA) based MTT technique is presented. Additionally, a solution to combine ARCE and SPA-based MTT is investigated in order to boost the accuracy of the overall surveillance system. Simulated experiments show the benefit of the combined algorithm in comparison with the conventional baseline SPA-based MTT and the stand-alone ARCE localization, in a 3D sensing scenario.
IEEE Signal Processing Magazine, Sep 1, 2018
Proceedings of the IEEE
T oday, the maritime domain is at the cusp of a new era, driven by technological advances in auto... more T oday, the maritime domain is at the cusp of a new era, driven by technological advances in automation, robotics, multisensor
2015 18th International Conference on Information Fusion (Fusion), 2015
We propose a method for multisensor-multitarget tracking with excellent scalability in the number... more We propose a method for multisensor-multitarget tracking with excellent scalability in the number of targets (which is assumed known), the number of sensors, and the number of measurements per sensor. Our method employs belief propagation based on a “detailed” factor graph that involves both target-related and measurement-related association variables. Using this approach, 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. We observed very low runtimes of the proposed method; e.g., our MATLAB simulation of a scenario of 30 targets and 10 sensors without gating required less than one second per time step. The performance of the proposed method in terms of mean optimal subpattern assignment (OSPA) error compares well with that of state-of-the-art methods whose complexity scales exponentially with the number of targets. In particular, we observed that our method can outperfo...
2016 19th International Conference on Information Fusion (FUSION), 2016
We propose a multisensor method for tracking an unknown number of targets. Low computational comp... more We propose a multisensor method for tracking an unknown number of targets. Low computational complexity and very good scalability in the number of targets, number of sensors, and number of measurements per sensor are achieved by running a belief propagation (BP) message passing scheme on a suitably devised factor graph. Using a redundant formulation of data association uncertainty and “augmented target states” including target indicators allows the proposed BP method to leverage statistical independencies for a drastic reduction of complexity. The proposed method is shown to outperform previously proposed multisensor methods for multitarget tracking, including methods with a less favorable scaling behavior.
IEEE Transactions on Signal Processing, 2018
Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, as... more Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, assuming that the order of the time indexes is completely unknown. First, maximum likelihood (ML) estimators are utilized to estimate both the permutation matrix and unknown signal amplitude under arbitrary, but known signal shape and quantizer thresholds. Sufficient conditions are provided under which an ML estimator can be found in polynomial time and an alternating maximization algorithm is proposed to solve the general problem via good initial estimates. In addition, the statistical identifiability of the model is studied. Furthermore, the generalized likelihood ratio test (GLRT) detector is adopted to detect the presence of signal. In addition, an accurate approximation to the probability of successful permutation matrix recovery is derived, and explicit expressions are provided to reveal the relationship between the number of signal samples and the number of quantizers. Finally, numerical simulations are performed to verify the theoretical results.
IEEE Transactions on Signal Processing, 2017
We propose a method for tracking an unknown number of targets based on measurements provided by m... more We propose a method for tracking an unknown number of targets based on measurements provided by multiple sensors. Our method 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 sensors. 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.
IEEE Open Journal of Signal Processing
We study the performance of Machine Learning (ML) classification techniques. Leveraging the theor... more We study the performance of Machine Learning (ML) classification techniques. Leveraging the theory of large deviations, we provide the mathematical conditions for a ML classifier to exhibit error probabilities that vanish exponentially, say exp(−n I), where n is the number of informative observations available for testing (or another relevant parameter, such as the size of the target in an image) and I is the error rate. Such conditions depend on the Fenchel-Legendre transform of the cumulant-generating function of the Data-Driven Decision Function (D3F, i.e., what is thresholded before the final binary decision is made) learned in the training phase. As such, the D3F and the related error rate I depend on the given training set. The conditions for the exponential convergence can be verified and tested numerically exploiting the available dataset or a synthetic dataset generated according to the underlying statistical model. Coherently with the large deviations theory, we can also establish the convergence of the normalized D3F statistic to a Gaussian distribution. Furthermore, approximate error probability curves ζ n exp(−n I) are provided, thanks to the refined asymptotic derivation, where ζ n represents the most representative sub-exponential terms of the error probabilities. Leveraging the refined asymptotic, we are able to compute an accurate analytical approximation of the classification performance for both the regimes of small and large values of n. Theoretical findings are corroborated by extensive numerical simulations and by the use of real-world data, acquired by an X-band maritime radar system for surveillance.
IEEE Transactions on Aerospace and Electronic Systems
Recent deep learning methods for vessel trajectory prediction are able to learn complex maritime ... more Recent deep learning methods for vessel trajectory prediction are able to learn complex maritime patterns from historical Automatic Identification System (AIS) data and accurately predict sequences of future vessel positions with a prediction horizon of several hours. However, in maritime surveillance applications, reliably quantifying the prediction uncertainty can be as important as obtaining high accuracy. This paper extends deep learning frameworks for trajectory prediction tasks by exploring how recurrent encoder-decoder neural networks can be tasked not only to predict but also to yield a corresponding prediction uncertainty via Bayesian modeling of epistemic and aleatoric uncertainties. We compare the prediction performance of two different models based on labeled or unlabeled input data to highlight how uncertainty quantification and accuracy can be improved by using, if available, additional information on the intention of the ship (e.g., its planned destination).
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Journal papers by Peter Willett
Papers by Peter Willett