The Sensing Capacity of Sensor Networks

This paper demonstrates fundamental limits of sensor networks for detection problems where the number of hypotheses is exponentially large. Such problems characterize many important applications including detection and classification of targets in a geographical area using a network of sensors, and detecting complex substances with a chemical sensor array. We refer to such applications as largescale detection problems. Using the insight that these problems share fundamental similarities with the problem of communicating over a noisy channel, we define a quantity called the sensing capacity and lower bound it for a number of sensor network models. The sensing capacity expression differs significantly from the channel capacity due to the fact that a fixed sensor configuration encodes all states of the environment. As a result, codewords are dependent and non-identically distributed. The sensing capacity provides a bound on the minimal number of sensors required to detect the state of an environment to within a desired accuracy. The results differ significantly from classical detection theory, and provide an ntriguing connection between sensor networks and communications. In addition, we discuss the insight that sensing capacity provides for the problem of sensor selection.Comment: Submitted to IEEE Transactions on Information Theory, November 200

Performance bounds for expander-based compressed sensing in Poisson noise

This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable. In this paper, we develop a novel sensing paradigm based on expander graphs and propose a MAP algorithm for recovering sparse or compressible signals from Poisson observations. The geometry of the expander graphs and the positivity of the corresponding sensing matrices play a crucial role in establishing the bounds on the signal reconstruction error of the proposed algorithm. We support our results with experimental demonstrations of reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process.Comment: revised version; accepted to IEEE Transactions on Signal Processin

Ant-Inspired Density Estimation via Random Walks

Many ant species employ distributed population density estimation in applications ranging from quorum sensing [Pra05], to task allocation [Gor99], to appraisal of enemy colony strength [Ada90]. It has been shown that ants estimate density by tracking encounter rates -- the higher the population density, the more often the ants bump into each other [Pra05,GPT93]. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides new tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using $local\ mixing\ properties$ of the underlying graph. Our results extend beyond the grid to more general graphs and we discuss applications to size estimation for social networks and density estimation for robot swarms

Space-Time Sampling for Network Observability

Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and less fragile to where and when samples are collected. It is shown that under what conditions taking coarse samples from a network will contain the same amount of information as a more finer set of samples. Our goal is to estimate initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space-time sampling strategies with explicit error bounds.Comment: Submitted to IEEE TAC (Revised Version

Quality of Information in Mobile Crowdsensing: Survey and Research Challenges

Smartphones have become the most pervasive devices in people's lives, and are clearly transforming the way we live and perceive technology. Today's smartphones benefit from almost ubiquitous Internet connectivity and come equipped with a plethora of inexpensive yet powerful embedded sensors, such as accelerometer, gyroscope, microphone, and camera. This unique combination has enabled revolutionary applications based on the mobile crowdsensing paradigm, such as real-time road traffic monitoring, air and noise pollution, crime control, and wildlife monitoring, just to name a few. Differently from prior sensing paradigms, humans are now the primary actors of the sensing process, since they become fundamental in retrieving reliable and up-to-date information about the event being monitored. As humans may behave unreliably or maliciously, assessing and guaranteeing Quality of Information (QoI) becomes more important than ever. In this paper, we provide a new framework for defining and enforcing the QoI in mobile crowdsensing, and analyze in depth the current state-of-the-art on the topic. We also outline novel research challenges, along with possible directions of future work.Comment: To appear in ACM Transactions on Sensor Networks (TOSN

Dynamic Arrival Rate Estimation for Campus Mobility on Demand Network Graphs

Mobility On Demand (MOD) systems are revolutionizing transportation in urban settings by improving vehicle utilization and reducing parking congestion. A key factor in the success of an MOD system is the ability to measure and respond to real-time customer arrival data. Real time traffic arrival rate data is traditionally difficult to obtain due to the need to install fixed sensors throughout the MOD network. This paper presents a framework for measuring pedestrian traffic arrival rates using sensors onboard the vehicles that make up the MOD fleet. A novel distributed fusion algorithm is presented which combines onboard LIDAR and camera sensor measurements to detect trajectories of pedestrians with a 90% detection hit rate with 1.5 false positives per minute. A novel moving observer method is introduced to estimate pedestrian arrival rates from pedestrian trajectories collected from mobile sensors. The moving observer method is evaluated in both simulation and hardware and is shown to achieve arrival rate estimates comparable to those that would be obtained with multiple stationary sensors.Comment: Appears in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). http://ieeexplore.ieee.org/abstract/document/7759357