Improving Localization in Geosensor Networks Through ... - Uni Rostock

Improving Localization in Geosensor Networks Through Use of Sensor Measurement Data Frank Reichenbach1 , Alexander Born2 , Edward Nash2 , Christoph Strehlow1 , Dirk Timmermann1 , and Ralf Bill2 1

University of Rostock, Germany Institute of Applied Microelectronics and Computer Engineering {frank.reichenbach,christoph.strehlow,dirk.timmermann}@uni-rostock.de 2 University of Rostock, Germany Institute for Management of Rural Areas {alexander.born,edward.nash,ralf.bill}@uni-rostock.de

Abstract. The determination of a precise position in geosensor networks requires the use of measurements which are inherently inaccurate while minimizing the required computations. The imprecise positions produced using these inaccurate measurements mean that available methods for measurement of distances or angles are unsuitable for use in most applications. In this paper we present a new approach, the Anomaly Correction in Localization (ACL) algorithm, whereby classical trilateration is combined with the measurements of physical parameters at the sensor nodes to improve the precision of the localization. Simulation results show that for localization using triangulation of distance measurements with a standard deviation of 10% then the improvement in precision of the estimated location when using ACL is up to 30%. For a standard deviation in the measurements of 5% then an improvement in positioning precision of ca. 12% was achieved.

1

Introduction

In the near future masses of tiny smart electronic devices will be placed ubiquitously in the environment surrounding us. These so called geosensor networks (GSN) sustainably measure mechanical, chemical or biological conditions, aggregate the important information and transmit it over neighboring sensor nodes to a data sink where it can be collected and then analyzed. GSNs are evolving as a promising technique for industry, modern life science applications or natural disaster warning systems. One of the most important issues in GSNs is the localization of each node using distances or angles to neighbors as the geographical position is required to make use of the measurements. Due to the large errors which are caused by available methods for the measurement of distances or angles, the expected precision, particularly indoors, is insufficient for most applications. In our new approach we take advantage of the fact that sensor measurements are related to their position in a pattern that can be largely determined in advance. We have therefore developed a model that combines spatial sensor information and classical localization approaches such as trilateration to increase the overall precision.

This paper is structured as follows. In Section 2 the fundamentals of localization in geosensor networks are summarized. Section 3 introduces the basic concept by which we hope to improve the precision of localization and Section 4 describes the new ACL algorithm in detail. Section 5 then presents simulation results before Section 6 summarizes the results presented in this paper. Finally, Section 7 discusses some ideas for future work in this area.

2

Fundamentals of Localization

The task of the described networks consists of the collection with sensors of a phenomena with a certain spatial dimension. The capability to self-determine the position of each sensor is an essential feature of the sensors because measurements are only useful if connected to a time and a place. A potential method would be the use of the Global Positioning System (GPS) or in future Galileo [1]. Because of the additional costs and the required small size of the sensor nodes these techniques are only feasible if used on a small number of more powerful nodes, further called Beacons. These Beacons determine their positions with such methods and make this information available to all other sensor nodes in the network. For the localization of the other nodes, different methods are available and can be separated into approximate and exact methods. An overview can be found in [2],[3]. Simple exact methods are the well known trilateration or triangulation, using measurement of distances or angles respectively. Due to the fact that measuring angles requires additional hardware (e.g. antenna arrays on each node), triangulation has not been subject to intensive investigation and the trilateration approach is favored. In the case of 2D localization, a system of three equations may be constructed using Euclidian distances [4]. Subtracting one equation from the other two and insertion of one of the remaining unknowns produces a quadratic equation which may be uniquely resolved. This method requires a low calculation and memory effort, but the measurement of the distances results in systematic and stochastical errors. These errors influence the results of the trilateration and significantly decrease the accuracy of the determined position because of the lack of robustness of the trilateration. In the worst case the localization process can fail if the Beacon positions are also subject to errors. Two methods to overcome these problems exist in the literature. Approximative algorithms use coarse positions or distances as start values and determine relatively inaccurate results, but with a minimum of calculation cost. Algorithms used include e.g. (weighted) centroid determination (CL,WCL) [5, 6] or overlapping areas (APIT) [7] and are more error resistant and therefore robust, but the approximate nature of the algorithms themselves means that even with error-free start values an exact position can never be determined. This is an advantage of the second class of methods - the exact algorithms. These can produce exact positions if accurate start values are used. The disadvantage is that they require a higher calculation and memory effort. They are therefore not appropriate to be used at resource-limited sensor nodes. There are however some algorithms which overcome these problems by distributing the tasks [8–11].

Additional to further developments of the algorithms we follow up a completely different approach - the use of spatial information inherent in sensor measurements. We will discuss this concept in the next section.

3

Basic Concept

In Section 2 we explained the problems affecting the positioning process. Intensive efforts have been made to reduce these errors using better localization algorithms. However, these algorithms all base on the same data such as Beacon positions and distance measurements. Even with the best measurement methods some error sources cannot be eliminated. Further available sources of information must therefore be considered. With the large amount of sensor data collected it is possible to draw conclusions about the environment in which the sensor nodes are located. In many cases there will be a correlation between the collected data and the sensor location. This information can be used to increase the position accuracy if it is possible to mathematically define this correlation. For a better understanding we will give an application example from Precision Agriculture, where the use of GSNs is currently a topic of research [12],[13]. In the future a large number of sensor nodes may be deployed, e.g. by aeroplane, over cropland. The sensor nodes measure chemical or biological soil composition as well as typical physical parameters such as temperature, light intensity or air pressure. Nodes which settle in areas of dense plant canopy, e.g. under trees, will measure a consistently lower light intensity, caused by the shadowing effects of the vegetation. On the other hand the sensor nodes in an open area without plant coverage would measure a consistently higher light intensity. Combining the estimated position with the sensor data and a surface model would allow us to draw conclusions about the localization. If a sensor node estimates a position in an open area but records a very low light intensity then an outlier is highly probable. Although this example is highly specialized, due to the fact that the sensor nodes may carry a large number of different sensors many potential classes of measurements could be used for an outlier detection. In this paper this principle is used as follows. Usually a sensor network contains redundant Beacons. Using trilateration, different positions can be estimated followed by the elimination of errors. In Section 4 we will introduce an algorithm with which it is possible to filter values which are subject to errors and thus improve the localization result. This approach is based on the idea that it is possible to define location-dependent ranges for measurement of certain phenomena. Using these ranges the sensor nodes can exclude certain areas for determining their own position, leading to a decrease in the localization error.

4

Anomaly Correction in Localization (ACL)

In this section we describe the Anomaly Correction in Localization (ACL) method. The aim can be summarized as to produce a very resource-saving trilateration, requiring only minimal additional calculation on the nodes whilst still determining a precise position. In particular, single outliers from the distance measurement may significantly affect the

Fig. 1. Resulting discrepancy in position between sensor measurement and calculated trilateration

result of the trilateration. This effect should be reduced or removed by the use of the ACL algorithm as described here. 4.1

Prerequisites

ACL realizes an improvement in the localization through elimination of highly inaccurate estimated positions based on sensor measurements and some previous knowledge of the measurement environment. Figure 1 illustrates how a sensor node with light sensor may reject false positions when the light conditions for cropland and forest are known. In this case, based on the measured light conditions, only positions in the forested area will be accepted. Prerequisites for a successful application of ACL are: – there must be sufficient sensors installed on the sensor nodes which measure a spatially-related phenomenon (exact numbers and densities are likely to be application dependent and further investigation is required), – and it must be possible to clearly define the spatial relation of the phenomenon being used using discrete (or potentially, with an extension of the model, fuzzy) zones linked to expected observation values which can be determined independent of the current sensor network (e.g. zones for expected soil moisture content may be derived from a digital terrain model through use of the topographic wetness index). Additionally it must be possible to allocate a specific region of space to each environmental parameter. This important relationship between a defined spatial region and a sensor value range is hereafter referred to simply as ’sensor interval’. Potential environmental parameters which may be used are temperature, light intensity, moisture, pH, pressure, sound intensity and all other physical parameters which may be metrically defined. A sensor interval is then defined as matching to a region when the expected measurement value lies within the delimited range with a high degree of probability.

A further important prerequisite is an inhomogeneity in the relevant environmental parameter. If the entire measurement field belongs to a single sensor interval or the measured variable may not be classified then this parameter is not suitable for use in the localization. It is therefore only possible to use parameters which may be divided into two or more intervals with a high significance. The ACL algorithm bases on the previous trilateration. Since normally more than the three required Beacons (n Beacons), are available within n the range of a sensor node, it is possible to perform multiple trilaterations. In total, 3 different trilaterations may be calculated. The question however remains as to which trilateration will produce the best (most precise) result, as it is important to minimize the computational effort. This optimum may be expressed by the question as to which trilateration produces a result which does not violate the clear rules of the ACL algorithm. Based on our previous example, this means that there would be a conflict when an estimated position lies in an open area, but the light sensor measures a very low value. This indicates that this trilateration is unreliable. The mathematical background is described in the following Section. 4.2

Construction of the Model

A model has been developed which abstracts real given environmental parameters and allows a variable allocation to intervals. For this, a rectangular measurement area is defined in which the sensor nodes are placed. The whole area is subdivided using an arbitrarily scalable raster, which may be represented using a square matrix. This allows both a very flexible configuration and a fast computation. Sensor intervals do not have preassigned values but may be indicated by a region in which the sensor values cluster within a certain interval. These regions may be formed by a set of adjacent cells, whereby each cell is represented by a logical ”1” in the relevant position in the matrix. This significantly simplifies the required calculations as no geometrical tests (e.g. point-in-polygon) must be performed but only a simple mapping of the spatial coordinates to the dimensions of the matrix and a logical comparison. The size, number and position of the sensor intervals may be generically defined. The measurement of sensor values is modeled through the allocation of the nodes to the sensor intervals in which the actual position of the sensor lies. A potential measurement error is thereby excluded, i.e. each sensor delivers values from the exact interval corresponding to its position. The measured sensor information are further referred to as ’sensor profile’ and are considered to be a defined spatially-variable property. Figure 2 illustrates an example measurement area. Each node has a 1D vector which defines its allocation to each sensor interval. Node 1 (N1 ) has in this case the vector V (N1 ) = (1, 0, 0) which indicates that N1 is located in sensor interval 1, but outside intervals 2 and 3. It is also possible that a sensor interval is distributed over multiple spatially discrete regions in order to allocate the same sensor profile to multiple areas. Such discrete regions may generally be considered as separate sensor intervals, with the difference that calculated positions which lie in one sub-region, but where the actual position lies in a different sub-region, will not be recognized as outliers.

Berechnung liefert eine mögliche Position des Sensorknotens, die jedoch durch die Distanzfehler verfälscht ist. Deshalb wird jede Position hinsichtlich ihres Sensorprofils überprüft, indem für jede der Positionen der Vektor der Intervallzugehörigkeiten berechnet und mit dem Vektor der tatsächlichen Position verglichen wird. Stimmt das Sensorprofil mit dem gemessenen Profil überein, so ist die Position gültig, falls der Vektor nicht übereinstimmt wird die Position als Ausreißer markiert. (siehe Abschnitt 4.1)

y

N2

N1 a

N3

b c

Interval 2

Ni

Node i

b

possible position for N4

a,c

Outlier

Interval 1

N4

Interval 3

N5

x Abb. 10: Schematische Darstellung der Lokalisierung und Ausreißerdetektion

Fig. 2. Schematic of a localization with outlier detection by ACL Anhand des Knotens N4 aus Abb. 10 sei dies einmal exemplarisch gezeigt. Es ergibt

sich V(N4)=(1,0,1). Für die möglichen Positionen a, b und c werden ebenfalls die

4.3

Algorithm Description

Vektoren berechnet. V(a)=(0,0,0), V(b)=(1,0,1), V(c)=(0,0,1). Da nur V(b) mit V(N4)

There now follows a step-by-step the algorithm. There are two possible übereinstimmt wird N4 an der description Position b of lokalisiert. Die beiden verbleibenden sequences which should be considered. Positionen a und c werden ignoriert, da sie nicht die gleiche Zugehörigkeit zu den drei Sensorintervallen aufweisen wie die Messwerte des Knotens N4.

ACL with Averaging The following sequence is more computationally expensive, but potentially more accurate as all available information is used. 22 nodes in the transmission range t . 1. Beacons send their position to the sensor x 2. Sensor nodes save the received position and measure the distance to the Beacons using a standard measurement technique such as signal-strength measurement. 3. After all data are saved, n i.e. all Beacons have finished transmitting, the sensor nodes calculate all q = 3 possible positions by repeated trilateration. 4. All resulting positions are tested using the ACL algorithm. The actual measured sensor value is compared to the previously defined sensor interval. If it matches then the position is considered as valid, otherwise as invalid. 5. After all positions have been tested using ACL, an average of all valid positions is calculated. This average is then used as the final estimated position.

ACL with First Valid Position As the previously described algorithm has the disadvantage of requiring that all trilaterations are calculated, we introduce a version which may be interesting for practical use. In this version, the calculation is stopped as soon as a valid trilateration is found. The sequence is identical to that previously described,

except that the result of each trilateration (stage 3) is immediately validated using ACL (stage 4) until a valid position is found. This position will then be used as the estimated position of the node and the algorithm terminates. Using this version then a greater localization error is to be expected. This is explained in the following Section.

5

Simulation and Results

For simulation we have used the packet simulator J-Sim from the Ohio State University [14]. Details of the implementation can be found in [15]. At this point we wish to present the simulation conditions and the results. The necessary distance measurement for the trilateration is modeled through calculation of the Euclidean distance, adjusted using a normally-distributed (Gaussian) random value to represent measurement error. The simulated distance d is thus calculated using the following formula: q 2 2 (1) d = (x − x0 ) + (y − y0 ) + rGauss · σd where x, y are the coordinates of the unknown node, x0 , y0 are the coordinates of the Beacons, rGauss is a normally distributed random number between zero and one and σd is the standard deviation of distances. For the localization an even distribution of nodes is assumed, resulting in an equal distribution of favorable and unfavorable alignments for the trilateration. This means that even with this idealized normally-distributed error model then significant outliers in the localization are to be expected. In the simulations then the localization errors of the initial position Ef and the localization error of the first correct position (without outliers) Ef,ACL are determined. It can therefore be seen, by how much the mean localization error is reduced when the ACL algorithm with version 1 and 2 is applied. The improvement is shown in the diagrams in meters, although since a sensor field of 100m × 100m is used then this may also be interpreted as percent. Similarly, the standard deviation may also be interpreted as percent values. A 100m × 100m sensor field with a cell size of 5m × 5m was used for all simulations. Figure 3 shows a typical visualization window of the results achieved by the J-Sim tool. 5.1

Mean Improvement with 10 Beacons

In the first simulation, 10 Beacons and 20 sensor nodes are distributed in the field. Three sensor intervals with range 49 and a distance error of σd = 1.0 are used. In the case that all three sensor intervals do not overlap, their area represents ca. 36% of the total area. In a simulation with 10 Beacons there are 120 possible trilaterations. At this point, only the mean improvement V = E − E ACL is considered. The data are sorted based on the proportion of outliers, i.e. it is calculated how many of the 120 possible positions lie outside the correct sensor interval. For each of the 20 nodes used there is a particular percentage of outliers and therefore a line in the diagram (figure 4). Each line represents the absolute value of the mean

euklidische Entfernungsberechnung und Überlagerung mit einem zufälligen gaußverteilten Fehler simuliert. (siehe Abschnitt 4.2) Jeder Knoten führt eine Liste mit Beaconpositionen und seiner jeweiligen Entfernung zu diesen Beacons. Sobald ein Knoten keine weiteren Beacons mehr empfängt, beginnt er mit der Lokalisierung. Diese erfolgt unter Anwendung des in Abschnitt 4.3 beschriebenen Modells und liefert die Simulationsergebnisse, welche im nächsten Kapitel näher erläutert werden. Gleichzeitig werden die graphische Ausgabe des Sensorfeldes

und

der

Fehlerdiagramme erzeugt.

Zur

Auswertung

späteren werden

diese Daten in externen Dateien abgespeichert. Nebenstehend in Abb. 13 ist eine solche graphische Ausgabe dargestellt. Die Sensorintervalle

sind

grau unterlegt und die einfachen Knoten zeigen mit Linien zum Ort ihrer Abb. 13: Graphische Ausgabe eines Sensorfeldes mit 3 Sensorintervallen, 10 Beacons Knotenand points withLokalisierung. Fig. 3. Screenshot of simulation results in J-Sim; trianglesund are 20 Beacons lines are

sensor nodes with its error-vector; three darker areas represent sensor intervals

Das angezeigte Raster entspricht einer Einteilung in 10 m Abschnitte, sodass sich 100 m xnode 100 achieves m Feld with ergibt, auf dem 10 Beacons 20of einfache Sensoren improvement ein which each 120 trilaterations and the givenund number outliers. In thezufällig case thatverteilt multiplesind. nodesDie haveDistanzabweichung the same number of outliers a mean value beträgt σd = 1.0. in diesem Beispiel is calculated. dreishow dargestellten Sensorintervalle haben eine jeweilige Größe von 49 Since the Die raw data a high scattering, a linear regression is used to emphasize the trend. TheRasterquadraten improvement increases withwobei an increasing number of outliers. This á 25 m², das interne Raster auf 5 m x 5trend m eingestellt ist. is not demonstratably linear, but a similar trend is observed over many simulations, leading to the assumption that the improvement is at least linear or even exponential. Similarly it can be seen that with a low number of outliers, up to ca. 15%, there is a negative improvement (i.e. a worsening). This shows that there is a certain minimum number of outliers under which the use of the ACL algorithm is not appropriate. This limit is dependent on the particular configuration and can not therefore be generally 28 specified. 5.2

Correlation Between Number of Outliers and Distance Errors

The number of outliers is dependent on the error in the distance measurement, in this case the standard deviation σd . In the following simulation the same configuration as in Section 5.1 is used with different distance errors. The parameter σd is varied between 1.0 and 10.0 with an interval of 1.0. The number of outliers is calculated as a function of this parameter.

verteilt. Es wurde hier mit drei Sensorintervallen der Größe 49 und einem Distanzfehler mit σd = 1.0 gerechnet. Für den Fall, dass alle drei Sensorintervalle sich nicht überschneiden, entspricht deren Fläche etwa 36 % der Gesamtfläche. In

( )

Optimierung des ACL-Algorithmus

einer Simulation¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ mit 10 Beacons gibt es 103 = 120 mögliche Trilaterationen. Es

Bei mehreren Knoten mit mittlere gleicherVerbesserung Anzahl an Ausreißern wurde Verbesserung wurde zunächst allein die V ¯ untersucht. Diedie Daten sind nach gemittelt. dem Anteil der Ausreißer sortiert, das heißt es wurde berechnet, wie viele der 120 möglichen Positionen des korrekten Sensorintervalls lagen. eine lineare Da die reinen Datenaußerhalb sehr hohe Streuungen aufweisen, wurde

Regressionsgerade eingefügt, welche den Trend verdeutlicht. Mit zunehmender Average Improvement

Improvement [m]

Anzahl von Ausreißern steigt die Verbesserung an. Dieser Trend ist nicht Linear Regression (Average Improvement) 250 nachweislich linear, jedoch wurde bei vielen Simulationen ein ähnliches Verhalten

beobachtet, sodass die Vermutung nahe liegt, dass die Verbesserung mindestens 200

linear oder sogar potentiell ansteigt. Gleichfalls zeigt sich bei geringem Anteil von 150 Ausreißern, bis etwa 15 %, dass die Verbesserung negativ ist. Das zeigt, dass eine

bestimmte untere Grenze für die Ausreißer existiert, unterhalb der die Anwendung 100 des ACL-Algorithmus nicht sinnvoll ist. Diese Grenze ist von der jeweiligen 50

Konfiguration abhängig und kann deshalb nicht allgemein angegeben werden. 0

6.3.2 Abhängigkeit der Anzahl der Ausreißer vom Distanzfehler -50

0 10 Ausreißer 20 40 vom 50 Fehler 60 bei der 70 Distanzmessung, 80 90 Der Anteil der ist30wiederum hier Outlier [%] also von der Standardabweichung σd abhängig. In den nächsten Simulationen

wurde die gleiche Konfiguration wie in Abschnitt 6.3.1 bei veränderlichen DistanzAbb. 14: Durchschnittliche Verbesserung über dem Anteil an Ausreißern bei 10 Beacons, 20 Knoten

fehlern untersucht. Der Parameter von 1.020bis 10.0nodes in Einerschritten d wurde und einer Standardabweichung σd =σ1.0 Fig. 4. Average improvement over outliers with 10 Beacons, sensor and a standard deviation σd Als = 1.0 eingestellt. Funktion davon wurde der Anteil der Ausreißer aufgenommen. Für jeden der verwendeten 20 Knoten ergibt sich ein bestimmter Prozentsatz an

Ausreißern und damit eine Linie im Diagramm. (siehe Abb. 14) Jede Linie .

Outlier Linear (Outlier) kennzeichnet Outlier [%] den absoluten Wert der mittleren Verbesserung, die einer der Knoten

bei50% 120 Trilaterationen mit dem entsprechenden Anteil an Ausreißern erzielt hat. 45%

31

40% 35% 30% 25% 20% 15% 10% 5% 0% 1

2

3

4

5

6

7

8

9

10

Standard deviation [%]

Abb. 15: Mittlerer Anteil der Ausreißer in Abhängigkeit von der Standardabweichung σd für 10 Beacons und 20depending Knoten Fig. 5. Average outliers on the standard deviation σd with 10 Beacons and 20 sensor

nodes

32

Figure 5 shows the mean number of outliers in relation to σd over multiple simulations. It shows that the number of outliers increases with an increasing standard deviation. Again a trend line is shown to illustrate the trend. This emphasizes that the values have a high random component and deliver different results in each simulation. It is however clear that the mean proportion of 15% outliers is rapidly exceeded, which indicates that the ACL algorithm will only be ineffective, or detrimental as in figure 4, where there is a very small σd . 5.3

Influence of the Size and Number of Sensor Intervals

Further important factors in the effectiveness of ACL are the size, number and position of the sensor intervals. For the simulations, the intervals were individually parameterized by size and number, but randomly positioned. Alongside the random distribution of the sensors, this is one of the main reasons for the high variability of the resulting data. There is therefore no explicit results from which a formula for the accuracy of the ACL in relation to these parameters can be derived. An investigation of the influence of size and number of sensor intervals however resulted in the expected results. An increasing number of sensor intervals results in an increasing fragmentation of the measurement field into smaller sections with different sensor profiles. This is particularly the case where the sensor intervals are larger and therefore overlap more. The number of outliers thus increases with an increasing size and number of sensor intervals, which results in a greater improvement. It is also important to note that sensors which lie near to an interval boundary profit most from the outlier detection because the probability of an outlier is higher in these locations than in a homogenous region. des ACL-Algorithmus Optimierung ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Outlier [%] Average Improvement [m] 30 25 20 15 10 5 0 3

6

9

Number of sensor intervals Abb. 16: Anteil der Ausreißer und mittlere Verbesserung in Abhängigkeit von der Anzahl der Sensorintervalle beiimprovement 10 Beacons und 20 Knotenon the number of sensor intervals with 10 Fig. 6. Outlier and average depending

Beacons and 20 sensor nodes

In Abb. 16 ist diese Abhängigkeit dargestellt. Mit dem Anteil der Ausreißer steigt auchFigure die mittlere V ¯ bei zunehmender Anzahl von 6 showsVerbesserung this relationship. With an increasing number of Sensorintervallen. outliers, the mean improvement V also increases with anmit increasing number ofder sensor intervals.Größe For this Es wurde dazu ein Sensorintervall drei Teilflächen jeweiligen 49 erzeugt. Im zweiten Schritt wurde ein weiteres gleichartiges Sensorintervall hinzugenommen und dann ein drittes, während die vorherigen jeweils in konstanter Anordnung gehalten wurden. Des Weiteren wurden 10 Beacons, 20 Knoten und σd = 1.0 verwendet, was bedeutet, dass bei höheren Distanzfehlern beide Kurven einen größeren Anstieg aufweisen würden.

6.3.4 Vergleich von mittlerer Verbesserung und Erstverbesserung Aufgrund der verschiedenen Möglichkeiten eine endgültige Schätzposition zu

case a sensor interval with three sub-regions of size 49 was created. In a second step a further similar sensor interval was introduced and subsequently a third, whereby the previous intervals were retained with a constant configuration. Furthermore, 10 Beacons, 20 nodes and σd = 1.0 were used, which indicates that with increasing distance errors both curves would show an increased slope. 5.4

Comparison of Mean Improvement and First Improvement

Due to the various possibilities for determining a final estimated position, experiments were made which should favor each method. For this a field with three sensor intervals of size 49 with 10 Beacons and 20 nodes was used to compare the mean improvement V with the first improvement Vf . The mean values from the 20 nodes were used to reduce the weight of the variation. The standard deviation of the distances was again varied between 1.0 and 10.0. Optimierung des ACL-Algorithmus ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ First Improvement Average Improvement Linear (First Improvement) Linear (Average Improvement)

Improvement [m]

35 30 25 20 15 10 5 0 -5 1

2

3

4

5

6

7

8

9

10

Standard deviation [%]

Abb. 17: Vergleich der mittleren Verbesserung und der Erstverbesserung in Abhängigkeit von der Standardabweichung σd Fig. 7. Comparison of the average improvement and the first improvement depending on the

standard deviation σd .

Es zeigt sich in Abb. 17 deutlich, dass die Erstverbesserung weit weniger stark wächst als die mittlere Verbesserung. Das liegt zum einen daran, dass bei der It is clear from figure 7 that the first improvement demonstrates a significantly lower Erstverbesserung weitin weniger Trilaterationen ausgewertet werden, anderen increase in precision comparison with the mean improvement. This zum is partly due to theauch fact that significantly fewer trilaterations considered,eine but also because only aber daran, dass nur wenige Knotenare überhaupt Erstverbesserung a few nodesweil show first not nearliegen the boundary of aufweisen, sie any nicht in improvement der Nähe desbecause Randes they einesare Intervalls und damit an interval and therefore have few or no outliers. The trends are also in this case not keine oder nur Ausreißer besitzen. Auch diese Trends unbedingt necessarily linearwenig and are emphasized using regression lines. The sind meannicht improvement is linear und wurden durch Regressionsgeraden verdeutlicht. Die mittlere Verbesserung erzielt hier erheblich bessere Ergebnisse und ist damit die Methode der Wahl, jedoch müssen in Bezug auf die Praxistauglichkeit zwei Punkte in Betracht gezogen werden: 1. Die Mittlere Verbesserung drückt eher aus, um wie viel der Algorithmus die Lokalisierung verbessern könnte und ist deshalb nicht als absolut zu betrachten 2. Die Ersparung an Berechnung bei der Erstverbesserung

demonstrated here to deliver significantly better results and is therefore the method of choice, although the increased computational expense must also be considered.

6

Conclusion

This paper presented a new approach to improve the precision of localization algorithms in sensor networks which were previously too inexact or calculation-intensive for use. The spatial correlation of the measured sensor values is used for this. The principle used is that sensor observations vary within defined boundaries depending on their location. We have presented a way to use this information by defining sensor intervals. These may be used after localization by trilateration to test the reliability of the resulting estimated positions by comparing the observed values with the sensor intervals. This method was presented as the ACL algorithm together with investigations as to its effectiveness. Simulations showed that the use of the ACL algorithm can improve the mean error of the localization using trilateration by up to 30% when the measured distances have a standard deviation of 10%. With a 5% standard deviation the improvement is ca. 12%. These results were obtained using three known sensor intervals, which coverered around one third of the measurement field. With further prerequisites the localization could be further improved. Only with very small distance errors with a standard deviation of under 1% is the use of the algorithm not appropriate as in this range an increased localization error was determined. In conclusion, it has been shown that using the sensor measurement data for localization is a sensible approach, particularly as these data are already available. A significant improvement is possible with minimal additional complexity of calculation on the sensor nodes. The concrete use is however very dependent on how accurate the available measurements are and how many prerequisites can be determined. An advantage of this method is that no additional errors are produced since it effectively involves no more than a filtering of the input values. This can have negative consequences in isolated cases, but from an overall standpoint leads to a more precise result. A further advantage of the model presented here is the possibility to formulate arbitrarily complex prerequisites. The ACL algorithm can be considered as an efficient additional method for localization. Even with relatively few preconditions it is possible to improve the localization or to verify the positions. In particular in combination with approximate algorithms it is possible to obtain good results, but also with exact positioning where large distance errors are present then the ACL is of benefit.

7

Future Work

The idea presented here is by no means optimally applied. It is necessary to find a better mathematical model on which the ACL algorithm may operate. Currently a simple comparison of measured values with sensor values is made. This is computationally easy, but the spatial information can only be very coarsely exploited. A model such as convex optimization should be considered instead.

Furthermore, the definition of sensor intervals is still very static and inflexible. This could also lead to problems at run-time as the sensor intervals may vary over time. To continue the example of light intensity sensors, the intervals may vary strongly between day and night or summer and winter. To solve this problem an automatic interval generation may be used, which may be possible with e.g. an evolutionary algorithm or simmulated annealing. Ultimately the additional information are used purely as a means of detecting outliers in the trilateration. The aim is to combine further localization algorithms with this information to obtain an increased precision and to possibly weight the defective distance measurements and error prone sensor data. It is conceivable that the briefly introduced WCL algorithm may be thus made more precise. This is however primarily reliant on the effectiveness of new mathematical models.

Acknowledgment This work was supported by the German Research Foundation under grant number TI254/15-1 and BI467/17-1 (keyword: Geosens). Thanks also to the reviewers who took the time to provide constructive criticism which has helped improve this paper.

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