Automatic self-calibration of ad-hoc sensor networks is a critical need for their use in military or civilian applications. In general, self-calibration involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. time delay or received signal strength between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of inter-sensor communication. We demonstrate that the information used for sensor calibration is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then demonstrate the utility of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multi-modal uncertainty. We illustrate the performance of NBP on several example networks while comparing to a previously published nonlinear least squares method.

Automatic self-localization is a critical need for the effective use of ad-hoc sensor networks in military or civilian applications. In general, self-localization involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. distance measurements between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of inter-sensor communication. We demonstrate that the information used for sensor localization is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then present and demonstrate the utility of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multi-modal uncertainty. Using simulations of small- to moderately-sized sensor networks, we show that NBP may be made robust to outlier measurement errors by a simple model augmentation, and that judicious message construction can result in better estimates. Furthermore, we provide an analysis of NBP’s communications requirements, showing that typically only a few messages per sensor are required, and that even low bit-rate approximations of these messages can have little or no performance impact.

This paper presents a technique for the Simultaneous Calibration of Action and Sensor Models (SCASM) on a mobile robot. While previous approaches to calibration make use of an independent source of feedback, SCASM is unsupervised, in that it does not receive any well calibrated feedback about its location. Starting with only an inaccurate action model, it learns accurate relative action and sensor models. Furthermore, SCASM is fully autonomous, in that it operates with no human supervision. SCASM is fully implemented and tested on a Sony Aibo ERS-7 robot.

Abstract — We consider the problem of estimating vectorvalued variables from noisy “relative ” measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables associated with the corresponding nodes (i.e., their relative values). This type of measurement model appears in several sensor networks problem. We take the value of one particular variable as a reference and consider the Unbiased Minimum Variance (UMV) estimators for the differences between the remaining variables and the reference. We establish upper and lower bounds on the estimation error variance of a node’s variable as a function of the Euclidean distance in a drawing of the graph between the node and the reference one. These bounds result in a classification of graphs: civilized and dense, based on how the variance grows with distance: at a rate greater than or less than linearly, logarithmically, or bounded. In deriving these results, we establish and exploit an analogy between the UMV estimator variance and the effective resistance in a generalized electrical network that is significant on its own. I.

for sensor networks. This paper studies the Cramér-Rao lower bound (CRB) for two kinds of localization based on noisy range measurements. The first is Anchored Localization in which the estimated positions of at least 3 nodes are known in global coordinates. We show some basic invariances of the CRB in this case and derive lower and upper bounds on the CRB which can be computed using only local information. The second is Anchor-free Localization where no absolute positions are known. Although the Fisher Information Matrix is singular, a CRB-like bound exists on the total estimation variance. Finally, for both cases we discuss how the bounds scale to large networks under different models of wireless signal propagation. Index Terms — Cramér-Rao bound, localization, estimation bounds, ranging information, sensor networks.

We examine the problem of estimating vector-valued variables from noisy measurements of the difference between certain pairs of them. This problem, which is naturally posed in terms of a measure-ment graph, arises in applications such as sensor network localization, time synchronization, and motion consensus. We obtain a characterization on the minimum possible covariance of the estimation error when an arbitrarily large number of measurements are available. This covariance is shown to be equal to a matrix-valued effective resistance in an infinite electrical network. Covariance in large finite graphs converges to this effective resistance as the size of the graphs increases. This convergence result provides the formal justification for regarding large finite graphs as infinite graphs, which can be exploited to determine scaling laws for the estimation error in large finite graphs. Furthermore, these results indicate that in large networks, estimation algorithms that use small subsets of all the available measurements can still obtain accurate estimates. I.

Abstract. We propose CaliBree, a self-calibration system for mobile wireless sensor networks. Sensors calibration is a fundamental problem in a sensor network. If sensor devices are not properly calibrated, their sensor readings are likely of little use to the application. Distributed calibration is challenging in a mobile sensor network, where sensor devices are carried by people or vehicles, mainly for three reasons: i) the sensing contact time, i.e., the amount of time nodes are within the sensing range of each other, can be very limited, requiring a quick and efficient calibration technique; ii) for scalability and ease of use, the calibration algorithm should not require manual intervention; iii) the computational burden must be low since some sensor platforms have limited capabilities. In this paper we propose CaliBree, a distributed, scalable, and lightweight calibration protocol that applies a discrete average consensus algorithm technique to calibrate sensor nodes. CaliBree is shown to be effective through experimental evaluation using embedded wireless sensor devices, achieving high calibration accuracy. 1

Geometric information is essential for sensor networks. We study two kinds of geometric information. One is the positions of the nodes. The estimation of the positions of the nodes is called the localization problem. The other is the positions of objects in the sensor network. For the localization problem, We will study the Cramer Rao lower bound on it. For the anchor-free localization problem where no nodes have known positions, we propose a new bound on the variance of the estimation error, because the Fisher In-formation Matrix is singular. For the anchored localization problem using only local information, we derive a lower bound to the Cramer Rao bound on the position estima-tion. We find that the Cramer Rao bounds in both cases are invariant under zooming of the whole sensor network. We will also propose a novel two-step localization scheme. In the first step, we estimate an anchor-free coordinate system around every node. In the second step, we combine all the anchor-free coordinate systems together. Then using the anchored position information of some nodes, we transfer the anchor-free coordinate system into an anchored coordinate system. For the object position estimation problem, we study it in different scenarios in terms of number of nodes. There are three scenarios: single transmitter and sin-gle receiver, multiple transmitter (receiver) and single receiver (transmitter), multiple transmitter and multiple receiver. For each scenario, we give a position estimation scheme and analyze the performance of our scheme. The Cramer Rao bound for each scenario is also computed. We are particularly interested in the behavior of the Cramer Rao bound when the number of sensors in the network grows to infinity. We find that ii the Cramer Rao bound on object tracking is proportional to the reciprocal of the total received SNR. iii To my parents.

Automatic self-calibration of ad-hoc sensor networks is a critical need for their use in military or civilian applications. In general, self-calibration involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. estimated distance between sensors) over regions of the network. We formulate the self-calibration problem as a graphical model, enabling application of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, can represent multi-modal uncertainty, and admits a wide variety of statistical models. This last point is particularly appealing in that it can be used to provide robustness against occasional highvariance (outlier) noise. We illustrate the performance of NBP using Monte Carlo analysis on an example network. 1.

for sensor networks. This paper studies the Cramér-Rao lower bound (CRB) for two kinds of localization based on noisy range measurements. The first is Anchored Localization in which the estimated positions of at least 3 nodes are known in global coordinates. We show some basic invariances of the CRB in this case and derive lower and upper bounds on the CRB which can be computed using only local information. The second is Anchor-free Localization where no absolute positions are known. Although the Fisher Information Matrix is singular, a CRB-like bound exists on the total estimation variance. Finally, for both cases we discuss how the bounds scale to large networks under different models of wireless signal propagation. Index Terms — Cramér-Rao bound, localization, estimation bounds, ranging information, sensor networks.