Position location via geometric loci construction
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 WO2006070211A1 WO2006070211A1 PCT/GR2005/000036 GR2005000036W WO2006070211A1 WO 2006070211 A1 WO2006070211 A1 WO 2006070211A1 GR 2005000036 W GR2005000036 W GR 2005000036W WO 2006070211 A1 WO2006070211 A1 WO 2006070211A1
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 ms
 transmitters
 attenuation
 pair
 points
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 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
 G01S5/00—Positionfixing by coordinating two or more direction or position line determinations; Positionfixing by coordinating two or more distance determinations
 G01S5/02—Positionfixing by coordinating two or more direction or position line determinations; Positionfixing by coordinating two or more distance determinations using radio waves
 G01S5/14—Determining absolute distances from a plurality of spaced points of known location

 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
 G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
 G01S11/02—Systems for determining distance or velocity not using reflection or reradiation using radio waves
 G01S11/06—Systems for determining distance or velocity not using reflection or reradiation using radio waves using intensity measurements

 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
 G01S5/00—Positionfixing by coordinating two or more direction or position line determinations; Positionfixing by coordinating two or more distance determinations
 G01S5/02—Positionfixing by coordinating two or more direction or position line determinations; Positionfixing by coordinating two or more distance determinations using radio waves

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04W—WIRELESS COMMUNICATIONS NETWORKS
 H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
Abstract
Description
DESCRIPTION
Position Location via Geometric Loci Construction.
The scientific field of the invention is wireless communications and electromagnetic waves propagation. More specifically, part of the invention falls into the field of position location, or estimation of the location of a wireless device.
The calculation of the propagation attenuation factor, in relative research, is usually performed as part of a larger procedure, related to propagation modeling. In the literature, there are a large number of relative papers, such as in [l][8]. In these papers, the positions of both transmitter and receiver are known, and the object of research is the extraction of a law of propagation, and/or the calculation of the propagation attenuation factor, which determines the loss of signal strength with respect to the transmitterreceiver distance.
Location of a wireless unit is also subject of extended research during the last years. As an example, consider the development of Global Positioning System (GPS). In GPS, an extra component, known as GPS receiver, is needed at the user's side, in order for the system to work. This means extra cost and size for the wireless unit. Furthermore, GPS suffers in indoor environments, due to large loss of signal strength during penetration of concrete walls, which means that GPS can not be used in indoor LANs.
There are a number of advanced position location (PL) techniques, alternative to GPS, for wireless device positioning. These techniques are known as RadioFrequency (RF) or network based techniques, and are categorized as Direction Finding systems (DF systems) and Range Based systems (RB systems) [9]. DF techniques estimate the position location of a mobile station (MS) by measuring the AngleOfArrival (AOA) of the incoming signal, from the MS to a sufficient number of Base Stations (BSs). (Hereinafter, the term BS will generally refer to a fixed transceiver, with known position, and not only to cellular systems BSs.) On the other hand, RB techniques estimate the position of a MS by measuring the distance between the MS and a sufficient number of BSs. RB techniques may be further categorized as ranging, range sum or range difference, if range estimates are based on TimeOfArrival (TOA), TimeSum OfArrival (TSOA) or TimeDifferenceOfArrival (TDOA) measurements of the incoming signal, respectively. Furthermore, distance measurements may be implemented based on the signal strength of the incoming signal. DF techniques are used in macrocell networks, such as cellular telephony networks, where
BSs and the MS are located at large distances, and there is also a large difference between the heights of the antennas of the BSs and that of the MS. Advanced AOA measurement techniques, such as MUSIC or ESPRIT are used [9J[Il]. A major disadvantage of these techniques is the need for expensive equipment and hardware for the AOA estimation [12], such as accurately calibrated antenna arrays etc. Furthermore, in microcells, BSs may be placed at heights below building rooftops. This case also occurs in indoor networks (such as WLANs). In this and other cases, multipath propagation strongly affects AOA techniques, because multiple replicas of the signal arrive at the receiver from different directions [12]. Therefore, DF systems may not perform accurately in such cases.
RB techniques based on TOA measurements are also widespread. These techniques also suffer from multipath propagation, because multiple replicas of the signal arrive at the receiver at different times of arrival. Furthermore, in NonLineOfSight (NLOS) conditions, only reflected and scattered replicas of the signal arrive at the receiver, making TOA measurements and position location even more inaccurate. Finally, these techniques also need expensive and accurately synchronized hardware (clocks) at the BSs.
RB techniques, which utilize signal strength measurements, have the advantage that they do not need expensive hardware, because signal strength measurement is implemented using inexpensive offtheshelf components. These systems use either models of propagation and topographical maps of the area of coverage, or insitu signal strength measurements in selected locations. In the literature, these systems are used in outdoor [13] and indoor environments [14][18]. The disadvantage of these techniques is exactly the need for topographical maps or insitu measurements. Using a statistical propagation model only, yields large inaccuracies, due to the largescale fading phenomenon. Largescale fading is caused by shadowing effects of large buildings or natural features [19][21]. Even when topographical maps are available, the achieved accuracy is usually not adequate. Furthermore, insitu measurements are an extremely expensive procedure, and are not always applicable, such as in emergency situations.
The invention, with minimum input the positions of a sufficient number of BSs, and the signal strength from each BS atthe MS's position, determines which of the BSs have the same (or contiguous) attenuation factor to the MS, calculates these factors and estimates the MS's position. This is accomplished by using propagation laws and constructing proper geometric loci. The core of the invention is the construction of the geometric loci, as well as a method for revealing the values of the attenuation factors and the position of the MS. The invention may be incorporated into any wireless network (cellular networks, wireless local area networks, sensor networks etc.), since it may be embodied into existing and inexpensive network equipment (e.g. 802.11 standard mandates on received signal strength indicators [RSSI]). Furthermore, the invention may be incorporated to already existing and functional networks. It is especially suited for operation in unknown environments (e.g. sensor networks), since topographical maps are not needed. The costly and sometimes impracticable procedure of onthefield premeasurements is avoided. Additionally, expensive equipment, such as directional, or switchedbearn, or adaptive antenna arrays, is no longer required. The invention overcomes most of these problems, which are characteristic of existing location methods, as aforementioned. For these reasons, the invention offers the possibility of locating a wireless unit with minimum prerequisites and inexpensive equipment.
Attached figures present the principles of the invention, and offer an intuitive understanding.
In figure 1, an example of two Base Stations (BSs), namely BSl, BS2, with the same attenuation factor to a Mobile Station (MS) is presented.
The example of figure 1 is further analyzed in figure 2. If an arbitrary attenuation factor is presumed, then, by measuring the received signal strength by the MS from each BS, two circles will be created. The MS must lie on these circles. Therefore, for this arbitrary attenuation factor, the MS must lie on either of the two intersection points, Pl, P2, of these circles (see figure 2). If no intersection point exists, then the presumed attenuation factor is a priori rejected. In figure 3, the evolution of the case study presented in figure 2 is illustrated. If the arbitrary attenuation factor scans an (arbitrary) interval, then, two circle groups, Cl , Cl , are constructed. The circles of these groups are centered at the fixed positions of BSl and BS2 respectively, and their radii are calculated using the instantaneous hypothetical value of the attenuation factor (similarly to figure 2 description). The geometric locus of the intersection points of the groups Cl, Cl is denoted by T_{a}__{C2} in figure 2. The MS must lie on this locus, and the locus represents all possible locations of the MS.
In figure 4, the case study becomes a little more complicated. Let there be a third BS, namely BS3, with the same attenuation factor to the MS as BSl and BS2. Then, similarly as aforementioned, a third circle group, namely C3 , is constructed. In figure 4, the geometric loci T^{1} _{C}i_{C}i ' ^cic_{3} of the intersection points of the groups C1C2 and Cl C3 respectively are illustrated. The locus T_{C2}__{C3} of the intersection points of the groups C2 C3 is not illustrated for clarity, since it bears no further information on the location of the MS. The MS must lie on the intersection points between the loci T_{cι}__{C2} , ^_{1}._{C3}, T_{C1}__{C3}, which are illustrated in figure 4 as Pl and P2. The reason why T_{C2}__{C3} bears no further information, is because the intersection points between the loci are not further restricted if T_{C2}__{C3} is used instead of T_{C1}__{C2} or T_{C1}__{C3}. The case of a fourth BS, namely BS4, with the same attenuation factor to the MS as BSl,
BS2 and BS3, is presented in figure 5. Similarly, the circle group C4 is constructed. Figure 5 presents the geometric loci T_{cι}__{C2} , T_{cι}__{C3} , T_{cι}__{C4}. The locus T_{CX}__{CA} corresponds to the intersection points of the groups ClCA . The MS possible location is restricted to an unambiguous location, namely the joint intersection point of the loci T_{cι}__{C2} , T_{cι}__{C3}, T_{cι}__{C4} .
This point is denoted as P in figure 5.
The case of four BSs, which have similar (contiguous) but not equal attenuation factors to the MS, is presented in figure 6. The geometric loci T_{cι}__{C2} , T_{cι}__{C3} , T_{cι}__{C4} do not have a joint intersection point, as they did in figure 5. But, as the invention scans the estimator of the contiguous attenuation factors, there is a value of the estimator for which the sum of distances between the loci is minimal. This value may be used as the estimate of the contiguous attenuation factors, and the position of the device may be estimated as the average of the points
Pl, P2 and P3 of figure 6. The points Pl, P2 and P3 are the points of the geometric loci which correspond to the minimum sum of distances between these loci. The real MS position is not displayed for clarity.
In figure 7, another case study is presented. In this study, there are five BSs, namely BSl,
BS2, BS3, BS4, BS5. Let BSl, BS2 and BS3 have contiguous attenuation factors to the MS.
Let BS4 and BS5 have contiguous attenuation factors to the MS, but not contiguous to the ones of BSl, BS2 and BS3. The invention scans all possible values of the two estimators of these factors. Thus, the circle groups Cl , Cl , C3 , CA , C5 and the geometric loci T_{cι}__{C2} , T_{cι}__{C3} ,
T_{CA}__{C5} are constructed, in a way similar to the one aforementioned. The locus T_{C4}__{C5} corresponds to the intersection points between the groups CA  C5 . The values of the estimators which correspond to the minimum sum of distances between the respective points of the loci, are used as the estimates of the real attenuation factors. The location of the device is estimated as the average of the point Pl, P2 and P3 of figure 7. These points correspond to the estimates of the real attenuation factors. The real location of the MS is not displayed for clarity.
The case of six BSs, namely BSl, BS2, BS3, BS4, BS5, BS6, is presented in figure 8. Let
BSl and BS2 have contiguous attenuation factors to the MS. Let BS3 and BS4 have contiguous attenuation factors to the MS, but not contiguous to the ones of BSl and BS2. Finally, let BS5 and BS6 have contiguous attenuation factors to the MS, but not contiguous to the ones of BSl, BS2, BS3 and BS4. Similarly as in the four and five BSs cases, the circle groups Cl, C2, C3 ,CA, C5 , C6 and the loci T_{cι}__{C2} , T_{C3}__{C4} , T_{C5}__{C6} are constructed. Again, the values of the attenuation factors estimators, which correspond to the minimum sum of distances between the loci, are used as the estimates of the real attenuation factors. The location of the device is estimated as the average of the points Pl, P2 and P3 of figure 8. These points correspond to the estimates of the real attenuation factors. The real location of the MS is not displayed for clarity.
Hereinafter, it is assumed that there are a number of fixed transmitters, referred to as BSs, and a mobile receiver or wireless device/unit, referred to as MS. The terms BS and MS will generally refer to a transmitter and receiver, respectively, and should not be confused with cellular networks terminology. A number of assumptions need to be made prior to the presentation of the invention.
The MS is assumed to be placed at the unknown position (x_{AiS} , y_{MS} ) , in an arbitrary, but known, coordinates system. The MS can sense signals from a maximum number of BSs, namely N_{BSMAX} . Let N_{BSMAX} e N and N_{BSMAX} ≥ 4. The received signal strength measurement from each BS can be performed by the MS, since most current MSs have the capability of signal strength indication. However, this is not a prerequisite for the invention. Let i e {l,...,N_{BSjiWC}}, and let the ith transmitter be placed at the known position
(x_{BS j},y_{BS j}), of the same coordinates system to the MS (the ith transmitter's position can be provided by the network administrator). Consequently, the unknown distance d_{t} between the
MS and the ith transmitter will be given by d, =
•The BSs transmit to a known output power (easily provided by the network administrator). The antennas of the BSs and the MS are considered to be omnidirectional and their respective gains are considered to be known. Therefore, the reference power level, that the MS theoretically receives at Im distance from each BS, is known and denoted by P_{01}. The received signal strength at the MS's position, from each BS, is denoted by P_{1}.
The invention selects a number of BSs, namely N_{BS} , which will be used for the position location of the MS. The selection of the specific N_{BS} transmitters is based on criteria that are irrelevant to the algorithm of the invention. The main reason for restricting the number of BSs to be taken into account is computational burden, which means more time needed for the algorithm to be executed. On the other hand, a more accurate result is expected as N_{BS} increases. The user of the invention will determine the value of N_{BS} . A possible criterion for selecting transmitters is to select those transmitters with the strongest signal strength received by the MS, up to a maximum of e.g. nine transmitters (the maximum depends on the computational power available to the user of the invention). Furthermore, it should be noted, that the attenuation factor between the MS and the ith transmitter, namely n,, ranges vastly, depending on the propagation channel. Evidently, ^{n}ι ^{e} [^_{m}i_{n} '^{w} _{raa}χ] • Determining the bounds of n_{t} is irrelevant to the invention, and should be performed by the user of the invention. In practical cases, w_{min} will be around 2, and w_{raax} will be around 7 to 8, or more.
Based on the assumptions made above, consider the simple case of two BSs, namely BSl and BS2, placed at (x_{BS}ι ,y_{B}si) ^{m}d (^{x}as_{2 >}>as_{2}) respectively, and a MS placed at
(^{X} _{MS >}y_{M}s) _{>} as illustrated in figure 1. The positions of BSl and BS2 are considered known, while the position of the MS is considered unknown. The distance between the
MS and BSl, BS2, is denoted by d_{x} , d_{2} respectively, and given by:
^{d}i = T](^{X}BS2  ^{X}MS f + iy_{BS}2  y_{MS} Y (^{2})
Hereinafter, the theoretical received signal strength by the MS, at Im distance by any BS, will be assumed to be equal to P_{0} , without loss of generality. The received signal strength from
BSl and BS2, is denoted by P_{1} , P_{2} respectively, and given by [19]:
^{p}>  % ^{(3)} ^{ p}> =f ^{(4)}
From equations (3) and (4), it is shown that the received power is inversely proportional to the distance raised by an exponent. This exponent is the attenuation factor, and is denoted by W_{1}, n_{2} for BS1,BS2 respectively. The received signal strength exhibits large scale and small scale fading [19], which will be discussed further below.
The factors W_{1} , W_{2} and the distances d_{x} , d_{2} are unknown. Let W_{1} , W_{2} be equal to each other, Le. W_{1} = W_{2} = w . By using the equations (3) and (4), estimates for d_{x} , d_{2} can be
obtained, for any arbitrary value of the estimator w of w . The estimates of d_{x} , d_{2}, for an
arbitrary value of w , are denoted by d_{x} (w) , d_{2} (w) and given by:
dM) (5)
As the estimator n scans the interval [«„,_{;}„ ,«_{max}] with step n_{step} , the estimates
d_{x} in) , d_{2} (ή) are calculated by equations (5) and (6).
(The value of n_{step} is irrelevant to the algorithms of the invention. Evidently, a larger value of n_{step} implies faster execution of the algorithm and a less accurate result. On the other hand, a smaller value of n_{step} implies more accurate results with the cost of increased execution time. Determining the value of n_{step} should take into account the computational power available to the user of the invention.)
The estimates d_{x} in) , d_{2} (n) define circle groups, centered at the BSs locations. These
groups are denoted by C_{1} (x_{BSl} , y_{BSl} , d_{x} («)) , C_{2} (x_{BS2} , y_{BS2} , d_{2} O)) , i.e. by their respective centers and radii. The MS must he on the intersection points of these circles. This is illustrated
in figure 2, where an arbitrary value of n is selected (different to the real value of n ). The
intersection points Pl and P2 constrain the possible MS locations, for the specific value of n .
If for a value of n the corresponding circles do not intersect each other, then this value is discarded. If the circles are adjacent, there is only one "intersection" point and one possible MS location.
The set of all intersection points, so far defined, for all values of n e [n_{min},n_{max}] , determines a geometric locus. This locus, displayed in figure 3, is denoted by T_{C1}__{C2} . The geometric locus is a closed curve, definitely passes by the MS location, and encloses one BS. The BS enclosed is the one closest to the MS. Note that figure 3 displays a geometric locus and not a circle centered at BS2. Evidently, the MS location lies on the locus T_{CX}__{C2} .
Let there be a third BS, namely BS3, placed at (x_{BSi} , y_{BS}z ) , at a distance d_{3} from the MS, transmitting at the same power level as BSl and BS2. Let the attenuation factor of BS3 to the MS be n , equal to the ones of BSl and BS2. The power P_{3} that the MS receives from BS3 is given by:
"3 while the estimate of the distance d_{3} for an arbitrary value of the estimator n e [n_{min} , n_{maκ}] , is
denoted by di{ri) and given by:
Similarly to the aforementioned analysis, a circle group C_{3}(x_{BS3},y_{BS3},d3(n)) is constructed. Furthermore, the geometric locus T_{C1}__{C3} of the intersection points between
Q (^{X} _{BSI} j yεsi _{>} di («)) and C_{3} (x_{BS3} , J^_{53} , ds (/?)) , as well as the geometric locus T_{C2}__{C3} of the
intersection points between C_{2}(x_{BS2},y_{BS2},d2(n)) and C_{3}{x_{BS3},y_{BS3},dτ,{nγ) are constructed. The loci T_{C1}__{C2} and T_{C1}__{C3} are displayed in figure 4. The locus T_{C2}__{C3} is not displayed for clarity. The locus T_{C1}__{C3} is a closed curve, enclosing BSl, since BSl is closer to the MS than BS3. The intersection points of the two loci, denoted by Pl and P2, are also displayed in figure 4. The points Pl and P2 of figure 4, are the only possible locations of the
MS. Thus, the location of the MS and the value of n are significantly restricted. It should be noted that the locus T_{C2}__{C3} is also a closed curve, enclosing BS2. However, the locus T_{C2}__{C3} will have the same intersection points Pl and P2 with the other two loci. Therefore, the locus Zc_{2}_{C3} does ^{not} b∞e any further information on the MS location or the attenuation factor value, and is not displayed in figure 4 for clarity.
Let there be a fourth BS, namely BS4, placed at (x_{BS4}, JF^_{4}), at a distance d_{4} from the MS, and let the attenuation factor between BS4 and the MS be also n . The received power by the MS, from BS4, is denoted by P_{4} and given by:
P_{4} = ^ (9) d_{A} while the estimate of the distance between the MS and BS4, for a value of the estimator
« ^{€} Kin '"max ] ' ^{is} gϊ^{Ven b}y ^{:}
d*{n) = ( MpM Y" (10) Similarly, the circle group C_{4}(x_{BS4},y_{BS4},d4(n)) is created, and the geometric locus
!T_{C1}__{C4} of the intersection points between the groups C_{1} (X_{381}, y_{BSι},dι(n)) and
C _{4} (^{X} _{BS45} ^_{545} ^ 4 (n)) is constructed. The geometric loci T_{02}^_{3} , T_{C2}__{C4}, T_{C3}__{C4} may also be constructed. Figure 5 displays the loci T_{C1}__{C2} , T_{C1}__{C3} , T_{cι}__{C4}. Evidently, these loci have a joint intersection point, which is denoted by P in figure 5. The loci T_{C2}__{C3} , T_{C2}__{CA}, T_{C3}__{C4} do not bear additional information on the MS's location, and are not displayed in figure 5, for clarity. Consequently, the only possible location of the MS is the joint intersection point P, and the only possible attenuation factor value, is the estimate that corresponds to this point. Thus, an estimate of the attenuation factor n , and also an estimate of the MS's position, are specified. The existence of more than four BSs with the same attenuation factor to the MS_{5} will not improve the estimation of the MS's location.
The invention can also estimate the attenuation factors between four BSs and the MS, in the case where these factors are contiguous to one another instead of equal. In this case, the received signal strength from each BS is given by:
P p_{1}, = ^ d_{x} r (H)
P_{0}
P_{2} (12) d α_{2}"^{2}
Po
Ps (13) d_{3}
where n_{1},n_{2},n_{3},n_{A} are the attenuation factors between the MS and BSl, BS2, BS3 and
BS4 respectively. In this case, a common estimator n ≡ [n_{min},n_{max}] of W_{15}W_{25}W_{35}W_{4} is
generated. For each value of « e [w_{min},w_{max}] , the estimates
di(n) , di(ή) , d4(n) of the distances d_{x} , d_{2} , d_{3} , d_{4} respectively are calculated:
In this case, the constructed loci T_{cι}__{C2} , T_{cι}__{C3} , T_{cι}__{C4} do not present a joint intersection
point. However, as n scans [n_{mia} ,n_{maκ}] with step n_{step} , there are up to two corresponding
points on each locus. Therefore, the distance between two loci, for a value of n , is defined as
the minimum distance between the points of these loci, for this value of n . If for a value
72_{rø/ 1} & [n_{min} ,n_{max}] the corresponding points on locus 1 are A and B, and for a value
^{n} _{vα}i_{,2} ^{e} [^{w} _{m}i_{n} '^{ra} _{ma}χ] ^^{e} corresponding points on locus 2 are C and D, the distance between these two loci, for the specific values of attenuation factor estimators, is the minimum among the distances AC, AD, BC and BD, i.e. the distance given by:
Distαnce{n_{v} ^{~} _{αU},n ^{~} _{αh2}) = min{d(A, C)_{5} J(A_{5} D)_{5}J(B_{5} C)_{5} J(B_{3}D)) (19) where J(X_{5} Y) denotes the distance between the points X and Y. Hereinafter, the term distance between two loci will refer to the distance defined by equation (19).
Consequently, the loci T_{C1}__{C2} , T_{CX}__{C3 >} ^cic_{4} ^{me} characterized by a distance between each
other, which is a function of n . The sum of these distances is also a function of n . The
minimum distant points of the loci T_{cι}__{C2} , T_{C1}__{C3} , T_{cι}__{C4} , as n scans [^_{m}i_{n} ,^_{max}] , are used for the estimation of the MS's location. The term "minimum distant points" means that the sum of distances between the loci T_{cι}__{C2} , T_{0103} , T_{cι}__{C4} is minimum. The corresponding value of
the estimator n e [n_{min},n_{maκ}] is the estimate of the contiguous factors «_{l5}«_{25}κ_{35}«_{4}. Furthermore, the MS's location is estimated by the average of the corresponding "minimum distant" points of the loci T_{cι}__{C2} , T_{C}\__{C3} , T_{cι}__{C4} . This case is illustrated in figure 6, where the "minimum distant points" are denoted by Pl, P2 and P3. Thereby, the estimate of the MS's location is (x,y), where x and y are given by: _{χ =} X_{1} + X_{2} +X_{3} y = *±ψ* (21) where (X_{1}^_{1}) , (x_{2} ,y_{2}), C^, ^) are tlie coordinates of the points Pl, P2, P3 in figure 6, respectively.
It should be noted that in figure 6, the loci intersect. In another case study, the loci will possibly not intersect, but the attenuation factors and the MS's location are estimated using the minimum sum of distances between the geometric loci in any case. If one or more of the loci
^_{C2}_{C3} > ^_{C2}_{C4}> ^_{C3}_{C4} ^ ^{usec}* alternatively, the estimation outcome may be slightly different.
The invention uses an internal criterion in order to estimate the accuracy of the attenuation factor and the MS's position estimation procedure. Evidently, this criterion cannot be the true accuracy of position location, since the position of the MS is unknown. Thereby, it should be noted that when the attenuation factors M_{1} , n_{2} , n_{3} , n_{4} are equal to one another, there is only one joint intersection point, while the same is not true when the factors n_{γ},n_{2},n^,n_{4} are contiguous. The minimum sum of distances between the "minimum distant points" will be larger for more dissimilar attenuation factors. Therefore, the Measure of Applicability (MA) is defined as:
where (X_{1}^_{1}) , (x_{2},y_{2}), (x_{3},y_{3}) are the coordinates of the "minimum distant points" (e.g. the points Pl, P2, P3 in figure 6, respectively). The Measure of Applicability is an alternative to the real accuracy and can be used in order to evaluate the result of the overall estimation procedure. Evidently, the MA in equation (22) is the inverse of the minimum sum of distances between the geometric loci. A larger MA corresponds to a more accurate estimation.
The invention, described so far, is able of revealing the MS's location, in the case where there are four BSs, as long as these BSs are characterized by similar attenuation factors to the
MS. In the case where more than four BSs are available, the invention is able to categorize BSs with contiguous attenuation factors, estimate these factors, and also estimate the MS's position.
The cases of 5, 6 or more BSs are now described.
Let there be five BSs, namely BSl, BS2, BS3, BS4, BS5, characterized by the attenuation factors n_{x}, n_{2} , W_{3}, n_{4} , n_{5} to the MS, at a distance of d_{x} , d_{2} , d_{3} , d_{A} , d_{5} away from the MS, placed at (x_{BSl} , y_{BSl} ) , (x_{BS2} , y_{BS2} ) , (X_{j383} , y_{BS3} ) , (x_{BS4} , y_{BS4} ) , (x_{BS5} ,y_{BS5}) respectively. The received power by the MS, from each BS, is given by:
P P P P P
P  ° P  ° P — 0 P _ 0 p _ ^{r}O (r)n\
M ~ U J_{1}ill ' ^{r}2 ^{*} d ,_{2}„2 ' ^{r}3 ~ d J_{3}iH ' ^{r}4 ~ d J_{A}»4 ' ^5 ~ d ,_{5}„5 V^
Let the factors W_{1}, W_{2} , W_{3} be contiguous to each other, and the factors W_{4} , W_{5} be contiguous to each other, but not contiguous to W_{1} , W_{2} , W_{3}. The estimator n_{A} e [w_{min} , w_{max} ] of
W_{1}, W_{2} , W_{3}, and the estimator n_{B} e [w_{min} , w_{max}] of W_{4} , W_{5} are generated. Using the method that was described for the case of three BSs (refer to figure 4), the geometric loci
T_{cι}__{C2} , T_{C1}__{C3} are constructed. Then, the method that was used in the case of two BSs (refer to figure 3) is applied, and the locus T_{C4}__{C5} is constructed. Thus, three loci are constructed, which ideally should have a joint intersection point. Practically, as n_{A} scans [w_{min},w_{max}] with step ^{n} step _{^} and ^{n} _{B} ^{scans} [«_{ffl}i_{n} ^_{m}aχ] ™& ^{ste}P ^{n} step _{^} ^{raere} is & value for U _{A} and a value for n_{B} , for which the sum of distances between the loci is minimum. These values are the estimates of the attenuation factors. It should be noted, that the sum of distances is now a function of n_{A} and n_{B} . The case study is illustrated in figure 7, where the points Pl, P2 and P3, of the loci T_{cι}__{C2} , T_{cι}__{C3} , T_{C4}__{C5} , corresponding to the minimum sum of distances, are displayed. The
MS's position is estimated as the average of Pl, P2 and P3, as defined by equations (20) and (21). Finally, theM4 of the specific tripletpair combination is calculated.
The invention is functional even in the case where it is not known which exactly of the five BSs are characterized by contiguous attenuation factors. In this case, all possible combinations of five BSs taken three at a time are configured (the order of selection is immaterial). Then, the MA is calculated for each tripletpair combination. The combination corresponding to the optimum (maximum) MA, among the configured tripletpair combinations, is the dominant combination, and is used in order to estimate the MS's position.
Let there be 6 BSs, namely BSl, BS2, BS3, BS4, BS5, BS6, with attenuation factors W_{1},
W_{2} , w_{3}, W_{4} , W_{5}, W_{6} , at a distance d_{x}, d_{2} , d_{3}, d_{4} , d_{5} , d_{6} away from the MS, placed at
(^{X}BSI > yβsi ) > (^{X}BS2 > yΕs2 ) ' (^{X}BS3 > Λ53 ) > (^{X}BS4 > y>BS4 ) ' (^{x}Bss > Xros ) > (^{X}BS6 > ^6 ) respectively. The received power by the MS, from each BS, is given by:
P P P P P P
P  ^{Q} p  ° p  ^{Q} p  o p  ^{Q} p  ^{Q} OΛ\
^{1} 1 ~ _{JB}l ' ^{r}2 ~ ,«2 ' ^3 ~ ,„3 ' ^{r}4  ,nA ' ^{λ} 5 ~ ,„5 ' ^{T}6 ~ ,_{n6} V") ^{a}i ^{a}2 ^{U}3 ^{a}4 ^{U}5 ^{U}6 Let the factors H_{1} , n_{2} be contiguous to each other, the factors n_{3}, n_{4} be contiguous to each other but not contiguous to W_{1}, n_{2} , and the factors n_{5}, W_{6} be contiguous to each other, but not contiguous to W_{1} , W_{2} , W_{3} , W_{4}. The estimator n_{A} e [n_{min} , w_{max} ] of W_{1} , W_{2} , the estimator ^{n} _{B} ^{e} K_{πn >} ^{w} _{ma}J °^{f} «_{3 >} ^{U} _{A} ^{aad me} estimator w_{c} e [w_{min},w_{max}] of n_{5}, n_{6} are generated. Similarly to the case of two BSs (refer to figure 3), the geometric loci T_{cι}__{C2} , T_{C3}__{C4} , T_{C5}__{C6} are constructed. Thus, three loci are constructed, which ideally should have a joint intersection point. Practically, as n_{A} scans [w_{min} ,w_{max}] with step n_{slep} , n_{B} scans [w_{min} ,w_{ma}j with step n_{step} , and n_{c} scans [w_{min} , w_{raax}] with step n_{slep} , there is a value for n_{A} , a value for n_{B} and a value for n_{c} , for which the sum of distances between the loci is minimum. These values are the estimates of the attenuation factors. It should be noted, that the sum of distances is now a function of n_{A} , n_{B} and n_{c} . This case is illustrated in figure 8, where the points Pl, P2 and P3 of the loci T_{C1}__{C2} , T_{C3}__{C4} , T_{C5}__{C6} correspond to the minimum sum of distances. The MS's position is estimated as the average of Pl, P2 and P3, as defined by equations (20) and (21). Finally, the MA of the specific pairpairpair combination is calculated. The invention is functional even in the case where it is not known which exactly of the six
BSs are characterized by contiguous attenuation factors. In this case, all possible combinations of six BSs taken two at a time are configured (the order of selection is immaterial). Thus, a pair and a remaining quadruplet are configured. Then, all possible combinations of the remaining four BSs, taken two at a time, are configured (the order of selection is immaterial). Thus, all possible combinations of the type pairpairpair are formed, and the MA is calculated for each one of them. The combination corresponding to the optimum (maximum) MA, among the configured pairpairpair combinations, is the dominant combination, and is used in order to estimate the MS's position.
Evidently, the invention may be developed, in order to categorize any number of BSs
(greater than six) with respect to the propagation attenuation factor to the MS. Based on the analysis of four, five and six BSs, all combinations of the BSs, taken four, five or six at a time are configured (the order of selection is immaterial). Each combination is scrutinized, properly analyzed, if needed, to tripletpair and pairpairpair combinations (in the case of pentad or hexads, respectively). The invention measures the MA of each subcombination, and determines the optimum group of BSs. Thus, the unknown attenuation factors are estimated, and the MS position is located. The residual attenuation factors, after the MS is located, are calculated, using the equation: log^hlogrø
logtø) where «, is Hie attenuation factor of the Mh BS to the MS, and d. is calculated considering the estimated MS position and the known position of the Mh BS.Finally, a discussion follows, regarding technical issues that may arise during the employment of the invention to realworld problems, and ways of overcoming these issues.
If the number of BSs that the MS can sense is too large, the execution of the algorithm may significantly delay. A number of BSs needs to be selected, in order to provide proper input to the algorithm. A smaller number of BSs means less accuracy but smaller execution time, while a larger number of BSs improves accuracy but execution time delays significantly. A possible criterion for BS selecting, is to select those BSs whose received signal is strongest. Another criterion is to select those BSs, whose signal strength fluctuation, as measured by the MS, is minimum. Actually, the criterion that the user of the invention will adopt is irrelevant to the algorithm of the invention. Smallscale fading refers to the rapid fluctuations of the received signal in space, time and frequency, and is caused by the signal scattering off objects between the transmitter and receiver [19], [20], [21], [22]. The large signal fluctuation introduced by smallscale fading means that the instantaneous value of the received signal strength may be very different than the local mean, and that this value changes rapidly with time and with movement of the order of wavelength. Performance degradation of the proposed algorithm may appear under strong fading conditions. In order to mitigate the consequences of smallscale fading, antenna diversity may be utilized at the transmitter, receiver, or both. Furthermore, a large number of signal samples from all BS's may be collected by the MS, in order to affront timevarying fading. Also, a large number of signal samples may be collected while moving slightly the MS, at distances of the order of wavelength. The invention can be used together with any of the techniques of smallscale fading mitigation described herein.
Largescale fading or shadowing is caused by buildings or natural features and is determined by the local mean of a smallscale fading signal [19], [20], [21]. Largescale fading means that the mean signal strength value varies from the value predicted by path loss slope [23]. In other words, largescale fading describes the effect which occurs over a large number of measurement locations, which have the same transmitterreceiver separation, but have different levels of clutter on the propagation path. Consequently, even after mitigating small scale fading using the techniques described above, the local mean signal strength may be measured to be different than predicted by the slope of the path loss diagram. However, large scale fading does not need to be resolved when using the invention method. Rather, the invention dynamically resolves any changes to the effective attenuation factors by anew estimating the MS location.
When the transmitted power by each BS is not constant, the invention uses the information of the theoretical received power at Im transmitterreceiver separation (provided by the administrator of the network), in order to categorize the BSs and locate the MS. The equations
(3) to (18), and (23) to (25) are used with no modification other than the power received at Im distance.
In some cases there is prior information on the position of the MS. As an example, consider the case of cellular systems, where the MS position is restricted into the cell of the associated BS. In a case like this, this information may be combined with the MS location provided by the invention, in order to ameliorate the accuracy of the location system.
If the orientation of the MS user affects the received power, the invention may sample the received power for different user orientations. This case is relevant to spaceselective fading. In any case, the orientation with the optimum MA is selected.
The resolution of the estimator n may also be an issue. The computational burden of the algorithm increases as the value of n_{step} decreases. Consequently, there is a trade off between the precision of the estimated attenuation factors and execution time. The selection of n_{step} values should be performed by the invention user, and is irrelevant to the algorithm of the invention.
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