1. Authors: Sheng-Po Kuo, Yu-Chee Tseng, Fang-Jing Wu, and Chun-Yu Lin
A Probabilistic Signal-Strength-Based Evaluation Methodology for Sensor Network Deployment
Authors: Sheng-Po Kuo, Yu-Chee Tseng, Fang-Jing Wu, and Chun-Yu Lin
Department of Computer Science and Information Engineering National Chiao-Tung University
My name is ShengPo Kuo.
Today, I will present our work about the deployment issue in the wireless sensor networks. The title is “A Probabilistic Signal-Strength-Based Evaluation Methodology for Sensor
Network Deployment”.

2. Outline Introduction Problem statement and assumptions
Wireless ad hoc sensor network overview
Motivation and goal
Problem statement and assumptions
Error estimate model and algorithm
Applications
Conclusions
This is the outline of this presentation.
First, I will give a brief introduction of the wireless sensor networks and mention our motivation and goal of this paper.
Then, I will explain the problem statement and the assumptions.
Third, we propose an error estimate model to evaluate the location positioning or location tracking capability of a specific sensor network.
Then, I will present some applications.
Finally, I will draw a conclusion.
Introduction:說明我們的work的motivation & 定位系統的overview
Problem statement and assumptions:說明要解的問題和assumption
Error estimate model and algorithm:我們的algorithm & model
Applications and experimental Results: demo一些實驗結果 & 我們model的應用

3. Wireless Ad Hoc Sensor Network Overview
A collection of sensor nodes
Each sensor node is a tiny device which has capability:
Sensing
Computation
Communication
A number of sensors could perform particular tasks collaboratively, such as target detection, location tracking, environment monitoring and controlling.
Wireless ad hoc sensor network has a collection of sensor nodes.
Each sensor node is a tiny device. These sensors can sense, compute, and communicate with each other.
So, it is usually to use a number of sensors to perform particular tasks, such as target detection, location tracking, environment monitoring and controlling.
In this paper, we focus on the location tracking application.
Wireless ad hoc sensor network overview
由一群sensor node組成
每個sensor有
Sensing環境資訊的能力，e.g, 訊號強度，溫度，壓力等變化
Computation能力
Communication:透過wireless link和neighbor作溝通
在ad hoc sensor network, sensor透過彼此之間的合作,可以tracking或是detection環境中的物體，或是去monitor環境，並作控制。

4. Motivation and Goal Motivation: Our Approach:
For location tracking applications, given a sensor deployment:
How to find the location of the object in the environment.
How to evaluate the performance or error degree of the sensor deployment?
Where to add more sensors to improve the performance of the sensor deployment?
Our Approach:
Introduce a probabilistic location estimation model to perform location tracking
Moreover, propose an error model to evaluate the performance of the sensor deployment, and try to reduce the error degree.
So, for a location tracking application, given us a sensor deployment, we can ask:
How to find the location of the object in the environment? and
How to evaluate the performance or error degree of the sensor deployment? And
Where to add more sensors to improve the performance of the sensor deployment?
To answer these questions, we introduce a probabilistic location estimation model and then propose an error model to evaluate the performance of the sensor deployment, and then try to reduce the error degree.
*強調deployment
motivation:給一組sensor deployment，要對環境中的物體坐定位，會有幾個問題：
1.如何找出物體所在位置？
2.如何評估這樣的deployment在定位時performance的好壞？
3.如何加入sensors來改善performance？
Our Approach :
1.建立一個機率的location estimation model來對環境中的物體作定位
2.建立一個Error model來評估sensor deployment在作定位時performance的好壞，並改善error degree

5. Outline Introduction Problem statement and assumptions
Error estimate model and algorithm
Applications
Conclusions
Here, I will define the problem and describe the assumptions.
對問題的說明和assumption

6. Tracking result is error！
Problem Statement :
Given a sensor network, taking RSSI (Received Signal Strength Indicator) to perform positioning is inaccurate.
It is because of the signal propagation model is sensitive to many factors, such as obstacles, distance, interference, fading, and multipath effect…
Tracking result is error！ s1 d1
Taking received signal strength indicator to perform positioning task is usually inaccurate.
This is because of interference, fading, and multipath effect.
We can see this figure.
If there are three sensors and one object located here.
Each sensor measure the distance to the object.
So, we can expect to get three circles to locate object’s position.
However, because of the unreliable RSSI, the estimation may be incorrect.
For example, if the sensor s_3 measure a smaller signal strength value, then the positioning result will be wrong.
一般用RSSI(訊號強度)作定位不準，原因是:
受環境因素影響，ex:1.障礙物多寡，2.距離和環境的interference，3.signal propagation的固有特性，像是multipath和fading
動畫：
1.一般作triangulation方式是
2.當物體出現，並發出訊號
3.Sensor s1會根據收到的訊號強度定出物體距離我d1，畫出一個圓
4.同樣的s2，s3也會如此，利用3個圓來決定物體位置
5.但是由於環境因素影響，造成訊號強度不穩定，像是s3若收到強度較弱的訊號，就認為物體在更遠處，發生三圓不交於一點的情形
6.此種情形，可能透過一些algorithm來決定一個物體位置，這時，tracking結果是error的
7.同樣的，當物體在其他位置出現時，
8.也可能發生error
9.Informally來說，我們可說，此組sensor deployment在tracking OB這位置的物體，有較大的error degree。
(這是因為距離越大，sensor測量的誤差就越大) d3 s3 d2 OA s2

7. Problem Statement :
Apply a probabilistic location estimation model to illustrate the inaccuracy caused by the unstable RSSI.
For sensor deployment S, how to evaluate the performance:
Formally, we define sound region A as:
unsound region has some locations with high error degree for location tracking (i.e, could not satisfy the predefined threshold)
In this paper, we use a probabilistic location estimation model to illustrate the inaccuracy caused by the unstable RSSI.
So, based on the probabilistic location estimation model, we want to evaluate the positioning capability of a sensor network.
Formally, we can define as follows:
Given a sensor network deployment S, we want to use an error degree Es of o to express the positioning performance when the object is at location o.
So, if the error degree of any location o within an area A is smaller than a predefined threshold Et, then we call region A is sound.
On the contrary, we call this region unsound region.
因此，我們要做的是：
1.用一個機率的Location estimation model來定出物體所在位置，以解決RSSI不精確的問題
2.給一組sensor deployment S，我們要評估S的performance
首先，我們來formally的定義，什麼是此組sensor deployment performance的break points/regions.
在此之前，我們先定義，什麼是”sound region”：
若是物體在region A中各位置的error degree都小於threshold Et，就說region A是sound region。
反之，若是存在某些點或是某些region，作location tracking時的error degree大於threshold，我們就說是break points/regions
3.對error degree Es(o)在之後會有明確的定義

8. Environment Assumptions:
An ad hoc sensor network with n nodes
Each sensor node location is known (by manually input, GPS ….etc )
This is our assumption:
There are many sensor nodes and their location are known.
These location information can be obtained from manually input or GPS devices.
n個sensor 的ad hoc sensor network
每個sensor node位置已知(透過預先設定，或是sensor上掛GPS)

9. Outline Introduction Problem statement and assumptions
Error estimate model and algorithm
Path loss model
Distance estimation model
Location estimation model
Error model
Applications
Conclusions
Then, I will use a simple path loss model to introduce the decay of signal strength over distance.
Also I will mention how to model the unstable signal strength.
Then, I will transform the unstable phenomenon from signal space to distance space.
Based on this model, we can derive we can derive the location estimation model and error model.
介紹我們的Algorithm & model
Path loss model：介紹一個常見的path loss model
Distance estimation model：我們將訊號的signal space轉到distance space來看
Location estimation model：我們如何找出物體所在位置
Error model：我們如何評估error

10. Path Loss Model What is path loss:
set a pair of the distance d between transmitter and receiver, the signal strength is fading with the distance
In general, the decay of signal strength over distance can be modeled as this equation.
Path loss of distance d equals to the path loss of a reference distance d_0 plus 10 times a path loss decay exponent n times log d over d_0 and finally plus a Gaussian random variable.
When we only consider the first two parts. The signal strength decays from a reference distance d_0. d_0 is closed to the transmitter, such as 1 meter. One example of the first two part is shown in this figure. The signal strength decays as a log function.
The final part is our concern. We usually uses a gaussian distribution to model the unstable signal strength.
This unstable fact can be illustrated in this figure.
When an object is fixed at this location. We collect all signal strength. And, in theory, we can get a distribution like this figure.
什麼是path loss：
(上圖)：1.固定一對transmitter和receiver的距離d，訊號強度會隨距離衰減，它的fading是follow一個log函數
(下圖)： 2.假如，來看物體在距離sensor 30m處發訊號，s,s不是穩定的衰減(不是d=30,穩定衰減多少dB)
說明式子：
(上式)：基本上，是以mean值 PL(d) follow一個Gaussian normal distribution震盪，
(下式)：和距transmitter很近的距離d0做比較，程log函數衰減
(動畫)：因為環境干擾，造成訊號震盪，若是d=30，但sensor收到強度PL(70)，會以為物體離我70m處發訊號
我們要得到的是sensor以為物體在70m處發訊號的機率有多少？
所以要把signal space轉到distance space去看
If Sensor receive signal strength is dB, it will regard as the object at d’ =70
What is the probability that sensor regard as the object at d’=70m?
Sensor

11. Distance Estimation Model
set a pair of the distance d between transmitter and receiver, for distance d’, the signal probability is
The previous slide shows the unstable effect is modeled by a gaussian distribution.
Now, we transform the gaussian distribution from signal space to distance space.
Using the path loss equation, we can derive a log-Normal distribution.
This figure shows an example. We can see the x-coordinate is distance.
我們轉換到distance space的結果：
固定一對transmitter和receiver的距離d
利用X(d’)可以的到sensor認為物體在d’ 處發射訊號的機率是X(d’)
Sensor
Informally speaking, the signal probability appeared at d’ is

12. Location Estimation Model
Notation:
Using the derived distance estimation model, we can proceed to derive the location estimation model in theory.
I declare some notation first.
有了之前 距離 和 signal出現機率 的mapping後，利用此機率來定出環境中物體所在位置
介紹notation：
S：n個sensor，分別放在(xi, yi)
o：物體實際位置在(xo, yo)
di：物體與sensor si 的距離
li：l這個位置與sensor si 的距離
A：是我們要評估的region

13. Location Estimation Model
When object be placed at o, sensor si estimate the signal strength probability of location l is:
The signal-strength probability of location l that be accumulated by the sensor set S is:
Ok, now I introduce how to derive the location estimation model.
The first equation is the distance estimation model mentioned before.
For positioning, each sensor will give its distance estimation result.
So, for each location, we product all probability from each sensor and finally do a normalization.
We note it Go(l).
I use an example to let this location estimation model clearer.
物體放在o，sensor si 認為在 l 處出現訊號的機率，也就是 si 認為物體在l 的機率是g_o^i(l)
(上圖)：sensor s1認為物體在各個位置的機率
有n個sensors，將他們的機率accumulate起來，再作normalized後得Go(l)
(下圖)： Go(l)：此組sensor deployment認為物體在l 的機率，
機率最高位置即是物體最有可能的位置

14. Example 1: Environment: Location Estimation model： 50*50 grids
Parameter:
Location Estimation model：
Object s1
In this figure, we place the object at (20,35). And the first sensor S1 is located at (15,25).
Then, we use the G_o(l) to compute the probability of each location.
The result is shown in the figure.
We can see the cross-section from sensor s_1 to object is similar to the figure of the distance estimation model.
環境是50*50
n=2是 free space, variance=11
物體在(20，35)
Sensor在(15，25)
出現訊號的機率，成火山口狀分佈
Object=(20,35)
S1=(15,25)

15. Example 1: object=(20,35) Sensor s1=(15,25) s2=(35,25) object=(20,35)
Then, we can use the same way to compute the probability of each location when there are two, three or more sensors.
Intuitively, if there are three or more sensors, we can estimate an unique location.
物體位置一樣，2顆sensor，物體的可能位置有2個機率的最高點
Sensor個數3個以上，可以決定出一個最有可能的物體位置

16. Error Estimation Model
Es(o,l) expresses a kind of expected value for error meaning:
We define the error degree of the object placed at location o when performing location tracking by sensor set S:
object l
Until now, given us a sensor network deployment, we can derive G_o(l) to represent the probability of each location in theory.
Then, we focus on the error estimation model.
We use Es(o,l) to express a kind of expected value for error meaning.
Es(o,l) is defined as Go(l) times d(l,o).
This means the error expected value of location l when the object is at location o.
So, we can define another notation Es(o) by the summation of all locations within the area A to express the error degree of the object placed at location o when performing location tracking by sensor set S. Like the following equation.
接下來，介紹我們的error model，來評估sensor deployment在作定位時performance的好與壞 1.
(左圖)：首先，我們要先計算，物體放在o，sensor set S，對每個位置 l 的誤差期望值=(機率)*(誤差距離)
(右圖)：物體在o，各位置 l ，的誤差期望值 Es (o,l)
2.再來，去定義此組sensor deployment S在tracking 物體在o這個位置的能力
也就是說，物體在o時的error degree Es(o)=各個location l 誤差期望值的和，上例中，和為1.4181

17. Error Estimation Model
Formally, we define to express the overall performance of the sensor deployment S for location tracking:
Finally, we can define Es hat to express the overall performance of the sensor deployment S for location tracking.
It sums up the Es(o) of all possible object location within the area A.
最後，我們來評估此組sensor deployment S，的整體performance，是將各個物體位置的error degree加起來=Es^
Example：上例中，此組sensor deployment s1，s2，s3，的整體performance=

18. Example 2:
Error model：
The error degree of the sensor deployment S in location tracking :
This is an example of the error estimation model.
We can see the location near by the sensors has smaller error degree.
1.(圖)：Example1的deployment在作location tracking時，各物體位置error degree分佈：
2.這樣deployment的作location tracking時，overall performance是5.7316乘以10的4次方
The overall performance of the sensor deployment S in location tracking:

19. Problem statement and assumptions Error estimate model and algorithm
Introduction
Problem statement and assumptions
Error estimate model and algorithm
Applications
Application1:Deploying Sensors at the Weakest Points
Application2:Awake and Sleep Protocol using Voronoi Diagram
Conclusions
In the following presentation, I will introduce two applications using the derived error estimation model.
1.Demo實驗結果
2.我們的error model的應用在改善performance的方法

20. Application 1: Deploying Sensors at the Weakest Points
The policy for improve the error degree：
Add a new sensor node on the location o with maximum error degree Es(o)
The first application is a deployment strategy. Its purpose is to deploy more sensors for a given deployment.
We can see initially there are only one sensor.
Based on the error estimation model, we can see the surrounding of this environment has higher error degree.
So, we greedily deploy extra sensors at the weakest points for accuracy improvement.
This is the final result after we deploy ten sensors.
These figures show the improvement of this deployment strategy.
利用error model來改善tracking的performance
改善的策略：在max error degree的位置加一個sensor幫忙定位
(動畫)：第一個sensor的位置是random的在(10，10)的位置，加sensor的過程，error的變化。
(動畫的最後一張)：來看max error degree和average error degree的變化，越後面加的sensor，改善的幅度越不明顯
First one at sensor=(10,10)

21. Application 2: Awake Protocol in Voronoi Diagram
Voronoi diagram characteristic:
Awake protocol:
: network configuration
such as sensor set S, network topology (Voronoi), backoff timers.
: predefined threshold
Each active sensor node has a unique backoff timer ti
when timer reach 0, a active sensor will calculate two value in its monitor area:
the overall performance in the si monitor area
If , si will awake a sensor which is the closest to the location Locationmax in its area, and broadcast the updated network configuration .
The second application is a power-saving protocol.
This power saving protocol let sensors change to sleep mode when there are enough sensors for the location tracking application and let sensor change to active mode when there are not enough sensors for the location tracking application.
Here we use the derived error estimation to determine whether the sensors can satisfy the accuracy requirement or not.
First, I will introduce the awake protocol.
This protocol is based on the Voronoi diagram.
Voronoi diagram is a graph. This graph algorithm can partition the sensor network into several polygons and all points in a polygon are closest to only one sensor in this polygon.
Error model 的另一個應用在改善performance的方法是，搭配awake protocol，來awake某特定sensor來幫助定位
Voronoi diagram的特性：(看圖)
環境中，已放好sensor，點是sensor，黑點：active sensor形成Voronoi幾何圖形，將平面劃分成各自的region，各自region內的任一點，最靠近的sensor一定是si自己
Awake protocol
1.Vt：network configuration，包括，sensor set S，topology，backoff timer
2.Et：預先定的threshold
3.每個active sensor有自己的unique的backoff timer ti
4.當backoff timer達0時，si會計算2個值：
Sensor會去計算自己monitor區域的performance Ei (epsilon i)
Location_max：自已region內，最大error degree的位置
5.若performance Ei (epsilon i) 不滿足threshold Et時，
si會去awake自己區域中，最靠近Location_max的sensor來幫助定位

22. Application 2: Awake Protocol in Voronoi Diagram
We can see this figure. The network is partitioned by the active sensors.
We use black node to represent active sensors and the other gray nodes are inactive sensors.
So, each active sensor calculate the error degree of each location in its polygon.
If it detect that any location has error degree higher than the threshold, it will find one closest inactive and awake it.
For example, if the red node in this figure has too high error degree, the sensor Si will find the closest sensor Sj and then awake it to improve the accuracy.
若performance Ei (epsilon i) 不滿足threshold Et時，
si會去awake自己區域中，最靠近Location_max的sensor sj 來幫助定位

23. Application 2: Sleep Protocol in Voronoi Diagram
Each active sensor node has a unique backoff timer ti
when timer reach 0, a active sensor will check its monitor area:
If :
Sensor Si sent Sleep_Request message to all neighbors
When a node receive a Sleep_Request message , it will presume the node Si is sleep, and check its area.
Sleep_Accept message: agree Si is going to sleep
Sleep_Reject message: Si can’t to sleep
Si turn off itself : only when it aggregates all Sleep_accept message form its neighbors, and broadcast the updated network configuration .
On the other hand, if all location in a polygon satisfies the error threshold, the active sensor in that polygon should try to change to sleep mode.
應用error model來關掉redundant sensor：
參數同awake protocol，timer=0時會去檢查自己區域
若performance達 threshold Et，會發出sleep_request message給所有neoghbor
Neighbor收到sleep_request message會先假設si是sleep，去檢查自己新的monitor 區域是否ok？
若ok：回sleep_accept message 給si，同意si sleep
否則：回sleep_reject message
Si 必須要收到所有neighbor的sleep_accept message，才能將自己sleep

24. Application 2: Sleep Protocol in Voronoi Diagram
We use this example to illustrate this protocol directly.
If sensor Si detects that all locations in its polygon are sound, it will try to go to sleep mode.
Why not directly go to sleep mode?
This is because this sleep decision may make some location cannot satisfy the error threshold.
So, the sensor Si needs to send a sleep_request message to its neighbors to make sure its decision will not make some location unsound.
(左圖)：Si發sleep_request message給所有neighbor，企圖要sleep
(右圖)：
所有neighbor先假設si是sleep，各自check此新的topology，自己的區域是否ok，若是ok，回si sleep_accept message.
si 收到所有neighbor的sleep_accept message後，關掉自己，並將新的network configuration Vt’ broadcast出去

25. Conclusions
Translate the Gaussian distribution in signal space to log-Gaussian distribution in distance space in order to model the distribution of distance measurement.
Use a probabilistic approach to model location estimation.
For location tracking requirement, propose a error model to evaluate the performance of the sensor deployment.
Combine error model with awake/sleep protocol to control network topology.
Ok, this slide shows some conclusions.
轉換到distance space
2.用機率model定出物體位置
3.用error model來評估某個sensor deployment performance的好壞
4.結合error model跟protocol，來control network topology