Wireless Indoor Localization with Dempster-Shafer Simple Support Functions

Wireless Indoor Localization with Dempster-Shafer Simple Support Functions∗ Vladimir Kulyukin Amit Banavalikar John Nicholson Computer Science Assistive Technology Laboratory Department of Computer Science Utah State University Logan, Utah, U.S.A {vladimir.kulyukin}@usu.edu Abstract— A mobile robot is localized in an indoor envi-ronment using IEEE 802.11b wireless signals. Simple supportfunctions of the Dempster-Shafer theory are used to combine ev-idence from multiple localization algorithms. Emperical resultsare presented and discussed. Conclusions are drawn regardingwhen the proposed sensor fusion methods may improve perfor-mance and when they may not. Index Terms— localization, sensor fusion, Dempster-Shafertheory I. I NTRODUCTION In May 2003, the Assistive Technology Laboratory ofthe Department of Computer Science (CS) of Utah StateUniveristy (USU) and the USU Center for Persons withDisabilities (CPD) started a collaborative project whose ob-jective is to build an indoor robotic guide for the visuallyimpaired in dynamic and complex indoor environments, suchas grocery stores and airports. A proof-of-concept prototypehas been deployed in two indoor environments: the USU CSDepartment and the USU CPD. The guide’s name is RG,which stands for “robotic guide.”A. RFID-based localization Fig. 1. RG: A Robotic guide for the visually impaired. RG, shown in Fig. 1, is built on top of the Pioneer 2DXcommercial robotic platform from the ActivMedia Corpo-ration (See Fig. 1). What turns the platform into a robotic objects in the environment or worn on clothing. They do notguide is a Wayfinding Toolkit (WT) mounted on top of the require any external power source or direct line of sight toplatform and powered from the on-board batteries. As can be detected by the RFID reader. The tags are activated bybe seen in Fig. 1, the WT resides in a polyvinyl chloride the spherical electromagnetic field generated by the RFID(PVC) pipe structure and includes a Dell T M Ultralight X300 antenna with a radius of approximately 1.5 meters. Each taglaptop connected to the platform’s microcontroller, a laser is programmatically assigned a unique ID.range finder from SICK, Inc., and to a radio-frequency RFID tags are viewed as stimuli that trigger or dis-identification (RFID) reader. The TI Series 2000 RFID reader able specific behaviors, e.g., follow-wall, turn-left, turn-right,is connected to a square 200mm × 200mm antenna. The avoid-obstacle, make-u-turn, etc. The robot’s knowledge baseupper left part of Fig. 1 depicts a TI RFID Slim Disk consists of a connectivity graph of the environment, tag totag attached to a wall. These tags can be attached to any destination mappings, and behavior trigger/disable scripts as- sociated with specific tags. Each node of the graph represents ∗ This work is supported, in part, by NSF Grant IIS-0346880 and, in part, a location marked with a tag. The robot’s location withby two Community University Research Initiative (CURI) grants (CURI2003 and CURI 2004) from the State of Utah. Copyright c 2005 USU respect to the graph is updated as soon as RG detects a tag.Computer Science Assistive Technology Laboratory (CSATL). During experimental runs described elsewhere [6], the

RFID tags were successfully detected with the exception of been much debated in the literature [17], [21], [5]. Attemptsthree runs in crowded environments. During these runs, the were made to reduce DST to the fundamental axioms ofrobot missed a total of five RFID tags, because it had to classical probability theory [10]. However, belief functions,navigate around groups of people standing near the tags. The a fundamental concept underlying DST, were shown not todetection failures happened when the tags were outside of be probability distributions over sample spaces [13].the effective range of the robot’s RFID antenna. The robot DST was chosen for three reasons. First, in DST, itsuccessfully navigated around each group of people using its is unnecessary to have precise a priori probabilities. Thisobstacle avoidance routines. However, the obstacle avoidance was considered an advantage, because the propagation ofmaneuver would put a blocked tag outside of the RFID wireless signals indoors is affected by dead spots, noise,antenna’s electromagnetic sphere, which caused the robot to and interference. Second, Laplace’s Principle of Insufficientmiss an important maneuver, e.g., turn in the right direction Reason, i.e., a uniform distribution of equal probability to allor make a u-turn [8]. Consequently, the robot would become points in the unknown sample space, is not imposed and,lost and would have to stop and re-plan its path after detecting as a consequence, there is no axiom of additivity. Third,that it had become lost. DST evidence combination rules have terms indicating when multiple observations disagree.B. Wireless localization To overcome RFID detection failures in crowded environ- C. Related workments, it was decided to supplement RFID-based localization The research presented in this paper contributes to the bodywith wireless localization. The working hypothesis was that of work on indoor localization done by assistive technologyindoor localization can be done by using wireless signals and robotics researchers. Ladd et al. [12] used Bayesianalready available in many indoor environments due to the reasoning combined with Hidden Markov Models (HMMs)ubiquitous use of wireless Wi-Fi (IEEE 802.11b) Ethernet to determine the orientation and position of a person usingnetworks. One advantage of this approach is that it does not wireless 802.11b signals. The person wore a laptop with arequire any modification of the environment, e.g., deployment wireless card and was tracked in an indoor environment. Theof extra sensors or chips, which may disrupt routine activities assumption was made that people were minimally present inof organizations and expose the robot to potential vandalism. the environment. It should be noted that wireless localization is similar to Serrano [19] uses IEEE 802.11b wireless network signalsRFID-based localization in that it localizes the robot to a to determine the position of a robot inside a building. Thelocation. No attempt is made to determine the robot’s pose conducted experiments show that wireless indoor localization(x, y, θ). In keeping with the principles of the Spatial Seman- may not be possible without a preconstructed sensor signaltic Hierarchy [9] on which RG’s knowledge representation is map. However, if a motion model is available, Markovbased, once the robot is localized to a location, the location localization techniques can be used to localize the robotspecific behavior scripts are triggered to achieve a global accurately. Howard et al. [4] also investigated the use ofnavigation objective [7]. Markov localization techniques in wireless robot localization. Kismet, an open source wireless network analyzer, was Talking SignsT M is an infrared localization technologyused to detect and digitize wireless signal strengths. The developed at the Smith-Kettlewell Eye Research Institute insoftware runs on the robot’s Dell T M Ultralight X300 laptop San Francisco [2]. The system is based on infrared sensorsequipped with the Orinoco T M Classic Gold PC 802.11b card. and operates like the infrared remote control device forD-LinkT M 802.11b/2.4GHz wireless access routers were television channel selection. Infrared beams carry speechused as access points, i.e., signal sources. A set of locations signals embedded in various signs to hand-held receivers thatis selected in a target environment. The wireless signature of speak those signals to users. Marston and Golledge [14] usedeach location consists of a vector of signal strengths from Talking SignsT M in their Remote Infrared Audible Signageeach access point detected at that landmark. At run time, (RIAS) system. RIAS was installed at the San Franciscosignal strengths are classified to a location. CalTrain station to conduct several field tests with legally While much effort has been put into modelling wireless blind individuals.radio signals, no single consistent model exists that can The BAT system is an indoor localization system de-reliably describe the behavior of wireless signals indoors[12]. veloped at the AT&T Cambridge Research Laboratory [1].Consequently, it was decided to use sensor fusion to localize The system uses ultrasonic sensors that are placed on thethe robot. Sensor fusion is a post-processing technique that ceiling to increase coverage and obtain sufficient accuracy.combines and refines initial sensor readings. The Dempster- The receiver detects ultrasonic signals and uses triangula-Shafer theory (DST) of evidence [20] was chosen as a tion to position itself. The Atlanta Veterans Administrationtheoretical framework for sensor fusion. The relative advan- (VA) R&D Center proposed the concept of Talking Brailletages and disadvantages of DST and Bayesian theory have infrastructure [18]. Talking Braille is a method for providing

access to Braille/Raised Letter (BRL) signage at a distance. as its subset. Formally, a simple support function S : 2 Θ →Talking Braille is an adaptation of electronic infrared badge [0, 1], A = , A ∈ Θ, is defined as S(B) = 0, if ¬(A ⊆ B);technology developed by Charmed Technologies, Inc. The S(B) = s, 0 ≤ s ≤ 1, if A ⊆ B, and B = Θ; S(B) = 1,infrastructure consists of small digital circuits embedded in if B = Θ. If S is focused on A, S’s BPAs are defined asstandard BRL signs. Small badges worn by users remotely follows: m(A) = S(A); m(Θ) = 1 − S(A); m(B) = 0,trigger signs in the user’s vicinity. Using buttons on the B = A and B ∈ Θ. A separable support function is thebadge, the user requests that signs either voice their message orthogonal sum of two or more simple support functions.or transmit their message to the user’s device over an infrared Simple support functions can be homogeneous or hetero-beam. geneous. Homogeneous simple support functions focus on As regards sensor fusion, the research presented here the same subset of Θ, whereas heterogeneous simple supportcontributes to the body of work done by robotics researchers functions focus on different subsets of Θ.who used DST to fuse information from multiple robotic Let S1 and S2 be two simple support functions focused onsensors. In particular, Murphy [16] used DST as a framework A so that S1 (A) = s1 and S2 (A) = s2 . It can be shown thatfor the Sensor Fusion Effects (SFX) architecture. In the SFX, the BPA m corresponding to S 1 ⊕ S2 is defined as follows:the robot’s execution activities used DST beliefs generated m(A) = 1 − (1 − s1 )(1 − s2 ) and m(Θ) = (1 − s1 )(1 − s2 ).from a percept to either proceed with a task, terminate the If S1 is focused on A and S 2 is focused on B = A, thentask, or conduct more sensing. Other robotics researchers also it can be shown that the BPA m corresponding to S 1 ⊕ S2used DST for sensor fusion [3]. depends on whether A ∩ B = . If A ∩ B = , m(A) = The remainder of this paper is organized as follows. s1 (1 − s2 ); m(A ∩ B) = s1 s2 ; m(B) = s2 (1 − s1 ); andFirst, a brief review of the salient aspects of DST is given. m(Θ) = (1 − s1 )(1 − s2 ), which gives rise to the followingSecond, the details of the proposed approach to wireless support function:indoor localization are presented. Third, the results of the ⎧experiments are discussed. ⎪ 0 ⎪ ⎪ ⎪ s1 s2 ⎪ ⎪ II. D EMPSTER -S HAFER T HEORY ⎨ s1 S(C) = (2) In DST, knowledge about the world is represented as a ⎪ s2 ⎪ ⎪ ⎪ 1 − (1 − s1 )(1 − s2 )set of elements, Θ, called the frame of discernment (FOD). ⎪ ⎪ ⎩Each element of Θ corresponds to a proposition. For example, 1 .Θ = {θ1 , θ2 } can be a FOD for a coin tossing experiment The first case arises when ¬(A ∩ B ⊆ C); the second caseso that θ1 is heads and θ2 is tails. Each subset of Θ can be arises when A ∩ B ⊆ C ∧ ¬(A ⊆ C) ∧ ¬(B ⊆ C); theassigned a number, called its basic probability number, that third case arises when A ⊆ C ∧ ¬(B ⊆ C); the fourth casedescribes the amount of belief apportioned to it by a reasoner. arises when B ⊆ C ∧ ¬(A ⊆ C); the fifth case arises when The assignment of basic probability numbers is governed A ⊆ C, B ⊆ C∧ = Θ; the sixth case arises when C = Θ.by a basic probability assignment (BPA) m : 2 Θ → [0, 1] so If A ∩ B = , S1 ⊕ S2 has the following BPA: m(A) =that m( ) = 0 and ΣA⊆Θ m(A) = 1. Each BPA describes a s1 (1 − s2 )/(1 − s1 s2 ); m(B) = s2 (1 − s1 )/(1 − s1 s2 );belief function over Θ. A subset A of Θ is a focal point of a m(Θ) = (1 − s1 )(1 − s2 )/(1 − s1 s2 ), which correspondsbelief function Bel if m(A) > 0. Suppose that m 1 and m2 to the following support function:are two BPAs for two belief functions Bel 1 and Bel2 over Θ,respectively. Let A1 , A2 , ..., Ak , k > 0 be the focal points of ⎧Bel1 and B1 , B2 , ..., Bn , n > 0 be the focal points of Bel 2 . ⎪ 0 ⎪ ⎪ ⎪ s1 (1 − s1 )/(1 − s1 s2 )Then Bel1 and Bel2 can be combined through the orthogonal ⎨sum Bel1 ⊕ Bel2 whose BPA is defined as follows: S(C) = s2 (1 − s1 )/(1 − s1 s2 ) (3) ⎪ ⎪ (s1 (1 − s2 ) + s2 (1 − s1 ))/(1 − s1 s2 ) ⎪ ⎪ ⎩ ΣAi ∩Bj =A m1 (Ai )m2 (Bj ) 1 m(A) = (1) 1 − ΣAi ∩Bj = m1 (Ai )m2 (Bj ) The first case arises when ¬(A ⊆ C) ∧ ¬(B ⊆ C); the Once the pairwise rule is defined, one can orthogonally second case arises when A ⊆ C ∧ ¬(B ⊆ C); the third casesum several belief functions. A fundamental result of the DST arises when B ⊆ C ∧ ¬(A ⊆ C); the fourth case arises whenis that the order of the individual pairwise sums has no impact A ⊆ C ∧ B ⊆ C ∧ C = Θ; the fifth case arises when C = Θ.on the overall result [20]. A simple support function S provides evidential support III. W IRELESS L OCALIZATIONfor one specific subset A of Θ. S is said to be focused on The target environment for localization experiments wasA. The function provides no evidential support for any other the USU CS Department. The department occupies an indoorsubset of Θ unless that set is implied by A, i.e., contains A area of approximately 6,590 square meters. The floor contains

example, if a hall’s orientation was from north to south, two sets of samples were collected: one facing north, the other facing south. A set of samples consisted of two minutes worth of data. An individual sample was a set of five wireless signal strengths, one from each wireless access point in the department. Samples were collected at a rate of approximately one sample every ten microseconds. Different sets of data for a single collection position were collected on different days in order to see a wider variety of signal strength patterns. Each collection position and direction combination had 10 total sets of data, which amounted to a total of twenty minutes worth of data. Therefore, the total data collection Fig. 2. Wi-Fi access points at the USU CS Department. time was 260 minutes, which resulted in a total of 1,553,428 samples. These samples were used for training purposes. To obtain the validation data, RG was made to navigate the route that contained all the selected locations 5 times in each direction. Four pieces of masking tape were placed at each collection position: two at 0.5 meter from the collection position and two at 1 meter from the collection position. The pieces of tape marked the proximity to the collection position, i.e., the robot is within 0.5 meter of the collection position and the robot is within 1 meter of the collection position. As the robot crossed a tape, a human operator following the robot Fig. 3. Data collection at a location. would press a key on a wearable keypad to mark this event electronically. Thus, in the validation file, the readings at each position were marked with the proximity to that position.23 offices, 7 laboratories, a conference room, a student Unlike in the wireless localization experiments conductedlounge, a tutor room, two elevators, several bathrooms, and by Ladd et al. [12], people were present in the environmenttwo staircases. during the robot runs. Five wireless access points were deployed at various A. Localization algorithmsoffices in the USU CS Department. The offices are shown The following algorithms were used for localization:in Fig. 2 with black circles. The offices were selected on Bayesian, C4.5, and an artificial neural network (ANN) [15].the basis of their availability. No other strategy was used The Bayesian algorithm considered the access points to befor choosing the offices. Five locations were then selected. independent of each other. At each location, the priors wereEach location was at a corner. Corners were selected because acquired for the probabilities of specific signal strengthsin indoor environments they are very useful decision points. from each sensor at that location, i.e., P (s i |L), where siIn Fig. 2, the locations are shown as circles with crosses. is the signal strength from the i-th sensor at location L.Each location had several (two or more) collection positions At run time, the standard Bayes rule was used to classifymarked. A collection position was the actual place where received signal strengths with respect to a specific location.wireless signal strengths were collected. Each collection posi- The C4.5 algorithm inductively constructed a decision treetion was located 1.5 meters away from a corner. Fig. 3 shows for classifying the signal strengths into five locations. Onehow wireless signal strength data were collected at a hall backpropagation ANN was trained for each location. Eachcorner. The bullets represent three collection positions. The ANN had 5 input nodes, i.e., 1 node for each access point,width of the hall determined how many collection positions 2 hidden layers of 10 nodes each, and 1 output node. Atwere needed. If the hall was narrow (width < 2 meters), run time, the outputs from each ANN were taken and theonly one collection position was chosen in the middle of the final classification was decided by the activation levels ofhall. If the hall was wider than 2 meters, then there were the output nodes of the individual ANNs. The winner ANNtwo collection positions, which were positioned to divide the determined the result location.hall width into thirds. A total of 13 collection positions waschosen for the five selected locations. Thus, each location B. Two evidence combination algorithmscorresponded to at least two collection positions. Evidence from the algorithms was combined as follows. Two sets of samples were taken at each collection position, Let Θ = {L1 , L2 , L3 , L4 , L5 }, where Li , 1 ≤ i ≤ 5,one for each direction of the hall’s orientation. So, for corresponds to the proposition that the robot is at location

Algorithm PositionLi . Let X be a vector of wireless signal strength readings 1 2 3 4 5such that X = [s1 , s2 , s3 , s4 , s5 ], where 0 ≤ si ≤ 130. BAY 0.98 0.95 0.79 0.65 0.91Let A be a localization algorithm such that X is its input C45 0.94 0.95 0.77 0.67 0.95 ANN 0.98 0.94 0.81 0.72 0.88so that A(X) ∈ Θ, i.e., the output of A is a possibly DST1 1.00 0.97 0.84 0.84 0.99empty set of locations. Let T be the target location, i.e., the DST2 1.00 0.98 0.79 0.67 0.99current location of the robot. Let all available algorithms beenumerated as A1 , ..., An , n > 0. TABLE I The performance of each localization algorithm at L i can TABLE I: PPV AT 0.5 METER . Aibe represented as a simple support function S B={Li } , whereB = {Li } is the focus of S and A i is a localization algorithm. Algorithm PositionFor example, if there are five locations and three localization 1 2 3 4 5algorithms, there are fifteen simple support functions: one BAY 0.93 0.91 0.82 0.68 0.91simple support function for each location and each localiza- C45 0.87 0.91 0.78 0.64 0.95 ANN 0.92 0.93 0.82 0.67 0.89tion algorithm. DST1 0.72 0.89 0.82 0.80 0.99 At run time, given X, A j (X) is computed for each L i DST2 0.91 0.90 0.81 0.68 0.97and for each localization algorithm A j . If Aj (X) is greater Aj TABLE IIthan the threshold, S {Li } ({Li }) = sij , where sij is the basic Aj TABLE II: PPV AT 1.0 METER .probability number with which S {Li } supports its focus. Oth- Ajerwise, S{Li } ({Li }) = 0. The support for L i is computed as A1 AjS{Li } ⊕...⊕S{Li} . After such orthogonal sums are computed Let T P , T N , F P , and F N be the number of truefor each location, the location whose orthogonal sum gives it positives, true negatives, false positives, and false negatives,the greatest support is selected. This method of combination respectively. Using T P , T N , F P , and F N , one can defineis called homogeneous insomuch as the orthogonal sums are four evaluation statistics: sensitivity, specificity, positive pre-computed of simple support functions with the same focus. dictive value (PPV), negative predictive value (NPV) [11]. There is another possibility of evidence combination. From Sensitivity, T P/(T P + F N ), estimates the probability of Apreliminary tests it is possible to find the best localization saying that the signal receiver is at location L given thatalgorithm for each location according to some criterion C. the signal receiver is at location L, i.e., P [A(X) = L|T =Suppose that A1 , ..., An are the best localization algorithms L]. Specificity, defined as T N/(T N + F P ), estimates thefor each of the n locations. Note that the same algorithm probability of A saying that the signal receiver is not at Lcan be best for several locations. Suppose further that given that the signal receiver is not at L, i.e., P [A(X) =these algorithms are represented as simple support function L|T = L]. PPV, defined as T P/(T P + F P ), estimates theS{L1 } , ..., S{Ln } . Given X, Ai (X) is computed for each L i , probability that the receiver is at L given that A says that thewhere Ai (X) is the output of the best algorithm for L i . If receiver is at L, i.e., P [T = L|A(X) = L]. Finally, NPV,Ai (X) is greater than some threshold, S {Li } ({Li }) = si . defined as TN/(TN + FN), estimates the probability that theOnce each of the n support degrees are computed, the signal receiver is not at L given that the algorithm says thatorthogonal sum S = S {L1 } ⊕ ... ⊕ S{Ln } is computed. The the receiver is not at L, i.e., P [T = L|A(X) = L].result sum is heterogeneous, because each simple support The PPV was chosen as the metric for computing basicfunction has a different focus. The best location is the probability numbers, because it simulates the run-time per-location with the highest degree of support according to S. formance of a localization algorithm. In particular, the PPV estimates the likelihood of the signal receiver being at LC. Assigning basic probability numbers when the algorithm states that the receiver is at L. If one is to represent each localization algorithm as asimple support function, the question arises as to how to IV. E XPERIMENTSassign the basic probability numbers with which each simple Tables I and II show the PPV numbers computed from thesupport function supports the location on which it is focused. robot’s validation runs. Table I shows the PPV numbers forOne possibility is to compute the basic probability numbers in the 0.5 meter proximity and Table II shows the PPV numbersterms of true and false positives and true and false negatives. for the 1 meter proximity. In both tables, DST1 denotes theA true positive is defined as A(X) = L and T = L, where homogeneous combination of simple support functions whileT is the true location and L is a location output by the DST2 denotes the heterogeneous combination. To analyze thealgorithm. A true negative is defined as A(X) = L and results, it was agreed to discretize the performance R of eachT = L. A false positive is defined as A(X) = L and T = L. algorithm into three intervals: strong (0.90 ≤ R), averageA false negative is defined as A(X) = L and T = L. (0.80 ≤ R < 0.90), and weak (R < 0.80).

The following observations were made. First, when the term sensor fusion in the presented conclusions refers onlyperformance of all three algorithms is strong, DST1 and to the sensor fusion methods described in this paper, i.e.,DST2 either maintained the same level of performance or when the fused algorithms are represented as DST simpleslightly improved it. For example, Table I column 1 shows support functions that subsequently are fused homogeneouslythat, at location 1, the three algorithms, i.e., Bayesian, C4.5, or heterogeneously.and ANN, performed at 0.98, 0.94, and 0.98, respectively.The performance numbers for DST1 and DST2 at the same R EFERENCESlocation and proximity are both 1.0. The same behavior can [1] M. Addlesee, R. Curwen, S. Hodges, J. Newman, P. Steggles, and A.be observed within 0.5 meter and 1 meter of location 2. As Ward, “Implementing a Sentient Computing System,” IEEE Computer,shown in Table I column 2, within 0.5 meter of location 2, pp. 2-8, August 2001.the three algorithms performed at 0.95, 0.95, and 0.94. At [2] R.G. Golledge, J.R. Marston, and C.M. Costanzo, “Assistive Devices and Services for the Disabled: Auditory Signage and the Accessible Citythe same location and proximity, DST1 performed at 0.97 for Blind and Vision Impaired Travelers,” Technical Report UCB-ITS-and DST2 at 0.98. As shown in Table II column 2, within PWP-98-18: Department of Geography, University of California Santa1 meter of location 2, the three algorithms performed at Barbara, 1998. [3] T. Henderson and E. Shilcrat, “Logical Sensor Systems,” Journal of0.91, 0.91, and 0.93. At the same location and proximity, Robotic Systems, 2(1):169-193, 1984.DST1 performed at 0.89 and DST2 at 0.9. Second, when [4] A. Howard, S. Siddiqi, and G. S. Sukhatme, “An experimental study ofall three algorithms performed weakly, DST1 significantly localization using wireless Ethernet,” The 4th International Conference on Field and Service Robotics, July 2003, Lake Yamanaka, Japan.improved performance, while DST2 remained on the same [5] I. Kramosil, Probabilistic Analysis of Belief Functions, Kluwer Aca-weak level. For example, Table I column 4 shows that within demic Publishers: New York, NY, 2001.0.5 meter of location 4, the three algorithms performed at [6] V. Kulyukin, C. Gharpure, J. Nicholson, and S. Pavithran, “RFID in robot-assisted indoor navigation for the visually impaired,” IEEE/RSJ0.65, 0.67, and 0.72. At the same location and proximity, Intelligent Robots and Systems (IROS 2004) Conference, September -DST1 achieved 0.84, a significant improvement, while DST2 October 2004, Sendai, Japan: Sendai Kyodo Printing Co.remained at 0.67. Similarly, as shown in Table II column [7] V. Kulyukin, C. Gharpure, N. De Graw, J. Nicholson, S. Pavithran, “A Robotic guide for the visually impaired in indoor environments,”4, within 1 meter of location 4, the performance levels of Rehabilitation Engineering and Assistive Technology Society of Norththe three algorithms were 0.68, 0.64, and 0.67. At the same America (RESNA 2004) Conference, June 2004, Orland, FL: Avail. onlocation and proximity, DST1 achieved 0.80, a substantial CD-ROM. [8] V. Kulyukin, C. Gharpure, P. Sute, N. De Graw, J. Nicholson, and S.improvement, while DST2 remained at 0.68. Third, when Pavithran, “A Robotic wayfinding system for the visually impaired,”two algorithms performed strongly and one averagely, DST2 Innovative Applications of Artificial Intelligence (IAAI-04) Conference,improved the overall performance or kept on the same level July 2004, San Jose, CA: AAAI/MIT Press. [9] B. Kupiers, “The Spatial Semantic Hierarchy,” Artificial Intelligence ,while DST1 behaved inconsistently. For example, as shown 119:191-233, 2000.in Table II column 1, DST2 remained on the same level, [10] H.E. Kyburg, “Bayesian and Non-Bayesian Evidential Updating,”while DST1’s performance worsened. However, as shown in Artificial Intelligence, 31(3):271-293, 1987. [11] http://www.medicine.uiowa.edu/Path_Handbook/,Table I column 5 and Table II column 5, both DST1 and Laboratory Services Handbook, Department of Pathology, TheDST2 raised the performance level significantly at location University of Iowa.5. Fourth, localization at the proximity of 0.5 meter was [12] A.M. Ladd, K. Bekris, A. Rudys, G. Marceau, L. Kavraki, and D. Wallach, “Robotics-Based Location Sensing using Wireless Ethernet,”overall better than at the proximity of 1 meter, because the Eighth Annual International Conference on Mobile Computing andlocation areas were further apart and the wireless signals were Networking (MobiCom), September 2002, Atlanta, GA: ACM.not confounded. Fifth, the localization performance dropped [13] J.F. Lemmer, “Confidence Faction, Empiricism, and the Dempster- Shafer Theory of Evidence,” in Uncertainty in Artificial Intelligence,at locations 3 and 4, because the locations were only 3 L.N. Kanal and J.F. Lemmer, Eds. Elsevier Scientific Publishers: Ams-meters apart from each other and cross misclassification was terdam, The Netherlands, 1986.frequently observed. [14] J.R. Marston and R. G. Golledge, “Towards an Accessible City: Removing Functional Barriers for the Blind and Visually Impaired: A Case for Auditory Signs,” Technical Report: Department of Geography, V. C ONCLUSION University of California at Santa Barbara, 2000. [15] T. Mitchell, Machine Intelligence, McGraw Hill: New York, NY, 1997. The following tentative conclusions can be made from the [16] R.R. Murphy, “Dempster-Shafer Theory for Sensor Fusion in Au-above observations. First, when all algorithms whose outputs tonomous Mobile Robots,” IEEE Transactions on Robotics and Automa- tion, 14(2), April 1998.are fused perform strongly, the addition of sensor fusion is [17] J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks oflikely to improve the overall performance and move it to 1.0. Plausible Inference, Morgan Kaufmann: San Mateo, CA, 1988.When all algorithms perform weakly, homogeneous sensor [18] D.A. Ross, “Talking Braille: Making Braille Signage Accessible at a Distance,” Rehabilitation Engineering and Assistive Technology Societyfusion is likely to improve performance significantly. Third, of North America (RESNA-2004) Conference, Orlando, FL, June 2004.if possible, locations should be selected further apart so as [19] O. Serrano, “Robot localization using wireless networks,” Technicalnot to confound wireless signals. It should be noted that these Report: Departmento de Informatica, Estadistica y Telematica, Univer- sidad Rey Juan Carlos, Mostoles, Spain, 2003.conclusions apply only to wireless localization indoors and [20] G. Shafer, A Mathematical Theory of Evidence, Princeton Universityare not to be interpreted as general recommendations. The Press: Princeton University, 1976.

[21] P. Smets, “The Combination of Evidence in the Transferrable Belief Model,” IEEE Transactions on Pattern Analysis and Machine Intelli- gence, 12:447-458, 1990.

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Wireless Indoor Localization with Dempster-Shafer Simple Support Functions

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Wireless Indoor Localization with Dempster-Shafer Simple Support Functions — Document Transcript