Mini Project Report by: Hersh Vardhan Shukla ; Guides : Jun Luo, Jacques Panchard ;
Professor : Dr. Jean-Pierre Hubaux
School of Computer and Communication Sciences
Ecole Polytechnique F´ed´erale de Lausanne (EPFL) , CH-1015 Lausanne, Switzerland
We plan to use base station mobility for localizing nodes using the mobility of the Base
Station to our advantage. In the process we also end up synchronizing the network. The scheme provides for distributed, fast and fairly accurate localization and the significant part of the scheme is that localization takes place in the passive mode such that no node compromises its position by broadcasting during localization phase.
Our new proposal builds upon the work done in
In this paper the authors show that if mobile BS is used to collect data from the sensors then the power saving for the nodes is of the order of 500%..Besides they also prove that the optimal path for such a data collection is a circular path along the periphery of the network.
In our proposal using this path we prove that besides efficient data collection the Base station can achieve much more; it can localize the nodes as well as synchronize them.
This paper deals with localization using diffusion technique. Diffusion techniques employ movement of mobile nodes to impart the static nodes of their position wrt to anchored access points. However most of the techniques employ signal sensing techniques to ascertain position which leads to slow convergence to correct positions.
Such techniques are useful for environments where not very exact positioning is required and delay in convergence to correct value is acceptable.

This paper proposes a scheme for distributed localization using constraints imposed by radio signal sensing, however this scheme also leads to slow convergence besides it also assumes symmetric radio propagation model and same sensing range for all nodes which will not be the case in real life sensor networks due to topology and battery strength of the motes.
In this paper the authors come with a novel scheme to localize nodes using Robust
Kilman Filter for Delay Tolerant Sensor Networks however they use a centralized approach in which the mobile robot goes about determining the locations of the nodes which has inherent scalability problem besides the operation requires active involvement by the nodes in form of RSSI broadcast thereby exposing their position.
In this paper the authors propose a scheme based on RSSI signal strength measurement and the constraints imposed by the node being in the sensing distance of the mobile beacon. They then use Bayesian probability distribution to calculate how close the node can be wrt to the node with a given RSSI. Such an approach requires some extensive calculation on the part of the nodes and does not yield very accurate results with errors in the margin of few meters as proclaimed by the authors themselves.
In this paper the authors propose a scheme to find the inter node distances.
The above paper use a distance measuring device using TDOA between ultrasound and radio signal and the concept of Closest Point of Approach (CPA) for measuring the distance from a mobile target. Then the two neighbors compare their estimates of how close the target came to each of them and in this light find the distance between each other. The authors leave it to the user to apply existing localization algorithms to henceforth find the position of the nodes.

1.
The Base Station has GPS installed on it.
2.
The ultrasonic transmitter at the base station is capable of transmitting at powers capable to reach distance of the order of Network radius; this assumption can be done away with if required.
The nodes determine their position w.r.t. the centre of the network
The base station synchronizes itself wrt to the Base station clock.
1.
The Base station moves in a circle circumscribing the network i.e. at the periphery of the network. This path has been shown to be optimal as in “ Joint
Mobility and Routing for Lifetime Elongation in Wireless Sensor
Networks” Jun Luo and Jean-Pierre Hubaux.
2.
The Base station continuously broadcasts :a.
b.
Its position wrt the centre of the Network circum-circle.
It time stamps its broadcast message with its local clock.
The time interval after which it is planning to broadcast again.
c.
T-> Local Clock of Node A t-> Clock of Base Station
BS-> Base Station/ Mobile Node
P-> Position of node in concern

3.
Say the first broadcast is heard by P from BS has a time stamp t1. Node P then initializes its clock to t1 i.e. T1=t1. But actually T1 is [t1+ δ (propagation time) ].The packet tells P that the next broadcast is after ∆t. So P expects the packet to arrive at T2 such that T2-T1=∆t if the propagation time is the same in both the cases but owing to the mobility of BS around the circum-circle the BS is now at a different distance from P, hence δ changes with mobility. P uses this notion to calculate its position w.r.t. centre of the network circle. It also uses the property that the node will be nearest to it when the centre of the circle, P and BS are in a straight line.
a.
P notes the position for the first receive of message from the BS (x,y) b.
P notes the difference in expected time of arrival and actual time of arrival (∆δ=T2-T1-∆t). As the BS nears the point B (as shown in figure) where B is the point such that it is collinear with the centre of the circle ‘O’ and the node P) P observes that the ∆δ becomes more and more negative and achieves its minima at B(owing to the property

of circles). P identifies B’s coordinates as (x2,y2) from the packet it received when BS transmitted at B.
4.
Solution for P’s coordinates are :-
Consider a circle centered on P with radius d. Let OPBC be a straight line intersecting the
Network circle at B and the circle centered on P at C(x3, y3).
(x3,y3) are unknown so we first determine them.
Then PB will be d-∆d.
Hence BC is ∆d
Using concept external partition of line we get x3= (1+(∆d/R))x2…………………………………….…………….1(a) y3=(1+(∆d/R))y2…………………………………………………...1(b)
Calculating Angle(AOB)= α = tan
-1
[(x1y2-y1x2) / (x1x2+y1y2)]….2
Now consider ∆ABC
We know all the vertices so we calculate angle (ACB) =β using sine rule
β = sin -1 [(c sin(90+α/2)/b]…………………………………………..3
Now consider ∆APC
Angle(APC)=180-2β……….since ∆APC is isosceles
Angle(ACP)= 90-α/2……….since ∆AOC is isosceles
Hence Angle(PAC)=
Ƴ =2β+α/2…………………………………….4
Slope of line OB is m1 = y2/x2…………………………………….5
Hence equation of line OB is y=m1x………………………………6
Slope of line AB is m2= (y2-y1)/(x2-x1)…………………………..7
Slope of line AP is m3= (m2-tan
Ƴ
)/ (1+m2.tan
Ƴ
)…………………8
Hence equation for AP is :- y-y1=m3(x-x1)………………………………………………………9
Hence from (6) and (9) P’s co-ordinates are :-

Px = [y1-m3.x1] / [m1-m3]……….………………………………..10
Py = m1[y1-m3.x1] / [m1-m3]……………………………………..11
1.
Now since the nodes know their position wrt to the centre of the network, the
BS position (from the beacon), the time at which the beacon was sent(from the timestamp on the beacon). Hence the nodes can calculate the propagation delay and adjust their local clock accordingly to synchronize with the BS clock.

The error margin in our scheme is based on the granulity of the transmission points of the BS; this granulity is essential owing to the hardware constraints of the BS and the ability of the node to differentiate between any two subsequent positions of the BS.
However we can incrementally decrease the error margin depending upon the accuracy desired by our application. The incremental error model can be realized as follows:-
We can visualize the circum-circle (on which the BS moves) dotted with transmission points. The gap between these dots represents the granulity and hence the Least Count of our scheme .If we assume the speed of BS as constant and transmission time too as a constant, then these dots are evenly distributed. Now our aim is to reduce this granulity or in other words reduce these inter dot distances as part of our incremental error reduction scheme or put more dots on this circum-circle provided they do not overlap each other. This can be achieved if the BS does a tiny phase shift after completion of each round. If the granulity be ∆DOT and the start position be R then after the completion of the round the BS starts at R+(∆DOT)/N i.e.
R+(∆DOT)/N is regarded as the start point for the next round. The BS henceforth maintains the same speed and time spacing (as it did in previous rounds).A given node observes over N rounds and takes the (x,y)
BS
pair for min(∆δ) among these N rounds to be the position where the centre of the network, the BS and itself are collinear.

1.
Jun Luo ,Jean-Pierre Hubaux.
2.
Michael Spratt
3.
Aram Galstyan, Bhaskar Krishnamachari,
Kristina Lerman, and Sundeep Pattem
4.
Pubudu N Pathirana, Andrey V Savkin, Sanjay Jha, Nirupama Bulusu
5.
Mihail L. Sichitiu and Vaidyanathan Ramadurai
6.
Prabal Dutta, Sarah Bergbreiter