Abstract:
With the increasing usage of mobile devices for communication, the need for wireless base-stations deployed in strategic locations is becoming increasingly important. The increased bandwidths being transmitted between the base-station and the mobile device has mandated that enhanced transmission formats and techniques be deployed, and, in order to operate correctly, these techniques require a tight synchronization in both time/phase, and in frequency, between the various base-stations serving a general area. Due to the need to establish the geographic location of the mobile device with a high degree of accuracy, it is also necessary to establish the location of the serving base-stations with a high degree of accuracy. The invention disclosed herein provides robust and practical methods for synchronizing base-stations, as well as providing for accurate location, by leveraging the usage of global navigation satellite systems receivers in conjunction with network based schemes for packet-based (time/phase/frequency) synchronization.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a divisional application of co-pending U.S. patent application Ser. No. 14/582,147, filed Jan. Dec. 23, 2014 and entitled “Method and System for Synchronizing Base Station and Establishing Location,” which is based upon and claims the benefit of U.S. Provisional Patent Application No. 61/920,176, filed on Dec. 23, 2013, the entire contents of each of which are incorporated by reference herein. 
     
    
     BACKGROUND OF THE INVENTION 
     Description of the Related Art 
       [0002]    With the increasing usage of mobile devices for communication, the need for wireless base-stations deployed in strategic locations is becoming increasingly important. Such base-stations are often referred to as “small cells” since they cover a limited geographic area and are often, but not always, paired with a “macro cell” that involves a base-station with much larger geographic coverage. The increased bandwidth being transmitted between the base-station and the mobile device has mandated that enhanced transmission formats and techniques be deployed, and, in order to operate correctly, these techniques require a tight synchronization in both time/phase, and frequency, between the various base-stations serving a general area. 
         [0003]    The need for providing emergency services (also referred to in the USA as E-911) has mandated that the geographic location of the mobile device signaling an emergency be established to a high degree of accuracy. In order to universally achieve this location accuracy, it is necessary to establish the location of the serving base-stations to a high degree of accuracy. 
         [0004]    The use of GNSS for providing location and time at a receiver is known. The most common GNSS in use is the Global Positioning Satellite (GPS) system. The use of navigational satellites to establish the position and time in a receiver is briefly explained with reference to panel A of  FIG. 1 . For specificity, the satellite constellation considered is GPS. 
         [0005]    As shown in  FIG. 1 , the receiver (REC)  110  can establish its position and time by observing 4 satellite vehicles (SVs) denoted in  FIG. 1  as SV- 1   121 , SV- 2   122 , SV- 3   123 , and SV- 4   124 . Each SV is broadcasting a signal that includes suitable time markers and messages indicating the time at the marker. At any particular point in time, t, the four satellite vehicles are at a particular distance (range) from the receiver  110 . In  FIG. 1  the actual range of the four satellite vehicles is denoted by R 1 (t)  131 , R 2 (t)  132 , R 3 (t)  133 , and R 4 (t)  134 . The range can be expressed either in terms of distance (e.g., meters) or in terms of time (e.g., seconds). Here we assume that the range is in terms of time because a time formulation permits the inclusion of correction terms related to effects of the ionosphere. The relationship between time and distance follows the speed of propagation of the radio signal, essentially the speed of light (nominally 3×10 8  m/s). 
         [0006]    Denote the time offset of the receiver clock as δ. The receiver estimates the range from SV-k by establishing the time-of-arrival of the time marker event contained in the broadcast signal from SV-k. This time-of-arrival is based on the receiver clock. The range estimate, PR k , is called “pseudo-range” because of the receiver time offset. Thus at some point in time, T, the receiver has four range estimates, {PR k (T); k=1,2,3,4}. Since, in principle, the location in space of the four satellite vehicles is known, the receiver can develop a set of four simultaneous equations and solve for the four unknowns corresponding to position (x R , y R , z R ) of the receiver and δ, the receiver clock offset (relative to the satellite timescale). 
       Packet-Based Methods for Time/Phase/Frequency Synchronization 
       [0007]    The distribution of time over packet networks is now ubiquitous. The dominant method is the use of Network Timing Protocol (NTP) for support of general timing applications in general computing applications. However, these implementations, based on existing standards and conventions, are suitable for time alignments on the order of (several) milliseconds. Over the last decade, a new protocol, Precision Timing Protocol (PTP) has emerged supported by industry standards (IEEE 1588v2, ITU G.827x series). The key differentiator between NTP and PTP is the levels of precision obtainable with PTP can support the needs of a variety of new applications and services. Both PTP and NTP are protocols for exchanging time-stamps associated with time-of-arrival and time-of-departure of designated packets and are thus, in principle if not practice, capable of similar performance levels. 
       Combined Methods for Synchronization 
       [0008]    U.S. Patent Application Publication 2014/0192826, entitled “UNIVERSAL ASYMMETRY CORRECTION FOR PACKET TIMING PROTOCOLS” provides methods for utilizing both GPS/GNSS methods and packet-based methods in a collaborative manner to provide a robust scheme for distributing time/frequency between devices. The description of such techniques is provided in U.S. Patent Application Publication 2014/0192826, which is incorporated by reference herein in its entirety. 
         [0009]    In all network-based synchronization schemes the single, dominant, source of time error, error that cannot be corrected by the protocol, is asymmetry. Asymmetry as considered here is the difference in transit delay of the designated event packets in the two directions between the communicating clocks. Whereas packet delay variation is an expected phenomenon in packet networks and contributes to asymmetry, there is an underlying asymmetry component that is entirely independent of the network loading and depends substantively only on the path between the clocks. The path, as considered here, includes all transmission links, including multiplexers and signal-format converters and transmission media, and intermediate network elements, such as switches and routers, between the communicating clocks. 
         [0010]    One approach known in the art that provides both time and frequency alignment involves computing an aligned time signal based on a master timing signal from a primary reference clock, such as a GNSS satellite timing signal, which is held in precise alignment with a global clock reference. This is depicted in panel B of  FIG. 1 . 
         [0011]    The two clocks, CLOCK- 1   110  and CLOCK- 2   120  both receive timing signals  130  from the GNSS system  150 . By aligning themselves to the GNSS timescale, the two clocks are, albeit indirectly, aligned to each other. Using GPS signals or other master timing signals at each network element to achieve time or frequency alignment is generally prohibitively expensive and requires each network element to be able to receive satellite time signals from GPS satellites. There are many situations where visibility of GPS satellites may be compromised, interfered with, or interrupted. It is generally accepted that, whereas GPS is a reliable and robust system, in many installations the visibility of a sufficient number of satellites simultaneously may not be available continuously. 
         [0012]    As described in U.S. Patent Application Publication 2014/0192826, the two clocks  110  and  120  can ascertain the network asymmetry between them by first aligning themselves to the common GNSS timescale. This enables the clocks to synchronize themselves when the GNSS signal is compromised, interfered with, or interrupted. 
       SUMMARY OF INVENTION 
       [0013]    Embodiments disclosed provide robust and practical methods for synchronizing base-stations (“small cells” and “macro cells”) as well as providing for accurate location. Some embodiments leverage the usage of global navigation satellite systems (GNSS) receivers in conjunction with network based schemes for packet-based (time/phase/frequency) synchronization. 
         [0014]    We assume that the receiver is (nominally) fixed in position. By repeatedly developing range estimates and solving for location/time-offset, the receiver can mitigate the impact of noise associated with (range) measurement and clock noise in the receiver clock subsystem. 
         [0015]    Very often the receiver has multiple, possibly more than four, satellites in view and can develop pseudo-range estimates to more than 4 satellites. This results in more than 4 equations and this permits the application of mathematical techniques for noise mitigation. 
         [0016]    This disclosure describes several additional methods for developing multiple equations, the premise being that having an “over-determined” set of equations (more equations than unknowns) enables the use of known mathematical tools for minimizing the impact of measurement and/or clock errors. 
         [0017]    One of the enabling items is that the different receivers/clocks can be operated in a collaborative manner and thereby certain measurements that have significant error can be detected and not used in the solution. 
         [0018]    Another one of the enabling items is that the different clocks can syntonize (i.e. synchronize in terms of frequency) themselves and thus have a common frequency-base. This syntonization is achieved using packet-based methods over the network. This permits the group of clocks to be syntonized (frequency alignment) using packet-based methods (PTP) and synchronized (time alignment) using GNSS or PTP. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]    So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
           [0020]      FIG. 1  depicts the notion of a receiver obtaining its time and frequency from the GNSS system and the notion of two devices synchronizing with each other by simultaneously obtaining time and frequency from the same navigational satellite system. 
           [0021]      FIG. 2  depicts how, depending on the mounting location of the GNSS antenna, part of the sky may be obscured. 
           [0022]      FIG. 3  depicts the urban canyon effect wherein part of the sky may be obscured and satellites in some parts of the sky may be visible via a non-line-of-sight or multipath signal. 
           [0023]      FIG. 4  depicts the case of multipath associated with a particular satellite vehicle as it traverses the sky. 
           [0024]      FIG. 5  depicts a situation where multipath in the case of two receivers in relatively close proximity can be detected by the receivers operating collaboratively. 
           [0025]      FIG. 6  provides a simplified block diagram depicting the generation of the GPS L1 signal. 
           [0026]      FIG. 7  provides a simplified block diagram of the GPS correlation receiver. 
           [0027]      FIG. 8  illustrates the correlation pattern computed via the correlation block. 
           [0028]      FIG. 9  depicts the situation of a collection of clocks with GNSS/GPS Receivers with one Master clock in the set. 
           [0029]      FIG. 10  identifies the case where two clock devices with GNSS/GPS receivers maintain a packet-based timing signal communication that is affected by asymmetry as well as a communication channel to pass parameters related to timing, location, and GNSS receiver signals. 
           [0030]      FIG. 11  depicts a method for iteratively estimating the location/time of GNSS receivers. 
       
    
    
       [0031]    For clarity, identical reference numbers have been used, where applicable, to designate identical elements that are common between figures. It is contemplated that features of one embodiment may be incorporated in other embodiments without further recitation. 
       DETAILED DESCRIPTION 
     The Urban Canyon Effect 
       [0032]    One of the important considerations in deploying small cells with GPS receivers is the “urban canyon effect”. In an ideal situation, the receiver would have a good view of the sky and thereby have a direct line-of-sight path to the satellites. In some cases the receiver antenna is not mounted with a clear view of the sky. For example, the antenna may be mounted on the side of a building and the building may thus appear as an obstruction. This is depicted in  FIG. 2 . 
         [0033]    As shown in  FIG. 2 , the receiver  110  may be on the side of a building  210  that could obstruct the view of some satellites. In  FIG. 2 , the building  210  obstructs the view of satellites SV- 3  and SV- 4  at time t. This obstruction is indicated by the range vectors R 3 (t)  233  and R 4 (t)  234  being depicted with dashed lines. As shown, the receiver  110  can observe the signals from SV- 1   121  and SV- 2   122 . Consequently the receiver  110  can make only 2 pseudo-range estimates. The two equations developed are insufficient to evaluate four unknowns, namely position (x,y,z) and time-offset (δ). 
         [0034]    In practice, if the receiver antenna is fixed then the position may be known and, further, can be assumed to be “constant”. If this is a valid assumption then even though the receiver can observe just two satellites, there is only one unknown, namely time-offset and this can be estimated provided that there is at least one satellite in view. When the primary utility of the receiver is to establish time and frequency, such obstruction can be considered relatively benign if the position of the receiver has been accurately established. 
         [0035]    In the simple configuration of  FIG. 2 , exemplifying cases where the receiver antenna is mounted on the side of a building, the receiver has view of about one-half of the sky, assuming that the building depicted by its outline  210  is impermeable to the radio frequency (RF) signal. Depending on the orbit of a particular satellite vehicle, it is possible that the satellite is observable for much less of the time as compared to the case where there is no obstruction. 
         [0036]    In cases where the receiver antenna is mounted on the side of a building in an urban environment, there can be situations of multipath. This is depicted in  FIG. 3 . 
         [0037]    Of particular importance in  FIG. 3  is the impact of obstruction  310  that may block the signal from the position of SV-1. It can result in reflections as well as blockage. In particular,  FIG. 3  indicates the path  333  that the signal from SV- 3  can take to reach the receiver  110 . Instead of being blocked from view, the receiver sees SV- 3  over a path that is longer than line-of-sight. This is the impact of multipath. Multipath is thus the phenomenon whereby signal from a satellite arrives at the receiver but along a path that is other than line-of-sight and thereby provides an incorrect estimate of the true range, the estimate being greater than the estimate provided by the direct path. 
         [0038]    Whereas the examples given above assume that the satellite constellation at a particular time instant is considered, a similar example can be generated by considering a particular satellite vehicle, say SV-N, as it traverses its orbit. There may be particular times when the satellite is clearly visible, other times when the satellite vehicle is blocked, and yet other times when the satellite signal arrives at the receiver via a non-line-of-sight path (multipath). An example of this situation is depicted in  FIG. 4 . 
         [0039]    As depicted in  FIG. 4 , one satellite, namely SV-N, is present at several different locations in the sky at different times. At time t 1 , satellite SV-N is at location  421  and the range is R N (t 1 )  431 , depicted as a dashed line to point out that the satellite SV-N may be obscured by obstruction  310 . From location  422 , the range R N (t 2 )  432  is representative of line-of-sight. From location  423 , the range R N (t 3 )  433  is not representative of line-of-sight transmission but is observed via a reflected ray. At location  424 , the signal is obscured by obstruction  210 . 
         [0040]    Of particular significance is the situation where there may be two GPS receivers that are in relatively close geographical proximity. This provides the opportunity to utilize the two receivers operating in a collaborative manner in order to mitigate the impact of multipath, which is depicted in  FIG. 5 . 
         [0041]    In  FIG. 5 , there are two receivers REC- 1   511  and REC- 2   512  that are both receiving a signal from SV-N that is at position  523  in the sky. The path to REC- 2   512  is a line-of-sight path  543 , whereas the path to REC- 1   511  is a non-line-of-sight path  533 . The benefit of detecting the multipath nature is that REC- 1   511  can account for that in its solution for time (and location). 
         [0042]    In addition,  FIG. 5  depicts another GPS receiver REC-M  550  located such that it is reasonably close to REC- 1   511  (and REC- 2   512 ) but has a clear view of the sky, particularly for satellite SV-N  523 . This situation is common in base-station deployments wherein the “macro-cell” is generally the large base-station that is deployed to support a wide geographical area and engineered such that it has an unobstructed view of the sky. For improving coverage and additional traffic, several “small cells” are deployed in the general area but it may not be feasible to provide each small cell unobstructed sky view. The small cells and macro-cell collaborate to provide suitable wireless coverage and can also collaborate to improve location/timing performance as described herein. Generally the device with the best sky view is the Master clock of the collection and the other devices function as Slave clocks. 
       Estimating Range 
       [0043]    The GPS signal structure is based on direct sequence spread spectrum modulation. The principal features of the GPS transmit signal are shown in  FIG. 6  by way of a simplified block diagram indicating the manner in which the GPS signal is constructed. 
         [0044]    Each satellite vehicle has a designated spreading code from a collection of Gold codes. The chip-rate used for the direct sequence spreading is 1023 kHz so that there are exactly 1023 chips in a period of 1 ms. The chosen Gold codes have a period of 1023 chips so that the period of the Gold code in time is 1 ms. The information bit rate is 50 b/s so that there are 20 Gold code periods per information bit. 
         [0045]    The clock generator  620  provides the clocking information to generate the Gold code at the correct rate via the CHIP-CLK  622  and the 1 ms period definition via CODE-SYNC  623  and the bit-clock BIT-CLK  624  to the information generator DATA GEN  640 . The direct sequence spreading is achieved by the mixer  630 . The composite (spread-spectrum) signal at the chip rate is applied to a BPSK (binary phase shift keying) modulator  650  and the appropriate L1 carrier signal RF-CLK  625  to establish the composite RF signal  660 . It should be noted that this is the C/A signal defined in the GPS specifications. 
         [0046]    A simplified block diagram of the receiver section that detects the presence of the signal from the particular satellite vehicle and estimates the effective time delay and thereby the “pseudo-range” to the particular satellite vehicle is depicted in  FIG. 7 . The basis of the receiver is the correlation operation whereby the incoming signal is applied to a “matched filter” that is matched to the particular spreading code of the particular satellite vehicle. 
         [0047]    The antenna  710  receives the RF signal from the air and this is down-converted to a suitable intermediate frequency (IF) signal. This IF signal is converted into digital format using an analog-to-digital converter (ADC) to create a digital IF signal  725 . The down-conversion and ADC is depicted as block  720 . 
         [0048]    The digital IF signal  725  is further demodulated to base-band using digital means with a Numerically Controlled Oscillator (NCO)  735 . This approach permits Doppler effect related to satellite motion to be addressed. The demodulation is done in both in-phase and quadrature to create a complex baseband signal  736  that is fed to the complex correlator  750 . The other leg of the correlator  750  is provided with the reference Gold code for this particular satellite vehicle being searched/tracked. The code generator  740  develops the chip pattern against which the incoming RF signal, in the form of the complex baseband signal  736 , is compared. It is well known that the correlation operation is associated with the matched filter, and this operation provides the best signal-to-noise ratio for ascertaining whether the satellite vehicle is being detected/tracked. The NCO  745  serves as the code NCO and is adjusted to provide the code at the appropriate phasing. 
         [0049]    Provided the signal from the satellite under observation is present, the correlator  750  may provide information such as that depicted in  FIG. 8 . The correlation pattern  820  is developed by the correlator  750  which computes the correlation over 1 ms between the received signal  736  and a local replica of the code developed by code generator  740  for different time lags. The correlation pattern  820  represents the magnitude of the correlation. The receiver estimates the time lag T peak    840  by picking the peak value  825  of the correlation pattern. This time lag corresponds to the receivers estimate of the distance (range), expressed in time units, between the receiver and the satellite. Since there may be an offset in the local receiver clock, this range estimate is referred to as “pseudorange”. 
         [0050]    The pseudorange and true range are related by the equation: 
         [0000]      PR( t )= R ( t )+δ( t )   (Eq. 1)
 
         [0000]    where PR(t) is the pseudorange, R(t) is the actual range, and δ(t) is the receiver clock offset. Depending on the convention used, the +sign in the right-hand-side of (Eq. 1) may be changed to a −sign. 
         [0051]    In practice, the estimate may be corrupted by multipath and, further and noise in the correlation estimate. Consequently, the actual estimate of pseudorange is related to the other terms as shown in (Eq. 2): 
         [0000]                ( t )= R ( t )+δ( t )+ m ( t )+ε( t )   (Eq. 2)
 
         [0000]    In (Eq. 2) the pseudorange estimate is affected not just by the local clock offset, δ(t); but also the impact of multipath, m(t); and possible error introduced by noise that introduces an apparent shift of the correlation peak, e(t). If the error introduced by multipath is significant, then the location/time solution will have error in both position and time. Further, note that the multipath error is always positive (or always negative depending on the prevailing convention) and therefore conventional noise mitigation techniques such as averaging are not very useful. 
         [0052]    In some instances position is known to a reasonable accuracy and time is the principal desired result from the calculation. Since, in principle, only one equation is required and additional equations serve to mitigate noise (mainly the measurement noise ε(t)), it is advantageous to identify the subset of pseudoranges that are substantively free of multipath error. 
       Receiver Coordination 
       [0053]    Consider the case when multiple receivers, for example REC- 1   511  and REC-M  550 , can collaborate and exchange information regarding the pseudorange estimate to the same satellite from the multiple receiver locations. 
         [0054]    That is, using the subscripts 1 and M to represent the entities in the two receivers at time t=T 1 , (Eq. 3A) represents the apparent pseudorange PR 1  and (Eq. 3B) provides the pseudorange for REC-M, PR M : 
         [0000]                  1 ( t )= R   1 ( t )+δ 1 ( t )+m 1 ( t )+ε 1 ( t )   (Eq. 3A)
 
         [0000]      PR M ( t )= R   M ( t )+δ M ( t )+ε M ( t )   (Eq. 3B)
 
         [0000]    Since REC-M has a clear view of the sky, there is no multipath term m M (t). 
         [0055]    Given that the two receivers are in reasonably close geographic proximity, the ranges R 1 (t) and R M (t) are related. Specifically, for a given general location on earth, the following limit can be established: 
         [0000]      | R   M ( t )− R   1 ( t )|≦ρ M    (Eq. 4)
 
         [0056]    The subscript M is used to refer to the notion that the range difference ρ M  is associated with the receiver that has the clear view of the sky, although it is not necessary for one or both of the receivers to have a clear view of the sky for a relationship as expressed by (Eq. 4) to apply. 
         [0057]    If it can be ensured that the time errors δ 1 (t) and δ M (t) are close, namely 
         [0000]      |δ M ( t )−δ 1 ( t )|&lt;ε M    (Eq. 5)
 
         [0000]    and the measurement errors ε 1 (t) and ε M (t) can be bounded as 
         [0000]      |ε 1 ( t )|&lt;ε MAX  
 
         [0000]      |ε M ( t )|&lt;ε MAX    (Eq. 6)
 
         [0000]    then by examining the apparent pseudorange for REC- 1  and the pseudorange for REC-M, it can be concluded that if 
         [0000]      |           1 ( t )−PR M ( t )|&gt;THRESHOLD HI    (Eq. 7)
 
         [0000]    then the particular pseudorange measurement is excessively corrupted by multipath. In one embodiment, the receiver may output a signal reflective of such multipath corruption. The value of THRESHOLD HI  is related to the known, pre-determined, limit ρ M  and the estimated time errors and estimated measurement errors. Furthermore, if 
         [0000]      |           1 ( t )−PR M ( t )|&lt;THRESHOLD LO    (Eq. 8)
 
         [0000]    then it is very likely that the particular pseudorange measurement is not corrupted by multipath. 
       Timing Collaboration 
       [0058]    In order to utilize receiver coordination, it is necessary to coordinate the receiver clocks to a level close enough to reject multipath. As will be shown, by coordinating the clocks of the various receivers, all receiver clocks can be syntonized. This syntonization provides additional benefits as will be explained later. 
         [0059]    As depicted in  FIG. 9 , the GPS receiver with the clear (or at least the best) view of the sky is configured as a PTP Master Clock  550  and the other GPS receivers REC- 1 , REC- 2 , and REC- 3  are configured as slave clocks  511 - 513 . These elements are interconnected over a packet network. Given the geographic proximity of the receivers (PTP clocks), the number of intervening switches between the clocks is likely to be small, typically 3 or less. PTP streams  910 ,  920 , and  930  interconnect the slave clocks  511 - 513  to the master clock  550  and deliver timing references that allow the slaves to synchronize with the master. 
         [0060]    Given that the master has a GPS receiver that has a clear view of the sky, the time-clock  550  is accurate. It is generally accepted that a clock with a good GPS receiver with a clear view of the sky can maintain time with an accuracy of better than 100 ns. That is, |δ M (t)|&lt;100 ns. Given that the packet network interconnecting the clocks is small, the syntonization that can be achieved between the slave clocks  511 - 513  and the master clock  550  is excellent. That is, all the slave clocks  511 - 513  may have frequency offsets that are essentially negligible. The time offset between the slave clocks  511 - 513  and the master clock  550  is because the asymmetry of transmission paths between the clocks is unknown. 
         [0061]    Given that the slave clocks are syntonized with the master and, further, that the master is locked to GPS, the slave clock time offset, for example of slave clock  511 , δ 1 (t), remains constant unless and until a correction is applied. 
         [0062]    The architecture is depicted in  FIG. 10  showing one slave clock  511  with its associated GNSS (e.g., GPS) receiver. The intervening network between the slave clock  511  and the master clock  550  may have multiple network elements as well as multiple inter-machine transmission links. All these intervening items can introduce asymmetry. 
         [0063]    The packet network  900  enables the establishment of a (logical) communication channel referred to as the “Optional Asymmetry Messaging Channel”  1065  that can be used to signal between the master and the slave and include information related to asymmetry as well as information regarding satellite information, particularly pseudo-range measurements, as well as the current best approximation of the geographical location. In the scenario being discussed the various receivers are assumed to be stationary and the location is, nominally, a constant. 
       Enhanced Algorithm for GPS Solution 
       [0064]    These observations form the basis of the following approach to establishing and improving location estimates and time offset estimates. For purposes of explanation, the approach is described for receiver REC- 1   511 . 
         [0065]    Denote the location and time offset of REC- 1   511  by the quartuple (x 1 , y 1 , z 1 , δ 1 ), where the location is expressed in Cartesian coordinates with respect to a suitable reference frame. 
         [0066]    The GPS receiver REC- 1   511  continually estimates the pseudorange to all visible GPS satellites. For explanatory purposes assume that these pseudorange estimates are made on a time grid {T n }, where T n  is the GPS time associated with the n th  pseudorange measurement interval. 
         [0067]    At time T n , there may be K satellites visible that are indexed for convenience as j 1 , j 2 , . . . , j K . The receiver REC- 1  and the master clock REC-M generate pseudorange estimates for the K satellites at time T n . As mentioned before, it is possible to eliminate pseudorange measurements that are corrupted by multipath. For sake of example, assume that just one satellite pseudorange associated with satellite j 1  is retained. In GPS methodology, the orbital information available for the satellite vehicles provides a position (x j1 , y j1 , z j1 ) for the satellite at time T n . 
         [0068]    The following equation(s) can be developed for the pseudorange between the receiver and the visible satellite(s) that are deemed to be uncorrupted by multipath (only one equation, representing j1, is shown; additional equations may be available for additional cases where multipath is minimal): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
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                     9 
                   
                   ) 
                 
               
             
           
         
       
     
         [0069]    In (Eq. 9) the term “c” represents the speed of light, δ 1  is the time offset of the clock  511  (REC- 1 ), PR 1j1 (T n ) is the pseudorange (in time units) as computed in REC- 1  for satellite vehicle j1, and ε 1j1 (T n ) represents the remaining error(s) due to measurement inaccuracies after known corrections to the range such as ionospheric corrections have been accounted for. 
         [0070]    Over an extended period, there may be several such equations developed for distinct values of T n . Of special interest is that the same satellite vehicle may be utilized more than once in the set of equations developed. This is permissible because the receivers are syntonized and therefore have a good frequency base so that δ 1  does not change with time (until corrected). 
         [0071]    There are 4 principal unknowns: (x 1 , y 1 , z 1 , δ 1 ) and, consequently, there need to be at least 4 equations to establish these values. If there are only four equations then it is conventional to assume that measurement errors are “zero” and the solutions are therefore colored by the measurement errors. If there are more than 4 equations available, conventional techniques will establish a solution for these four unknowns that minimizes the impact of the measurement error. The equations are not linear equations, but there are conventional methods available to linearize the equations or to solve them using iterative methods such as the Newton-Raphson technique. 
         [0072]    Having several equations, with satellite positions that are diverse, permits choosing a suitable subset of the equations. Given the satellite positions and the approximate location of the receiver REC- 1 , the chosen equations will provide the best Geometric Dilution of Precision (GDOP). 
       Iterative Approach to Improve Location Estimation 
       [0073]    A collection of clocks and receivers may be considered as a self-organizing network. In particular, it is possible for the collection to detect whether a particular clock/receiver has moved. 
         [0074]    At any given time of day, say T n , the location of the satellites in space can be computed. Given the (approximate) location of two receivers, say (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ), and a particular satellite whose location (x S , y S , z S ) is known, the pseudo range differential can be computed and bounded (see Eq. 4). The pseudo range differential can also be measured. If the measured value of the pseudo range differential is substantively different from the computed value, then two possibilities arise. One is that the signal to one or both receivers has been corrupted by multipath and the second is that one, or both, receivers has been moved. Over the course of a day it is very likely that there will be at least some interval where the signal is not corrupted by multipath and within this interval the determination can be made whether the receiver was moved or is in its expected location. Establishing multipath may involve comparing pseudo range residuals between several receivers in the collection. 
         [0075]    An iterative procedure can be used to continually improve the location/time estimates of the receivers. In one embodiment, the iterative procedure may include the steps of  FIG. 11 , which depicts the following method  1100  for iteratively estimating the location/time of GNSS receivers: 
         [0076]    Step  1101  is a background operation in which the receivers are all syntonized using PTP over the network. Although depicted as a first step, it should be understood that PTP may run continually, maintaining syntonization between all the clocks. PTP is also used to estimate the time offset between the various clocks. Until asymmetry of network paths is estimated, the time offset of a particular Slave clock relative to the Master could be incorrect by the amount related to asymmetry. 
         [0077]    At step  1102 , a Master receiver communicates its location to Slave receivers, which use the Master&#39;s location as initial estimates of their own locations. One of the receivers is designated as the Master. This is generally the receiver that has the clearest view of the sky. In wireless deployments this would be the macro-cell in a collection of macro- and small cells. The location of the receiver is established using conventional GPS/GNSS methods and used as a first approximation of their own location. In many cases this approximation may be adequate. PTP provides a time synchronization between the receivers that is reasonably accurate with the principal source of error being the asymmetry. 
         [0078]    At step  1103 , equations, discussed above, are established based on pseudoranges between the Slave receivers and satellites estimated at distinct times or estimated by a plurality of the Slave receivers, and the equations are solved to estimate the time and location at each Slave receiver. Essentially this provides for better estimates of the time and location for the receiver that improve upon the initial estimate of step  1102 . 
         [0079]    At step  1104 , each Slave receiver may output a signal reflective of the time and/or location estimated at that receiver. In turn, such time and location estimates may be used to support enhanced transmission formats and techniques which require tight synchronization between receivers in time/phase and frequency, emergency services such as the E-911 system, among other things. 
         [0080]    After step  1104 , the method  1100  returns to step  1103 , where additional equations are established and used to solve for the time and location at the Slave receivers. 
         [0081]    While the forgoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof. For example, aspects of the present invention may be implemented in hardware or software or in a combination of hardware and software. One embodiment of the invention may be implemented as a program product for use with a computer system. The program(s) of the program product define functions of the embodiments (including the methods described herein) and can be contained on a variety of computer-readable storage media. Illustrative computer-readable storage media include, but are not limited to: (i) non-writable storage media (e.g., read-only memory devices within a computer such as CD-ROM disks readable by a CD-ROM drive, flash memory, ROM chips or any type of solid-state non-volatile semiconductor memory) on which information is permanently stored; and (ii) writable storage media (e.g., floppy disks within a diskette drive or hard-disk drive or any type of solid-state random-access semiconductor memory) on which alterable information is stored. Such computer-readable storage media, when carrying computer-readable instructions that direct the functions of the present invention, are embodiments of the present invention.