Diversity techniques for signal-strength based indoor location determination

Transcription

1 Scholars' Mne Masters Theses Student Research & Creatve Works Sprng 2007 Dversty technques for sgnal-strength based ndoor locaton determnaton nl Ramachandran Follow ths and addtonal works at: Part of the Computer Engneerng Commons Department: Electrcal and Computer Engneerng Recommended Ctaton Ramachandran, nl, "Dversty technques for sgnal-strength based ndoor locaton determnaton" (2007). Masters Theses Ths Thess - Open ccess s brought to you for free and open access by Scholars' Mne. It has been accepted for ncluson n Masters Theses by an authorzed admnstrator of Scholars' Mne. Ths work s protected by U. S. Copyrght Law. Unauthorzed use ncludng reproducton for redstrbuton requres the permsson of the copyrght holder. For more nformaton, please contact scholarsmne@mst.edu.

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3 DIVERSITY TECHNIQUES FOR SIGNL-STRENGTH BSED INDOOR LOCTION DETERMINTION by NIL RMCHNDRN THESIS Presented to the Faculty of the Graduate School of the UNIVERSITY OF MISSOURI-ROLL In Partal Fulfllment of the Requrements for the Degree MSTER OF SCIENCE IN COMPUTER ENGINEERING 2007 pproved by Jagannathan Sarangapan, dvsor Can Saygn Scott Chrstopher Smth

4 2007 nl Ramachandran ll Rghts Reserved

5 PUBLICTION THESIS OPTION Ths thess conssts of the followng two artcles that have been submtted for publcaton as follows: Pages 1-52 are ntended for submsson to the CM TRNSCTIONS ON SENSOR NETWORKS. Pages are ntended for submsson n INTERNTIONL JOURNL OF DISTRIBUTED SENSOR NETWORKS.

6 v BSTRCT Dversty technques have been found n the lterature to be sutable for compensatng channel uncertantes such as multpath fadng. In ths thess, we explot spatal and frequency dversty technques for mprovng accuracy n locatng statonary and moble objects n the ndoor envronment. Frst, spatal and frequency dversty technques are ntroduced for small scale and temporal varaton compensaton of receved sgnal strength and t s demonstrated analytcally that t n fact enhances locaton accuracy. novel metrc s ntroduced n selecton combnng n order to acheve locaton accuracy through the addton of dversty upon two of the avalable locaton determnaton schemes. The results are evaluated expermentally aganst the case where there s no dversty for recepton by usng low cost wreless RF devces such as motes. n asset locaton trackng system s then devsed to both mprove accuracy and predct asset movement. Spatal dversty on the order of twce the wavelength and frequency dversty n terms of channel spacng of 55 MHz are evaluated and shown to provde a reducton n locaton determnaton error of 36% and 20%, respectvely, when compared to a system wthout dversty. Fnally, results from frequency dversty are compared aganst the spatal dversty technques n terms of mprovement n locaton accuracy, transmtter power consumpton, and hardware and processng costs.

7 v CKNOWLEDGMENTS I am extremely grateful to my advsor, Dr. Sarangapan, for the encouragement and gudance he has gven me and the extreme patence he has shown n my completng ths work. He has also gven me suffcent freedom to explore avenues of research whle correctng my course and gudng me at all tmes. I thank Dr. Saygn and Dr. Smth, my commttee members, for the help and support they have provded throughout my Masters degree program. I should especally menton Kanan Cha, Maheswaran Thagarajan, James Fonda, and Dr. Macej Zawodnok, wthout whose help, ths effort and ts successful completon would not have been possble. Specal thanks go to all members of the IMS and utoid research groups who have stood by me at all tmes. I express my grattude to l Salour, Douglas Trmble, and Bryan Dods of Boeng for fnancal support durng my program, the opportunty to work wth Boeng on ther RTLS solutons and the valuable experence I ganed from t. On a personal note, I thank my roommates at Rolla and the Keralte communty here who have been supportve n all my ventures. Last, but at the top of my lst, I thank my parents S. Ramachandran and Dr. Lakshm Ramachandran, and my sster rchana Ramachandran, for the tremendous encouragement and support I have receved throughout my lfe whch has enabled me to face the challenges and acheve success.

8 v TBLE OF CONTENTS Page PUBLICTION THESIS OPTION... BSTRCT... v CKNOWLEDGMENTS... v LIST OF ILLUSTRTIONS... x LIST OF TBLES... x PPER 1. ccuracy Improvement Usng Spatal Dversty For Sgnal Strength Based WLN Locaton Determnaton Systems...1 BSTRCT... 1 I. INTRODUCTION... 2 II. BCKGROUND Defntons... 7 B. Overvew of Spatal Dversty... 8 III. PROPOSED METHODOLOGY Source of Locaton Determnaton Errors B. Spatal Dversty and Locaton Determnaton C. Number of Recevers D. Locaton Determnaton lgorthm ) Probablstc technque ) Determnstc technque E. Dversty and Combnng F. Trackng, veragng and Predcton IV. EXPERIMENTL RESULTS ND NLYSIS... 38

9 v. Testbed and Implementaton B. lgorthm Pseudocode C. sset Locaton Trackng and veragng D. Results and nalyss ) Spatal dversty and locaton determnaton accuracy ) Comparson of HORUS vs. spatal dversty ) Locaton trackng, averagng and predcton V. CONCLUSIONS REFERENCES Use of Frequency Dversty n Sgnal Strength Based WLN Locaton Determnaton Systems...56 BSTRCT I. INTRODUCTION II. BCKGROUND Defntons B. Overvew of Frequency Dversty III. PROPOSED METHODOLOGY Source of Locaton Determnaton Errors B. Frequency Dversty and Locaton Determnaton C. Number of Recevers D. Locaton Determnaton lgorthm ) Probablstc technque ) Determnstc technque ) Dversty and combnng E. Locaton Update Rate and Power Consumpton F. Trackng, veragng and Predcton... 75

10 v IV. EXPERIMENTL RESULTS ND NLYSIS Testbed and Implementaton B. lgorthm Pseudocode C. sset Locaton Trackng and veragng D. Results and nalyss ) Frequency and spatal dversty and locaton determnaton accuracy ) Locaton update rate and power consumpton ) Locaton trackng, averagng and predcton V. CONCLUSIONS REFERENCES VIT... 94

11 x LIST OF ILLUSTRTIONS Fgure Page PPER 1 1. Normalzed correlaton coeffcent between fadng envelopes as functon of separaton between the antennas (a) Two locatons and B and a sngle recever (b) probablty densty functons of sgnal strength receved from each locaton at the recever Probablty Densty Functons of RSSI from locatons and B (a) at Recever 1 and (b) at Recever Reducton n error area from spatal dversty (a) Hardware mplementaton of spatal dversty and proposed selecton combnng approach (b) software mplementaton Layered representaton of the proposed method of selecton combnng Calculaton of averaged cumulatve x and y moton for nne tme unts veragng of located coordnates to report poston (lag of 9 unts) UMR G4-SSN embedded wreless sensor networkng platform UMR-SLU G4-SSN motes arranged for creatng spatal dversty wth a separaton of 25 cms Floor plan of ERL thrd floor Floor plan of ERL second floor Probablstc technque- offgrd ponts - (a) cumulatve dstrbuton functon of locaton error (b) locaton error as a functon of number of recevers Probablstc technque, ongrd ponts - (a) cumulatve dstrbuton functon of locaton error (b) locaton error as a functon of number of recevers Determnstc technque, offgrd ponts - (a) cumulatve dstrbuton functon of locaton error (b) locaton error as a functon of number of recevers... 44

12 x 16. Determnstc technque, ongrd ponts - (a) cumulatve dstrbuton functon of locaton error (b) locaton error as a functon of number of recevers Successful detecton of moble and statonary assets ccuracy levels of averagng and predcton technques for moble assets ccuracy levels of averagng and predcton technques for statonary nodes PPER 2 1. (a) Tmer-based mplementaton of frequency dversty and proposed selecton combnng approach (b) dual recever mplementaton Layered representaton of the proposed method of selecton combnng UMR G4-SSN embedded wreless sensor networkng platform Floor plan of ERL thrd floor Floor plan of ERL second floor Determnstc technque (a) cumulatve dstrbuton functon of locaton error (b) locaton error as a functon of number of recevers Probablstc technque - (a) cumulatve dstrbuton functon of locaton error (b) locaton error as a functon of number of recevers Battery lfetme vs. locaton update nterval Successful detecton of moble and statonary assets ccuracy levels of averagng and predcton technques for moble assets ( Determnstc technque) ccuracy levels of averagng and predcton technques for moble assets (Probablstc technque)

13 x LIST OF TBLES Table Page PPER 1 I : Pseudocode for probablstc locaton determnaton II : Pseudocode for determnstc locaton determnaton III : Performance comparson wth and wthout spatal dversty and number of recevers IV: Summary of locaton determnaton error levels PPER 2 I Pseudocode for probablstc locaton determnaton II Pseudocode for determnstc locaton determnaton III : Performance comparson wth and wthout dversty and number of recevers IV: Summary of locaton determnaton error levels... 84

14 PPER 1 ccuracy Improvement Usng Spatal Dversty For Sgnal Strength Based WLN Locaton Determnaton Systems 1 nl Ramachandran and S. Jagannathan * Embedded Systems and Networkng Laboratory Department of Electrcal and Computer Engneerng Unversty of Mssour-Rolla BSTRCT The lterature ndcates that spatal dversty can be utlzed to compensate channel uncertantes such as multpath fadng. Therefore, n ths paper, spatal dversty s exploted for accuracy mprovement n locatng statonary and moble objects n the ndoor envronment. Frst, space dversty technque s ntroduced for small scale and temporal varaton compensaton of receved sgnals and demonstrated analytcally that t n fact enhances locaton accuracy. novel metrc s ntroduced for selecton combnng n order to mprove locaton accuracy through the addton of spatal dversty upon two of the avalable locaton determnaton schemes. The results are evaluated expermentally aganst a sngle antenna system for recepton by usng low cost wreless RF devces such as motes. lternatvely, the mpact of the number of locaton determnaton devces n a probablstc WLN network based on pre-proflng of sgnal strength s analyzed and t s demonstrated analytcally that locaton accuracy mproves wth the number of recevers used. n asset locaton trackng system s then devsed to both mprove accuracy and predct asset movement. Spatal dversty n terms of the antenna spacng of 2λ s evaluated and shown to provde a reducton n locaton determnaton error between 30 % and 40 % when compared to a sngle antenna system. Fnally, t s shown that t s cheaper to create dversty compared to ncreasng the number of locatng devces. Key words Indoor Geo-locaton, WLN Locaton Determnaton, Spatal Dversty, Locaton ccuracy. 1 Research supported n part by an r Force Research Laboratory Grant F C-704.

15 2 I. INTRODUCTION In ndustral and servce sectors, real-tme locatng, trackng of assets and personnel s fast becomng a necessty. Several technologes have been developed and mplemented wth varyng degrees of success. Whle efforts started wth nfrared and ultrasonc technologes [1], [2], t was recognzed that use of rado frequency (RF) technologes, beng easly scalable and deployable, was the opton of choce [3], [4] due to low cost and mnmal safety concerns because of the absence of wrng. Subsequently, dfferent locaton determnaton schemes n the RF doman were developed, whch nclude tme of arrval (TO), tme dfference of arrval (TDO), angle of arrval (O), and receved sgnal strength (RSSI) etc. [5], [6]. Bult-n RF networks now exst n most ndoor envronments for communcaton and networkng applcatons and therefore t would be advantageous to utlze the same networks for locaton determnaton n the manufacturng shop floor, buldngs and other places. Towards ths end, tme and angle based systems have been developed but they ([5],[6]) are dffcult to mplement because they requre specalzed hardware. Sgnal strength based systems, on the other hand, can be used on all RF networks wthout addtonal hardware and are therefore beng addressed by many researchers as a cost effectve soluton for locaton determnaton. The fundamental premse of sgnal strength-based locaton determnaton s that receved sgnal strength ndcator (RSSI) at a recever s a functon of the locaton of the transmtter and thus can be used to dentfy the locaton of objects or assets. Therefore, for the past few years, consderable nterest has evolved n usng RSSI for locaton determnaton. RSSI-based locaton determnaton systems are classfed nto

16 3 nfrastructure and clent based systems dependng upon where the locaton determnaton occurs. In a clent-based system, the tracked object measures sgnal strength receved from varous access ponts and usng pror nformaton about the poston of the access ponts and pre-profled data, locaton determnaton s performed. RDR and HORUS are examples of the clent based system. RDR was developed as a determnstc locaton determnaton system based on average sgnal strength receved from each reference locaton [7]. On the other hand, HORUS [8] uses a probablstc algorthm for locaton determnaton. It s mportant to notce that, n the clent-based locaton determnaton system, each tracked object computes ts own locaton. Whle ths opton has the advantage of dstrbuted computaton, each tracked object platform must have suffcent computatonal power to dentfy ts locaton. Ths mght be dffcult to mplement n power constraned devces such as actve RTLS tags whch are normally beng used for ndoor locaton determnaton envronments, for nstance, on a manufacturng shop floor. In addton, the requrements on pror storage are also large. nother ssue s that t s dffcult to make locaton nformaton on all assets avalable n a centrally avalable nterface. There s also a securty ssue n allowng each devce to fnd ts own locaton snce each devce would then be aware of coordnates of the area and the rado map. By contrast, n nfrastructure-based locaton determnaton, the asset tags / moble unts ether report the receved sgnal strength vectors or they act as transmtters and the receved sgnal strength from them are recorded at snffers placed around the area. The locaton computaton s performed on a central server and s made accessble globally. Such an opton enables the use of power constraned transmtter tags to reman n very-

17 4 low-power standby modes and transmt ther nformaton perodcally. Therefore, an nfrastructure-based system s addressed n [9]. The work n ths paper refers to an nfrastructure based system because the current trends n ndustral applcatons warrant the need for such a technology snce t mnmzes securty concerns. We consder the system n whch the electroncs on the tracked asset act as a transmtter sendng ts own dentty perodcally, where the frequency vares dependng on how often the applcaton requres updated locaton nformaton. ddtonally, n the avalable works such as RDR and HORUS, the effect of the number of recevers on locaton accuracy s not dscussed and analytcal justfcaton s not ncluded. By contrast, n the proposed work, we analytcally prove that accuracy mproves wth the number of recevers even though ths may be costly. Therefore, we show that by usng spatal dversty the cost s mnmzed whle achevng the desred locaton accuracy. One of the major challenges facng WLN locaton determnaton s that sgnal strength of receved rado sgnals s a dynamc parameter and vares wdely wth changes n the envronment due to fadng, shadowng etc. [10]. These factors nclude both smallscale and temporal effects, and such varaton puts a lmt on the resoluton achevable by the locaton determnaton system. The developers of HORUS suggest a small scale compensaton method [11] based on observng the determned locaton of each object and perturbng the sgnal strength vector to better sut a reference locaton. However, there are several ssues wth such an approach appled to an nfrastructure based system. Frst, the object has to be located ether contnuously or often to detect unexpected changes n locaton. Unfortunately, tags attached to assets for trackng n manufacturng shop floor envronments are often energy-constraned and do not transmt frequently [12], makng

18 5 the perturbaton based contnuous trackng a practcally unvable soluton. Second, the suggested perturbaton technque s not based on any true physcs of rado communcaton. Fnally, the computatonal overhead due to the perturbaton technque s sgnfcantly hgh. By contrast, a novel approach based on space dversty and modfed selecton combnng s ntroduced n order to overcome the above lmtatons. Dversty has been a well-researched topc n the feld of communcatons wth the vew of combatng fadng. It nvolves combnng multple uncorrelated sgnal envelopes n order to obtan a sgnal wth a hgher sgnal to nose rato (SNR). Several methods for sgnal combnng have been developed [13] targetng SNR mprovement. For locaton determnaton, achevng hgher SNR does not automatcally result n better accuracy unless consstent receved sgnal strength s acheved. In the proposed work, t s demonstrated that spatal dversty can be employed to effectvely reduce the varaton n receved sgnal strength values and as a result, mproved accuracy s acheved n locaton determnaton. new combnng method s ntroduced and s shown to reduce varance n sgnal strength when used wth spatal dversty. The combnaton of spatal dversty and the proposed combnng s shown to enhance the locaton accuracy of objects or assets. The mpact of the number of recevers on locaton determnaton accuracy s analyzed and t s shown that dversty technques provde an effectve method for compensatng small scale and temporal varatons and locatng objects accurately. It s shown that, for a gven number of recevers, a system usng spatal dversty wth the proposed combnng wll perform better than one wthout dversty. Expermental results usng wreless UMR motes are ncluded and demonstrate hghly satsfactory performance, whch ndeed verfes our theoretcal conjecture.

19 6 The paper s organzed as follows. Secton II presents the background on spatal dversty. Secton III presents the proposed methodology, analytcal results and the mplementaton. Secton IV presents and dscusses hardware results. Secton V concludes the paper and dscusses avenues for future work.

20 7 II. BCKGROUND In order to proceed, the followng defntons are requred. Subsequently, an overvew of spatal dversty s dscussed.. Defntons RSSI (Receved Sgnal Strength Indcaton): The average receved sgnal strength at a gven recever durng the recepton of a packet, expressed n dbm, s known as RSSI. Dversty: The use of multple sgnal sources n order to mprove the qualty of the receved sgnal s known as dversty. The dfferent sgnal sources are referred to as dversty branches. Spatal Dversty: n antenna confguraton of two or more sgnal sources that are physcally spaced apart (spatally dverse) to combat sgnal fadng s known as Spatal Dversty. Uncorrelated fadng envelopes: When a dversty scheme s capable of ensurng mnmal correlaton between the receved sgnal strength values from multple nput sgnal sources (multple antennas n case of spatal dversty), such a scheme s sad to result n uncorrelated fadng envelopes. When the nput channels n a dversty scheme are uncorrelated, effectve mtgaton of fadng can be accomplshed. Selecton Combnng: The method of selectng one out of multple sgnal sources n a dversty scheme by usng SNR (select the one wth hgher SNR) as a crteron s known as Selecton Combnng. In the proposed approach, the SNR crteron s replaced by RSSI (select the one wth hgher RSSI) snce RSSI, and not SNR, s a representatve functon of transmtter locaton.

21 8 B. Overvew of Spatal Dversty The varatons n sgnal strength can be classfed nto large-scale, small-scale and temporal varatons [8]. Sgnal strength dependent locaton determnaton s based on large-scale varatons of sgnal strength wth dstance, snce ths allows dstncton between dfferent locatons. Small-scale varatons n sgnal strength are caused by asset movements of the order of a fracton of a wavelength and are detrmental to accuracy n locaton determnaton. ddtonally, temporal varatons happen over tme due to human actvty and envronmental changes. In other words, the source of error n both smallscale and temporal varatons n terms of sgnfcant reducton n receved sgnal strength s caused by destructve fadng occurrng at the recever from multple paths. To combat such fadng of wreless sgnals, multple uncorrelated fadng channels are employed at each recever. Motvaton for use of dversty technques stems from the fact that the probablty of smultaneous deep fadng occurrng on two uncorrelated fadng envelopes (resultng from spatal dversty) s much lower than the probablty of a deep fadng occurrng on a sngle branch system [15]. Thus, employng a new selecton combnng approach on top of any dversty technque whch assures suffcently uncorrelated channels wll reduce the varance n sgnal strength owng to small scale factors whch appears to be the major source of locaton determnaton errors. The normalzed correlaton coeffcent ρ( ξ ) between the two fadng envelopes from the nput sources provded by spatal dversty s expressed as a functon of antenna separaton [16] as ρ( ξ ) J (2 πξ ) (1) 2 0

22 9 whereξ s the separaton between two vertcal monopole antennas expressed n terms of multples of the wavelength n use, n our case 2.4 GHz, and J 0 s the Bessel functon of the frst knd and order zero [17]. Based on ths dervaton, the normalzed correlaton coeffcent between the fadng envelopes drops wth antenna separaton k as depcted n Fg. 1. Normalzed correlaton coeffcent ntenna separaton n multples of wavelength Fg. 1. Normalzed correlaton coeffcent between fadng envelopes as functon of separaton between the antennas From Fg. 1, t s clear that for a separaton of 2λ between the antenna elements, the correlaton coeffcent s around and hence the fadng envelopes can be shown to be uncorrelated. Further, n [18] expermental results at 1800 MHz ndcate that 2λ s an acceptable value of separaton to ensure almost totally uncorrelated channels.

23 10 Hence, n the proposed work, spatal separaton of 2λ (25 cms for 2.4 GHz) s used to ensure uncorrelated fadng channels. Secton III shows how the proposed selecton combnng, employed wth a two-branch dversty system, lowers the varaton n receved sgnal strength. Consequently, t wll be proven that reduced varance n sgnal strength renders mproved locaton accuracy.

24 11 III. PROPOSED METHODOLOGY We prove that use of selecton combnng over two uncorrelated channels results n reduced varance n sgnal strength provded the selecton combnng s performed by usng the approprate metrc and n an adequate manner. lternatvely, t s demonstrated that by ncreasng the number of recevers the accuracy can be further enhanced but wth an ncreased cost. Based on ths lne of thought, actual mplementaton detals of spatal dversty are gven. RSSI values from the transmtter are used to arrve at an estmate of ts locaton. n asset locaton trackng system s developed to determne whether the located asset s movng or statonary. veragng of consecutve estmated locatons of the transmtter s performed to mprove locaton accuracy. For moble assets, a predcton scheme s developed to dentfy future locaton of the asset for trackng applcatons. Frst, the source of errors n locatng objects s dscussed.. Source of Locaton Determnaton Errors The work descrbed n [14] dscusses locaton accuracy for dentfyng two gven ponts referred to n Fg. 2 (a) as Locaton and B wth one recever. Let us consder ths basc system for error analyss. Intally, a transmtter s placed at locaton and made to transmt repeatedly for a perod of tme, durng whch the RSSI values observed at the recever are recorded. These values are now stored as a sgnal strength dstrbuton wth probablty densty functon (PDF) f. Smlarly, the transmtter s placed at locaton B and made to transmt for the same perod of tme and the observed RSSI values at the recever are stored as a probablstc dstrbuton wth the PDF f B. Ths completes the offlne phase. In the onlne phase, the recever s placed at locaton and made to

25 12 transmt. Let us assume ths transmsson s collected at the recever wth a RSSI value of S. Now, based on the stored sgnal strength dstrbutons at the recever from a transmtter placed at locatons and B, the lkelhood of the transmsson havng orgnated from a transmtter located at or B can be evaluated. Let f ( S ) and fb( S ) be the values on the PDFs f and f B, respectvely, at the RSSI value of S. Now, f fb( S) > f ( S) for the observed RSSI value of S, then the locaton determnaton system would wrongly decde that the transmsson has orgnated from locaton B. Such a case s shown as example n Fg. 2 (b). The ntegral of f ( S ) over the range of S for whch f ( S ) > f ( S ) gves the probablty of wrong dentfcaton of a transmsson B from locaton as f t s orgnatng from the locaton B. Ths probablty s expressed by the shaded area n Fg. 2 (b). f B(S ) Locaton Locaton B f B f f (S ) Recever +1 Recever (a) S Sgnal Strength (b) Fg. 2. (a) Two locatons and B and a sngle recever (b) probablty densty functons of sgnal strength receved from each locaton at the recever

26 13 Ths probablty can be mathematcally expressed as ( ) B P 1 = P f ( S) < fb( S) (2) where 1 B P s the probablty of wrongly dentfyng a transmsson arrvng from locaton as f t s arrvng from locaton B whle usng one recever for dstncton, the observed RSSI from locaton, s a random varable obeyng the PDF f of the S, RSSI, f ( S ) s the value of the PDF f at the RSSI value S ; and f ( S ) s the value B of the PDF f B at the RSSI value S. Now let us add one more recever to the scenaro. In the offlne phase, the RSSI values from a transmtter at both locatons and B observed at both recevers are ndvdually recorded and stored as PDFs. Let 1 f and 1 f B represent the PDFs of observed RSSI values at recever 1 from locatons and B, respectvely, and 2 f and 2 f B be the PDFs of observed RSSI values at recever 2 from locatons and B, respectvely. These are depcted n Fg. 3. The recevers are assumed to be lnked to a central server through a backbone network. The RSSI values are brought to the server for buldng and storng the dstrbutons as well as computng the locaton n the onlne phase. In the onlne phase, the transmtter s placed at locaton and made to transmt. Let the observed sgnal strength values at recevers 1 and 2 be 1 S and 2 S respectvely. These values follow the PDFs 1 f and 2 f respectvely. Here, f ( S ) and 1 1 f ( S ) are the 1 1 B values of the PDFs 1 f and 1 f B at the observed RSSI value 1 S at recever 1 and f ( S ) 2 2 and f ( S ) are the values of the PDFs 2 2 B 2 f and 2 f B at the observed RSSI value 2 S at recever 2.

27 14 f ( S ) 1 1 B f ( S ) 2 2 B 1 f 1 f B f ( S ) f 2 f B f ( S ) S 2 S Fg. 3. Probablty Densty Functons of RSSI from locatons and B (a) at Recever 1 and (b) at Recever 2 Unlke the sngle recever case, here, the product of f ( S ) and 1 1 B f ( S ) has to be 2 2 B greater than the product of f ( S ) and 1 1 f ( S ) for the transmsson from locaton to 2 2 be wrongly dentfed as f t s orgnatng from locaton B. Ths probablty can be represented mathematcally as P = P f S f S < f S f S (3) B ( ( ) ( ) B ( ) B ( )) B P where 2 s the probablty of wrongly dentfyng a transmsson from locaton as beng orgnated from locaton B. Now, the scenaro s scaled to k recevers whch are assumed to be lnked to the central server. In the offlne phase, the transmtter s placed at both of the reference locatons and made to transmt for a perod of tme. The receved RSSI values on the k recevers are brought to the central server and RSSI PDFs are computed for both reference grd locatons at each recever. These PDFs are labeled as f and f B where = 1L k s the recever number and f represents the PDF of the RSSI from a

28 15 transmtter placed at locaton observed at recever and f B represents the PDF of the RSSI from a transmtter placed at locaton B observed at recever. In the onlne phase, the transmtter s placed at locaton and made to transmt. RSSI values at recevers = 1L k, where S follows PDF S are receved f. By nducton from (3), the probablty of wrongly dentfyng a transmsson orgnatng from locaton as f t s orgnatng from locaton B can now be expressed as k k B Pk = P f ( S ) < fb( S ) = 1 = 1 (4) where B P k s the probablty of wrongly dentfyng a transmsson from locaton as f t s comng from locaton B wth k recevers n use; recever from locaton ; f ( S ) s the value of the PDF S s the RSSI observed at f at the RSSI value S ; and f ( S ) s the value of the PDF B f B at the RSSI value S. Equaton (4) quantfes probablty of erroneous dentfcaton n a probablstc locaton determnaton system. Ths equaton helps n further analyss of the locaton error wth and wthout spatal dversty and to understand the mpact of number of recevers on the locaton accuracy, whch are presented n subsequent sectons. Next we present analytcal results wth our proposed scheme wth spatal dversty where we demonstrate that spatal dversty enhances locaton accuracy and mnmzes error. B. Spatal Dversty and Locaton Determnaton Lemma 3.1 (Varance Reducton wth Spatal Dversty): For an ndoor transmtter and recever locaton par wth Raylegh dstrbuton of sgnal strength, the varance n the sgnal strength dstrbuton s reduced when the proposed selecton combnng approach

29 16 wth hghest RSSI beng the crteron s employed on two uncorrelated fadng envelopes, compared wth usng a sngle nput source. Proof: Let the PDFs of RSSI from a gven transmtter locaton for the two uncorrelated fadng channels be gven by f 1 and f 2, and the cumulatve dstrbuton functons (CDF) by F 1 and F 2. But snce the spatally dverse antennas provdng the uncorrelated fadng channels are closely located, we assume that these two antennas share smlar probablty dstrbutons of RSSI for a gven transmtter locaton. Hence, f ( S) = f ( S); F ( S) = F ( S); S (5) It s to be noted that though the dstrbutons are smlar, the sgnal strength at any gven tme from the dstrbutons resultng from the antennas nputs s completely ndependent and uncorrelated (dfferent) due to separaton between them. t any gven tmet, let S ( t ) and 1 S ( ) 2 t represent the observed RSSI values on the two ndependent uncorrelated channels. By applcaton of the proposed selecton combnng approach where the antenna wth hgher nstantaneous RSSI s selected at all tmes, we now evolve a new RSSI parameter S ( t) from the RSSI values observed on the two antennas where select S ( t) = max( S ( t), S ( t)) (6) select 1 2 Let the PDF and CDF of ths resultng RSSI parameter S ( t) from the proposed selecton combnng be gven by f new select and F new respectvely. By defnton of the cumulatve dstrbuton functon, f F represents the CDF of a random varable x, for any value x, F( x ) represents the probablty that the random varable x s less than x. Hence by defnton, the CDF Fnew ( S ) represents the probablty that Sselect ( t) s less than S.

30 17 Snce, Sselect ( t) s the maxmum of S ( t) and S ( t ), t follows that both S ( t) and S ( ) 2 t have to be less than S. Therefore, F ( ) ( ) ( ) ( ( )) new S F S F S F S 2 = 1 2 = 1 (7) where F ( S) s the cumulatve dstrbuton functon of RSSI of the new parameter from new the proposed selecton combnng approach and F ( ) 1 S s the CDF of RSSI on ether of the nput sources. It has been shown n the lterature that ndoor propagaton follows a Raylegh model and results n a Raylegh dstrbuton of receved sgnal strength [19]. Let us assume, therefore wthout loss of generalty, that the RSSI dstrbutons on the nput sources follow a Raylegh dstrbuton wth a scale factor of s. Then the cumulatve dstrbuton functon [20] can be defned as 2 2 2s S F ( ) 1 1 S = e (8) Substtutng (8) nto (7)results n 2 S 2 S 2 2 2s 2 s F ( S) = ( F ( S)) = 1 2e + e (9) new s Dfferentatng (9) yelds f ( S) = 2 f ( S) f ( S) (10) new s s 2 where f ( S ) s the PDF of the Raylegh dstrbuton wth the scale parameter of s 2 s 2 and f ( S ) s the PDF of the Raylegh dstrbuton wth a scale parameter of s whch s s the same as f ( ) 1 s. The orgnal dstrbuton wth a scale parameter of s and probablty densty functon f 1 ( s) = f ( s) has a varance of s π σ1 = s 2- = s whle the

31 18 probablstc dstrbuton of the evolved RSSI parameter from the proposed selecton combnng method wth probablty densty functon fnew( S) = 2 fs( S) f ( S) can be s 2 shown to have varance of 2 2 (12+(4 2-9) π ) 2 σ new = s = s. Snce the scale 4 parameter of the Raylegh dstrbuton, s, s a real number, t s obvous that f ( S) has a lower varance than f 1 ( S ). Thus, the proposed method of selecton combnng of two uncorrelated fadng channels wth smlar sgnal strength probablty dstrbutons results n a lower varance wth a factor of approxmately 13% compared to the sngle branch new case. Theorem 3.1 (Improved Locaton Determnaton wth Spatal Dversty): For a gven number of recevers, use of spatal dversty renders mproved locaton accuracy for a pre-proflng based probablstc WLN locaton determnaton system. Proof: Let us consder a smple locaton dentfcaton system agan wth two locatons and B and a sngle recever. Let the sgnal strength dstrbutons from both locatons and B be profled at recever n the offlne phase as detaled n Secton III. Let these dstrbutons have probablty densty functons f and f B, as shown n Fg. 4 Let the mean of f be µ and ts standard devaton be σ. Smlarly, let the mean of f B be µ B and ts standard devaton beσ B. Let us ntally assume µ < µ (The opposte case s also handled later). We defne S( f = f ) as the B value of RSSI at whch f ( S) = f ( S). B B

32 19 fb new f f B S( f = f ) B S( f = ) fb new Fg. 4. Reducton n error area from spatal dversty s derved n Secton III, the probablty that a transmsson from locaton s wrongly dentfed as orgnatng from locaton B usng only the sngle recever n the onlne phase s gven by the probablty of obtanng an RSSI value S from locaton at recever, for whch the condton f ( S ) > f ( S ) s satsfed. It can be seen from Fg. 4 B that the range of S over whch f ( S ) > f ( S ) s gven by S( f = f ) < S <. The B B probablty of observng an RSSI value n ths range at recever from a transmtter placed at locaton s gven by the ntegral of f ( S ) over ths nterval. The ntegral s gven as B P = f ( S) ds (11) S ( f = fb ) where B P represents the probablty of dentfcaton of a transmtter at locaton as f t s at locaton B based on the prevously recorded sgnal strength dstrbutons from

33 20 locatons and B at recever, S( f = f ) represents the RSSI value at the recever B where the PDFs from locatons and B are equal to each other, and f ( S) represents the PDF of the RSSI dstrbuton at the recever from locaton. Now, consder that by a sutable method (n our case, spatal dversty and the proposed selecton combnng approach), the varance of the sgnal strength dstrbuton at the recever from locaton B s reduced to σ B new and the PDF correspondng to ths dstrbuton s fb new as shown n Fg. 4 where σ σ B new < B (12) We also defne the RSSI value at whch the PDF as S( f = ). f B new Now, fb new meets f S( f = f ) > S( f = f ) (13) B new B On smlar lnes as n (11), the probablty of wrongly dentfyng a transmsson from locaton as orgnatng from locaton B can be derved as B Pnew = f ( S) ds (14) S ( f = fb new ) where B P new s the probablty of dentfcaton of locaton as locaton B based on the new sgnal strength dstrbuton from a transmtter at locaton B at recever wth reduced varance. But, from (13) and snce f ( S) s always postve, P B < P. (15) B new

34 21 Now consder the second case where µ 1 > µ 2. The error s gven by S ( f = fb ) B P = f ( S) ds (16) Once agan, we assume that the sgnal strength dstrbuton at the recever from locaton B s by sutable means (n our case, Spatal dversty), altered to fb new wth varance σ B new where σ σ B new < B (17) Then t follows that S( f = f ) > S( f = f ) (18) B new B The error now becomes S ( f = fb new ) B Pnew = f ( S) ds (19) But from (18) and snce f ( S ) s always postve, P < P. Thus for B B new both µ 1 > µ 2 and µ 1 < µ 2, the probablty of locaton beng wrongly dentfed as locaton B s shown to be reduced f the varance of the RSSI dstrbuton from locaton B s reduced. Smlarly, t can be shown that reducng the varance of f ( S ) wll reduce the probablty of wrongly dentfyng a transmsson from an object at locaton B as orgnatng from locaton. Thus, reducton n varance of both dstrbutons s proven to effectvely reduce locaton determnaton error. Lemma 3.1 ndcates that the proposed method of selecton combnng of two uncorrelated nput sources from applcaton of spatal dversty reduces the varance of the receved sgnal strength dstrbutons. On the other hand, Theorem 3.1 shows that by

35 22 usng spatal dversty, the accuracy of determnng locaton of an asset equpped wth a transmtter s enhanced. Hence, use of spatal dversty wth proposed method of selecton combnng s shown to reduce error n locaton determnaton n sgnal strength based systems. Next we present how ncreasng the number of recevers wll ndeed enhance the locaton accuracy. C. Number of Recevers Theorem 3.2 (Locaton ccuracy wth Number of Recevers): For a pre-profled sgnal strength based probablstc WLN locaton determnaton system, the locaton accuracy wth k+1 recevers s better than the locaton accuracy wth k recevers for all k > 0. Proof: Consder frst the smple case of a system wth two locatons and B and k recevers. s derved n (4), the probablty P B k of a transmsson orgnatng from a transmtter at locaton beng wrongly dentfed as orgnatng at locaton B n ths system wth k recevers s gven by k k B Pk = P f ( S) < fb( S ) = 1 = 1 (20) where f s the PDF of the pre-profled RSSI dstrbuton at recever from a transmtter at locaton obtaned n the offlne phase, f B s the PDF of the pre-profled RSSI dstrbuton at recever from a transmtter at locaton B obtaned n the offlne phase, s the RSSI value receved from locaton at recever n the onlne phase, f ( S ) s S the value of the probablty densty functon f at RSSI value of S, and f ( S ) s the B B

36 23 value of the probablty densty functon f at RSSI value of S. Now, consder addng a B recever to the system resultng n k + 1 recevers. The probablty of a transmtter located at beng wrongly dentfed as at B s gven by k+ 1 k+ 1 B Pk + 1 = P f ( S ) < fb( S ) = 1 = 1 (21) B where P k+ 1 s the probablty of wrongly dentfyng a transmsson from locaton as f t s comng from locaton B wth k + 1 recevers n use. Let k 1 S + be the observed RSSI value at recever k + 1 from locaton n the onlne phase, and thus also a random varable followng the dstrbuton wth PDF k 1 f +. Snce k 1 S + follows the dstrbuton wth PDF k 1 f +, t can be proved that k + 1 k + 1 ( B ( ) ) ( ( ) ) E f S E f S (22) From (20) through (22), t follows that B B Pk + 1 Pk (23) Hence, for a system wth two locatons, the probablty of a locaton beng dentfed wrongly as the other reduces wth an ncrease n the number of recevers. Now, consder a system wthl locatons 1, 2, 3L l and k recevers. In ths system, when a transmsson s observed, the measured RSSI values at each recever are conveyed to and compled at a central server. For each reference pont, the probablty of the transmsson havng orgnated at that pont s calculated. Ths probablty s gven by the product of ndvdual probabltes of observng the measured RSSI values at each recever ndvdually when the transmtter s at the specfc locaton. Fnally, the reference pont wth the maxmum probablty s selected as the estmated locaton of the

37 24 transmtter. For a transmsson from locaton to be correctly dentfed wth k recevers n the system, the estmated probablty of recevng the observed set of RSSI values at the k recevers must be greater than the estmated probablty of recevng them from any of the reference locatons ; j 1,2 L l; j. Ths s mathematcally gven as j P k j = (1 ) j 1,2, Ll ; j P k (24) j where P k s the probablty of dentfyng locaton as j wth k recevers n the system. The above equaton states that the probablty of correct dentfcaton s the product of complement of the probablty of all possble wrong dentfcatons. Now, by addng a recever to the system, the probablty of correct dentfcaton becomes j k 1 P + = k + 1 j 1,2, Ll ; j P (1 ) (25) P j where k+ 1 s the probablty of dentfyng locaton as for any j; j 1 L l, j, j wth k + 1 recevers. But j j k 1 Pk P + (26) Hence j j Pk + 1 > Pk j 1,2, Ll ; j j 1,2, Ll ; j (1 ) (1 ) (27) Therefore, P + P (28) k 1 k Hence, t s proven that the probablty of a locaton beng correctly dentfed mproves wth an ncrease n the number of recevers.

38 25 The theorems presented above show that the accuracy mproves both wth spatal dversty and ncreasng the number of recevers. Next the proposed locaton determnaton schemes are ntroduced, whch are bult upon the known schemes, determnstc and probablstc methods, from the lterature. D. Locaton Determnaton lgorthm Both probablstc and determnstc technques from the lterature are evaluated wth and wthout spatal dversty. Further, the applcaton of dversty and the proposed method of selecton combnng on top of ether technque s dscussed. 1) Probablstc technque smplfed verson of HORUS [8], whch s a probablstc technque, s consdered n ths work. grd s ntally constructed to provde the reference ponts for proflng. The coordnates of these reference ponts on the grd are measured and recorded for mappng RSSI values to the locaton. The technque begns wth an offlne phase where the grd ponts are profled for a perod of tme to record n samples of the sgnal strength value at each recever from each of the l reference grd ponts. To smplfy the storage problem, the sgnal strength values receved from each of the reference grd ponts at each recever are mapped to a Gaussan dstrbuton. The mean and varance of each of these dstrbutons s stored rather than storng all the RSSI values receved at each recever from each reference pont. In other words, gven n sgnal strength samples from locaton X at recever, the estmate for mean sgnal strength at recever from any locaton X s gven by n 1 ˆ µ = SX ( k) (29) n k= 1

39 26 where ˆµ s the estmated mean of the RSSI dstrbuton and S ( k) s the k th sgnal strength sample from locaton X at recever. The varance s estmated as X 1 ˆ σ µ (30) n 2 2 = [ S ( ) ˆ X k ] n k= 1 where ˆ σ 2 s the estmated varance of the RSSI dstrbuton and S ( k) s the k th sgnal strength sample from locaton X at recever. ctual locaton determnaton s accomplshed n the onlne phase by usng the mappng constructed from the offlne phase. For each recever, the probablty of recevng the observed RSSI value from each of the reference locatons s calculated usng the Gaussan probablty functon as S ( s ˆ µ x ) /(2 ˆ σ ) j x j P( S / x j) = e ds (31) S 0.5 σ x 2π x j x j j where ˆ µ and ˆ σ are the pre-profled estmates for mean and standard devaton of X receved sgnal strength at recever from locaton x and P( S / x ) s the probablty of j j recevng RSSI value S from locaton x j at recever. Snce the XBee modules quantze the RSSI values, the PDF values are ntegrated over a range of RSSI values between 0.5 to The process s repeated for all x ; j 1L N and for all recevers ; 1L k. j Now, the overall probablty P( S / x j ) that the set of observed RSSI values at all recevers orgnates from a reference locaton x j, s gven as k P( S / x ) P( S / x ) = (32) j j = 1 where S = { S}; 1L k and S s the observed RSSI at the th recever.

40 27 In the end, a sorted lst of the locatons s generated n descendng order of ther probabltes. The coordnates of only the four reference locatons wth the hghest probabltes are used n locaton determnaton. The use of four locatons makes ntutve sense snce any pont can be enclosed by a square wth four closest neghbors. The coordnates of each of these four locatons are multpled wth ther correspondng probabltes and a weghted averagng s performed. The result of ths operaton s returned as the locaton. Ths process s smlar to the center-of-mass technque [24]. 2) Determnstc technque The frst step n the determnstc technque [7] also nvolves constructon of a reference grd and generatng coordnates of reference grd ponts. In the offlne phase, RSSI sgnature vectors are collected from all reference grd ponts at dfferent tmes n a day and durng the week. These dfferent profles are used to arrve at the average sgnal strength value from each reference pont on the grd at each recever. In the onlne phase, a sgnal strength vector s constructed from the RSSI values observed from a transmtter at each of the recevers. The Eucldean dstance from ths vector to each of the averaged profle entres s taken. The reference ponts are now arranged n the order of descendng Eucldean dstances. The four reference ponts wth the lowest Eucldean dstance from ther RSSI vectors recorded n the offlne phase to the measured RSSI vector n the onlne phase are used n locaton determnaton. The coordnates of these four ponts are averaged to provde a locaton. E. Dversty and Combnng There are two methods of mplementng the proposed method of selecton combnng on top of spatal dversty usng the probablstc and determnstc schemes. It

41 28 can be mplemented on the hardware level usng a swtch for selectng the antenna wth hgher RSSI and usng a sngle recever as shown n Fg. 5 (a). second method of mplementaton would be at the software level, where sgnal strength values are recorded on two spatally separate recever unts and the hgher RSSI value s selected whle processng as shown n Fg. 5 (b). We use the latter mplementaton n our testbed as t s much easer to mplement, but from the vew of cost-effectve mplementaton, not requrng addtonal processng, the former mplementaton s more sutable to a true realtme locaton determnaton. Fg. 5. (a) Hardware mplementaton of spatal dversty and proposed selecton combnng approach (b) software mplementaton In locaton determnaton wthout usng dversty, only one recever from each par s used n analyss, n both the onlne and offlne phases. By contrast, n usng the system wth dversty appled, each par of recevers s vewed as a sngle recever. For every packet receved and RSSI reported, the maxmum of the two RSSI values s taken

42 29 for each par. Ths software-level selecton s appled before usng the RSSI values for processng n both onlne and offlne phases. Thus, the locaton determnaton algorthm becomes a hgher layer of processng when the combnng layer s added as shown n Fg. 6. Fg. 6. Layered representaton of the proposed method of selecton combnng F. Trackng, veragng and Predcton Detecton of movement of an asset, trackng t and predctng ts locaton are areas relevant to locaton determnaton. The frst applcaton of locaton trackng can be understood from [25] where a vterb-based scheme s developed to lmt unusual asset movement patterns by lmtng moblty between consecutve locatons n tme. Whle such an approach wll enhance the accuracy for a statonary or slow-movng asset, assets possessng consderable moblty are lkely to suffer from a loss of accuracy snce the system works on the bass of selectng the path that ensures least dstance of travel of the tracked asset. Further, the approach does not detect whether the asset s n moton or not.

43 30 Locaton determnaton based on sgnal strength results n scatterng of estmated locatons around a small area over tme. Over a small nterval of tme, such random scatterng may exhbt drectvty n moton. Usng a small tme wndow to observe estmated locaton coordnate varatons of a statonary asset to detect drected moton may lead to msnterpretng asset movement status as movng. Increasng the observaton wndow sze to a large value wll mprove detecton accuracy but wll cause a sluggsh response n the moton detecton algorthm. To solve ths problem, we ntroduce a twolevel system of observaton and averagng. Estmated moton trends over multple consecutve, yet overlappng observaton wndows are averaged. Ths process, whle elmnatng the sluggshness of response, ensures suffcent certanty n determnng movement status. The proposed algorthm s ntroduced as follows. In the moton detecton algorthm, cumulatve moton n ether the x or y drecton s observed for determnng movement status. RSSI values are obtaned from the asset every second and locaton determnaton s carred out usng ether the probablstc or determnstc method wth or wthout applyng dversty. Only contnuous cumulatve drected moton n the x or y drecton or both s treated as moton. t the observng level, a wndow sze of n s employed and at the averagng level, the wndow s of sze m. The moble transmtter s made to transmt once every second, resultng n one set of located coordnates every second. buffer of the last n sets of estmated locaton coordnates s mantaned n the system. The x and y coordnate varaton between each par of consecutve locatons n ths buffer s added up over all n 1 ntervals between the n locatons. Mathematcally, at tme t, these summed values can be evaluated as

44 31 ( ) xn( t) = x( t) x( t n + 1) (33) where x( t ) s the located x coordnate at tme t and x( t n + 1) s the located x coordnate at tme t n + 1. Smlarly, ( ) yn( t) = y( t) y( t n + 1) (34) where y( t ) s the located y coordnate at tme t and y( t n + 1) s the located y coordnate at tme t n + 1. Ths completes the lower level movng wndow average. Now, for the next level, the last m calculated values of xn and yn are stored n a second buffer. The mean values from these buffers provde the moton trend varables mean _ x and mean _ y for the system. These are formulated as t 1 mean _ x = xn( ) (35) m = t m + 1 where mean _ x s the estmated trend for the x coordnate varaton over n 1 tme ntervals. Smlarly, t 1 mean _ y = yn( ) (36) where mean _ m = t m + 1 y s the trend for the y coordnate varaton over n 1 tme ntervals. The resultant total movement from the trended x and y s calculated as the square root of the sum of squares of the two trend values. If ths value s above a gven threshold, t ndcates contnuous cumulatve drected moton of the tracked asset n a certan drecton. Hence, we determne that the asset s movng. If the total trended movement s below the threshold, the asset s declared statonary. Ths status reportng s based on the current and prevous m + n 2 estmated locaton coordnates and hence results n a delay

45 32 m + n of 1 tme unts n moton status reportng. In the system under test, we use a 2 value of 10 for both n and m. Ths value results n substantally szed averagng wndows at both levels whle not resultng n a huge delay n reportng the movement status of the asset. For example, a value of 10 for both n and m would result n a delay of nne tme unts (seconds) n reportng the movement status, whle usng a value of 15 for both n and m would result n a delay of fourteen tme unts (seconds). Further, a hgher averagng wndow sze results n a sluggsh response n the moton detecton algorthm when the state of the asset changes from movng to statonary or vce versa Thus a trend of x and y drecton movement of the asset over nne ( n 1) tme ntervals s obtaned as mean _ x and mean _ y, respectvely. The process s detaled n Fg. 7. smlar method s developed for averagng located coordnates to mprove accuracy. Once agan, an averagng system of small wndow sze wll not provde suffcent accuracy whle a large averagng wndow wll enhance accuracy, but result n sluggsh response n updatng the locaton when the tracked asset moves. To both mprove accuracy and locaton update response tme, we devse a lower averagng level to remove the small-tme-scale scatterng of located coordnates, and perform further averagng of the resultng averaged coordnates to enhance accuracy whle ensurng a quck system update when the asset locaton changes. Here, n and m are used as wndow szes for two levels of movng wndow averagng. In the frst movng wndow, at any gven tme, the set of current estmated locaton coordnates as well as the n 1 prevous located coordnates are averaged. Ths averagng process s mathematcally depcted as

46 33 t 1 x ( t) = x( ) (37) mean n = t n + 1 where xmean ( t) s the mean of the current and last n 1 located x coordnate values, and x( ) s the located x coordnate value at tme t =. Fg. 7. Calculaton of averaged cumulatve x and y moton for nne tme unts Smlarly, t 1 y ( t) = y( ) (38) mean n = t n + 1

47 34 where ymean( t) s the mean of the current and last n 1 located y coordnate values, and y( ) s the located y coordnate value at tme t =. In the hgher level movng wndow average, the mean of the current and prevous m 1 averaged x and y coordnate values s used as the estmated locaton. Ths secondary level of averagng s gven as t 1 mean _ x = x ( ) (39) m = t m + 1 mean where mean _ x s the averaged locaton x coordnate resultng as a functon of x coordnate values from the current and prevous m + n 2 locaton estmates. Smlarly, t 1 mean _ y = y ( ) (40) m = t m + 1 mean where mean _ y s the averaged locaton y coordnate resultng as a functon of y coordnate values from current and prevous m + n 2 locates. Thus, the reported m + n locaton suffers a tme lag of 1 tme unts from the current locaton n locaton 2 reportng, thus offerng mproved accuracy at the cost of delayed locaton reportng. In the system under test, parameters m and n are set to 10, resultng n a nne tme unt delay n locaton reportng. The averagng s detaled n Fg. 8. The reported trend varables mean _ x and mean _ y represent the expected movement n the x and y drectons from the averaged locaton estmate over a perod of n 1 seconds. To calculate the current locaton from the averaged locaton wth a m + n delay of 1 seconds, we assume lnear moton of the asset and proportonately 2 m + n scale the x and y movement trend values to account for x and y moton over 1 2

48 35 tme unts. Thus, addng these scaled trend values drectly to the averaged locaton allows an estmaton of the current poston of the asset wth a hgher level of accuracy. Thus, the current poston s predcted based on the averaged locaton estmate as m + n m + n 1 1 asset _ locaton( t) = [ mean _ x + 2 mean _ x, mean _ y + 2 mean _ y] n 1 n 1 (41) where asset _ locaton( t ) represents the estmate of the poston of the asset at tme t, m + n mean _ x and mean _ y represent the located coordnates of the asset at tme t based on averagng, and mean _ x and movement for a perod of n 1 tme unts. mean _ y are the expected trend values n asset Fg. 8. veragng of located coordnates to report poston (lag of 9 unts)

49 36 By smlar lnear scalng and assumpton of lnear asset movement, a trend value m + n can be developed for more than 1 seconds. Let us assume that we ntend to 2 predct the asset locaton k tme unts nto the future. Ths predcton requres an m + n estmaton of the asset movement for a tme perod of + k 1 tme unts from the 2 m + n averaged estmate snce t suffers a lag of 1 unts. Thus, the x and y movement 2 trends are scaled by a factor of m + n + k 1 2 n 1 for ths predcton. Thus, the poston of the asset k tme unts nto the future s gven as m + n m + n + k 1 mean _ x + k 1 mean _ y 2 2 asset _ locaton( t + k) = [ mean _ x +, mean _ y + ] n 1 n 1 (42) where asset _ locaton( t + k) s the estmated locaton of the asset k tme unts nto the future. For demonstraton, n the system under consderaton, we predct the asset locaton one tme unt nto the future. Ths mples a scalng factor m + n k of 2 = 2 =. Usng ths scalng factor and assumng lnear n moton of the asset, the asset locaton one second nto the future s estmated as 10 mean _ x 10 mean _ y asset _ locaton( t + 1) = [ mean _ x +, mean _ y + ] (43) 9 9 where asset _ locaton( t + 1) s the estmated locaton of the asset one tme unt nto the future (tme t+1), mean _ x and mean _ y represent the located coordnates of the asset based on averagng at tme t 9 and 10 mean _ y 10 mean _ y and are the scaled 9 9

50 37 trend values n asset movement n the x and y drectons, respectvely, for a perod of ten tme unts. The advantages of such a predcton are several. One of the possble applcatons s enhancement of network performance by optmzng access pont handovers based on estmated future poston. ccuracy of the moton detecton, trackng and predcton schemes are dscussed n Secton IV for statonary and movng targets for probablstc and determnstc methods wth and wthout applyng spatal dversty.

51 38 IV. EXPERIMENTL RESULTS ND NLYSIS. Testbed and Implementaton G4-SSN motes developed at UMR, shown n Fg. 9, were used for testng. They have been used n pror work relatng to wreless sensor networks [21], [22]. The wreless networkng medum chosen was IEEE PHY. ll nodes are equpped wth XBee pro rados from Maxstream [23] wth 18 dbm of transmt power. To generate spatal dversty, two motes were placed at a dstance of 25 cm ( 2λ ) from each other, as shown n Fg. 10. Fg. 9. UMR G4-SSN embedded wreless sensor networkng platform Fg. 10. UMR-SLU G4-SSN motes arranged for creatng spatal dversty wth a separaton of 25 cms