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The ability to automatically locate sensor nodes is essential in many Wireless Sensor Network (WSN) applications. To reduce the number of beacons, many mobileassisted approaches have been proposed. Current mobileassisted approaches for localization require special hardware or belong to centralized localization algorithms involving some deterministic approaches due to the fact that they explicitly consider the impreciseness of location estimates. In this paper, we first propose a rangefree, distributed and probabilistic Mobile Beaconassisted Localization (MBL) approach for static WSNs. Then, we propose another approach based on MBL, called Adapting MBL (AMBL), to increase the efficiency and accuracy of MBL by adapting the size of sample sets and the parameter of the dynamic model during the estimation process. Evaluation results show that the accuracy of MBL and AMBL outperform both Mobile and Static sensor network Localization (MSL) and Arrival and Departure Overlap (ADO) when both of them use only a single mobile beacon for localization in static WSNs.
Wireless Sensor Networks (WSNs) are composed of large numbers of tiny sensor devices with wireless communication capabilities. WSN systems have been developed recently for numerous applications such as military surveillance [
In most existing WSNs, sensors are static [
In this paper, we propose two mobile beaconassisted localization approaches,
This paper offers the following two major contributions:
We propose a rangefree, distributed and probabilistic MBL approach. This approach outperforms both Mobile and Static sensor network Localization (MSL) and ADO when both of them use only a single mobile beacon for localization in static WSNs.
We propose another approach based on MBL, called AMBL, to increase the efficiency and accuracy of MBL by adapting the size of sample sets and the parameter of the dynamic model during the estimation process.
The rest of this paper is organized as follows: Section 2 defines mobile beaconassisted localization problem from Bayesian filter and particle filter perspective. Section 3 presents details of the proposed MBL and AMBL algorithms. Section 4 shows and discusses our evaluation results. Section 5 gives an overview of related works. Finally, Section 6 concludes our work.
Let us consider a sensor network with
If we solve the abovementioned localization problem with a probabilistic approach, we are interested in estimating the unknown node’s
By
To address the complexity of the integration step in Bayesian filter, many optimal or suboptimal approaches are proposed. The recurrence relations
The Kalman filter assumes that the posterior density at every time step is Gaussian and, hence, parameterized by a mean and covariance, provided that certain assumptions hold:
The particle filter solutions offer a number of significant advantages compared with other techniques currently available, including the Kalman filter. These advantages arise principally from the generality of the approach, which allows inference of full posterior distributions in general statespace models, which may be both nonlinear and nonGaussian.
Thus, in this paper, we use a particle filter (also called
In order to develop the details of the algorithm, let
The proposal density is chosen to factorize such that:
To derive the weight update equation,
The weight update equation can then be shown to be (the proposal density is chosen to be dynamic model
The generic particle filter proceeds for localization are as follows:
The parameter
In order to state the description of observation
In this paper, we only rely on observations from the beacon. This has two advantages. First, the number of unknown nodes will not affect the accuracy of localization. Second, the computation and communication costs drop drastically, since nodes are no longer involved in the localization of other nodes [
Once the unknown node is in Insider state, it gathers this observation, i.e. the filter condition of the real location
When the unknown node is in Arriver or Leaver state, it gathers this observation, i.e. the filter condition of the real location
From an implementation perspective, in the first way, the beacon just transmits information about its own current location. Once the unknown node hears a location announcement from that beacon, an observation (also called
In the second way, the beacon transmits both its current location and its location at the previous time step in each announcement. The unknown node needs to save state (Insider or Outsider) in previous time step with a tag:
This procedure at an unknown node is then as described by
State at an unknown node.
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2:  StateTag=FALSE 
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4:  filter(R)=FALSE 
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6:  filter(R)=TRUE 
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9:  filter(R)=TRUE 
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12:  StateTag=TRUE 
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14:  StateTag=FALSE 
15: 
The first way was adopted by Monte Carlo Localization (MCL) [
Then, the weight of sample is determined by the filter condition:
Finally, in order to give more clear description of MBL, we describe the main stages as a state machine diagram with labeled transitions, see
For reference, we first evaluate the trend of location error defined by
As shown in
To judge the localization to reach the stable phase, a simple and intuitive approach is to adopt
We adopt two predefined adjustment tables in our approach, one for the number of samples
The implementation details are described in
adaptive step in unknown node.
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AMBL.
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The key metric [
In this section, we first evaluate MBL algorithm under various parameters configuration, such as the maximum speed of the beacon, the number of samples for an unknown node, and the impact of parameters
In order to compare different algorithms under the same conditions, MSL in our evaluation will only use a single mobile beacon for localization.
All of our previous experiments assumed an ideal scenario where location sensory data are not influenced by irregular radio range and any receiver within the radio range of sender will hear the packets from that sender. However, on the one hand, variability in actual radio transmission patterns can have a substantial impact on localization accuracy depending on the localization technique [
If the unknown node (receiver) within radio range of the beacon (sender) will not hear a location announcement (such as network collisions or missed packages) from that beacon at some time, the beacon must keep moving for longer time to send location information which the unknown node could receive them, i.e. the time to achieve final stable phase of accuracy as ideal state will be extended. The accuracy of MBL and AMBL will not be affected in such scenarios.
In this section, we provide a brief survey focusing on mobileassisted localization approaches suitable for WSNs. MAL [
Different from above rangebased deterministic mobile beaconassisted approaches, many rangebase probabilistic approaches have been proposed. Sichitiu
All above rangebased approaches are constrained by the expensive cost and high energy consumptions of the ranging hardware devices. Furthermore, in many practical situations, the measurements are far from accurate (and even sometimes unobtainable) due to highly dynamic environments [
Due to the hardware limitations and energy constraints of sensor nodes, rangefree localization approaches are costeffective alternatives to rangebased approaches. Walking GPS [
Our proposed method differs significantly from previous rangebase or rangefree mobileassisted localization works because we adopt rangefree techniques and solve the problem from particle filter perspective.
Our work is similar to that of Hang
Coates
The rangefree algorithm MCL proposed by Hu
In this paper, we propose two rangefree, distributed and probabilistic mobile beaconassisted localization approaches for static WSNs, MBL and AMBL. Evaluation results show that the accuracy of AMBL outperforms MBL, MSL and ADO in static WSNs when all of them use only a single mobile beacon for localization. As future work, two new issues will be considered. First, whether the use of information from unknown nodes (especially the neighbor nodes) which may have greater communication cost to increase efficiency and accuracy in mobile beaconassisted localization needs further research. Second, though adopting predefined adjustment tables in AMBL is convenient and effective, obtaining these tables is difficult. We will also consider some of selfadaptive mechanism in our approaches to achieve more flexibility.
This work is supported by the National Basic Research Program of China (973 Program) under grant No. 2006CB303000.
State machine diagram of MBL
Different exemplars of MBL.
Sum of weight for MBL.
Location convergence.
Impact of sample size.
Impact of parameter α.
Comparison of efficiency.
Comparison of accuracy.
Speed of beacon.
Number of unknown nodes.
Impact of Irregularity.
Predefined adjustment tables for N.
1  0  50 
2  2,000  20 
Predefined adjustment tables for α.
1  0  0.1 
2  1,500  0.01 