Localization in Sensor Networks BY: GAURAV KHANNA

15RE91R04

Introduction

In many applications of sensor networks it is required to automatically locate people, equipment, and other tangibles.

Various techniques have evolved over the years, such that sensor nodes can learn their location automatically.

Since each approach solves a slightly different problem or supports different applications, they vary in many parameters, such as the physical phenomena used for location determination, power requirements, infrastructure versus portable elements, and resolution in time and space.

Hence, determination of accurate location is a topic of keen interest among various researchers.

Properties of Localization [1]

Physical position and symbolic location Absolute versus relative Localized location computation Accuracy and precision Scale Recognition Cost Limitations

Localization sensing techniques

The major approaches to determine a node’s position are: Using information about a node’s neighborhood (proximity-based

approaches) Exploit finite range of wireless communication E.g.: Easy to determine location in a room with infrared room number announcements

Exploiting geometric properties of a given scenario (triangulation and trilateration) Using elementary geometry, the distance between two nodes or the angle in a triangle

can be estimated. When distances between entities are used, the approach is called lateration; when

angles between nodes are used, one talks about angulation. Trying to analyze characteristic properties of the position of a node in comparison

with premeasured properties (scene analysis).

Range based localization schemes

Received signal strength indication (RSSI)

Time of arrival (TOA) Time Difference of arrival

(TDOA) Angle of arrival (AOA)

Received Signal Strength (RSS) techniques measure the power of the signal at the receiver. Based on the known transmit power, the respective propagation loss can be calculated. Theoretical or empirical models are used to translate this loss into a distance estimate. This method has been used mainly for RF signals.

Friis Free Space Equation

Note: The Friis space equation above does not consider losses

RANGE BASED DISTANCE ESTIMATION [2],[3]

Time of arrival (ToA)/ Time difference of arrival (TDoA) [2],[4]

• In this case the distance between two nodes is directly proportional to the time the signal takes to

propagate from one point to another. • This way, if a signal was sent at time t1 and

reached the receiver node at time t2, the distance between sender and receiver is d = c(t2 – t1), where c is the propagation speed of the radio signal (speed of light), and t1 and t2 are the times when the signal was sent and received, Fig (a).

• In TDoA, nodes compute the difference in the arrival times of the two signals.

• The distance can now be computed by the formula: d = (sr – ss)*(t2 – t1), where sr and ss are the propagation speed of the radio and ultrasound Signals.

Angle of arrival (AoA) [2]

The estimation of the AoA is done by using directive antennas or an array of receivers — usually three or more — that are uniformly separated.

Based on the arrival times of the signal at each of the receivers, it becomes possible to estimate the AoA of this signal

Scene analysis

In scene analysis, pictures taken by a camera are analyzed to derive the position from this picture.

This requires substantial computational effort and is hardly appropriate for sensor nodes.

But apart from visual pictures, other measurable characteristic “fingerprints” of a given location can be used for scene analysis, for example, radio wave propagation patterns.

One option is to use signal strength measurements of (one or more anchors) transmitting a known signal strength and compare the actually measured values with those stored in a database of previously off-line measured values for each location.

The RADAR system is one example that uses this approach to determine positions in a building.

Multilateration

In reality, distance measurements are never perfect and the intersection of these three circles will, in general, not result in a single point.

To overcome these imperfections, distance measurements from more than three anchors can be used, resulting in a multilateration problem.

Angulation exploits the fact that in a triangle once the length of two sides and two angles are known the position of the third point is known as the intersection of the two remaining sides of the triangle.

The problem of imprecise measurements arises here as well and can also be solved using multiple measurements.

Mathematical basics for lateration [4] Assuming distances to three points with known location are exactly

given Solve system of equations (using Pythagoras Theorem)

(xi,yi) : coordinates of anchor point i, ri : distance to anchor i (xu, yu) : unknown coordinates of node

Subtracting eq. 3 from 1 & 2:

Rearranging terms gives a linear equation in (xu, yu)!

Trilateration as matrix equation

Rewriting as a matrix equation:

What if only distance estimation ri’ = ri + i available? Use multiple anchors, overdetermined system of equations

Use (xu, yu) that minimize mean square error, i.e, Given a matrix equation:

Ax = b, The normal equation is that which minimizes the sum of the square

differences between the left and right sides:

It is called a normal equation because b-Ax is normal to the range of A. Here, is a normal matrix.

Single Hop localization

Active Badge Active office RADAR CricketFew other techniques are: Overlapping Connectivity Approximate point in triangle Using Angle of Arrival information

Active Badge [5]

It is the first system for the location of people in an office environment.

Members of staff wear badges that transmit signals providing information about their location to a centralized location service, through a network of sensors.

It uses diffused infrared as transmission medium and exploits the natural limitation of infrared waves by walls as a delimiter for its location granularity.

A badge periodically sends a globally unique identifier via infrared to receivers, at least one of which is installed in every room. This mapping of identifiers to receivers (and hence rooms) is stored on a central server, which can be queried for the location of a given badge.

Active office [6]

It is a system that can determine the location and orientation of objects within a building.

The information provided by the system is sufficiently fine-grained to allow investigation of a new set of context aware applications.

Here, ultrasound is used, with receivers placed at well-known position, mounted in array at the ceiling of a room; devices for which the position is to be determined act as ultrasound senders.

Furthermore, the wireless, low-powered nature of the location sensors allows them to be integrated into an everyday working environment with relative ease.

RADAR [7]

The RADAR system is also geared toward indoor computation of position estimates.

Its most interesting aspect is its usage of scene analysis techniques, comparing the received signal characteristics from multiple anchors with premeasured and stored characteristic values.

Both the anchors and the mobile device can be used to send the signal, which is then measured by the counterpart device(s).

While this is an intriguing technique, the necessary off-line deployment phase for measuring the “signal landscape” cannot always be accommodated in practical systems.

Cricket [8]

In the Active Badge and active office systems described above, the infrastructure determines the device positions.

Sometimes, it is more convenient if the devices themselves can compute their own positions or locations – for example, when privacy issues become relevant.

Therefore, Cricket uses a combination of RF and ultrasound hardware to enable a listener to determine the distance to beacons, from which the closest beacon can be more unambiguously inferred.

Positioning in multi-hop environment [9] How to estimate range to a node to which no direct radio

communication exists? No RSSI, TDoA, … But: Multihop communication is possible

Idea 1: Count number of hops, assume length of one hop is known (DV-Hop)

Idea 2: If range estimates between neighbors exist, use them to improve total length of route estimation in previous method (DV-Distance)

Iterative multilateration

Assume some nodes can hear at least three anchors (to perform triangulation), but not all

Idea: let more and more nodes compute position estimates, spread position knowledge in the network Problem: Errors accumulate

Probabilistic position description

Similar idea to previous one, but, here position of nodes is only probabilistically known Represent this probability explicitly, use it to compute probabilities for further

nodes

Centroid Algorithm (Range-Free)[10]

The implementation of centroid algorithm contains below steps. All anchor nodes broadcast their location information and

identity to all sensor nodes in their transmission range. All nodes listens the signal for a fixed time t and collect the location information from various anchor nodes.

All un-localized nodes determine their position by forming a polygon shown in figure and calculate the centroid from all positions of anchor nodes in their range by using the below formula:

Xest = (X1+ X2…..+ Xn) /n Yest = (Y1+ Y2…..+ Yn) /n

Where (X1, Y1)… (Xn, Yn) are the anchor node’s coordinates and (Xest, Yest) is estimated coordinates of the node.

Major drawback is it produces large localization error.

Relative Neighborhood Graph[11]

In many problems one is given a set of points on the plane and it is desired to find some structure among the points in the form of edges connecting a subset of the pairs of points.

Edge between nodes u and v if and only if there is no other node w that is closer to either u or v

Formally:

RNG maintains connectivity of the original graph Easy to compute locally But: Worst-case

spanning ratio is (|V|) Average degree is 2.6

This region has to be empty for the two nodes to be connected

Voronoi Diagrams/ Delaunay Triangulation

Voronoi diagram: Assign, to each node, all points in the plane for which it is the closest node

Constructed in O(|V| log |V|) time Delaunay triangulation: Connect

any two nodes for which the Voronoi regions touch

Problem: Might produce very long links; not well suited for power control

Edges of Delaunay triangulation

Gabriel Graph

Gabriel graph (GG) similar to RNG Difference: Smallest circle with nodes u and

v on its circumference must only contain node u and v for u and v to be connected

Formally:

Properties: Maintains connectivity, Worst-case spanning ratio (|V|1/2), energy stretch O(1) (depending on consumption model!), worst-case degree (|V|)

This region has to be empty for the two nodes to be connected

Two algorithms for finding the RNG

Given: n points, their Cartesian coordinates p1(x1, y1), p2(x2, y2).... Pn (xn,yn)

Algo. 1: (1) Compute the distance between all pairs of points d(pi , pj), i, j = 1, 2, ... n, i ≠ j.

(2) For each pair of points (pi , pj) compute = max {d(pk, pi), d(pk, pj)} for k = 1, 2, ... n, k ≠ i, k ≠ j.

(3) For each pair of points (pi, pj) search for a value of that is smaller than d(pi, pj). If such a point is not found, an edge is formed between pi and pj.

Algo. 2: (1) Compute the Voronoi diagram of the set of points. (2) Obtain Delaunay triangulation from the Voronoi

diagram. (3) For each pair of points (pi, pj), associated with an

edge of the DT, compute = max {d(pk, pi), d(pk, pj)} for k = 1, 2, ... n, k ≠ i, k ≠ j.

(4) Same as step 3 of algorithm 1, with edges of DT only.

Mobile target tracking in WSNs

The RNG tessellates the plane into polygonal shapes called as “faces”. If every node is aware of its own location and of all its neighbors in the

faces by using global positioning system (GPS) or other techniques (already discussed), then, this can be exploited in tracking mobile targets.

Typical examples include establishing survivable military surveillance systems, environmental and industrial monitoring, personnel and wildlife monitoring systems requiring tracking schemes, capable of deducing kinematic characteristics such as position, velocity, and acceleration of single or multiple targets of interest.

Target Tracking with Monitor and Backup Sensors in Wireless Sensor Networks (TTMB)[12] If the number of active sensors is large, the tracking accuracy can be

high; however, with high energy consumption. So, for tracking a mobile target, the idea is to use as minimum no. of

sensors as possible. TTMB is a novel lightweight approach to implement target tracking in

WSNs combining Geographic routing and prediction methods. This protocol relies on accumulated information from a small number of

sensor nodes. It has low complexity prediction based cooperative tracking that compares the data received from different nodes.

TTMB Introduction

An entity that intends to track a target is called a tracker. A tracker is assumed to be a single generic source such as a mobile user

or a respective authority. A target can be any mobile entity such as enemy vehicle or an intruder. Each sensor in the network has the capability of sensing, communicating,

and computing. One of the active and working sensors is elected as a monitor, and

another one is elected as a backup for fault tolerance concern. The tracker queries the sensor network to follow a target, monitor works

on the request of tracker. All sensors can be in three states: awake, active or inactive.

Working (Outline) of TTMB protocol

A Tracker sends a query request to the sensor network Sensor receives a query request

Checks whether it is close to the target

If it is, it then becomes a “monitor”

Informs the trackerTracker moves towards the monitor and queries for the

target information.

If target is still in the face, monitor keeps tracking, and

also elects new monitor in other face using the proposed prediction mechanism

Monitor also elects a new backup

Planarization model

A sensor network can be modeled as a graph G = (V,E) by utilizing two well-known distributed planarization algorithms, Gabriel graph (GG) and relative neighborhood graph (RNG)(already discussed).

In the given Figure note that node v1 corresponds to 3 adjacent faces, namely, F1, F2, and F18.

Suppose a target is presently in F2 and v1 is a monitor node, then F1 and F18 are called neighbor faces.

So v1 stores information about 3 faces that are adjacent to it in the planar subgraph - (v1, v3, v4, v5), (v1, v5, v6, v7, v2) and (v1, v2, v3).

Node v1 has only 3 neighbor nodes v2, v3, and v5, but with respect to the target position, v1 has 2 neighbor nodes, v5 and v2 in F2, called immediate neighbors.

While the rest of v1’s neighbor nodes, v6 and v7 in F2 are called distant neighbors.

State transition and Energy consumption model Assume a tracking event is captured by a sensor node at

some time t0; processing is finished at time t1; and the next tracking event occurs at time t2 = t1 + ti.

According to the state transition diagram shown in Figure, each state Sk has a power consumption Pk, and the transition time to a state and return from the state is given by τd,k and τu,k, respectively.

Typically, in different node states, Pj > Pi, td,i > td,j and tu,i > tu,j for any i > j, and ΔP = P0 – Pk and ΔP’ = P0+Pk.

When the node changes state from s0 to, say, sk. The energy savings, Es,k, because of state transition given by the difference in the face and sleep thresholds Tth,k corresponding to the states sk are computed as follows:

Mobile target positioning and movement

Using these values, the predicted location for the target (xi+1, yi+1) after a given time t is given by:

The monitor can find out a target’s position, velocity and direction.

Given the target’s present location in oLi(xi, yi) at time ti and (xi−1, yi−1) in previous location oLi−1 at time ti−1, then we can estimate the target’s speed v and the direction as:

T sends request into the sensor network at time ti, requesting the

position of o. Since o is in Face F1, T is informed of o’s current location and that the closest sensor is v4

(see Figure a)

Thus, v4 becomes the monitor. In F1, v4 has 3 face neighbors that are v5, v1 and

v3, where its immediate neighbors are v5 and v3.

If o moves in the direction of v3, v4 is able to easily determine it. If the monitor v4 estimates that o is moving toward v1, v4 then communicates with v1 and v5.

Since T arrives at the vicinity of v4 after o has moved away,

v4 informs T to follow the same route i.e. go to v1 (o’s

current position).

When o moves from F1 to F2 along the route indicated in

Figure (b) at time ti+1, only the monitor v1 or both monitor v1

and backup v5 are already aware of o’s route.

As o moves from F1 to F2, a new monitor and backup are determined in the new

face by the old monitor

Meanwhile T reaches v1, now monitor v1 senses and

observes o in F2. This process continues as shown

in Fig. (c)

Interaction between Tracker (T), target (O), monitors and backups

When a new monitor fails to detect or is not close to o, the backup takes up the role of the monitor.

The relationship between the monitor, the new monitor, and the backup is maintained through a low cost implicit linked list among them, as shown in Figure.

When o moves across the sensing field, the monitor can construct a linked list automatically, there is a linear link between the monitor v4 and the new monitor v1, and another link between v4 and v5, also there is link between v1 and its backup v5.

Local area prediction-based mobile target tracking in wireless sensor networks (t-Tracking)[13]

T-Tracking: A modification in TTMB by target tracking using “face prediction”, instead of “target location prediction in faces”.

This achieves two major objectives: high QoT and high energy efficiency of the WSN.

Basic terms like: target, tracker etc. remains unchanged here, also assumptions are similar about RNG and query etc.

This protocol consists of seven algorithms, which are used for face prediction for localization of target. The outputs from one algo. Serves as some input for the other.

Here also, all nodes are aware of their geographic location, and a RNG is constructed at the initial step.

Rules for node organization into faces As T wishes, it issues a message to the WSN to assist to track t. Suppose that vi is any node of the WSN that can detect t as t appears in the vicinity

of vi, e.g., v1. Based on a detection probability (Pd), v1 becomes the monitor. Then, v1 starts finding face Fi on which t appears. v1 further updates the information

about faces. It corresponds to three adjacent faces, namely, F1, F2, and F18. F1 and F18 are called “neighboring faces.” The nodes in the three adjacent faces in

G’ are—(v1, v3, v4, v5), (v1, v5, v6, v7, v2), and (v1, v2, v3). v1 has only three direct neighboring nodes v2, v3, and v5, but here we only consider

the neighboring nodes with respect to t’s location in F2. Thus, the nodes v5, v6, v7, and v2 in F2, are called v1’s “face neighbors.”

v5 and v2 in F2, are called v1’s “immediate neighbors.” The rest of v1’s neighboring nodes, v6 and v7, are called “distant neighbors.”

One immediate neighbor (e.g., v2) becomes the backup, as the combined detection probability, denoted by , between the monitor and the immediate neighbor is the best.

Target detection inside a face (Algo. 1) Each node estimates a

detection probability Pd, which is “the probability that a node reports the presence of t when t is within its Rs.”

Here, Signal strength is modelled using:

Algorithm 1. Target Detection Input: A WSN of N sensor nodes observing the

target t; Output: t’s location li at time h; for each node vi of the WSN at the s1 state do Listen to the environment and start sensing; Measure Si; if t is found then Change the status to s0 state; Compute Pd; Run t’s moving face detection algorithm; //i.e.,

Algorithm 2 Compute current location li; // After Algorithm 2 runs end for

Target’s moving face detection (Algo. 2) Each node that already detected t makes a

decision on t: in which specific face t is currently moving and then localize t inside the face for the first time face detection.

Algorithm 2: Step 1. Node vi, e.g., v1, detects t by using

Pd at time instant h somewhere in the WSN. Similarly, some neighboring nodes, e.g., v5, v3, v4, v6, and so on, of v1 might be able to detect t at h and have Pd to some extents.

Step 2. v1 first interacts with its adjacent neighbors by issuing a request, containing the information that t is in the range. The information includes Pd and d(,). There are three adjacent neighbors of v1: v5, v2, and v3.

Step 3. After receiving the request messages from all of its neighbors (including the adjacent ones), node vi compares its Pd with another node vj that are paired up with it, e.g., v1<->v2; v1<->v3; v1<->v5.

Step 4. Among all the neighbors, v5 or v2 has the second best detection probability that are the immediate neighbors. v3 may have the lower detection probability than that of v5 or v2. Thus, t should be inside F2, instead of in F18 or in F11. To know the pair of the nodes, which have the best detection probability, we consider a “combine detection probability ()” of each pair.

Target’s moving face detection (Algo. 2) Finally, three conditions for any pair

of nodes such as v1 and v5 are set, to be the monitor and backup: (i) should be higher than other pairs of nodes; (ii) they should be the adjacent and also be the immediate neighbors; (iii) they should be in the same face Fi, e.g., F2.

Step 5. As the monitor and backup, v1 and v5 update the information of F2 and neighboring faces by following the rules described earlier. Then, the complete face Fi is

detected and nodes of the faces are organized to track t.

Note that the above steps are used for face Fi detection at the first time. t’s tracking can be easier in the WSN afterward, as another two nodes of F2 (e.g., v1 and v5) compute t’s movements and face prediction when t moves from Fi to Fj.

Target’s moving face detection (Algo. 2)

Computing t’s moving sequence inside a face (Algo. 3)

t may move in complex and stochastic ways in any direction from face Fi to a future face Fj, as shown in Fig.(a).

t’s velocity is unpredictable and it may be impossible to explicitly express the velocity. When t moves inside Fi and moves toward Fj, as shown in Fig. (b)

Fig.(a) Fig.(b)

Face prediction (Algo. 4)

Here, based on the movement sequence, the monitor and backup compute a probability of direction, denoted by p, where p is given by:

Tracking process through face prediction (Algo. 5 & 6)

Algorithm 6 provides the pseudocode of the interactions between the monitor and T for t’s tracking.

Robustness to special events in tracking (Algo. 7)

References

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References

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13. M. Z. A. Bhuiyan, G. Wang, A.V. Vasilakos, "Local Area Prediction-Based Mobile Target Tracking in Wireless Sensor Networks," in Computers, IEEE Transactions on , vol.64, no.7, pp.1968-1982, July 1 2015.

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