Dynamic Iterative Pursuit

For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able to incorporate sequential predictions, thereby providing better compressive sensing recovery performance, but not at the cost of high complexity. Through experimental evaluations, we observe that the new algorithm exhibits a graceful degradation at deteriorating signal conditions while capable of yielding substantial performance gains as conditions improve.Comment: 6 pages, 7 figures. Accepted for publication in IEEE Transactions on Signal Processin

Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing

In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure

Underwater mobile target tracking with particle filter using an autonomous vehicle

This paper describes an underwater mobile target localization and tracking by using an autonomous surface vehicle for which the successive ranges between the target and the reference are the only information. In a dynamic system, such as range-only single-beacon underwater target tracking, a statespace model can be characterized, where the state vector may include position, and velocity of the mobile underwater target. Moreover, the range observations can come from a mobile autonomous vehicle, which is used as a moving landmark. Then, a nonlinear Bayesian filtering algorithm can be used to make extrapolations on the state vector from the observations, in order to obtain the target position at each instant of time. In this paper we consider the use of Particle Filter (PF) to perform such localization and tracking where its performance and characterization is studied under different scenariosPostprint (published version

Distributed Estimation and Performance Limits in Resource-constrained Wireless Sensor Networks

Distributed inference arising in sensor networks has been an interesting and promising discipline in recent years. The goal of this dissertation is to investigate several issues related to distributed inference in sensor networks, emphasizing parameter estimation and target tracking with resource-constrainted networks. To reduce the transmissions between sensors and the fusion center thereby saving bandwidth and energy consumption in sensor networks, a novel methodology, where each local sensor performs a censoring procedure based on the normalized innovation square (NIS), is proposed for the sequential Bayesian estimation problem in this dissertation. In this methodology, each sensor sends only the informative measurements and the fusion center fuses both missing measurements and received ones to yield more accurate inference. The new methodology is derived for both linear and nonlinear dynamic systems, and both scalar and vector measurements. The relationship between the censoring rule based on NIS and the one based on Kullback-Leibler (KL) divergence is investigated. A probabilistic transmission model over multiple access channels (MACs) is investigated. With this model, a relationship between the sensor management and compressive sensing problems is established, based on which, the sensor management problem becomes a constrained optimization problem, where the goal is to determine the optimal values of probabilities that each sensor should transmit with such that the determinant of the Fisher information matrix (FIM) at any given time step is maximized. The performance of the proposed compressive sensing based sensor management methodology in terms of accuracy of inference is investigated. For the Bayesian parameter estimation problem, a framework is proposed where quantized observations from local sensors are not directly fused at the fusion center, instead, an additive noise is injected independently to each quantized observation. The injected noise performs as a low-pass filter in the characteristic function (CF) domain, and therefore, is capable of recoverving the original analog data if certain conditions are satisfied. The optimal estimator based on the new framework is derived, so is the performance bound in terms of Fisher information. Moreover, a sub-optimal estimator, namely, linear minimum mean square error estimator (LMMSE) is derived, due to the fact that the proposed framework theoretically justifies the additive noise modeling of the quantization process. The bit allocation problem based on the framework is also investigated. A source localization problem in a large-scale sensor network is explored. The maximum-likelihood (ML) estimator based on the quantized data from local sensors and its performance bound in terms of Cram\\u27{e}r-Rao lower bound (CRLB) are derived. Since the number of sensors is large, the law of large numbers (LLN) is utilized to obtain a closed-form version of the performance bound, which clearly shows the dependence of the bound on the sensor density, $i.e.,$ the Fisher information is a linearly increasing function of the sensor density. Error incurred by the LLN approximation is also theoretically analyzed. Furthermore, the design of sub-optimal local sensor quantizers based on the closed-form solution is proposed. The problem of on-line performance evaluation for state estimation of a moving target is studied. In particular, a compact and efficient recursive conditional Posterior Cram\\u27{e}r-Rao lower bound (PCRLB) is proposed. This bound provides theoretical justification for a heuristic one proposed by other researchers in this area. Theoretical complexity analysis is provided to show the efficiency of the proposed bound, compared to the existing bound

Statistical Filtering for Multimodal Mobility Modeling in Cyber Physical Systems

A Cyber-Physical System integrates computations and dynamics of physical processes. It is an engineering discipline focused on technology with a strong foundation in mathematical abstractions. It shares many of these abstractions with engineering and computer science, but still requires adaptation to suit the dynamics of the physical world. In such a dynamic system, mobility management is one of the key issues against developing a new service. For example, in the study of a new mobile network, it is necessary to simulate and evaluate a protocol before deployment in the system. Mobility models characterize mobile agent movement patterns. On the other hand, they describe the conditions of the mobile services. The focus of this thesis is on mobility modeling in cyber-physical systems. A macroscopic model that captures the mobility of individuals (people and vehicles) can facilitate an unlimited number of applications. One fundamental and obvious example is traffic profiling. Mobility in most systems is a dynamic process and small non-linearities can lead to substantial errors in the model. Extensive research activities on statistical inference and filtering methods for data modeling in cyber-physical systems exist. In this thesis, several methods are employed for multimodal data fusion, localization and traffic modeling. A novel energy-aware sparse signal processing method is presented to process massive sensory data. At baseline, this research examines the application of statistical filters for mobility modeling and assessing the difficulties faced in fusing massive multi-modal sensory data. A statistical framework is developed to apply proposed methods on available measurements in cyber-physical systems. The proposed methods have employed various statistical filtering schemes (i.e., compressive sensing, particle filtering and kernel-based optimization) and applied them to multimodal data sets, acquired from intelligent transportation systems, wireless local area networks, cellular networks and air quality monitoring systems. Experimental results show the capability of these proposed methods in processing multimodal sensory data. It provides a macroscopic mobility model of mobile agents in an energy efficient way using inconsistent measurements