Wireless sensor network localization techniques

TL;DR: An overview of the measurement techniques in sensor network localization and the one-hop localization algorithms based on these measurements are provided and a detailed investigation on multi-hop connectivity-based and distance-based localization algorithms are presented.

About: This article is published in Computer Networks.The article was published on 2007-07-01 and is currently open access. It has received 1870 citations till now. The article focuses on the topics: Key distribution in wireless sensor networks & Visual sensor network.

Summary

I. INTRODUCTION

• W IRELESS sensor networks (WSNs) are a significant technology attracting considerable research interest.
• Cheap, smart sensors, networked through wireless links and deployed in large numbers, provide unprecedented opportunities for monitoring and controlling homes, cities, and the environment.
• Sensor network localization algorithms estimate the locations of sensors with initially unknown location information by using knowledge of the absolute positions of a few sensors and inter-sensor measurements such as distance and bearing measurements.
• In applications where a local coordinate system suffices (e.g., smart homes), these anchors define the local coordinate system to which all other sensors are referred.
• In Section III, one-hop localization techniques based on these measurements are discussed.

B. Distance related measurements

• Distance related measurements include propagation time based measurements, i.e., one-way propagation time measurements, roundtrip propagation time measurements and timedifference-of-arrival (TDOA) measurements, and RSS measurements.
• One-way propagation time measurements measure the difference between the sending time of a signal at the transmitter and the receiving time of the signal at the receiver.
• When the receiver receives the RF signal, it turns on its ultrasonic receiver and listens for the ultrasonic pulse.
• Their method gave fairly accurate distance estimate at the cost of additional hardware and complexity of the system because ultrasonic reception suffers from severe multipath effects caused by reflections from walls and other objects.
• The optical beam rotates at an unknown angular velocity ω around the Z axis.

) Time-difference-of-arrival measurements :

• The most widely used method is the generalized cross-correlation method, where the cross-correlation function between two signals s i and s j received at receivers i and j is given by integrating the lag product of two received signals for a sufficiently long time period T , EQUATION Overlapping cross-correlation peaks due to multipath often cannot be resolved.
• Even if distinct peaks can be resolved, a method must be designed for selecting the correct peak value, such as choosing the largest or the first peak [7] .
• 4) Distance estimation via received signal strength measurements :.
• In free space, other things being equal the RSS varies as the inverse square of the distance d between the transmitter and the receiver.

C. RSS profiling measurements

• Yet another category of localization techniques, i.e., the RSS profiling-based localization techniques [42] - [46] , work by constructing a form of map of the signal strength behavior in the coverage area.
• In addition to there being anchor nodes (e.g., access points in WLANs) and non-anchor nodes, a large number of sample points (e.g., sniffing devices) are distributed throughout the coverage area of the sensor network.
• By referring to the RSS model, a non-anchor node can estimate its location using the RSS measurements from anchors.
• In summary, a number of measurement techniques are available for WSN localization.
• That accuracy is achieved at the expense of higher equipment cost.

A. AOA based one-hop localization techniques

• In the absence of noise and interference, bearing lines from two or more receivers will intersect to determine a unique location, i.e., the location estimate of the transmitter.
• In the presence of noise, more than two bearing lines will not intersect at a single point and statistical algorithms, sometimes called triangulation or fixing methods, are required in order to obtain the location estimate of the transmitter [47] , [48] .
• His approach has been further generalized in [50] , [52] and has been implemented in many practical systems.
• The 2D localization problem using bearing measurements can be formulated as follows.
• In that case an iterative procedure can be used to obtain the solution to the minimization problem, which has no advantage over the ML technique [48] .

B. TDOA-based one-hop localization techniques

• Moreover, in some situations this method can result in significant location estimation errors due to geometric dilution of precision (GDOP) effects.
• GDOP describes a situation in which a relatively small ranging error can result in a large location estimation error because the transmitter is located on a portion of the hyperbola far away from both receivers [7] , [53] .
• Chan et al. [57] developed a closed form solution valid for an arbitrary number of TDOA measurements and arbitrarily distributed transmitters.
• The computational complexity of Chan's method is comparable to the spherical interpolation method but substantially less than the Taylor-series method [47] .
• The hyperbolic curves are approximated by linear asymptotes.

C. Distance-based one-hop localization techniques

• The most well-known distance-based localization technique is based on use of GPS.
• The fourth distance measurement provides information from which the synchronization error of the receiver can be corrected and the receiver's clock can be synchronized to an accuracy better than 100ns.
• This minimization problem can be solved using a similar procedure described in Section III-A and Section III-B.
• The essence of using the Cayley-Menger determinant to reduce the impact of distance measurement errors is: the six edges of a planar quadrilateral are not independent, instead they must satisfy the equality constraint in Eq. 30.
• This equality constraint can be exploited to reduce the impact of distance measurement errors.

D. Lighthouse approach to one-hop localization

• The lighthouse approach uses a base station equipped with three mutually perpendicular parallel optical beams to locate all optical receivers within the range and line-of-sight of the beams in 3 .
• Without loss of generality, assuming the rotational axes of the three mutually perpendicular parallel optical beams are X, Y , and Z axes respectively.
• By using priori knowledge of which quadrant the receiver is located in, only one solution is chosen.
• Techniques dealing with non-ideal situations such as misalignment of the rotational axes of optical beams and nonparallel beams were also discussed in [24] .

E. RSS-profiling based localization

• Given the RSS model constructed using the procedure described in Section II-C, each non-anchor node unaware of its location uses the signal strength measurements it collects, stemming from the anchor nodes within its sensing region, and thus creates its own RSS finger print, which is then transmitted to the central station.
• The accuracy of this technique depends on two distinct factors: the particular technique used to build the RSS model, with the resultant quality of that model, and the technique used to fit the measured signal strength vector from a non-anchor node into the appropriate part of the model.
• The performance of all three algorithms was compared with the point based algorithm of [42] .
• Subsequent changes in the environment (e.g. inside a building, office occupancy can change) can affect the model, and so a static model derived from a single-shot experiment may be inadequate in some applications.
• Together with a large number of stationary emitters (anchor nodes) deployed at known locations, the "sniffers" can be used to construct and update the RSS model online.

F. Localization based on hybrid measurements

• There are a number of other localization algorithms based on data fusion [68] [71] .
• Thomas et al. considered the fusion of TDOA and AOA measurements [73] .
• Catovic [74] computed the Cramér-Rao bounds on the location estimation accuracy of two different hybrid schemes, i.e., TOA/RSS and TDOA/RSS, and found that hybrid schemes offer improved accuracy with respect to conventional TOA and TDOA schemes.
• Therefore errors in the location estimate for each measurement type are at least partially independent.
• Among those hybrid techniques, the fusion of RSS and TOA measurements appears to be the most attractive for a WSN because of its relatively simple hardware requirement.

IV. NONLINE-OF-SIGHT ERROR MITIGATION

• A common problem in many localization techniques is the nonline-of-sight (NLOS) error mitigation.
• NLOS errors between two sensors can arise when either the line-of-sight between them is obstructed, perhaps by a building, or the lineof-sight measurements are contaminated by reflected and/or diffracted signals.
• A typical approach is to assume that the measurement error has a Gaussian distribution, then the least-squares residuals are examined to determine if NLOS errors are present [76] , [80] , [81] (by regarding any large residual as due to the NLOS signals).
• In [79] , Venkatraman et al. employed a constrained nonlinear optimization approach for TOA NLOS error mitigation in a cellular network.
• Bounds on the NLOS error and the relationship between the true ranges are extracted from the geometry of the cell layout and the measured range circles to serve as constraints.

V. CONNECTIVITY BASED MULTIHOP LOCALIZATION ALGORITHMS

• In the following sections, the authors shall review multihop localization techniques in which the non-anchor nodes are not necessarily the one-hop neighbors of the anchors.
• Shang et al. [85] and Doherty et al. [88] developed centralized connectivitybased localization algorithms.
• The "DV(distance vector)-hop" approach developed by Niculescu et al. [87] starts with all anchors flooding their locations to other nodes in the network.
• The messages are propagated hop-by-hop and there is a hop-count in the message.
• The average node degree, i.e., average number of neighbors per node, is 7.6.

VI. DISTANCE-BASED MULTIHOP LOCALIZATION ALGORITHMS

• The core of distance-based localization algorithms is the use of inter-sensor distance measurements in a sensor network to locate the entire network.
• Based on the approach of processing the individual inter-sensor distance data, distance-based localization algorithms can be considered in two main classes: centralized algorithms and distributed algorithms.
• Centralized algorithms use a single central processor to collect all the individual inter-sensor distance data and produce a map of the entire sensor network, while distributed algorithms rely on self-localization of each node in the sensor network using the distances the node measures and the local information it collects from its neighbors.
• Next the authors review the main characteristics as well as relevant studies in the literature for each of the two classes and compare them at the end of the section.

A. Centralized algorithms

• In certain networks where a centralized information architecture already exists, such as road traffic monitoring and control, environmental monitoring, health monitoring, and precision agriculture monitoring networks, the measurement data of all the nodes in the network are collected in a central processor unit.
• Once feasible to implement, the main motive behind the interest in centralized localization schemes is the likelihood of providing more accurate location estimates than those provided by distributed algorithms.
• The whole sensor network is divided into smaller groups where adjacent groups may share common sensors.
• MDS is used to estimate the relative locations of sensors in each group and build local maps.
• Since a large number of iterations (implies a high communication cost) are required for the algorithm to converge, it is more appropriate to be implemented using a centralized architecture.

B. Distributed Localization

• Similarly to the centralized ones, the distributed distancebased localization approaches can be obtained as an extension of the distributed connectivity-based localization algorithms in Section V to incorporate the available inter-sensor distance information.
• The main idea in the "DV-distance" algorithm as compared to the "DV-hop" algorithm is propagation of measured distance among neighboring nodes instead of hop count.
• Two similar approaches are the two-stage localization scheme of Savarese et al. [95] and the four-stage algorithm of Savvides et al. [96] .
• The simulation results demonstrated that the algorithm is able to achieve an average location estimation error of less than 33% of the transmission range in the presence of 5% distance measurement error (normalized by the transmission range).
• In the final stage of the algorithm, the location of each node deemed not tentatively uniquely localizable in stage one is estimated using the location estimates of its tentatively uniquely localizable neighbors.

C. Centralized versus Distributed Algorithms

• Centralized and distributed distance-based localization algorithms can be compared from perspectives of location estimation accuracy, implementation and computation issues, and energy consumption.
• From the perspective of location estimation accuracy, centralized algorithms are likely to provide more accurate location estimates than distributed algorithms.
• Other disadvantages of centralized algorithms, as compared to distributed algorithms, are their requirement of higher computational complexity and lower reliability due to accumulated information inaccuracies/losses caused by multihop transmission over a wireless network.
• Error propagation is another potential problem in distributed algorithms.
• Depending on the setting, the energy required for transmitting a single bit could be used to execute 1,000 to 2,000 instructions [103] .

VII. GRAPH THEORETIC RESEARCH PROBLEMS IN DISTANCE-BASED SENSOR NETWORK LOCALIZATION

• There are still many unsolved problems in the area.
• TDOA and AOA), the authors focus on distance-based sensor network localization.
• A potential problem with using the Cramér-Rao bound to study the performance of a localization algorithm is that the Cramér-Rao bound assumes the underlying estimator is unbiased.
• This assumption needs to be validated with the estimators used in various localization algorithms, and in particular, the class of algorithms which minimize the sum of the square of the difference between measured distances and estimated distances.
• Since trilateration and quadrilateration representative graphs provide proven reduced computational complexity in localization and actually there are systematic methods to locate networks with such representative graphs, it is of interest to develop mechanisms to make these methods applicable for certain other classes of representative graphs as well.

VIII. SUMMARY

• Wireless sensor network localization has attracted significant research interest.
• This paper has provided a review of the measurement techniques in WSN localization and the corresponding localization algorithms.
• These localization algorithms were divided into one-hop localization algorithms and multi-hop localization algorithms.
• A detailed investigation on connectivity-based and distance-based localization algorithms were presented because of their popularity in wireless sensor network localization.
• A discussion on some fundamental research problems in distance-based location and possible approaches to these problem was also presented in this paper.

Figures

Fig. 5. In the presence of noise, bearing lines from three receivers will not interact at the same point.

Fig. 11. Localization of a non-globally rigid unit-disk framework in <2: assume that the location of vertices 1, 2, 3 and the lengths of the edges (2, 4) and (3, 4) are known and that there is no edge between 1 and 4. There exist two possible locations for vertex 4 in general: Case 1 and Case 2. We can eliminate Case 2 using the unit-disk property since for this case there had to be an edge between vertices 1 and 4 since d14 < R. Hence Case 1 gives the correct unique location of vertex 4.

Fig. 10. An illustration of discontinuous deformations on non-globally rigid frameworks: (a) Flip ambiguity: vertex 4 can be reflected across the edge (2,3) to a new location without violating the distance constraints. (b) Discontinuous flex ambiguity: removing the edge (1,4), flexing the edge triple (1,5), (1,2), (2,3), and reinserting the edge (1,4) so that the distance constraints are not violated in the end, we obtain a new new framework.

Fig. 1. An illustration of the horizontal antenna pattern of a typical anisotropic antenna.

Fig. 2. An antenna array with N antenna elements.

Fig. 9. Performance of SA algorithm with flip ambiguity mitigation and SDP algorithm with gradient search improvement.

Fig. 7. A fully-connected planar quadrilateral in sensor networks.

Fig. 3. An illustration of the lighthouse approach for distance measurement.

Fig. 8. An illustration of the lighthouse approach to localization.

Frequently asked questions

Q1. What have the authors contributed in "Wireless sensor network localization techniques" ?

This interest is expected to grow further with the proliferation of wireless sensor network applications. This paper provides an overview of the measurement techniques in sensor network localization and the one-hop localization algorithms based on these measurements. A list of open research problems in the area of distance-based sensor network localization is provided with discussion on possible approaches to them. 

Q2. What are the main approaches for designing centralized distance-based localization algorithms?

In the literature, there exist three main approaches for designing centralized distance-based localization algorithms: multidimensional scaling (MDS), linear programming and stochastic optimization approaches. 

Q3. What other techniques can deal with the more general situation with extra measurements?

Other techniques that can deal with the more general situation with extra measurements include the spherical interpolation method [55], which is derived from least-squares “equationerror” minimization, and the divide and conquer method [56]. 

Q4. What is the major error source in roundtrip propagation time measurements?

The major error source in roundtrip propagation time measurements is the delay required for handling the signal in the second sensor. 

Q5. How can the SDP approach be extended to incorporate distance measurements?

Similarly to the MDS approach, the semi-definite programming (SDP) approach used for connectivity-based localization algorithms can also be extended to incorporate distance measurements [88]. 

Q6. What is the problem with using the Cramér-Rao bound?

A potential problem with using the Cramér-Rao bound to study the performance of a localization algorithm is that the Cramér-Rao bound assumes the underlying estimator is unbiased. 

Q7. What are the disadvantages of centralized and distributed distance-based localization algorithms?

Other disadvantages of centralized algorithms, as compared to distributed algorithms, are their requirement of higher computational complexity and lower reliability due to accumulated information inaccuracies/losses caused by multihop transmission over a wireless network. 

Q8. How is the algorithm able to achieve an average location estimation error?

The simulation results demonstrated that the algorithm is able to achieve an average location estimation error of less than 33% of the transmission range in the presence of 5% distance measurement error (normalized by the transmission range). 

Q9. What is the definition of a constrained maximization problem?

If the authors set the element of c corresponding to xi (or yi) to be 1 (or -1) and all other elements of c to be zero, the problem becomes a constrained maximization (or minimization) problem. 

Q10. How can the improved algorithm achieve better performance on irregularly-shaped networks?

The improved algorithm can achieve better performance on irregularly-shaped networks by avoiding the use of distance information between far away nodes. 

Q11. How many anchors are used to estimate the location of a node?

The estimated distances to more than three anchors allow the location of the non-anchor node to be confined inside a rectangular box, which is the intersection of the squares corresponding to each of these anchors. 

Q12. What criteria are provided in selection of the subgraphs of the representative graph of a wireless?

In this paper, certain criteria are provided in selection of the subgraphs of the representative graph of a network to be used in a localization algorithm robust against such errors. 

Q13. What are the two performance parameters for the area based localization algorithm?

Two different performance parameters apply: accuracy, or the likelihood that an object is within the area, and precision, i.e., the size of the area.