Indoor Positioning Using Ultrasound and Radio Combination

Transcription

1 Inoor Positioning Using Ultrasoun an Raio Combination Gintautas Salcius, Evalas Povilaitis, Algimantas Tacilauskas Centre of Real Time Computer Systems, Kaunas University of Technology Stuentu St. 50, Kaunas, Lithuania ABSTRACT The paper introuces a metho of inoor positioning using a combination of ultrasoun an raio frequency. This metho allows for a more effective usage of raio frequency as it is employe for both object ientification an time synchronization by calculating ultrasoun propagation time, as well as object positioning using raio signal strength values. Application of this metho forms the basis of positioning system that can estimate the position of mobile an stationary objects when an object has been etecte by at least two ultrasoun listeners, while the systems that are in usage toay require for the object to be etecte by at least three listeners. Experiments on an object that was etecte by only two ultrasonic listeners resulte in a mean error of 34.1 cm, whereas consistent positioning woul not have been possible when limite only to ultrasoun technology. The aforementione mean error is also a few times lower than the one resulting from positioning when only raio frequency is use. KEYWORDS Inoor positioning, Ultrasoun, RF, Fingerprinting, RSSI. 1 INTRODUCTION Following the rapi evelopment of technology, more an more innovative solutions are being brought into our aily lives an homes. In orer to evelop cutting-ege, smart house management solutions, a precise object (people, evices, things, etc.) positioning an ientification system is require. There are several reasons for that: achieving maximum system precision; applying technologies that woul compensate their weaknesses with the strengths of other technologies; creating a more universal, ajustable an user-frienly system. At present, commonly use technologies for inoor positioning inclue Infrare, Ultrasonic, computer vision, ZigBee, RFID, UWB an WLAN [1]. GPS technology is not on the list because it is not suitable for inoor usage. Of existing technologies, position estimation using ultrasoun is appealing for its high accuracy rate (up to centimeters or even millimeters) an inexpensive equipment. However, when employe alone, ultrasoun technology oes not solve all problems that may arise: objects are not always in the line of sight, not to mention ifficulties in ientifying multiple mobile objects, time synchronization an such. These problems are effectively solve by combining ultrasoun with other technologies. This paper proposes a metho that combines best features of ultrasoun an RF technologies for effective inoor positioning. With the application of the suggeste metho, the potential of the active ultrasoun positioning system is realize. In the propose case, a beacon evice sening out ultrasonic an RF signals is attache to a mobile object. The beacon oes not perform any aitional calculations, resulting in reuce power consumption an extene battery life. Mobile object positioning using ultrasoun is one by calculating the istance between active (beacon) an passive (listener) evices. Different 3D positioning methos can be employe when the istance between evices is known. Aing RF technology solves three problems arising from ultrasoun usage: time synchronization is ensure when calculating ultrasoun time of ISBN: SDIWC 109

2 flight; mobile object is ientifie; position estimate even if ultrasoun signal coming from a mobile object oes not reach the listeners. A representative example of ultrasoun-rf technology combination is the Cricket system [2]. Cricket s accuracy rate is about 10 centimeters [3]. A Cricket evice can be use as both the beacon an the listener. Even though RF technology is employe in the Cricket system, its performance is limite only to the ientification of the object an time synchronization, one by calculating ultrasoun propagation time. There were several attempts to improve the Cricket system. Shin et al. [4] an Kim et al. [5] propose harware an software solutions to improve accuracy, operating range, ecrease time elay an sensitivity to interference. Other stuies present a solution on how to estimate the orientation of the positione object. Stuies show that this can be achieve by improving Cricket s algorithm [6] or by implementing a compass [7]. However, these solutions o not solve the main problem: a requirement for ultrasoun listener an beacon to be in line of sight. Often times in actual conitions this requirement cannot be met, which means that there will always be areas in the builing where object positioning will not be possible. This problem can be solve by a wier use of RF technology: applying RF not only for time synchronization as suggeste in [2, 4 7], but for positioning as well, in cases where position estimation is unsuccessful using ultrasoun. 2 METHOD OVERVIEW A positioning system is a complex compoun comprise of ifferent components. The key elements of this system are provie in Figure 1. These elements are as follows: mobile object (beacon) that nees to be etecte; listeners that are locate on the top plane, their coorinates are known; a room, the size is known an a number of listeners epening on that size; a computer running positioning software. There are a number of ways to estimate object s coorinates in space [2 5], but in our case the operation of the system is base on calculating the ultrasonic signal propagation time. We can conclue the following: Figure 1. Key Elements in a Positioning System 1. This is the most efficient scheme for achieving our goals (synchronization or complex equipment is not neee); 2. Receive time ifference ata enables the istances between all listeners to be calculate; Different istance parameters are use to fin the coorinates of the mobile object. These calculations prouce errors for several reasons: rouning of values; signal propagation in ifferent meiums (in case of a room its environmental characteristics); collisions; other factors. After evaluating the available methos an the accuracy of their calculation results, we have come to the conclusion that implementation of several methos is necessary in orer to achieve the following: Create a system that is simple to operate an can be easily moifie (by increasing or ecreasing the number of listeners). ISBN: SDIWC 110

3 Combine raio frequency an ultrasoun technologies for successful coorinate estimation in unfavorable circumstances. Achieve the maximum possible accuracy in coorinate estimation. In that case the positioning algorithm was that the system woul aapt to varying listener numbers on its own. Listener numbers can vary for the following reasons: room size; signal sent by the beacon oes not reach the listener. These factors were put into consieration when the following positioning methos were chosen: 1. trilateration metho; [8] 2. matrix metho; [8] 3. two points metho (supplemente with RSSI technology) [9]. The position estimation algorithm was create using these methos. The steps of this algorithm are presente in Figure Position estimation metho is chosen accoring to the etermine number of listeners. 4. Estimate coorinates returne. Accoring to known ata the coorinates of a moving object are calculate by estimating the istances between each of the listeners an their coorinates on the coorinate plane. Position estimation metho is chosen accoring to the number of listeners that are being use. These methos have ifferent mathematical expressions. The first part of the formula for the first two methos is the same: ( x xi ) + ( y yi ) + z zi = (i = 1, 2,, n), r istance between the listener an the mobile object. ( ) r 2 1 (1) Derivation of this formula (ifferent for each metho) can be use to estimate the coorinates of the moving object. 2.1 Position Estimation Using Trilateration Metho This metho requires for at least three listeners to see the moving object in space. Figure 2. Visualization of the position estimation algorithm This algorithm is use to calculate the coorinates of a mobile object, an is comprise of the following steps: 1. Distance between the mobile object an all of the listeners is etermine by calculating the signal propagation time. 2. The number of listeners that etecte the mobile object is etermine. Figure 3. Position Estimation Using Circles Metho The sequence in which those listeners etect the object is not important: the object can be etecte by the first, secon an thir listeners ISBN: SDIWC 111

4 or the secon, thir an fourth. What is important is for the arrangement of points to be maintaine, as shown in Figure 3. Stanar formulas are use to estimate the coorinates of the mobile object on a plane. Those formulas can be foun in [8]. 2.2 Position Estimation Using Matrix Metho The same conitions apply for this case as well: istances to all listeners an their coorinates on a plane are known. But in this case at least four listeners etecting the moving object are require for position estimation (Figure 4). frequency but the most efficient one for inoor positioning is the fingerprinting metho. However, in orer to apply this metho successfully, initial information on signal propagation of every raio evice is require. This information can be gathere experimentally (signal strength is measure in various inoor areas an entere into a atabase) or mathematically (signal propagation moel is create an signal strength in specifie room areas is estimate on a computer accoring to that moel). Determining signal strength experimentally is time-consuming, so in case of fingerprinting it was ecie to use signal propagation moels. 3.1 Preiction of Raio Signal Propagation Figure 4. Position Estimation Using Matrix Metho There is an aitional requirement: at least one of the listeners etecting the object must be place at a ifferent height from all the other listeners. The number of listeners is not limite as long as it is not less than four (>4). This metho is realize by implementing stanar formulas [8]. 3 POSITION ESTIMATION USING TWO POINTS AND RSSI METHOD In cases when successful positioning is impossible using ultrasoun, a metho implementing both RF technology an ultrasoun has been propose. There are several methos that can be implemente for position estimation using raio Using theoretical signal propagation moels base on empirical measurements is a relatively simple way to estimate inoor RF propagation. These moels o not require a lot of the initial parameters an can be calculate quite fast compare to the eterministic moels that are base on signal propagation an iffraction theories (Geometrical Optics an Uniform Theory of Diffraction formulations) [10]. Early empirical methos were erive from the Free Space Propagation moel. This moel is base on gathering measurement ata uner actual conitions an then using it to estimate unknown coefficient values. More complex moels were create later on, an they inclue a significant number of aitional parameters affecting signal propagation. Therefore, their results were far more accurate. These moels were chosen for further investigation on their application possibilities when raio beacons are use for positioning. Path-loss preiction is commonly expresse in the following way [11]: PL n P Q ( )[ B] = 10 log( ) + WAF( p) + p= FAF( q) 1 q= 1 (2) 0 PL() stans for receive signal strength in the istance between the beacon an the listener. ISBN: SDIWC 112

5 0 is istance between the beacon an a spot where the initial signal strength has been measure. Usually 0 is equal to 1 m, in such case only propagation effects are inclue in (2). p an q are the number of walls an floors between the beacon an the listener, respectively. The empirical parameters n, WAF (p) an FAF (q) are respectively the path-loss exponent, wall attenuation factor an floor attenuation factor. This moel oes not inclue signal propagation effects, such as attenuation from travele istance, angle of incience with walls an so on. This may lea to lower accuracy in calculation results in certain areas of the builing. These eficiencies were well note when creating the New Empirical Moel which is written in the following way [12]: PL( )[ B] = 10 log( + log( bp ) n2 ] U ( bp n1 bp n1 ) U ( bp ) + [log( ) WAF( p) FAF( q) ) + cos( θ ) P Q + p= 1 q= 1 cos( θ p ) q (3) PL() is the loss of signal strength at a point of istance from the beacon, 0 istance between the beacon an a spot where the initial signal strength has been measure, bp is the istance of the breakpoint from the beacon, n 1 is the first path-loss exponent (in front of the breakpoint), n 2 the secon path-loss exponent (behin the breakpoint), U is the unit step function, p the number of walls in signal propagation path, q - the number of floors in signal propagation path, WAF wall attenuation factor, FAF floor attenuation factor, θ p signal angle of incience with walls, θ q signal angle of incience with floors. WAF(p) an FAF(q) are the attenuation factor values for the signal when it is moving perpenicular to walls or floors, θ p an θ q are angles of incience between, respectively, the p-th wall an q-th floor an a straight line connecting the beacon an the listener. 3.2 Positioning Using RSSI an Propagation Moels Before object positioning can take place, a etaile builing plan is require along with a signal propagation moel for each RF listener. These moels are create in accorance with the previously escribe RF signal propagation formula (3). Once the aforementione ata is prepare, object positioning can take place. Object positioning algorithm iea is base on Eucliean istance calculation [9]. Algorithm is execute in the following orer: 1. All of the RF listeners connecte to the system sen the following information on every etecte beacon to the server: Receive signal strength inicator RSSI, Listener ientifier ID, Listener packet ientifier PID, use for correct time synchronization. 2. Positioning is performe only for those beacons that were last etecte (i.e., their transmitte raio packet was last receive) in a specifie amount of time by at least two listeners. 3. In orer to reuce the amount of calculations, the probable location of the beacon is estimate using signal propagation moels (instea of analyzing the entire plan of the builing) by excluing all the areas where the beacon coul not be locate. To o so, information from all of the listeners is use to etermine if the beacon was etecte by the listener or not. In orer to estimate the likely location of the beacon, the coverage area of each of the listeners is compare. Coverage area of the listeners is etermine by using their signal propagation moels. 4. In orer to etermine the actual position of the positione object, the Eucliean istance between the measure an calculate values is calculate using the following formula: ISBN: SDIWC 113

6 = n i= 1 2 ( q i p i ) (4) q i signal strength inex measure by the i- th listener, p i value of the i-th listener foun in its signal propagation moel, n number of listeners use in the positioning system. The number of Eucliean istances estimate epens on the number of signal propagation moels create an values calculate in them. 5. The minimum Eucliean istance is foun an the corresponing row an column inexes values are save. 6. The position is estimate in meters accoring to the row inex an column inex. Coorinates x an y are calculate in the following way: a x = c (5) n where a stans for the length of the room in meters, n number of columns in RSSI values file, c column inex. b y = r m (6) where b stans for the with of the room in meters, m number of rows in RSSI values file, r row inex. 3.3 Position Correction Using RF Positioning Position estimation using raio frequency is not as accurate as ultrasoun positioning. However, it can be very useful when the positioning algorithm etermines more than one likely position using ultrasoun, i.e., when a system of equations with several possible solutions is forme. Figure 5. Position Estimation Using Two Points Metho When we have only two points (listeners) we can estimate two area points where the mobile object is likely locate (Figure 5). In such case the accurate position cannot be etermine. Nonetheless, by employing RSSI the accurate position can be estimate by using coorinates of several possible locations. Calculations are one using the following formulas: e = c a where a is the x-coorinate of the first listener, c x-coorinate of the secon listener, e x-coorinates ifference. (7) f = b (8) where b is the y-coorinate of the first listener, y-coorinate of the secon listener, f y-coorinates ifference. p = e f (9) where p is the istance between the centers of two circles. 2 2 ( p + r s 2 ) k = 2 p where k is the istance between the center of one of the circles an the line connecting the points of intersection, r (10) ISBN: SDIWC 114

7 an s istance between both points an the mobile object. We can estimate the istance between two known points by using formulas given above. The coorinates of those points are use in orer to o so. All the estimate values are neee for fining the x an y coorinates of the mobile object. Formulas are given below: the position of the beacon. It can then sen this information to other systems. Local area network connecting the listeners an the server into a single network using a TCP/IP protocol. x = a + e k / p + f / p r k (11) y = b + f k / p e / p r k (12) or x y = a + e k / p f / p r k (13) = b + f k / p + e / p r k (14) Incorrect coorinates can be ismisse by taking into consieration the estimate position calculate with the help of RF positioning. This is one by following the steps outline below: 1. The istance between coorinates foun by the RF positioning an coorinates of all likely spots foun by the ultrasoun positioning algorithm is calculate. 2. The coorinates that have the smallest istance between them are chosen. The closest coorinates estimate by ultrasoun positioning is then presente as the actual position of the mobile object. Figure 6. Positioning System Structure Listeners that can receive ultrasonic an raio signals from a mobile beacon. Aitionally, each listener calculates the time of flight of the ultrasonic signal (the time it takes for the ultrasonic signal to reach the listener) an sens this information to the positioning server. A beacon that is usually attache to a mobile object minimizing the possibility of various obstacles interfering with ultrasoun an raio signals. The beacon sens out a ata packet (its structure is given in Figure 7) via raio frequency. Aitionally, it sens out an ultrasoun signal. 4 POSITIONING SYSTEM ELEMENTS AND THEIR APPLICATION The general structure of the positioning system is given in Figure 6. It is comprise of the following elements: Server running positioning software. The server receives ata packets sent from the listeners, processes this ata an estimates Figure 7. Beacon Data Packet Structure Beacon ata packet contains the basic information require for registering the ultrasonic propagation time an ientifying the object. Beacon ID ientifies both the beacon an the mobile object. Packet ID is use for correct time synchronization. With each ata packet an ultrasonic signal sent, packet ID is increase by ISBN: SDIWC 115

8 one. Beacon temperature reaings are require for further operations when the ultrasoun time of flight is calculate by the server. Data packets sent by the beacon are receive by the listener which processes the information an creates a new ata packet by supplementing the ol one an then sening it to the server. Listener ata packet structure is given in Figure 8. Figure 9. Beacon Operation Chart Figure 8. Listener Data Packet Structure Listener ID ientifies the listener. It is use by the server to etermine which listener sent the ata packet so it can associate known listener coorinates with the actual listener. Both beacon an listener temperature reaings are use in further calculations when the ultrasoun propagation istance is estimate by the server. BID (beacon ID), PID (beacon packet ID) an BT (beacon temperature) containe in the listener ata packet are the same as the ones receive from the beacon. When ata is receive from the beacon (a RF packet is receive), the receive signal strength inicator (RSSI) is measure for that packet as well. This value is then logge in the packet boun for the positioning server. The last measurement in the ata packet is t ultrasoun time of flight which is use for estimating the position of the object. As mentione earlier, the main task of the beacon is to sen out a raio ata packet an an ultrasoun signal. A etaile chart on the operation of the beacon is given in the following iagram (Figure 9). Time intervals between packets can be configure. For objects that move (for example, people) this time interval nees to be quite short (less than 1 s) in orer to maintain accuracy. For stationary or rarely move objects time interval can be prolonge to ecrease beacon energy consumption. In either case, energy consumption will be relatively low because the beacon will not perform any aitional calculations nor will it process large amounts of ata. This means that beacon performance can rely solely on batteries or an accumulator. Before the ultrasonic signal an RF packet is sent, the beacon checks if the raio channel is ile. It reuces the number of possible collisions in case there are several mobile objects in the room. The principle of operation for listeners is more complex. Not only oes the listener have to receive the ultrasonic an raio signals from the beacon, but it also has to calculate the ultrasonic signal time of flight. Ultrasoun time of flight measurements are use by the server in estimating listener s position using ultrasoun. Listener operation chart is given in Figure 10. ISBN: SDIWC 116

9 Figure 10. Listener Operation Chart The listener is constantly checking for an incoming signal. When it receives the RF packet, it knows that the beacon has sent out the ultrasoun signal as well, so it waits for its arrival. When the ultrasoun signal is receive, its time of flight (t) is calculate: t = t r t u (15) t r stans for the moment of time when the raio packet was receive, t u moment of time when the ultrasoun signal was receive. 5 EXPERIMENTAL SETUP AND RESULTS The general outline for the positioning system testing environment is given in Figure 11. Figure 11. Positioning System Testing Environment Testing environment comprise of four listeners attache to the ceiling in certain spots, beacon that is attache to a mobile object an positioning server. 5.1 Experimental Results Several experiments have been carrie out to test the ultrasonic positioning technology without position correction by raio frequency. During the first test, position estimation accuracy for a stationary object was teste in ifferent positions (A, B an C). In Figure 12 the actual position of the object is marke with a re cross, an the calculate ones with grey ots. In each case, the stationary object was left in the same position a sufficient perio of time in orer for 500 coorinates to be logge. ISBN: SDIWC 117

10 Figure 12. Test Results for Stationary Object Then the estimate coorinates were compare to actual ones an the positioning errors entere in Table 1. In each case, the object was iscovere by at least three ultrasonic listeners. As can be seen from the results, the mean error oes not excee 10 cm. Table 1. Position Estimation Errors (Stationary Object) Measurement location Maximum error cm Mean error cm SD cm Position A Position B Position C The secon test was one to fin out the positioning accuracy rate for a mobile object. In this case, the positione object moves aroun a table with roune eges (Figure 13). Figure 13. Position Estimation Results for a Mobile Object Moving Aroun an Oval Table Errors that were prouce when positioning a mobile object are given below (Table 2). Test results show that the mean error is even lower when estimating the position of a mobile object than that of a stationary object. Table 2. Position Estimation Errors (Mobile Object) Maximum error cm Mean error cm SD cm This may be ue to the fact that the test i not take a long time: moving an object aroun the table took much less time than estimating the position of a stationary object. Therefore, one can assume that larger errors coul not have forme in a short perio of time. Other tests were carrie out to etermine the accuracy rate when position is estimate using both ultrasoun an raio frequency. First, measurements for position estimation using only raio frequency were taken. Positioning using RF is performe by measuring the transmitte signal strength. Positioning results are given in ISBN: SDIWC 118

11 Figure 14 (the actual position of the object is marke by a re cross). Figure 14. Position Estimation Results Using Raio Frequency As can be seen from the test results, when limite only to raio technology position estimation prouce much larger errors than when positioning was performe using ultrasoun technology. Table 3. Position Estimation Errors When Raio Frequency Is Use Maximum error cm Mean error cm SD cm It is clear from the results in Table 3 that position estimation prouce much larger errors when raio frequency was use. However, raio frequency has its own avantages: it oes not require the line of sight zone between the beacon an the listener, whereas the ultrasoun technology is limite by this requirement. In the case of ultrasoun, even the smallest obstacles in ultrasonic signal s path may prevent it from reaching the listener. Generally, position estimation using raio frequency is impractical because it cannot prouce accurate results. Nevertheless, this metho is very useful when an ultrasoun beacon is etecte by an insufficient number of listeners. Figure 15. Position Estimation Results Using Ultrasoun an Raio Frequency In the case where the beacon is etecte by two listeners, accurate positioning by measuring ultrasoun time of flight is impossible because a system of equations with several solutions is forme. But if we a the approximate position estimate by using raio frequency into this equation, we can ismiss faulty solutions an calculate the value that is closest to the actual position of the object. Position estimation results in a case of ultrasoun beacon being etecte only by two listeners are shown in Figure 15. Position estimation accuracy for a stationary object was teste in ifferent positions (A, B an C) Estimation results iffer from the actual positions (marke by a re cross) by 52.5 cm at most, an the mean error is 34.1 cm. Table 4. Position Estimation Errors Using Ultrasoun an Raio Frequency Measurement location Maximum error cm Mean error cm SD cm Position A Position B Position C ISBN: SDIWC 119

12 As can be seen from test results (Table 4), position estimation errors are significantly lower than the ones prouce using only raio frequency. Comprehensive utilization of raio technology helps achieve goo positioning results with less equipment. 6 CONCLUSIONS A metho base on ultrasoun technology an ifferent positioning techniques was create to estimate the position of a mobile object. Several methos (trilateration, matrix, two points, RSSI calculation methos) were integrate an use epening on what amount of listeners are available for etermination of the coorinates of the mobile object. Integration was chosen in orer to achieve accuracy. It is also important to note that ue to the ifferent room sizes, their furnishings, an the trajectory of the mobile object, the ultrasoun an raio technology combination was employe. Position estimation in the case where the positione object is etecte by two listeners woul not have been possible if limite to ultrasoun technology. During experimentation, the metho was teste for positioning accuracy. The application of trilateration, matrix, two points an RSSI methos was teste to see how their results alter epening on the changing number listeners. The results showe that the positioning accuracy achieve by calculating the ultrasoun propagation time is not lower than the one achieve by other existing methos. The mean error for position estimation when the object is etecte by two ultrasoun listeners is 34.1 cm. It is about four times lower than in cases where position is estimate using only raio frequency, whereas position estimation using other methos in this case is impossible. 7 REFERENCES [1] Z. Song, G. Jiang, an C. Huang, A Survey on Inoor Positioning Technologies, in Theoretical an Mathematical Founations of Computer Science, vol. 164, Q. Zhou, E. Springer Berlin Heielberg, 2011, pp [2] N. B. Priyantha, The cricket inoor location system, Massachusetts Institute of Technology, [3] H. Balakrishnan, R. Baliga, D. Curtis, M. Goraczko, A. Miu, B. Priyantha, A. Smith, K. Steele, S. Teller, an K. Wang, Lessons from Developing an Deploying the Cricket Inoor Location System, [4] S. Shin, J. Choi, B. Kim, an M. Park, Improve ultrasonic beacon systems for inoor localization, in Proc. of International Conference on Control, Automation an Systems, [5] B. Kim, J.-S. Choi, S.-I. Ko, an M. Park, Improve active beacon system using multi-moulation of ultrasonic sensors for inoor localization, in SICE- ICASE, International Joint Conference, 2006, pp [6] A. Kitanov, V. Tubin, an I. Petrovic, Extening functionality of RF Ultrasoun positioning system with ea-reckoning to accurately etermine mobile robot s orientation, in Control Applications, (CCA) Intelligent Control, (ISIC), 2009 IEEE, 2009, pp [7] H. Kim an J.-S. Choi, Avance inoor localization using ultrasonic sensor an igital compass, in Control, Automation an Systems, ICCAS International Conference on, 2008, pp [8] William S. Murphy Jr., Willy Hereman, Determinattion of a Position in Three Dimenesions Using Trilateration an Approximate Distances, [9] S. Gansemer, U. Grossmann, an S. Hakobyan, RSSI-base Eucliean Distance algorithm for inoor positioning aapte for the use in ynamically changing WLAN environments an multi-level builings, in Inoor Positioning an Inoor Navigation (IPIN), 2010 International Conference on, 2010, pp [10] A. J. Lopez-Barrantes, O. Gutierrez, F. S. D. Aana, an R. Kronberger, Comparison of empirical moels an eterministic moels for the analysis of interference in inoor environments, in Electromagnetic Compatibility (APEMC), 2012 Asia- Pacific Symposium on, 2012, pp [11] A. Golsmith, Wireless Communications. Cambrige University Press, [12] K.-W. Cheung, J. H.-M. Sau, an R. D. Murch, A new empirical moel for inoor propagation preiction, Veh. Technol. IEEE Trans. On, vol. 47, no. 3, pp , ISBN: SDIWC 120