Digital Signal Processing Research Program

Contains table of contents for Section 2, an introduction, reports on twenty-one research projects and a list of publications.U.S. Navy - Office of Naval Research Grant N00014-93-1-0686Lockheed Sanders, Inc. Contract P.O. BY5561U.S. Air Force - Office of Scientific Research Grant AFOSR 91-0034National Science Foundation Grant MIP 95-02885U.S. Navy - Office of Naval Research Grant N00014-95-1-0834MIT-WHOI Joint Graduate Program in Oceanographic EngineeringAT&T Laboratories Doctoral Support ProgramDefense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research Grant N00014-89-J-1489Lockheed Sanders/U.S. Navy - Office of Naval Research Grant N00014-91-C-0125U.S. Navy - Office of Naval Research Grant N00014-89-J-1489National Science Foundation Grant MIP 95-02885Defense Advanced Research Projects Agency/U.S. Navy Contract DAAH04-95-1-0473U.S. Navy - Office of Naval Research Grant N00014-91-J-1628University of California/Scripps Institute of Oceanography Contract 1003-73-5

Some Models for Count Time Series

There has been growing interest in modeling stationary series that have discrete marginal distributions. Count series arise when describing storm numbers, accidents, wins by a sports team, disease cases, etc. The first count time series model introduced in this paper is the superpositioning methods. It have proven useful in devising stationary count time series having Poisson and binomial marginal distributions. Here, properties of this model class are established and the basic idea is developed. Specifically, we show how to construct stationary series with binomial, Poisson, and negative binomial marginal distributions; other marginal distributions are possible. A second model class for stationary count time series -- the latent Gaussian count time series model -- is also proposed. The model uses a latent Gaussian sequence and a distributional transformation to build stationary series with the desired marginal distribution. This model has proven to be quite flexible. It can have virtually any marginal distribution, including generalized Poisson and Conway-Maxwell. It is shown that the model class produces the most flexible pairwise correlation structures possible, including negatively dependent series. Model parameters are estimated via two methods: 1) a Gaussian likelihood approach (GL), and 2) a particle filtering approach (PF)

Some contributions to model selection and statistical inference in Markovian models

The general theme of this thesis is providing and studying a new understanding of some statistical models and computational methods based on a Markov process/chain. Section 1-4 are devoted to reviewing the literature for the sake of completeness and the better understanding of Section 5-7 that are our original studies. Section 1 is devoted to understanding a Markov process since continuous and discrete types of a Markov process are hinges of the thesis. In particular, we will study some basics/advanced results of Markov chains and Ito diffusions. Ergodic properties of these processes are also documented. In Section 2 we first study the Metropolis-Hastings algorithm since this is basic of other MCMC methods. We then study more advanced methods such as Reversible Jump MCMC, Metropolis-adjusted Langevin algorithm, pseudo marginal MCMC and Hamiltonian Monte Carlo. These MCMC methods will appear in Section 3, 4 and 7. In Section 3 we consider another type of Monte Carlo method called sequential Monte Carlo (SMC). Unlike MCMC methods, SMC methods often give us on-line ways to approximate intractable objects. Therefore, these methods are particularly useful when one needs to play around with models with scalable computational costs. Some mathematical analysis of SMC also can be found. These SMC methods will appear in Section 4, 5, 6 and 7. In Section 4 we first discuss hidden Markov models (HMMs) since all statistical models that we consider in the thesis can be treated as HMMs or their generalisation. Since, in general, HMMs involve intractable objects, we then study approximation ways for them based on SMC methods. Statistical inference for HMMs is also considered. These topics will appear in Section 5, 6 and 7. Section 5 is largely based on a submitted paper titled Asymptotic Analysis of Model Selection Criteria for General Hidden Markov Models with Alexandros Beskos and Sumeetpal Sidhu Singh, https: //arxiv.org/abs/1811.11834v3. In this section, we study the asymptotic behaviour of some information criteria in the context of hidden Markov models, or state space models. In particular, we prove the strong consistency of BIC and evidence for general HMMs. Section 6 is largely based on a submitted paper titled Online Smoothing for Diffusion Processes Observed with Noise with Alexandros Beskos, https://arxiv.org/abs/2003.12247. In this section, we develop sequential Monte Carlo methods to estimate parameters of (jump) diffusion models. Section 7 is largely based on an ongoing paper titled Adaptive Bayesian Model Selection for Diffusion Models with Alexandros Beskos. In this section, we develop adaptive computational ways, based on sequential Monte Carlo samplers and Hamiltonian Monte Carlo on a functional space, for Bayesian model selection

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

Mathematics and Digital Signal Processing

Modern computer technology has opened up new opportunities for the development of digital signal processing methods. The applications of digital signal processing have expanded significantly and today include audio and speech processing, sonar, radar, and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. This Special Issue is aimed at wide coverage of the problems of digital signal processing, from mathematical modeling to the implementation of problem-oriented systems. The basis of digital signal processing is digital filtering. Wavelet analysis implements multiscale signal processing and is used to solve applied problems of de-noising and compression. Processing of visual information, including image and video processing and pattern recognition, is actively used in robotic systems and industrial processes control today. Improving digital signal processing circuits and developing new signal processing systems can improve the technical characteristics of many digital devices. The development of new methods of artificial intelligence, including artificial neural networks and brain-computer interfaces, opens up new prospects for the creation of smart technology. This Special Issue contains the latest technological developments in mathematics and digital signal processing. The stated results are of interest to researchers in the field of applied mathematics and developers of modern digital signal processing systems

Passive acoustic monitoring for assessment of natural and anthropogenic sound sources in the marine environment using automatic recognition

In the marine environment, sound can be an efficient source of information. Indeed, several marine species, including fish, use sound to navigate, select habitats, detect predators and prey, and to attract mates. Therefore, all the abiotic, biotic and manmade sounds that comprise the soundscape, have the potential to be used to assess and monitor species and marine environments. Passive acoustic monitoring (PAM) involves the use of acoustic sensors to record sound in the environment, from which relevant ecological information can be inferred. This thesis studied marine soundscapes, with special attention on fish communities, anthropogenic noise, and applied several methods to analyse acoustic recordings. Most of the focus was on the Tagus estuary, where the presence of two highly vocal species is known: the Lusitanian toadfish (Halobatrachus didactylus) and the meagre (Argyrosomus regius). Azorean and Mozambique soundscapes were also analysed. Several methods were applied to extract information and to visualize soundscape characteristics, including sound recognition systems based on hidden Markov models to recognize fish sounds and boat passages. Analysis of several types of marine environments and time scales showed several advantages and disadvantages of different methods. The use of sound pressure level on different frequency bands allowed the quantification of daily and seasonal patterns. Ecoacoustic indices appear to be cost-effective tools to monitor biodiversity in some marine environments. Using automatic recognition, vocal rhythms (diel and seasonal patterns) and vocal interactions among individuals were also characterized. Furthermore, boat noise effects on fish were studied: we encountered impacts on the audition, vocal behaviour and reproduction. Overall, we used PAM as a tool to remotely assess and monitor soundscapes, biodiversity, fish communities’ seasonal patterns, fish behaviour, species presence, and the effect of anthropogenic noise aiming to contribute for the management and conservation of marine ecosystems

Automatic Detectors for Underwater Soundscape Measurements

Environmental impact regulations require that marine industrial operators quantify their contribution to underwater noise scenes. Automation of such assessments becomes feasible with the successful categorisation of sounds into broader classes based on source types – biological, anthropogenic and physical. Previous approaches to passive acoustic monitoring have mostly been limited to a few specific sources of interest. In this study, source-independent signal detectors are developed and a framework is presented for the automatic categorisation of underwater sounds into the aforementioned classes

A Bayesian approach to simultaneously characterize the stochastic and deterministic components of a system

The present work provides a Bayesian approach to learn plausible models capable of characterizing complex time series in which deterministic and stochastic phenomena concur. Two main approaches are actually developed. The first approach, is a simple superposition model grounded on the hypothesis that the interactions between the stochastic and deterministic phenomena are negligible. To enable this model to capture complex dynamics, the stochastic part is assumed to be a fractal signal. Under the assumptions of this model, an analysis method is proposed, enabling the characterization of the fractal stochastic component and the estimation the deterministic part. The second main approach relies on Stochastic Differential Equations (SDEs) to model systems where the stochastic and deterministic part interact. First, a non-parametric estimation method for SDEs is developed, using recent advances from Gaussian processes. Finally, the thesis studies how to overcome the main constraint that the use of SDEs imposes: the Markovianity assumption. To that end, a new structured variational autoencoder with latent SDE dynamics is proposed. All the methods are tested on both synthetic and real signals, demonstrating its ability to capture the behavior of complex systems

Information fusion architectures for security and resource management in cyber physical systems

Data acquisition through sensors is very crucial in determining the operability of the observed physical entity. Cyber Physical Systems (CPSs) are an example of distributed systems where sensors embedded into the physical system are used in sensing and data acquisition. CPSs are a collaboration between the physical and the computational cyber components. The control decisions sent back to the actuators on the physical components from the computational cyber components closes the feedback loop of the CPS. Since, this feedback is solely based on the data collected through the embedded sensors, information acquisition from the data plays an extremely vital role in determining the operational stability of the CPS. Data collection process may be hindered by disturbances such as system faults, noise and security attacks. Hence, simple data acquisition techniques will not suffice as accurate system representation cannot be obtained. Therefore, more powerful methods of inferring information from collected data such as Information Fusion have to be used. Information fusion is analogous to the cognitive process used by humans to integrate data continuously from their senses to make inferences about their environment. Data from the sensors is combined using techniques drawn from several disciplines such as Adaptive Filtering, Machine Learning and Pattern Recognition. Decisions made from such combination of data form the crux of information fusion and differentiates it from a flat structured data aggregation. In this dissertation, multi-layered information fusion models are used to develop automated decision making architectures to service security and resource management requirements in Cyber Physical Systems --Abstract, page iv