Localizing a Wheelchair Indoors with MagneticSensors

Ruolin Fan, Silas Lam, Oleksandr Artemenko†, Emanuel Lin, You Lu, Mario GerlaDepartment of Computer Science

University of California, Los Angeles

Los Angeles, CA 90095, USA

Email: {ruolinfan, silaslam, emanuel, youlu, gerla}@cs.ucla.edu† Ilmenau University of Technology, 98693 Ilmenau, Germany

Email: oleksandr.artemenko@tu-ilmenau.de

Abstract—Indoor localization with conventional GPS devicesis too difficult because the satellite signals are too weak. Severalalternate schemes have been proposed, from RF signal strength toradio signatures. In this paper we consider the indoor localizationof a wheelchair. This is important to guide the handicapped onpredefined wheelchair-friendly routes in a building, for example.For indoor wheelchair positioning we explore a new odometry-like approach based on a cyclometer. Namely, the system detectswheel rotations from uniformly distributed magnets around thecircumference of the two large wheels. Distance traveled andturning degrees can be computed by analyzing how much thewheels have rotated. This allows the tracking of the path. Thispaper reports the system implementation and preliminary results.

I. INTRODUCTION

Localization is the process of knowing ones location, whichis critical for anyone wishing to reach a specific destinationin a timely manner. Global positioning system (GPS) is oneof todays most common solutions for obtaining a positionalfix. Commercial GPS devices, typically used for driving,are readily available from companies such as TomTom andMagellan [1]. Most mobile phones also contain built-in GPSunits. The ubiquitous nature of GPS greatly helps solve thelocalization problem in most cases.

Unfortunally, GPS is not well suited for the indoors en-vironment for lack of satellite signals [2]. In our research,we consider a specialized problem, the indoor localizationof the physically handicapped, wheelchair bound individuals.Instead of relying on existing non-GPS solutions, such as radioreceivers, accelerometers and even cameras, we created a newsystem that could transform measured wheel rotations into bothdistance and angular displacement. The scheme is inspired bythe odometer. However, an odometer can only measure totaldistance travelled and not angular displacement. Specifically,our solution adds evenly spaced magnets on the two largerwheels of the wheelchair. A reed switch detects when a magnetpassed near it. By performing simple calculations on the rawdata, we can obtain an estimate of the wheelchairs location.

The main contribution of this work is introduce a newpositioning scheme that does not use previously investigatedsensors. The current system implementation can be summa-rized as follows. Raw data from the magnets is collectedby smartphone at regular intervals through a PHP webpagecombined with JavaScript and MySQL. The data is processed

and the webpage displays the wheelchairs current location.Error is estimated by comparing our results with physicaltape measurements. Results are very encouraging for straightforward motion at slow to normal speeds. However, we foundthat while turning angles are not accurately estimated, witherrors up to 10 degrees. These errors can be disastrous whenamplified by dead reckoning.

The rest of the paper is organized as follows. SectionII gives some background information on the problem ofindoor localization in general. This is followed by section IIIwhich gives a brief description on related work on localization.Section IV presents our design and how we translated physicalcharacteristics into formulas for calculation. Sections V and VIdeal with our implementation and evaluation, respectively. Weend with discussion and conclusion in sections VII and VIII,respectively.

II. BACKGROUND

As previously stated, GPS is good enough for outdoor usebut does not suit our purposes for the indoors. The medianhorizontal error of mobile-GPS units ranges from 5-8.5 meterswhen tested outdoors [3]. This degree of error is acceptablein an outdoor setting, as the system can still place the user onthe same street or block. In an indoor scenario, however, suchan error may place the user in the wrong room or wrong aislein the grocery store. In addition, this estimation of error inan indoor scenario is actually optimistic because GPSs tend tohave an even larger range of errors on average when operatedindoors, assuming that it can actually obtain a readable signal.

GPS is based on triangulation from satellites whose po-sition is known. When GPS fails, a possible solution is toredefine other landmarks. One obvious method is to use 3Gand 4G repeaters of known position as landmarks and usesignal strength to approximate distance. Similarly, indoor Wi-Fi access points can be used. Another method often used forpositioning relative to radio access point is radio signaturematching, exploiting the fact that the combination of signalstrength levels received from the station uniquely defines theposition. Other schemes yet use a combination of acousticsignals (say smart phone ring tones) and radio signals to obtaina more precise position fix. Generally, triangulation methodsare quite complex and require previous mapping of the site,acquisition of landmarks and/or sophisticated equipment.

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In our application we choose to rely on methods that donot use landmarks. These methods are often categorized asdead reckoning methods. Dead reckoning is the process ofcomputing ones current position based on a previously knownposition and incremental displacement. Because each positionestimate is relative to its previous estimate, errors will magnifyas they accumulate in the calculation. This means that if therewas a previous turning angle error of several degrees at aprevious position, the current estimate will have the turn errorfrom the current calculation added with the previous turn error.In order to correct for this error, dead reckoning works bestwhen alongside a system such as GPS. This would be akin tousing the GPS for positioning whenever a signal is present.

Inertial navigation systems use computers and sensors tocalculate position via dead reckoning [4]. They are commonlyused in vehicles such as ships, aircraft, submarines, missiles,and spacecraft. Unfortunately, they are inconvenient to use fora single person because it would require a person to carrya device specifically for the purpose of navigation. We wouldlike to avoid this and use whatever a person may already have,such as a wheelchair and smartphone.

III. RELATED WORK

Localization is the core of any navigation system. Much ef-fort has been put into the indoor localization problem. Almostall the approaches are based on dead reckoning and utilize asmartphone device for data capture and processing. They canbe grouped into three major classifications: smartphone-basedindoor navigation systems, wardriving, and optical flow.

Almost all smartphones (especially of the Android orApple variants) contain built-in measurement devices such asaccelerometer, gyroscope, and compass. The measurements ofany combination of these instruments can be utilized to com-pute a position through dead reckoning [5]–[7]. Gyroscopesmeasure angular momentum, which can be used to obtain abearing. Compasses can also obtain a bearing but by detectingmagnetic fields. Accelerometers measure acceleration, whichcan be used to compute speed. Unfortunately, using only a sin-gle type of measurement is error-prone because of the noise inthe raw data from the sensor. Each of the types of sensors haveits own disadvantages with respect to our scenario. Gyroscopesrequire frequent calibration because their error increases overtime [8]. Compass measurements are difficult to use becauseof the magnetic inference of metallic objects, such as stairwayrails or electronics, which are widespread within buildings.This causes wildly varying readings in bearing that cannotbe relied upon [9]. Accelerometer measurements depend onthe orientation of the phone. This orientation easily changesinside a person’s pocket, causing a skew in the data [10]. Inour research, we did not integrate these sensors into our systembecause we wished to analyze the accuracy of our proposedsolution in isolation.

Wardriving positions an entity according to stationary Wi-Fi hotspots [11]. By pinging surrounding hotspots and mea-suring the signal strength, you can triangulate your location.An inconvenience of wardriving is the inherent requirementfor massive amounts of infrastructure. Large Wi-Fi coverageof a building is not possible without significant cost andmany access points. Many wardriving techniques also require

calibration of the hotspots, such as a known location of thehotspot (like a latitude/longitude tuple). Even the accuracy ofwardriving is in question, as it also must deal with the problemof signal degradation and interference.

The third kind of localization is optical flow. It works bycalculating the distance between two images taken at differenttimes. This distance can be analyzed to compute an estimatedspeed of the viewer. The calculations tend to be too CPU-intensive for smartphones, making the program too slow forreal-time applications [12]. One group has succeeded withFlowpath, a system that analyzes H.263 video motion vectorsin real-time [6]. However, the system requires a map, eitherpublically available or user-created, of the building to function.This requirement is not practical for people visiting a buildingfor the first time.

Our work falls most closely with the smartphone-basedindoor navigation systems. Although we do not utilize any ofthe sensors in the smartphone, we do use its web browsingcapabilities in order to access our server to send/display thedata. Our major contribution is using the physical attributes ofa wheelchair to our advantage in creating an indoor localizationsystem.

IV. DESIGN

With a wheelchair, we use features unique to this deviceto help us achieve our goal. Assuming that the wheelchairwas outside at some point in time, we record the movementsof the wheelchair and use them in combination with the lastknown GPS coordinates to find out the actual position ofthe wheelchair. Therefore, from a high level perspective, welocalize the wheelchair using a known initial position and addon vectors to find its new positions. The bulk of the algorithmlies in recording these movements.

To track the wheelchair’s movements, we take advantageof its mode of travel. Since wheelchairs travel by rotationof its wheels, we can then track all movements by countingthe rotations of the wheels and analyzing them. For example,we can immediately infer straight forward movement if bothwheels rotate at the same rate in the same direction. Tocalculate the magnitude of movement, we simply record theamount of rotations and multiply it by the circumference of thewheels. In this way, we develop a simple mathematical modelof the wheelchair’s movement, consisting of simple straightforward movement and turns. To make the distances morefine-grained than entire circumference of the wheel, we placemarkers on the wheels equally spread apart. We then are ableto increment the travelling distance by the arc lengths betweenthese marks rather than entire wheel circumferences, yieldingmore accurate results.

For straight forward movement, we utilize the followingequation:

dtravelled =cwheel

n× ticks, (1)

where cwheel is the circumference of the wheel, n is thenumber of marks we place on the wheel, and ticks is thenumber of times each mark on the wheel passes by a point ofreference to indicate motion.

Turns are a little more complex to think about. We placethem into two different categories, one easy case which we call

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Fig. 1. An illustration of a generic turn with the two wheels of a wheelchair

a sharp turn, and a more difficult case which is the generic turn.The sharp turn is where one of the wheels is moving, whilethe other one stays completely still. The generic turn, on theother hand, has both wheels moving at the same time, but oneof the wheels rotates faster than the other one, thus creating aturn. For sharp turns, we utilize the following equations:

cchairTurn = 2πwchair, (2)

θ◦turn =dtravelledcchairTurn

× 360◦, (3)

where cchairTurn is the circumference when the chair turns afull circle by keeping one wheel still. This is calculated withthe standard circumference formula, using the width of thechair, wchair, as the circle radius. dtravelled used in (3) is thedistance travelled by the rotating wheel during the turn, whichin this case is the arc of the turning circle.

For a generic turn, we use the definition of radians to derivethe turning model. When the wheelchair makes a generic turn,we assume that the two wheels follow the curvature of twocircles, in the fashion as illustrated in Figure 1. In this scenario,the known variables are Δr, which is just the distance betweenthe two wheels, and d1, and d2, the arc distance travelled byeach wheel during the turn. By definition of radians, is

θrturn =d1r1

=d2r2

. (4)

Substituting in Δr to get r2 = r1 + Δr and rearrangingthe terms, we end up with

r1 =d1Δr

d2 − d1. (5)

Therefore,

θrturn =d1r1

= d1(d2 − d1d1Δr

) =d2 − d1Δr

, (6)

and the equation for calculating the turning angle, indegrees, is

Fig. 2. Placement of magnets and reed switch on one of the wheels

θ◦turn =d2 − d1Δr

× 180◦

π. (7)

With these equations in place to model the overallwheelchair movement, we know what distance and in whichdirection the wheelchair has moved from its initial positionand thus find its location inside the building.

V. IMPLEMENTATION

Our implementation of the wheelchair localization systemconsists of both a hardware part and software part. The radiusof the wheel is 0.29m, and the width of the chair from wheelto wheel is 0.53m. Thus, the circumference for each wheel isabout 1.8m, and the circumference of a turn for the wheelchairis 3.3m, as seen in (2).

To keep track of the ticks for calculating the distance awheel has travelled, we placed a magnet on each of the eightspokes of each wheel, and ran two reed switches down eachside of the wheel chair to detect as the magnets pass by it(see Figure 2). The reed switches are then connected to aBluetooth mouse on the wheelchair where the left reed switchis connected to the left click and the right one to the rightclick. In this way, we record the rotation for each wheel basedon the left and right clicks of the mouse.

We differentiate between straight forward movement andturns by comparing the number of left clicks LC with thenumber of right clicks RC. If they are equal, we infer that thewheelchair is moving forward and can thus use (1) to calculatethe new position of the wheelchair. On the other hand, wecan infer a simple turn if the click count for either left orright was 0. In this case, the wheelchair is turning toward thedirection of the 0 click. For example, if LC = 2, while RC =0, we can infer that the wheelchair has turned right. Oncewe make the inference on the direction of turn, we can use

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TABLE I. INACCURATE INFERENCES FOR STRAIGHT FORWARD

MOVEMENT CAUSED BY UNSYNCHRONIZED WHEEL MOVEMENTS

# Left Clicks # Right Clicks State Distance

...1 1 F 11 1 F 11 0 R 00 1 L 01 1 F 1

...

TABLE II. INACCURATE INFERENCES CAUSED BY WHEEL SLIPPING

# Left Clicks # Right Clicks State Distance

...2 2 F 23 3 F 33 2 R 02 2 F 2

...

(3) to calculate the magnitude of the turn. Because the venuefor which we conduct our indoor localization experiments isnarrow and crowded, the more complicated “fast turn” cannotbe easily maneuvered. Thus, we decided to not implement itas of yet to keep our testing simple.

Unfortunately, this simple design does not work as intendedby itself. When the wheels rotate, in most cases they do notrotate in a synchronized fashion. Therefore, it is impossiblefor the left and right clicks to always happen at the same timewhen the wheelchair moves forward. Table I, which presentsa portion of collected data during straight forward movement,gives a good example of this. In the table, the State columnindicates the nature of the movement. F means a forwardmovement; L means a left turn; R means a right turn. Thistable displays a series of normal forward movements followedby an unsynchronized movement of the wheel rotations, whichare incorrectly inferred to be a slight left turn followed by aslight right. As a result, although the total distance travelledby the wheelchair should be 1+ 1+ 1+ 1 = 4 units, we inferonly 3 units because we miss the 1 unit distance travelled fromthe unsynchronized move. When this happens many times,our movement accuracy will sharply decrease. In additionto this, because of imperfections in the wheelchair design,sometimes one wheel will slip and we would permanentlymiss a click. This does not happen often, but if it occurs in ahigh aggregate scenario, as indicated in Table II, it can causelarge underestimates in movement distances. Here, the actualdistance travelled by the wheelchair is 2 + 3 + 3 + 2 = 10units, but because of the 0 unit distance inferred by the unequalnumber of left and right clicks, we get a total distance of only7 units.

We solve this problem by implementing a so-called “ap-proximate equality filter” and use it instead of the normal e-quality to infer a straight forward movement by the wheelchair.Under our new system, we define two numbers as being equalif their difference is below a threshold value. We use this newequality system to compare LC with RC, and take the greaterof the two as the movement magnitude. However, to make surethat we are not ignoring what may be the beginning of an actualturn, we designate such unequal but close wheel rotations as a“forward left” or “forward right” movement and use the nextmove to check the correctness of our decision. On the nextmove, if the inequality was towards the other direction or if

TABLE III. CORRECTING A WRONG INFERENCE

# Left Clicks # Right Clicks State Distance Turn

...2 2 F 2 01 0 F/R 1 02 0 R -1 32 2 F 2 0

...

the difference between the LC and RC was 0, then we assumethat we have guessed correctly in the previous move.

Here we must handle each success case separately. As anexample, during a straight forward movement, if the (LC,RC)pair was (x, x− 1) in the previous move, then we guess thatthis inequality was due to either unsynchronized rotation ofthe wheels or to slippage in the wheels, and read it as ifthe pair was (x, x) as according to our rules. On the nextmove, we may see the (LC,RC) pair as either somethinglike (y, y) or (y − 1, y). The (y, y) case is easier to handlebecause we can just record a movement forward of y units asusual. To handle the (y, y + 1) case, however, we must checkthe previous move to know whether or not the wheelchair isactually moving forward. We can assume this if the directionof inequality is opposite from the previous one. In this case, wecan take the new click pair as if it were (y, y) to balance outthe extra distance given from the previous movement inference.Therefore, we develop the rule of thumb, where we always takethe bigger of the first L-R inequality and the smaller of theone after it.

However, if the inequality was toward the same direction,then we “undo” all the movement inferred in the previousmove, and aggregate what was supposed to be the previousturning degree with the next one to correct the movementinference. An example of this is seen in Table III, wherethe second (1,0) click pair corrected the previous incorrectinference of forward movement by moving −1 units andturning 1 + 2 = 3 units to the right. Thus, we must saveall the inferred movements of wheelchair in a database andwhenever we get an unequal number of clicks, we alwayscheck the previous entry to infer the next movement as wellas to see if any corrections need to be made. In this way, weimplement our “approximate equality filter” to have a moreaccurate reading of the wheelchair’s movements.

VI. EVALUATION

We tested the accuracy of our system by pushing thewheelchair around the third floor of the UCLA main engi-neering building, Boelter Hall. In our general trial, we beganon the south-western section of Boelter Hall, near the balcony,and walked in a counter-clockwise direction at a normal paceto see how well our localization techniques are and recordedthe route on a map. As Figure 3 shows, our mathematicalmodel works well for straight forward movements, but breaksdown during turns. We attribute this to the fact that there areonly eight spokes on the wheels and thus are limited in ourability to find out the turning degree in a fine-grained manner.Since there are 8 magnets spread equally apart each wheel, andthe circumferences of the wheels are 1.8m, the arc distancebetween any two magnets are 1.8m ÷ 8 = 0.225m. Using (3)from the Design section, we see that the smallest angle of turnwe can record is (0.225m ÷ 3.3m) × 360◦ = 24.5◦. Note

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Fig. 3. Counter-clockwise run inside Boelter Hall

that the the circumference of a 360◦ turn of the wheelchair is3.3m, as established in the beginning of Section V. This meansthat we are very limited in the number of turning angles thatwe can record. Specifically, we cannot record the angle of 90◦.Instead, the wheelchair records the angle that is closest to 90◦,which turns out to be 24.5◦ × 4 = 98◦. It is for this reasonthat our results seem to be very inaccurate. Simply addingmore magnets to the wheels should improve accuracy by agreat amound. Enabling generic turns can also increase turnaccuracy, as the turning degrees can be more fine-tuned in thatcase. Another way to improve this condition is to incorporateother features in the smartphone into calculating the turns.Extra data from the built-in compass in combination with thegyroscope would allow our system to perform sanity checksperiodically to make sure that the system is still on the righttrack.

Despite our system’s relative inaccuracy in decipheringturns, it has a satisfactory performance with straight forwardmovements. We test its accuracy by moving in a straight linefor 100ft (30.48m) at three different speeds and compare theerror rates between our system fitted with the “approximateequality filters” against that of the simple design of recordingLC or RC whenever they equal. Using an update frequencyof one update per second, we conducted the evaluation withspeeds of 0.56m/s, 0.92m/s, and 1.52m/s. As Figure 4 shows,the addition of a filter improves the system’s accuracy bya very high percentage. When the filter is used, the errorrates for slow and normal movement speeds are less than 5%.Thus, the system works equally well for both slow and normalmovements, with the difference between the perceived distanceand actual travelled distance being less than 2m. For fastmovements, however, the perceived distance is much shorterthan the actual distance. The recorded data show that this erroris caused by many false positive turns, where missing left orright clicks trick the system into believing that it is a genericturn, which is not implemented by our implementation andthus ignored.

In our experiment of moving at fast speeds, we were

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

10%

20%

30%

40%

50%

60%

70%

80%

90%

Travelling Speed (m/s)

Erro

r Rat

e

FilteredUnfiltered

Fig. 4. Localizaton accuracy vs. moving speed for straight forward move-ments

0 0.2 0.4 0.6 0.8 1 1.2 1.40

10%

20%

30%

40%

50%

60%

70%

80%

90%

Update Period (s)

Erro

r Rat

e

FilteredUnfiltered

Fig. 5. Localization accuracy vs. mouse click update rate for fast straightmovement

consistently missing right clicks. Though we hypothesized inour design that wheels may slip and thus miss a click, therewere far too many missed right clicks to be coincidental.We attribute this problem directly to the hardware itself. Theproblem most likely stems from the way that the magnets andreed switches are attached to the wheelchair (tape the magnetsonto the wheels and zip ties to hold the reed switches inplace against a cylindrical bar), which cause them to be easilymoved. When this happens, it becomes difficult for the reedswitch to detect the magnetic fields of certain magnets and thusmisses them as they passes through too quickly. Fortunately,such a problem can be easily fixed with better equipments.For example, simply having a wheelchair with a built-in setof magnets and reed switches to detect wheel rotations mayfix this problem. In addition, motorized wheelchairs that usethings like stepper motors will not have the problem of missingcounts at all, as the motor can be made to rotate at veryprecise intervals, which, incidentally, also solves the problemof inaccurate measurements of the wheelchair turning [13].

We also found a way to decrease the effects of this problemwith our equipment by increasing the update frequency of theclicks. In this way, though the magnets may still be missedin a similar way, the clicks would be recorded in a way thatcan be partially corrected by our approximate equality system.Figure 5 shows an error rate reduction of as much as 10%by increasing the update rate of the mouse clicks. Of course,an error rate of over 30% (about 10 meters for the tested 30

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Fig. 6. Projected results for right angle correction

meters) is still unacceptable for a localization system, but thetechnique can be applied in combination with a better set ofhardware for maximal benefits. Also note that without filtering,the percent error rate is consistenly high, and changing thefrequency of updates has no effect on localization.

In all, we find that the wheelchair localization systemperformes satisfactorily as a proof-of-concept. For straightforward movements at slow to normal travelling speeds, thesystem allows the user with accurate enough results for navi-gation. Accuracy for faster movements can be easily improvedwith better hardware, and turns is an area of further research.

VII. DISCUSSION

Here we will further discuss some issues with our imple-mentation.

A. Inaccurate Turn Calculation

The most obvious problem with our solution is its inaccu-racy in turn calculation. Although with better hardware comesa more accurate solution, we would like to briefly discuss analternative way to improve turning accuracy without makingany hardware changes.

First, we can make slight improvements by making theassumption that most of the turns required inside a building are90◦ turns. Under this assumption, we may round all turns closeto 90◦ to just simply 90◦. With this, we can fix the problem ofthe pathway drawn out by the map running through walls, andthe resulting graph may look something like Figure 6. Thewheelchair trace path shows how the localization techniquecan utilize this idea to improve accuracy. However, it has adrawback in that the underlying assumption is too broad. If thisassumption is applied to buildings that have irregular shapes,the wheelchair would again to seem to run through walls onthe GPS display. Further, even with the rounding correction,it is possible for the chair to seem to hit walls if the distancemeasurement was off by even a few meters.

Fig. 7. Projected results for boundary detection and correction

To solve this, we can enlist the help of floor plans madeavailable by building authorities and use them to detect travel-ling boundaries. If the wheelchair runs over the boundaries, thesystem can then automatically correct for it by showing thatthe wheelchair is traveling along the boundary. It can do this bychanging its travelling distance at the smallest angle possibleto make it run along the boundary. An example of this is seenin Figure 7, which illustrates how localization system wouldshow the wheelchair path after it detects that the wheelchairhas run through the boundary of the wall on the west sidecorridor. It must be noted that such a technique requires theknowledge of the building for which the system is trying tolocalize. Fortunately, such information is readily available inUCLA, and should be available in most other buildings in theworld as well.

With a combination of these two techniques, we should seea great improvement in our localization systems in its detectionof turns, and will be a large part of our future research work.

B. Backward Motion

Our current localization system does not support detectionof backward motion. This is due to the nature of the hardwaresetup. Reed switches can only detect the proximity of magnets,but cannot detect the direction which they come from or thedirection that they are going towards. For this reason, it isimpossible to detect the rotational direction of the wheels withonly reed switches and magnets. In our solution, we makethe simplified assumption that the wheels will never rotatebackwards, so the wheelchair cannot go backwards. However,with the additional use of accelerometers in smart phones,we can, in the future, add support to detect if the wheelchairhas moved backwards. Another implication of this is that thesystem cannot detect an “on the spot turn” of the wheelchair,where one wheel of the wheelchair moves forward and theother one moves backwards. This may be fixed in the futurewith the combined use of compass and gyroscope.

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VIII. CONCLUSION

Indoor localization for a wheelchair presents unique op-portunities to capitalize upon. Our main contribution is totranslate wheel rotation measurements into distance and di-rection traveled, and implement it using a webserver. Thiswork can possibly be ported to other vehicles that have wheelson axles. We showed that the accuracy of our localizationsystem in its current state is high for slow to medium speeds,and decreases in higher ones. However, with the increasein the number of measurements, possibly by using moremagnets, we are confident in the ability of our system tofurther increase its accuracy. In addition, we believe that ourwork can be improved even further by complementing it withsensors in the smartphone, such as compasses, gyroscopes, andaccelerometers. The incorporation of such sensors will be alarge portion of our future work.

ACKNOWLEDGMENT

We would like to thank the UCLA Office for Students withDisability (OSD) for providing us with the wheelchair for ourexperiments. Further, we thank Katherine Tai and Yi Tyan Tsaifor editing our bar graphs to make them more readable.

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