Patent Publication Number: US-9900784-B2

Title: Geo-location in a wireless communication network

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 13/144,130, filed Sep. 19, 2011 (now U.S. Pat. No. 9,462,482), which is a 371 application of PCT/EP2010/000072, filed Jan. 9, 2010, which claims priority under 35 U.S. C. § 119 to U.S. Provisional Patent Application No. 61/144,242, filed Jan. 13, 2009, the entire disclosures which are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     Aspects of the invention relate to the geo-location of wireless communication units, and the planning of wireless networks. 
     The invention is applicable to mobile telephones. The invention is also applicable to other types of wireless digital communication units, including both personal digital assistants (PDAs) and laptop computers with wireless communications capability. The invention is not however limited to these applications. 
     BACKGROUND OF THE INVENTION 
     A wireless communication unit usually forms part of a wireless communication system. The wireless communication unit communicates through a wireless communication network, which also forms part of the wireless communication system. 
     The wireless communication network normally comprises a network of base stations. Each base station enables communication within an area referred to as a cell-site. Each cell-site may comprise multiple sectors. There are usually three sectors in a cell-site, each served by a dedicated antenna. 
     In some countries, it is a legal requirement that wireless communication systems be able to provide accurate information about the location of wireless communication units. This information may serve, for example, to expedite the arrival of assistance to a user of a wireless communication unit who calls the emergency services, using the ‘911’ number in the United States. 
     Information about the location of a wireless communication unit can be derived in many ways. At any particular time, various forms of measurement information may be available from: 
     (i) The wireless communication unit; 
     (ii) The wireless communication network, and particularly from one or more base stations with which the wireless communication unit is communicating; or 
     (iii) Both of (i) and (ii). 
     This measurement information can be processed to provide an estimate of the location of the wireless mobile communication unit. 
     Considering the measurement information in more detail, this information may be available either: 
     (i) Directly. This means that the information is included in the measurement made. The measurement may be made either by the wireless communication unit, or by another part of the wireless communication system, such as the wireless network. 
     (ii) Indirectly. This means that the information is derived from the measurements made. An example would be an estimate of the distance between a wireless communication unit and the base station of a wireless communication system. Such an estimate might be calculated by multiplying the speed of propagation of the signal by a measured time difference between transmission and receipt of a signal. 
     So some or all of the following mobile measurement information may be available: 
     (i) The absolute distance(s) from the wireless communication unit to one or more network sectors. 
     (ii) Differential distances between the wireless communication unit and one or more pairs of network sectors. 
     (iii) Received signal powers recorded by the wireless communications unit from one or more network sectors. 
     (iv) Received signal-to-noise ratio measurements recorded by the wireless communication unit from one or more network sectors. 
     In addition, the following network information may be available: 
     (i) Antenna locations per sector. This information may be provided in latitude and longitude, or as ‘Easting’ and ‘Northing’ directions, or the equivalent. 
     (ii) Antenna properties. This information may include height above ground, azimuth, tilt, horizontal and vertical beam pattern, transmitted power levels for control and traffic channels. 
     A combination of the mobile measurement information and the network information is often used to provide geometric interpretations of the mobile device location. 
     So prior art geo-location methods have as their inputs various forms of directly- and indirectly derived measurement information. That measurement information may have come from the wireless communication unit, the wireless communication system, or both. Some wireless communication units may be able to provide further information that originates from direct communication links between the wireless communication unit and other wireless communication units. Such direct communication links do not pass through the wireless communication network. 
       FIG. 1  shows a simple example of a wireless communication system  100 . Wireless communication unit  110  communicates with base station  120 . Base station  120  is one of many base stations that together comprise the wireless communication system  100 . Base station  120  is the nearest base station to wireless communication unit  110 , and is located a distance ‘R’ from wireless communication unit  110 . 
       FIG. 1  shows one problem with prior art geo-location methods. If the base station  120  has an omni-directional antenna, and no other measurement information is available, then any attempt to provide a single estimate of the location of the wireless communication unit  110  is very difficult. The information available from the wireless communication unit  110  and/or from base station  120  allows prior art geo-location methods to calculate only the absolute value of distance R. This distance is measured relative to the known location of base station  120 , which might be at coordinates (x B , y B ). However, all that is known is that the wireless communication unit  110  is located somewhere on a circle of radius R, centred on (x B , y B ), which is the circle  130  in  FIG. 1 . 
     The single estimate of the location would have to be a point chosen at random on the circle  130 . The error in this estimate could be up to 2R, because the wireless communication unit might in fact be located on circle  130  at a point diametrically opposite to the estimated location. 
       FIG. 2  considers another simple example of a wireless communication system  200 .  FIG. 2  also shows a wireless communication unit  210  and base station  220 . Base station  220  has a directional antenna. It is statistically most likely that wireless communication unit  220  is being served by the main lobe  230  of the directional antenna. So a single estimate of the location of the wireless communication unit  210  can be made with greater certainty than was the case with the wireless communication system of  FIG. 1 . However, it is also possible, but less likely, that wireless communication unit  210  is being served by a ‘side-lobe’ or ‘back-lobe’ of the directional antenna. A back-lobe is shown as reference  240  in  FIG. 2 . 
     A prior art geo-location method would provide an estimate of the location of wireless communication unit  210  based on the distance R and the direction of the antenna&#39;s main lobe. This estimate is shown as point (x 1 , y 1 ) on  FIG. 2 . However, the wireless communication unit  210  might provide the same measurement information, such as a received signal to noise ratio, if it were in fact being served by the back-lobe  240  of the antenna. In this case, it would be located at a distance less than R from base station  220 , in the opposite direction. Such a location is shown as point (x 2 , y 2 ) on  FIG. 2 , which is located 0.25R from base station  220 . If wireless communication unit  210  were in fact located at point (x 2 , y 2 ), then the estimated location (x 1 , y 1 ) would be in error by a distance of 1.25R. 
     In general terms, prior art geo-location techniques usually deliver a single point in space as their estimate of the location of the wireless device. This point may, for example, be described by an x coordinate and a y coordinate, as in  FIGS. 1 and 2 . However, such an approach does not give the user information about the reliability of the estimate of the location. Reliability, in this example, means both ‘accuracy’ and ‘precision’. 
     ‘Accuracy’ concerns whether the estimated location is the correct one, or not. In the example of  FIG. 1 , it was explained that the measurement of the location of mobile communication unit  110  might be inaccurate by as much as 2R. 
     ‘Precision’ is the exactness of the measurement. Both  FIGS. 1 and 2  assumed that the distance R could be determined very precisely, i.e. that an exact value for R could be derived. 
     Both accuracy and precision depend on the type and quality of data on which the measurement estimate is based. 
     Whereas  FIGS. 1 and 2  assumed that distance R could be determined reliably, there is in fact an error range associated with the measurement of R itself. The measurement of R is in fact imprecise. 
       FIG. 3  illustrates the imprecision in the measurement of R.  FIG. 3  corresponds generally to the arrangement of  FIG. 1 . A base station  320  located at point (X B , Y B ) might measure the distance to a communication unit  310  as R. Circle  330  shows the locus of all points at the distance R, which is the distance from base station  320  at which the mobile is most likely to be located. Due to the measurement collection process, however, the user  310  might actually be at a distance of between (R−e1) and (R+e2) from base station  320 . So it is not possible even to say with certainty that the user  310  lies on circle  330 . 
     An error function describes the probability that communication unit  310  is located at each particular distance from base station  320 . The error function is usually complex. The details of the error function can be determined through a variety of means. One option is to place calls from a small number of locations, and compare the measurement data with the known locations. 
     Summing up the discussion of  FIGS. 1-3 , there is both inaccuracy and imprecision in the measurement of the location of a mobile communications unit. So some degree of error is likely in the measurement of the position of a mobile communications unit in most cellular communications systems. 
     These problems are greatest in the unusual case of: 
     (i) A base station with an omni-directional antenna, such as in  FIG. 1 ; and 
     (ii) When received signal strength is the only measurement data on which an estimate of the position of the mobile communications unit can be made. 
     In the preceding discussion and the discussion that follows, the term ‘communicating’ includes a variety of forms of communication. These forms include, but are not limited to, speech or data communication sessions on traffic channels, and communication on the control channel. So, for example, the communication may not require the user of a mobile telephone to actually place or receive a call. The communication may involve, for example, only the intermittent receipt by a mobile telephone of data over the wireless communication system&#39;s control channel. 
     Prior art U.S. Pat. No. 5,293,642 (Lo) describes a variety of approaches to estimating the location of a mobile communication unit. The approaches involve calculating a probability density function for the location of the mobile communication unit. A mobile station may be in communication with two or more base stations. In this case, several probability density functions can be calculated, each describing the location of the mobile calculated from measurements received from one of the base stations. These probability density functions may be combined, to provide a joint probability density function. U.S. Pat. No. 5,293,642 (Lo) may employ any of the following data in calculating a location probability density function: 
     Radio attenuation from RSSI measurements at the mobile station; 
     Radio attenuation from RSSI measurements at the base stations; 
     Direction of signal arrival at the base station; 
     Radio propagation delay from mobile signal arriving at the base station; and 
     Mobile transmission timing alignment. 
     Prior art United States patent application US2008080429 (Hart) describes a process of minimum variance location estimation in wireless networks. A probability density function is calculated, and a ‘probability surface’ is derived from the probability density function. A mean location of a wireless node is calculated from the probability surface. 
     SUMMARY OF THE INVENTION 
     In accordance with a first aspect of the present invention, there is provided a method for geo-location of a wireless communication unit in accordance with the description herein. 
     In accordance with a second aspect of the present invention, there is provided a wireless communication unit or a wireless communication system in accordance with the description herein. 
     In accordance with a third aspect of the present invention, there is provided a method of selecting enhancements to a wireless communication system in accordance with the description herein. 
     In accordance with a fourth aspect of the present invention, there is provided a computer program product in accordance with the description herein. 
     In accordance with a fifth aspect of the present invention, there is provided a wireless communication system in accordance with the description herein. 
     The geo-location method of the invention provides information, as part of its output, about more than one possible location for a wireless communication unit. The method therefore may retain more of the information associated with the measurements on which the location estimates are based than was the case with prior art geo-location methods, and use this information in its output. The output from the method of the present invention may provide information about second and third, etc., most likely locations for a device, and/or may keep uncertainty information and present this as part of the output. 
     The invention may, for example, indicate that there are two possible locations for a wireless communication unit, and that one of the two locations has only a slightly higher probability of being correct than the other. The user of a mobile communication unit, or the operator of a wireless communication system, may react very differently to this information than would be the case with information from a prior art geo-location method. 
     The present invention may therefore offer a number of advantages, for example in: 
     (i) Providing ‘real-time’ information to a user of a wireless communication unit about that user&#39;s current location; or 
     (ii) Searching for a user of a wireless communication unit who has requested emergency assistance. 
     The geo-location information provided by the present invention may also be used in ‘post-processing’. Such processing may be carried out by, amongst others, the following: 
     (i) operators of wireless communication networks when analysing telecommunications traffic patterns; 
     (ii) the emergency services; 
     (iii) general location based services; 
     (iv) organisations that monitor levels and speeds of vehicular road traffic by tracking ‘anonymised’ mobile phone signals, for example to measure or forecast road traffic delays. 
     The results of such post-processing are themselves used in decision making. Such decisions include decisions about enhancing networks, for example by adding new base stations, or upgrading an antenna in a network sector. The method of selecting enhancements to a wireless communication system in accordance with the invention shows advantages over prior art arrangements, and may result in more effective upgrades to the network being made, when they are needed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments of the present invention will now be explained with reference to the accompanying drawings. 
         FIGS. 1-3  show wireless communication systems, and illustrate the limitations of prior art geo-location methods. 
         FIG. 4  shows an exemplary embodiment of a wireless communications system in accordance with the invention. 
         FIG. 5  shows an exemplary embodiment of a method of geo-location in accordance with the invention. 
         FIG. 6  shows a flowchart for a method for geo-location of a wireless communication unit in accordance with the invention. 
         FIG. 7  shows a flowchart for a method of selecting enhancements to a wireless communication system in accordance with the invention. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG. 4  shows an exemplary embodiment of a wireless communications system  400  in accordance with the invention. 
     Wireless communication unit  410  is connectable via a wireless communication link  420  to a wireless communication network  430  of wireless communication system  400 . Base stations  432  and  434 , and control unit  436  all form part of wireless communication network  430 . 
     Communication link  420  may comprise a voice communication channel, or a data link. 
     In accordance with this exemplary embodiment of the invention, a probability density function is derived for the location of the wireless communication unit. The probability density function is derived from at least one of the group of: 
     (i) measurement information from the wireless communication unit  410 ; 
     (ii) network information about the wireless communication network  430 . 
     The probability density function may be derived by one of several of the components of the wireless communication system  400 . For example, a processor  438  located in control unit  436  may derive the probability density function. 
     The probability density function is sampled, to provide output information. This output information comprises both spatial information and probability information about each of at least two possible locations for the wireless communication unit  410 . Sampling of the probability density function may also occur in processor  438 . 
     In an alternative arrangement, the probability density function may be derived in a separate system, which is not shown on  FIG. 4 . Such a separate system is particularly likely to be used when the probability density function is derived as part of ‘post-processing’, which does not take place in real time. Such post-processing may be carried out in a dedicated system outside of wireless communication system  400 , using records of one or more communication links or calls. In some applications, the post-processing will be applied to several records, or to a large number of records. Here the ‘large number’ may include many thousands or millions of call records. When the invention is performed by a separate system, one or more computer workstations may be used. These workstations may be dedicated to this task, which would be the usual approach. Alternatively, these workstations may perform other tasks, such as fault management or compiling switch statistics and maintenance reports, in addition to the present invention. These workstations may consist of general-purpose computers. However, they could also be composed of custom hardware, with specially-built printed-wiring cards &amp; custom chips to accelerate the necessary calculations. Where all calls in a busy network are analysed, such a custom type arrangement may provide greater speed of implementation of the method. 
     One approach to implementing the invention would be simply to arrange for each of a group of mobiles of a mobile telephone system to provide data as an ‘input’. The mobile telephones would provide their measurements to the Radio Access Network (RAN) of the mobile telephone system, which in turn provides the mobile measurements to the Operations Support System (OSS) of the mobile telephone system. The calculations necessary to perform the invention would be carried out in the Operations Support System (OSS). The Operations Support System of a mobile telephone system is normally connected directly to the Radio Access Network (RAN), so it is easy to arrange for the Operations Support System to receive measurements from the Radio Access Network. 
     The probability density function may be derived from at least two individual probability density functions, each individual probability density function being based on either: 
     (i) the measurement information from the wireless communication unit  410 ; or 
     (ii) the network information about the wireless communication network  430 . 
     Various techniques are available for calculating probability density functions. However, in accordance with the invention, the probability density function, or the two or more individual probability density functions, may be created by parametric modelling. The parametric modelling may use one or more moments of a random variable distribution. The probability density function thus created will be such that the summation of the probabilities of all possible locations equals unity. 
     The spatial information and probability information about each of the at least two possible locations for the wireless communication unit may advantageously comprise: 
     (i) an x-coordinate and a y-coordinate for each possible location; and 
     (ii) a probability of the wireless communication unit  410  being located at the x-coordinate and y-coordinate, the probability being derived from the probability density function. 
     In order to make the output information from the invention more user-friendly, the possible locations for the mobile communication unit  410  with a probability less than a threshold value may be eliminated. This can be done, for example, using importance sampling. The output information would then comprise a list of all the possible locations for the wireless communication unit  410  with a probability greater than or equal to the threshold value. The user of the wireless communication unit  410  may be able to select how many possible locations for the wireless communications unit are included in the output information. 
     The output information of the invention may serve a wide variety of uses. However, the output information may be displayed on a screen of the wireless communication unit  410 . In an alternative arrangement to that described above, it is also possible for the wireless information unit  410  to calculate the probability density function, rather than this being a function of the wireless communication network  430 . 
     The invention may be arranged to operate with measurement information from the wireless communication unit  410  that comprises one or more of the following: 
     (i) one or more absolute distances from the wireless communication unit  410  to one or more network sectors of the wireless communication network  430 ; 
     (ii) one or more differential distances between the wireless communication unit  410  and one or more pairs of network sectors of the wireless communication network  430 ; 
     (iii) one or more received signal powers recorded by the wireless communication unit  410  from one or more network sectors of the wireless communication network  430 ; and 
     (iv) one or more measurements of the received signal-to-noise ratio recorded by the wireless communication unit  410  from one or more network sectors of the wireless communication network  430 . 
     In addition, the invention may be arranged to operate with network information about the wireless communication network  430  that comprises one or more of the following: 
     (i) antenna or base station location information; 
     (ii) antenna properties; 
     (iii) azimuthal and tilt pointing angles of a sector antenna; 
     (iv) transmitted power levels. 
       FIG. 5  shows an exemplary embodiment of a method of geo-location in accordance with the invention. 
       FIG. 5  shows first and second antennae  532 ,  534 , which are part of two base stations such as base stations  432  and  434  of  FIG. 4 . First and second antennae  532 ,  534  are sectorised antennae. First antenna  532  is located in a first sector, and second antenna  534  is located in a second sector. 
     Each of first and second antennae  532  and  534  focuses its transmitted energy. This focussing is such that most of the energy falls within a certain range of angles of azimuthal beam width. The range might be, typically, 45 to 90 degrees, centred about the azimuthal pointing angle. The direction of each of the arrows  532 ,  534  in  FIG. 5  shows the azimuthal pointing angle for that antenna. 
     Assume now that a wireless communications unit, such as unit  410  shown in  FIG. 4 , performs a first measurement, which is of the distance to first antenna  532 . The first measurement may be either a direct or an indirect measurement.  FIG. 5  has been provided to illustrate the probability information that is available from a wireless communications unit whose location is uncertain, so no wireless communications unit is actually shown on  FIG. 5 . 
     The first measurement results in a first probability density function. The solid double circle  540  illustrates the probability information, which is derived from the first probability density function. First antenna  532  lies at the centre of both of the circles  540 . The double circle  540  corresponds to two contours of equal probability of finding the wireless communications unit. This measurement is generally similar to that described in connection with  FIG. 3 . The two lines of double circle  540  may, for example, correspond to distances R+e and R−e in  FIG. 3 . 
     The mobile communications unit is also able to perform a second measurement, which is of the distance to the second antenna  534  in  FIG. 5 . However, the second measurement yields a differential distance measure, relative to the first sector that contains first antenna  532 . The differential distance measure might be obtained from the Time Difference of Arrival, the ‘TDOA’, of communication signals. The second measurement provides a second probability density function. The four dotted lines generally indicated by reference  550  in  FIG. 5  illustrate probability information, which is derived from the second probability distribution function. The four dotted lines are contours of equal probability, and each takes the form of a hyperbola. The geometrical parameters of the hyperbola depend on the locations of the first and second sectors, and the differential distance quantity. 
     Both double circle  540  and the four hyperbolae  550  are in fact a dense sampling of points from their respective probability density functions. 
     In order to locate the wireless communication unit, it is necessary to combine the first and second probability density functions. This is because the probability of the wireless communication unit being at a particular location is the conjunction of independent events, i.e.: 
     (i) The mobile communication unit being located a distance from antenna  532  corresponding to approximately the radius of one of the circles  540 ; 
     (ii) A Time Difference of Arrival of a given value; and 
     (iii) Mobile visibility of the first and second sectors. 
     The first and second probability density functions need to be suitably scaled when making this combination. 
     The example of  FIG. 5  shows directional antennae in each sector. In this case, the most precise information is derivable by combining the first and second probability density functions with the probability density functions associated with the antennae. This is because users are more likely to be served in the main lobe of each antenna than either in the back lobe, or in a side lobe of the antenna. If both first and second antennae had been identical omnidirectional antennae, there would be no need to include their probability density functions in the combination. 
     The possible locations for the wireless communications unit are in first and second ovals  560  and  570 . These show the locations where the combined probability density functions lead to the highest probability values. 
     In prior art geo-location approaches, the usual output would be a single point towards the centre of first oval  560 . The point would be in first oval  560 , because of the pointing angles of the antennae. Providing only the single point in first oval  560  as an output would discard useful information about the geo-location process, and limit its utility. For example, the probability of being at each possible location in second oval  570  might be nearly equal to the probability of being in corresponding points in upper oval  560 , but that information would be discarded by prior art approaches. 
     When the emergency services locate a user, for example, it is valuable for them to know if there is more than one very likely location that requires their attention. The present invention provides that information. The prior art method would not. 
     The invention therefore provides a method for geo-location of a wireless communication unit  410 . The steps of the method are summarised in the flowchart  600  of appended  FIG. 6 . In step  610 , the wireless communication unit  410  communicates with the wireless communication network  430 . In step  620 , a probability density function is derived from measurement and/or network information. In step  630 , the probability density function is sampled, to provide spatial and probability information about at least two possible locations for a wireless communication unit  410 . 
     The invention also provides a method of selecting enhancements to a wireless communication system  400 . An exemplary method in accordance with the invention is shown in flowchart  700  of  FIG. 7 . 
     Step  710  of the method of the invention comprises deriving a probability density function for a location of a wireless communication unit  410 , from at least one of the group of: 
     (i) measurement information from the wireless communication unit  410 ; 
     (ii) network information about the wireless communication network  430 . 
     Step  720  comprises sampling the probability density function to provide output information, the output information comprising spatial information and probability information about the location of the wireless communication unit  410 . 
     Step  730  comprises deriving a quality rating for the wireless communication link between the wireless communication unit  410  and the wireless communication network  430 . 
     Step  740  comprises using the output information and the quality rating in a decision on enhancements to the wireless communication system  400 . 
     The decision in step  740  on enhancements to the wireless communication system  400  may employ output information and quality ratings derived from many wireless communication units  410  and/or many wireless communication links. Generally, output information or quality ratings derived from larger numbers of units or links will lead to better decisions. 
     The decision in step  740  on enhancements to the wireless communication system  400  may comprise at least one from the group of: 
     (i) Deciding to re-direct an antenna in a base station  432 ,  434  of the wireless communication network  430 ; 
     (ii) Deciding to upgrade an antenna in a base station  432 ,  434  of the wireless communication network  430 ; 
     (iii) Deciding to change the transmission power level of an antenna in a base station  432 ,  434  of the wireless communication network  430 . 
     Alternatively, or in addition, the decision  740  on enhancements to the wireless communication system  400  may comprise at least one from the group of: 
     (i) Choosing a site for an additional base station in the wireless communication network; 
     (ii) Re-locating an existing base station  432 ,  434  to a new site; or 
     (iii) Moving a mobile or temporary base station. 
     The quality rating may be derived from at least one from the group of: 
     (i) Data about the number of times when it was not possible to establish a communication link  420 , and/or data about the number of times that the communication link  420  breaks; 
     (ii) Data about the number of times when it was not possible to place a call and/or data about the rate of calls being dropped during the call; 
     (iii) One or more received signal powers recorded by the wireless communication unit  410  from network sectors of the wireless communication network  420 ; 
     (iv) One or more measurements of the received signal-to-noise ratio recorded by the wireless communication unit  410  from network sectors of the wireless communication network. 
     It will be appreciated that, for clarity purposes, the above description has described embodiments of the invention with reference to different functional units. Hence, references to specific functional units are only to be seen as references to suitable means for providing the described functionality, rather than indicative of a strict logical or physical structure or organization. 
     Aspects of the invention may be implemented in any suitable form including hardware, software, firmware or any combination of these. Aspects of the invention may optionally be implemented, at least partly, as computer software running on one or more data processors and/or digital signal processors. Thus, the elements and objects of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way. Indeed, the functionality may be implemented in a single unit, in a plurality of units or as part of other functional units. 
     Although the invention has been described in connection with some embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the scope of the present invention is limited only by the claims. Additionally, although a feature may appear to be described in connection with particular embodiments, one skilled in the art would recognize that various features of the described embodiments may be combined in accordance with embodiments of the invention. 
     Additionally, although individual features may be included in different claims, these may possibly be advantageously combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. Also, the inclusion of a feature in one category of claim does not imply a limitation to this category, but rather the feature may be equally applicable to other claim categories, as appropriate. 
     The order of individual steps in a method claim does not imply that the steps must be performed in this order. Rather, the steps may be performed in any suitable order. In addition, singular references do not exclude a plurality. Thus, references to ‘a’, ‘an’, ‘first’, ‘second’, etc. do not preclude a plurality.