Analysis of error propagation in particle filters with approximation

This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense $L_p$ error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node particle filter and present numerical experiments exploring its performance and the relationship to the error bounds.Comment: Published in at http://dx.doi.org/10.1214/11-AAP760 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Designing Robust Collaborative Services in Distributed Wireless Networks

Wireless Sensor Networks (WSNs) are a popular class of distributed collaborative networks finding suitability from medical to military applications. However, their vulnerability to capture, their "open" wireless interfaces, limited battery life, all result in potential vulnerabilities. WSN-based services inherit these vulnerabilities. We focus on tactical environments where sensor nodes play complex roles in data sensing, aggregation and decision making. Services in such environments demand a high level of reliability and robustness. The first problem we studied is robust target localization. Location information is important for surveillance, monitoring, secure routing, intrusion detection, on-demand services etc. Target localization means tracing the path of moving entities through some known surveillance area. In a tactical environment, an adversary can often capture nodes and supply incorrect surveillance data to the system. In this thesis we create a target localization protocol that is robust against large amounts of such falsified data. Location estimates are generated by a Bayesian maximum-likelihood estimator. In order to achieve improved results with respect to fraudulent data attacks, we introduce various protection mechanisms. Further, our novel approach of employing watchdog nodes improves our ability to detect anomalies reducing the impact of an adversarial attack and limiting the amount of falsified data that gets accepted into the system. By concealing and altering the location where data is aggregated, we restrict the adversary to making probabilistic "guess" attacks at best, and increase robustness further. By formulating the problem of robust node localization under adversarial settings and casting it as a multivariate optimization problem, we solve for the system design parameters that correspond to the optimal solution. Together this results in a highly robust protocol design. In order for any collaboration to succeed, collaborating entities must have the same relative sense of time. This ensures that any measurements, surveillance data, mission commands, etc will be processed in the same epoch they are intended to serve. In most cases, data disseminated in a WSN is transient in nature, and applies for a short period of time. New data routinely replaces old data. It is imperative that data be placed in its correct time context; therefore..

Information theoretic sensor management

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 195-203).Sensor management may be defined as those stochastic control problems in which control values are selected to influence sensing parameters in order to maximize the utility of the resulting measurements for an underlying detection or estimation problem. While problems of this type can be formulated as a dynamic program, the state space of the program is in general infinite, and traditional solution techniques are inapplicable. Despite this fact, many authors have applied simple heuristics such as greedy or myopic controllers with great success. This thesis studies sensor management problems in which information theoretic quantities such as entropy are utilized to measure detection or estimation performance. The work has two emphases: Firstly, we seek performance bounds which guarantee performance of the greedy heuristic and derivatives thereof in certain classes of problems. Secondly, we seek to extend these basic heuristic controllers to nd algorithms that provide improved performance and are applicable in larger classes of problems for which the performance bounds do not apply. The primary problem of interest is multiple object tracking and identification; application areas include sensor network management and multifunction radar control.(cont.) Utilizing the property of submodularity, as proposed for related problems by different authors, we show that the greedy heuristic applied to sequential selection problems with information theoretic objectives is guaranteed to achieve at least half of the optimal reward. Tighter guarantees are obtained for diffusive problems and for problems involving discounted rewards. Online computable guarantees also provide tighter bounds in specific problems. The basic result applies to open loop selections, where all decisions are made before any observation values are received; we also show that the closed loop greedy heuristic, which utilizes observations received in the interim in its subsequent decisions, possesses the same guarantee relative to the open loop optimal, and that no such guarantee exists relative to the optimal closed loop performance. The same mathematical property is utilized to obtain an algorithm that exploits the structure of selection problems involving multiple independent objects. The algorithm involves a sequence of integer programs which provide progressively tighter upper bounds to the true optimal reward. An auxiliary problem provides progressively tighter lower bounds, which can be used to terminate when a near-optimal solution has been found.(cont.) The formulation involves an abstract resource consumption model, which allows observations that expend different amounts of available time. Finally, we present a heuristic approximation for an object tracking problem in a sensor network, which permits a direct trade-o between estimation performance and energy consumption. We approach the trade-o through a constrained optimization framework, seeking to either optimize estimation performance over a rolling horizon subject to a constraint on energy consumption, or to optimize energy consumption subject to a constraint on estimation performance. Lagrangian relaxation is used alongside a series of heuristic approximations to and a tractable solution that captures the essential structure in the problem.by Jason L. Williams.Ph.D

Design and implementation of a relative localization system for ground and aerial robotic teams

The main focus of this thesis is to address the relative localization problem of a heterogenous team which comprises of both ground and micro aerial vehicle robots. This team configuration allows to combine the advantages of increased accessibility and better perspective provided by aerial robots with the higher computational and sensory resources provided by the ground agents, to realize a cooperative multi robotic system suitable for hostile autonomous missions. However, in such a scenario, the strict constraints in flight time, sensor pay load, and computational capability of micro aerial vehicles limits the practical applicability of popular map-based localization schemes for GPS denied navigation. Therefore, the resource limited aerial platforms of this team demand simpler localization means for autonomous navigation. Relative localization is the process of estimating the formation of a robot team using the acquired inter-robot relative measurements. This allows the team members to know their relative formation even without a global localization reference, such as GPS or a map. Thus a typical robot team would benefit from a relative localization service since it would allow the team to implement formation control, collision avoidance, and supervisory control tasks, independent of a global localization service. More importantly, a heterogenous team such as ground robots and computationally constrained aerial vehicles would benefit from a relative localization service since it provides the crucial localization information required for autonomous operation of the weaker agents. This enables less capable robots to assume supportive roles and contribute to the more powerful robots executing the mission. Hence this study proposes a relative localization-based approach for ground and micro aerial vehicle cooperation, and develops inter-robot measurement, filtering, and distributed computing modules, necessary to realize the system. The research study results in three significant contributions. First, the work designs and validates a novel inter-robot relative measurement hardware solution which has accuracy, range, and scalability characteristics, necessary for relative localization. Second, the research work performs an analysis and design of a novel nonlinear filtering method, which allows the implementation of relative localization modules and attitude reference filters on low cost devices with optimal tuning parameters. Third, this work designs and validates a novel distributed relative localization approach, which harnesses the distributed computing capability of the team to minimize communication requirements, achieve consistent estimation, and enable efficient data correspondence within the network. The work validates the complete relative localization-based system through multiple indoor experiments and numerical simulations. The relative localization based navigation concept with its sensing, filtering, and distributed computing methods introduced in this thesis complements system limitations of a ground and micro aerial vehicle team, and also targets hostile environmental conditions. Thus the work constitutes an essential step towards realizing autonomous navigation of heterogenous teams in real world applications