10-01-2011, 12:07 PM
Jason A. Fuemmeler, Member, IEEE, and Venugopal V. Veeravalli, Fellow, IEEE
ABSTRACT
The problem of tracking multiple objects moving through a network of wireless sensors is studied. It is assumed that each sensor has a limited range for detecting the presence of the object, and that the network is sufficiently dense so that the sensors cover the area of interest. In order to conserve energy the sensors may be put into a sleep mode with a timer that determines the sleep duration. It is assumed that a sensor that is asleep cannot be communicated with or woken up, and hence the sleep duration needs to be determined at the time the sensor goes to sleep based on all the information available to the sensor. The objective is to track the location of the objects to within the accuracy of the range of the sensor. Having sleeping sensors in the network could result in tracking errors, and therefore there is a tradeoff between the energy savings and the tracking errors that result from the sleeping actions at the sensors. Sleeping policies that optimize this tradeoff are designed, and their performance analyzed. This work is an extension of previous work that considered the tracking of only a single object.
INTRODUCTION
ADVANCES in technology are enabling the deployment of vast sensor networks through the mass production of cheap wireless sensor units with small batteries. Such sensor networks can be used in a variety of application areas. Our focus in this paper is on applications of sensor networks that involve tracking, e.g., surveillance, wildlife studies, environmental control, and health care.
We study the problem of tracking multiple objects that are moving through a network of wireless sensors. Each sensor has a limited range for detecting the presence of the objects being tracked, and the objective is to track the location of the objects to within the accuracy of the range of a sensor. For such a tracking problem to be well-posed we need to assume that the sensor field is sufficiently dense so that the sensors cover the entire area of interest. The objects follow random paths through the sensor field whose statistics are assumed to be either known a priori or estimated online.
The sensor nodes typically need to operate on limited energy budgets. In order to conserve energy, the sensors may be put into a sleep mode. The use of sleeping sensors in sensor networks for tracking has been studied in the past. It appears that there have been two primary approaches. The first has been to assume that sleeping sensors can be woken up by external means on an as-needed basis (see, e.g., . Either the method used for this wakeup is left unspecified or it is assumed that there is some low-power wakeup radio at each sensor dedicated to this function. The second approach has involved modifications to power-save functions in MAC protocols for wireless ad hoc networks (see, e.g.,).
In this paper, we wish to examine the fundamental theory of sleeping in sensor networks for tracking, as opposed to the design of protocols for this sleeping. We will assume that the wakeup channel approach is impractical given current sensor technology. In other words, we assume it is not feasible to design a receiver that requires negligible power for operation. Thus, we must consider alternatives to the wakeup channel approach. A straightforward approach is to have each sensor enter and exit the sleep mode using a fixed or a random duty cycle. A more intelligent, albeit more complicated, approach is to use information about the objects’ trajectories that is available to the sensor from the network to determine the sleeping strategy. In particular, it is easy to see that the location of the objects (if known) at the time when the sensor is put to sleep would be useful in determining the sleep duration of the sensor; the closer an object is to a sensor, the shorter the sleep duration should be. We take this latter approach in this paper in designing sleeping strategies for the sensors.
In , we used the above approach for the tracking of a single object. An optimization problem was formulated that took the form of a partially observable Markov decision process (POMDP). While optimal solutions to this problem could not be found, suboptimal solutions were devised that could be demonstrated to be near optimal. In this paper, we extend our analysis to the tracking of multiple objects. A discussion of the tracking of multiple objects, often termed multitarget tracking (MTT), can be found in. Tracking multiple objects is not a simple extension of tracking a single object due to the data association problem. This problem arises whenever the identity of the objects cannot be determined from the observations. Thus, even if all locations where objects are located are known exactly, it may not be known which location corresponds to which object. This uncertainty leads to
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