Valentino Crespi

Tracking a moving object with a binary sensor network

In this paper we examine the role of very simple and noisy sensors for the tracking problem. We propose a binary sensor model, where each sensors value is converted reliably to one bit of information only: whether the object is moving toward the sensor or away from the sensor. We show that a network of binary sensors has geometric properties that can be used to develop a solution for tracking with binary sensors and present resulting algorithms and simulation experiments. We develop a particle filtering style algorithm for target tracking using such minimalist sensors. We present an analysis of fundamental tracking limitation under this sensor model, and show how this limitation can be overcome through the use of a single bit of proximity information at each sensor node. Our extensive simulations show low error that decreases with sensor density.

Top-down vs bottom-up methodologies in multi-agent system design

Abstract Traditionally, two alternative design approaches have been available to engineers: top-down and bottom-up. In the top-down approach, the design process starts with specifying the global system state and assuming that each component has global knowledge of the system, as in a centralized approach. The solution is then decentralized by replacing global knowledge with communication. In the bottom-up approach, on the other hand, the design starts with specifying requirements and capabilities of individual components, and the global behavior is said to emerge out of interactions among constituent components and between components and the environment. In this paper we present a comparative study of both approaches with particular emphasis on applications to multi-agent system engineering and robotics. We outline the generic characteristics of both approaches from the MAS perspective, and identify three elements that we believe should serve as criteria for how and when to apply either of the approaches. We demonstrate our analysis on a specific example of load balancing problem in robotics. We also show that under certain assumptions on the communication and the external environment, both bottom-up and top-down methodologies produce very similar solutions.

Efficient computation of the hidden Markov model entropy for a given observation sequence

Hidden Markov models (HMMs) are currently employed in a wide variety of applications, including speech recognition, target tracking, and protein sequence analysis. The Viterbi algorithm is perhaps the best known method for tracking the hidden states of a process from a sequence of observations. An important problem when tracking a process with an HMM is estimating the uncertainty present in the solution. In this correspondence, an algorithm for computing at runtime the entropy of the possible hidden state sequences that may have produced a certain sequence of observations is introduced. The brute-force computation of this quantity requires a number of calculations exponential in the length of the observation sequence. This algorithm, however, is based on a trellis structure resembling that of the Viterbi algorithm, and permits the efficient computation of the entropy with a complexity linear in the number of observations.

The theory of trackability with applications to sensor networks

In this article, we formalize the concept of tracking in a sensor network and develop a quantitative theory of trackability of weak models that investigates the rate of growth of the number of consistent tracks given a temporal sequence of observations made by the sensor network. The phenomenon being tracked is modelled by a nondeterministic finite automaton (a weak model) and the sensor network is modelled by an observer capable of detecting events related, typically ambiguously, to the states of the underlying automaton. Formally, an input string of symbols (the sensor network observations) that is presented to a nondeterministic finite automaton, M, (the weak model) determines a set of state sequences (the tracks or hypotheses) that are capable of generating the input string. We study the growth of the size of this candidate set of tracks as a function of the length of the input string. One key result is that for a given automaton and sensor coverage, the worst-case rate of growth is either polynomial or exponential in the number of observations, indicating a kind of phase transition in tracking accuracy. These results have applications to various tracking problems of recent interest involving tracking phenomena using noisy observations of hidden states such as: sensor networks, computer network security, autonomic computing and dynamic social network analysis.

Learning Hidden Markov Models Using Nonnegative Matrix Factorization

The Baum-Welch algorithm together with its derivatives and variations has been the main technique for learning hidden Markov models (HMMs) from observational data. We present an HMM learning algorithm based on the nonnegative matrix factorization (NMF) of higher order Markovian statistics that is structurally different from the Baum-Welch and its associated approaches. The described algorithm supports estimation of the number of recurrent states of an HMM and iterates the NMF algorithm to improve the learned HMM parameters. Numerical examples are provided as well.

Analyzing permutation capability of multistage interconnection networks with colored Petri nets

In a multistage interconnection network (MIN) the calculation of the number of permutations of the input terminals into the output terminals is a classic difficult problem. In this paper, we introduce an innovative technique based on Colored Petri Nets (known as CP-nets or CPNs) that will allow us to analyze the permutation capability of arbitrary MINs. We show how to verify whether a MIN is rearrangeable through the state space analysis of the associated CP-net and we measure the permutation capability of non-rearrangeable MINs in terms of the permutations that can be generated. The proposed approach takes advantage of powerful existing software tools, particularly, CPNTools, which is used to explore the occurrence graphs of CP-nets and determine the set of permutations performed by the modeled MINs. This new technique is easy to use and can be efficiently applied to MINs made of cross-bar switches.

Comparative analysis of top-down and bottom-up methodologies for multi-agent system design

Traditionally, top-down and bottom-up design approaches have competed with each other in Algorithmics and Software Engineering. In the top-down approach, design process starts with specifying the global system state and assuming that each component has global knowledge of the system, as in a centralized approach. The solution is then decentralized by replacing global knowledge with communication. In the bottom-up approach, on the other hand, the design starts with specifying requirements and capabilities of individual components, and the global behavior is said to emerge out of interactions among constituent components and between components and the environment. In this paper we present a comparative study of both approaches with particular emphasis on applications to multi-agent system engineering.

Sampling theory for process detection with applications to surveillance and tracking

In this paper, we investigate the link between the rate at which events are observed by a monitoring system and the ability of the system to effectively perform its tracking and surveillance tasks. In general, higher sampling rates provide better performance, but they also require more resources, both computationally and from the sensing infrastructure. We have used Hidden Markov Models to describe the dynamic processes to be monitored and (alpha,beta)-currency as a performance measure for the monitoring system. Our ultimate goal is to be able to determine the minimum sampling rate at which we can still fulfill the performance requirements of our system. Along with the theoretical work, we have performed simulation-based tests to examine the validity of our approach; we compare performance results obtained by simulation with the theoretical value obtained a priori from the scenario parameters and illustrate with a simple example a technique for estimating the required sampling rate to achieve a given level of performance.

Trackability analysis of multiple processes using multi-distributed agents

A framework of trackability analysis of tracking systems is established based on the information theoretic approach of estimation problems. The a posterior conditional entropy is linked to two principal factors of the tracking performance - the probability of error, and the complexity of hypothesis management. Quantitative boundaries of the two performance factors are induced from the entropy indicator. Analytic works focus on discrete state tracking problems with stationary property, verified by simulation results on finite alphabet hidden Markov models.

Distributed sensing and UAV scheduling for surveillance and tracking of unidentifiable targets

This paper presents an automated decentralized surveillance system for the problem of tracking multiple mobile ground targets with no signature in a bounded area. The system consists of unmanned aerial vehicles (UAVs) and unattended fixed ground sensors (UGSs) with limited communication and detection range that are deployed in the area of interest. Each component of the system (UAV and/or Sensor) is completely autonomous and programmed to scan the area searching for targets and share its knowledge with other components within communication range. UAV scheduling of the areas to search is stochastic and the characterizing probability distributions are determined through hypotheses of consistent tracks of target observations. Such hypotheses are formulated by a client subsystem called Process Query System, which is queried with streams of incoming observations of targets and stochastic models of their kinematics. The purpose of this work is also to provide a quantitative measure of the situational awareness of the monitoring system in relation to the accuracy of the target models and the degree of decentralization of the control.