Patent Publication Number: US-7899467-B2

Title: Estimating the location of a wireless terminal based on the traits of the multipath components of a signal

Description:
FIELD OF THE INVENTION 
     The present invention relates to telecommunications in general, and, more particularly, to a technique for estimating the location of a wireless terminal and using the estimate of the location in a location-based application. 
     BACKGROUND 
       FIG. 1  depicts a diagram of the salient components of wireless telecommunications system  100  in accordance with the prior art. Wireless telecommunications system  100  comprises: wireless terminal  101 , base stations  102 - 1 ,  102 - 2 , and  102 - 3 , wireless switching center  111 , assistance server  112 , location client  113 , and Global Positioning System (“GPS”) constellation  121 . Wireless telecommunications system  100  provides wireless telecommunications service to all of geographic region  120 , in well-known fashion. 
     The salient advantage of wireless telecommunications over wireline telecommunications is the mobility that is afforded to the users. On the other hand, the salient disadvantage of wireless telecommunications lies in that fact that because the user is mobile, an interested party might not be able to readily ascertain the location of the user. 
     Such interested parties might include both the user of the wireless terminal and remote parties. There are a variety of reasons why the user of a wireless terminal might be interested in knowing his or her location. For example, the user might be interested in telling a remote party where he or she is or might seek advice in navigation. 
     In addition, there are a variety of reasons why a remote party might be interested in knowing the location of the user. For example, the recipient of an E 9-1-1 emergency call from a wireless terminal might be interested in knowing the location of the wireless terminal so that emergency services vehicles can be dispatched to that location. 
     There are many techniques in the prior art for estimating the location of a wireless terminal. 
     In accordance with one technique, the location of a wireless terminal is estimated to be at the center of the cell or centroid of the sector in which the wireless terminal is located. This technique is advantageous in that it does not require that additional hardware be added to the wireless terminal or to the wireless telecommunications system, and, therefore, the first technique can be inexpensively implemented in legacy systems. The first technique is only accurate (in present cellular systems), however, to within a few kilometers, and, therefore, it is generally not acceptable for applications (e.g., emergency services dispatch, etc.) that require higher accuracy. 
     In accordance with a second technique, the location of a wireless terminal is estimated by triangulating the angle of arrival or multilaterating the time of arrival of the signals transmitted by the wireless terminal. This technique can achieve accuracy to within a few hundreds of meters and is advantageous in that it can be used with legacy wireless terminals. The disadvantage of this second technique, however, is that it generally requires that hardware be added to the telecommunication system&#39;s base stations, which can be prohibitively expensive. 
     In accordance with a third technique, the location of a wireless terminal is estimated by a radio navigation unit, such as, for example, a Global Positioning System (GPS) receiver, that is incorporated into the wireless terminal. This technique is typically accurate to within tens of meters but is disadvantageous in that it does not work consistently well indoors, in heavily wooded forests, or in urban canyons. Furthermore, the accuracy of this third technique can be severely degraded by multipath reflections. 
     Therefore, the need exists for a technique for estimating the location of a wireless terminal with higher resolution than the first technique and without some of the costs and disadvantages of the second and third techniques. 
     SUMMARY OF THE INVENTION 
     The present invention enables the construction and use of a system that can estimate the location of a wireless terminal without some of the costs and limitations associated with techniques for doing so in the prior art. 
     The present invention is based on the recognition that there are traits of electromagnetic signals that are dependent on topography, the receiver, the location of the transmitter, and other factors. For example, if a particular radio station is known to be received strongly at a first location and weakly at a second location, and a given wireless terminal at an unknown location is receiving the radio station weakly, it is more likely that the wireless terminal is at the second location than at the first location. 
     By quantifying “strongly” and “weakly” and extending this principle to multiple traits and multiple signals, the present invention can estimate the location of a wireless terminal with greater accuracy. 
     The illustrative embodiment comprises estimating the location of a wireless terminal based on a measured temporal difference of a pair of multipath components of a signal as processed by said wireless terminal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts a map of a portion of a wireless telecommunications system in the prior art. 
         FIG. 2  depicts a diagram of the salient components of wireless telecommunications system  200  in accordance with the illustrative embodiment of the present invention. 
         FIG. 3  depicts a block diagram of the salient components of location server  214 , as shown in  FIG. 2 , in accordance with the illustrative embodiment. 
         FIG. 4  depicts a flowchart of the salient processes performed in accordance with the illustrative embodiment of the present invention. 
         FIG. 5  depicts a flowchart of the salient processes performed in accordance with process  401  of  FIG. 4 : building Location-Trait Database  313 . 
         FIGS. 6   a  through  6   k  depict geographic regions and their deconstruction into a plurality of locations. 
         FIG. 6L  depicts an alternative partitioning of geographic region  220  into 64 square locations. 
         FIG. 6   m  depicts a graphical representation of an adjacency graph of geographic region  220  as partitioned in  FIGS. 6   c  through  6   e.    
         FIG. 6   n  depicts a graphical representation of an adjacency graph of the highway intersection partitioned in  FIGS. 6   h  through  6   k.    
         FIG. 7  depicts a flowchart of the salient processes performed as part of process  402  of  FIG. 4 : populating Trait-Correction Database  313 . 
         FIGS. 8   a  through  8   c  depict illustrative distortion and correction curves. 
         FIG. 9  depicts a flowchart of the salient processes performed in process  403  (of  FIG. 4 ): maintaining Location-Trait Database  313 . 
         FIG. 10  depicts a flowchart of the salient processes performed in process  701  of  FIG. 7 : estimating the location of wireless terminal  201 . 
         FIG. 11   a  depicts a flowchart of the salient processes performed in process  901  of  FIG. 9 : generating the probability distribution for the location of wireless terminal  201  based on the traits of one or more signals received by, or transmitted to, wireless terminal  201  at instants H 1  through H Y . 
         FIG. 11   b  depicts a flowchart of the salient processes performed in accordance with process  1104  of  FIG. 11   a : search area reduction. 
         FIG. 11   c  depicts a flowchart of the salient processes performed in accordance with process  1105 : generating the probability distribution for that wireless terminal  201  at each of instants H 1  through H Y . 
         FIG. 12  depicts a flowchart of the salient processes performed in process  902  of  FIG. 9 : generating the probability distribution for the location of wireless terminal  201  based on GPS-derived information (i.e., information from GPS constellation  221 ). 
         FIG. 13  depicts a flowchart of the salient processes performed in process  903  of  FIG. 9 : combining non-GPS-based and GPS-based probability distributions for the location of wireless terminal  201 . 
         FIG. 14  depicts a first example of combining non-GPS-based instants H 1  through H Y  and GPS-based instants G 1  through G Z  into composite instants J 1  through J F . 
         FIG. 15  depicts a second example of combining non-GPS-based instants H 1  through H Y  and GPS-based instants G 1  through G Z  into composite instants J 1  through J F . 
     
    
    
     DETAILED DESCRIPTION 
     For the purposes of this specification, the following terms and their inflected forms are defined as follows:
         The term “location” is defined as a one-dimensional point, a two-dimensional area, or a three-dimensional volume.   The term “staying probability” is defined as an estimate of the probability P S (b, T, N, W) that wireless terminal W in location b at calendrical time T will still be in location b at time T+Δt, given environmental conditions, N.   The term “moving probability” is defined as an estimate of the probability P M (b, T, N, W, c) that wireless terminal W in location b at calendrical time T will be in adjacent location c at time T+Δt, given environmental conditions, N.   The term “environmental conditions N,” are defined to include one or more physical aspects of the environment, and includes, but is not limited to, the weather, the astronomical conditions, atmospheric conditions, the quantity and density of radio traffic, the quantity and density of vehicular traffic, road and sidewalk construction, etc.   The term “calendrical time T” is defined as the time as denominated in one or more measures (e.g., seconds, minutes, hours, time of day, day, day of week, month, month of year, year, etc.).       

     Overview— FIG. 2  depicts a diagram of the salient components of wireless telecommunications system  200  in accordance with the illustrative embodiment of the present invention. Wireless telecommunications system  200  comprises: wireless terminal  201 , base stations  202 - 1 ,  202 - 2 , and  202 - 3 , wireless switching center  211 , assistance server  212 , location client  213 , location server  214 , and GPS constellation  221 , which are interrelated as shown. The illustrative embodiment provides wireless telecommunications service to all of geographic region  220 , in well-known fashion, estimates the location of wireless terminal  201  within geographic region  220 , and uses that estimate in a location-based application. 
     In accordance with the illustrative embodiment, wireless telecommunications service is provided to wireless terminal  201  in accordance with the Universal Mobile Telecommunications System, which is commonly known as “UMTS.” After reading this disclosure, however, it will be clear to those skilled in the art how to make and use alternative embodiments of the present invention that operate in accordance with one or more other air-interface standards (e.g., Global System Mobile “GSM,” CDMA-2000, IS-136 TDMA, IS-95 CDMA, 3G Wideband CDMA, IEEE 802.11 WiFi, 802.16 WiMax, Bluetooth, etc.) in one or more frequency bands. 
     Wireless terminal  201  comprises the hardware and software necessary to be UMTS-compliant and to perform the processes described below and in the accompanying figures. For example and without limitation, wireless terminal  201  is capable of:
         i. measuring one or more traits of one of more electromagnetic signals and of reporting the measurements to location server  214 , and   ii. transmitting one or more signals and of reporting the transmission parameters of the signals to location server  214 , and   iii. receiving GPS assistance data from assistance server  212  to assist it in acquiring and processing GPS ranging signals.
 
Wireless terminal  201  is mobile and can be at any location within geographic region  220 . Although wireless telecommunications system  200  comprises only one wireless terminal, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that comprise any number of wireless terminals.
       

     Base stations  202 - 1 ,  202 - 2 , and  202 - 3  communicate with wireless switching center  211  and with wireless terminal  201  via radio in well-known fashion. As is well known to those skilled in the art, base stations are also commonly referred to by a variety of alternative names such as access points, nodes, network interfaces, etc. Although the illustrative embodiment comprises three base stations, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that comprise any number of base stations. 
     In accordance with the illustrative embodiment of the present invention, base stations  202 - 1 ,  202 - 2 , and  202 - 3  are terrestrial, immobile, and within geographic region  220 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which some or all of the base stations are airborne, marine-based, or space-based, regardless of whether or not they are moving relative to the Earth&#39;s surface, and regardless of whether or not they are within geographic region  220 . 
     Wireless switching center  211  comprises a switch that orchestrates the provisioning of telecommunications service to wireless terminal  201  and the flow of information to and from location server  214 , as described below and in the accompanying figures. As is well known to those skilled in the art, wireless switching centers are also commonly referred to by other names such as mobile switching centers, mobile telephone switching offices, routers, etc. 
     Although the illustrative embodiment comprises one wireless switching center, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that comprise any number of wireless switching centers. For example, when a wireless terminal can interact with two or more wireless switching centers, the wireless switching centers can exchange and share information that is useful in estimating the location of the wireless terminal. For example, the wireless switching centers can use the IS-41 protocol messages HandoffMeasurementRequest and HandoffMeasurementRequest2 to elicit signal-strength measurements from one another. The use of two or more wireless switching centers is particularly common when the geographic area serviced by the wireless switching center is small (e.g., local area networks, etc.) or when multiple wireless switching centers serve a common area. 
     In accordance with the illustrative embodiment, all of the base stations servicing wireless terminal  201  are associated with wireless switching center  211 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which any number of base stations are associated with any number of wireless switching centers. 
     Assistance server  212  comprises hardware and software that is capable of performing the processes described below and in the accompanying figures. In general, assistance server  212  generates GPS assistance data for wireless terminal  201  to aid wireless terminal  201  in acquiring and processing GPS ranging signals from GPS constellation  221 . In accordance with the illustrative embodiment, assistance server  212  is a separate physical entity from location server  214 ; however, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which assistance server  212  and location server  214  share hardware, software, or both. 
     Location client  213  comprises hardware and software that use the estimate of the location of wireless terminal  201 —provided by location server  214 —in a location-based application, as described below and in the accompanying figures. 
     Location server  214  comprises hardware and software that generate one or more estimates of the location of wireless terminal  201  as described below and in the accompanying figures. It will be clear to those skilled in the art, after reading this disclosure, how to make and use location server  214 . Furthermore, although location server  214  is depicted in  FIG. 2  as physically distinct from wireless switching center  211 , it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which location server  214  is wholly or partially integrated with wireless switching center  211 . 
     In accordance with the illustrative embodiment, location server  214  communicates with wireless switching center  211 , assistance server  212 , and location client  213  via a local area network; however it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which location server  214  communicates with one or more of these entities via a different network such as, for example, the Internet, the Public Switched Telephone Network (PSTN), etc. 
     In accordance with the illustrative embodiment, wireless switching center  211 , assistance server  212 , location client  213 , and location server  214  are outside of geographic region  220 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which some or all of wireless switching center  211 , assistance server  212 , location client  213 , and location server  214  are instead within geographic region  220 . 
     Location Server  214 — FIG. 3  depicts a block diagram of the salient components of location server  214  in accordance with the illustrative embodiment. Location server  214  comprises: processor  301 , memory  302 , and local-area network transceiver  303 , which are interconnected as shown. 
     Processor  301  is a general-purpose processor that is capable of executing operating system  311  and application software  312 , and of populating, amending, using, and managing Location-Trait Database  313  and Trait-Correction Database  314 , as described in detail below and in the accompanying figures. It will be clear to those skilled in the art how to make and use processor  301 . 
     Memory  302  is a non-volatile memory that stores:
         i. operating system  311 , and   ii. application software  312 , and   iii. Location-Trait Database  313 , and   iv. Trait-Correction Database  314 .
 
It will be clear to those skilled in the art how to make and use memory  302 .
       

     Transceiver  303  enables location server  214  to transmit and receive information to and from wireless switching center  211 , assistance server  212 , and location client  213 . In addition, transceiver  303  enables location server  214  to transmit information to and receive information from wireless terminal  201  and base stations  202 - 1  through  202 - 3  via wireless switching center  211 . It will be clear to those skilled in the art how to make and use transceiver  303 . 
     Operation of the Illustrative Embodiment 
       FIG. 4  depicts a flowchart of the salient processes performed in accordance with the illustrative embodiment of the present invention. 
     In accordance with process  401 , Location-Trait Database  313  is built. For the purposes of this specification, the “Location-Trait Database” is defined as a database that maps each of a plurality of locations to one or more expected traits associated with a wireless terminal at that location. The details of building Location-Trait Database  313  are described below and in the accompanying figures. 
     In accordance with process  402 , Trait-Correction Database  314  is built. For the purposes of this specification, the “Trait-Correction Database” is defined as a database that indicates how the measurement of traits can be adjusted to compensate for systemic measurement errors. The details of building Trait-Correction Database  314  are described below and in the accompanying figures. 
     In accordance with process  403 , the location of wireless terminal  201  is estimated based on location-trait database  401 , trait-correction database  402 , and a variety of traits that vary based on the location of wireless terminal  201 . The details of process  403  are described below and in the accompanying figures. 
     In accordance with process  404 , the estimate of the location of wireless terminal  201  is used in a location-based application, such as and without limitation, E 9-1-1 service. The details of process  404  are described below and in the accompanying figures. 
     In accordance with process  405 , Location-Trait Database  313  and Trait-Correction Database  314  are maintained so that their contents are accurate, up-to-date and complete. Process  405  is advantageous because the effectiveness of the illustrative embodiment is based on—and limited by—the accuracy, freshness, and completeness of the contents of Location-Trait Database  313  and Trait-Correction Database  314 . The details of process  405  are described below and in the accompanying figures. 
     Building Location-Trait Database  313 — FIG. 5  depicts a flowchart of the salient processes performed in accordance with process  401 —building Location-Trait Database  313 . 
     In accordance with process  501 , geographic region  220  is partitioned into B(T,N) locations, wherein B(T,N) is a positive integer greater than one, and wherein B(T,N) varies as a function of calendrical time T and the environmental conditions N. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the number of locations that geographic region  220  is partitioned into is static. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the number of locations that geographic region  220  is partitioned into is not dependent on the calendrical time T or the environmental conditions N. 
     Some traits of the radio frequency spectrum and of individual signals are different at different locations in geographic region  220 . Similarly, some traits of the radio frequency spectrum and of individual signals transmitted by wireless terminal  201  change at base stations  202 - 1 ,  202 - 2 , and  202 - 3  when wireless terminal  201  is at different locations. Furthermore, some traits (e.g., hand-off state, etc.) of wireless telecommunications system  200  change when wireless terminal  201  is at different locations. 
     When wireless terminal  201  is at a particular location, the values of the traits that vary with the location of wireless terminal  201  represent a “fingerprint” or “signature” for that location that enables location server  214  to estimate the location of wireless terminal  201 . For example, suppose that under normal conditions the traits have a first set of values when wireless terminal  201  is at a first location, and a second set of values when wireless terminal  201  is at a second location. Then when wireless terminal  201  is at an unknown location and the traits at that unknown location match the second set of values, it is more likely that wireless terminal  201  is at the second location. 
     Although human fingerprints and handwritten signatures are generally considered to be absolutely unique, the combination of traits associated with each location might not be absolutely unique in geographic region  220 . The effectiveness of the illustrative embodiment is enhanced, however, as differences in the values of the traits among the locations increases. It will be clear to those skilled in the art, after reading this disclosure, how to select locations and traits in order to increase the likelihood that the values of the traits associated with each location are distinguishable from the values of the traits associated with the other locations. 
     Each location is described by:
         i. a unique identifier b,   ii. its dimensionality (e.g., one-dimension, two dimensions, three dimensions, four-dimensions, etc.),   iii. the coordinates (e.g., latitude, longitude, altitude, etc.) that define its scope (e.g., position, area, volume, etc.), which can be static or, alternatively, can vary as a function of calendrical time T or the environmental conditions N, or both the calendrical time T and the environmental conditions N.   iv. the expected value E(b, T, N, W, Q) for each trait, Q, when wireless terminal W is at location b at calendrical time T given environmental conditions, N,   v. the identities of its adjacent locations, and   vi. the staying and moving probabilities P S (b, T, N, W) and P M (b, T, N, W, c).       

     In accordance with the illustrative embodiment, the identifier of each location is an arbitrarily-chosen positive integer. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the identifier of some or all locations is not arbitrarily chosen. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the identifier of some or all locations is not a positive integer. 
     In accordance with the illustrative embodiment, the scope of each location is three-dimensional and is described by (i) one or more three-dimensional coordinates and geometric identifiers that define its boundaries, (ii) a three-dimensional coordinate that resides at the centroid of the location, and (iii) a description of how the scope changes as a function of calendrical time T and environmental conditions N. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the scope of some or all of the locations are one-dimensional or two-dimensional. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the scope of some or all of the locations are not a function of calendrical time T or environmental conditions N. 
     In accordance with the illustrative embodiment, the scope of two or more locations can overlap at zero, one, two, more than two, or all points of latitude and longitude (e.g., an overpass and underpass, different stories in a multi-story building as described below, etc.). 
     In accordance with the illustrative embodiment, the boundaries of each location are based, at least in part, on:
         i. natural and man-made physical attributes of geographic region  220  (e.g., buildings, sidewalks, roads, tunnels, bridges, hills, walls, water, cliffs, rivers, etc.),   ii. legal laws governing geographic region  220  (e.g., laws that pertain to the location and movement of people and vehicles, etc.),   iii. theoretical predictions and empirical data regarding the location and movement of individuals and groups of people and vehicles in geographic region  220 ,   iv. the desired accuracy of the estimates made by location server  214 , and   v. patterns of the location and movement of people and vehicles within geographic region  220 ,   vi. the calendrical time T, and   vii. the environmental conditions N,
 
subject to the following considerations:
       

     First, the accuracy with which wireless terminal  201  can be located potentially increases with smaller location sizes. Not all locations need to be the same size, however, and areas requiring greater accuracy can be partitioned into smaller sizes, whereas areas requiring less accuracy can be partitioned into larger sizes. 
     Second, as the number of locations in geographic region  220  increases, so does the computational burden on location server  214  as described below with respect to  FIG. 10 . 
     Third, as the size of adjacent locations decreases, the likelihood increases that the expected values for the traits in those locations will be identical or very similar, which can hinder the ability of location server  214  to correctly determine when wireless terminal  201  is in one location versus the other. 
     With these considerations in mind, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that partition geographic region  220  into any number of locations of any size, shape, and arrangement. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention in which the locations are identical in size and shape. 
       FIG. 6   a  depicts an isometric drawing of geographic region  220  and  FIG. 6   b  depicts a map of geographic region  220 . Geographic region  220  comprises water fountain  601 , park  602 , four-story building  603 , two-story building  604 , various streets, sidewalks, and other features that are partitioned into 28 locations as described below and depicted in  FIGS. 6   c  through  6   e . Although geographic region  220  comprises approximately four square blocks in the illustrative embodiment, it will be clear to those skilled in the art how to make and use alternative embodiments of the present invention with geographic regions of any size, topology, and complexity. 
     In accordance with the illustrative embodiment, the eight road intersections are partitioned into Locations  1  through  8 , as depicted in  FIG. 6   c . In accordance with the illustrative embodiment, the street sections and their adjacent sidewalks up to the edge of buildings  603  and  604  are partitioned into Locations  9  through  19 , as depicted in  FIG. 6   d . In accordance with the illustrative embodiment, water fountain  601  is partitioned into Location  20 , park  602  is partitioned into Location  25 , each floor of building  604  is classified as one of Locations  21 ,  22 ,  23 , and  24 , and each floor of building  603  is classified as of one of Locations  27  and  28 . It will be clear to those skilled in the art, however, after reading this disclosure, how to partition geographic region  220  into any number of locations of any size and shape. 
     In accordance with an alternative embodiment of the present invention, a geographic region that comprises a clover-leaf intersection of two, four-lane divided highways is partitioned into 51 locations.  FIG. 6   f  depicts an isometric drawing of the intersection, and  FIG. 6   g  depicts a map of the intersection. In accordance with the illustrative embodiment, the grass and medians have been partitioned into 15 locations as depicted in  FIG. 6   g , the four ramps have been partitioned into four locations as depicted in  FIG. 6   h , the inner or “passing” lanes have been partitioned into eight locations as depicted in  FIG. 6   i , and the outer or “travel” lanes have been partitioned into eight locations as depicted in  FIG. 6   j.    
       FIG. 6L  depicts an alternative partitioning of geographic region  220  into 64 square locations. 
     In accordance with process  502 , the expected values E(b, T, N, W, Q) for the following traits is associated with each location:
         i. the expected pathloss of all of the signals receivable by wireless terminal  201  when wireless terminal  201  is at the location, from all transmitters (e.g., base stations  202 - 1 ,  202 - 2 , and  202 - 3 , commercial television, commercial radio, navigation, ground-based aviation, etc.), as a function of the calendrical time, T, and the environmental conditions, N; and   ii. the expected pathloss of all of the signals transmitted by wireless terminal  201  when wireless terminal  201  is in the location as receivable at base stations  202 - 1 ,  202 - 2 , and  202 - 3 , as a function of the calendrical time, T, and the environmental conditions, N; and   iii. the expected received signal strength of all of the signals receivable by wireless terminal  201  when wireless terminal  201  is in the location, from all transmitters, as a function of the calendrical time, T, and the environmental conditions, N; and   iv. the expected received signal strength of all of the signals transmitted by wireless terminal  201  when wireless terminal  201  is in the location as receivable at base stations  202 - 1 ,  202 - 2 , and  202 - 3 , as a function of the calendrical time, T, and the environmental conditions, N; and   v. the expected received signal-to-impairment ratio (e.g., Eb/No, etc.) of all of the signals receivable by wireless terminal  201  when wireless terminal  201  is in the location, from all transmitters, as a function of the calendrical time, T, and the environmental conditions, N; and   vi. the expected received signal-to-impairment ratio of all of the signals transmitted by wireless terminal  201  when wireless terminal  201  is in the location as receivable at base stations  202 - 1 ,  202 - 2 , and  202 - 3 , as a function of the calendrical time, T, and the environmental conditions, N; and   vii. the expected received temporal difference of each pair of multipath components (e.g., one temporal difference for one pair of multipath components, a pair of temporal differences for a triplet of multipath components, etc.) of all of the signals receivable by wireless terminal  201  when wireless terminal  201  is in the location, from all transmitters, as a function of the calendrical time, T, and the environmental conditions, N; and   viii. the expected received temporal difference of each pair of multipath components (e.g., one temporal difference for one pair of multipath components, a pair of temporal differences for a triplet of multipath components, etc.) of all of the signals transmitted by wireless terminal  201  when wireless terminal  201  is in the location as receivable at base stations  202 - 1 ,  202 - 2 , and  202 - 3 , as a function of the calendrical time, T, and the environmental conditions, N; and   ix. the expected received delay spread (e.g., RMS delay spread, excess delay spread, mean excess delay spread, etc.) of all of the signals receivable by wireless terminal  201  when wireless terminal  201  is in the location, from all transmitters, as a function of the calendrical time, T, and the environmental conditions, N; and   x. the expected received delay spread (e.g., RMS delay spread, excess delay spread, mean excess delay spread, etc.) of all of the signals transmitted by wireless terminal  201  when wireless terminal  201  is in the location as receivable at base stations  202 - 1 ,  202 - 2 , and  202 - 3 , as a function of the calendrical time, T, and the environmental conditions, N; and   xi. the expected received relative arrival times of two or more multipath components of all of the signals receivable by wireless terminal  201  when wireless terminal  201  is in the location, from all transmitters (which can be determined by a rake receiver in well-known fashion), as a function of the calendrical time, T, and the environmental conditions, N; and   xii. the expected received relative arrival times of two or more multipath components of all of the signals transmitted by wireless terminal  201  when wireless terminal  201  is in the location as receivable at base stations  202 - 1 ,  202 - 2 , and  202 - 3 , as a function of the calendrical time, T, and the environmental conditions, N; and   xiii. the expected round-trip time of all of the signals transmitted and receivable by wireless terminal  201  through base stations  202 - 1 ,  202 - 2 , and  202 - 3 , as a function of the calendrical time, T, and the environmental conditions, N; and   xiv. the expected round-trip time of all of the signals transmitted and receivable by base stations  202 - 1 ,  202 - 2 , and  202 - 3  through wireless terminal  201 , as a function of the calendrical time, T, and the environmental conditions, N; and   xv. the identity of the base stations that provide telecommunications service to the location, as a function of the calendrical time, T, and the environmental conditions, N; and   xvi. the identities of the neighboring base stations that provide telecommunications service to the location, as a function of the calendrical time, T, and the environmental conditions, N; and   xvii. the handover state (e.g., soft, softer, 1×, 2×, etc.) of wireless terminal  201  and wireless telecommunication system  200  when wireless terminal  201  is in the location as a function of the calendrical time, T, and the environmental conditions, N.       

     In accordance with the illustrative embodiment of the present invention, all signals transmitted by wireless terminal  201  are for communicating with base stations  202 - 1  through  202 - 3 , and all of the signals received by wireless terminal  201  are:
         signals transmitted by base stations  202 - 1  through  202 - 3  for communicating with wireless terminal  201 ,   television signals,   radio signals,   aviation signals, and   navigation signals.
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use different signals.
       

     In accordance with the illustrative embodiment, the expected values of these traits are determined through a combination of:
         i. a plurality of theoretical and empirical radio-frequency propagation models, and   ii. a plurality of empirical measurements of the traits within geographic region  220 , in well-known fashion. The empirical measurements of the traits are stored within location-trait database  313  and updated as described below.       

     In accordance with the illustrative embodiment of the present invention, each location b is described by the identities of its adjacent locations, (i.e., the locations that wireless terminal  201  can reasonably move into from location b within one time step Δt.) In accordance with the illustrative embodiment, two locations are considered to be “adjacent” when and only when they have at least two points in common. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which two locations are considered adjacent when they have zero points or one point in common. 
     Adjacency Graph—In accordance with the illustrative embodiment, a data structure is created that indicates which locations are adjacent. This data structure is called an “adjacency graph” and it is stored within Location-Trait Database  313  in sparse-matrix format.  FIG. 6   m  depicts a graphical representation of the adjacency graph for the 28 locations that compose geographic area  220 , and  FIG. 6   n  depicts a graphical representation of the adjacency graph for the 51 locations that compose the highway intersection in  FIGS. 6   f  through  6   k.    
     As described in detail below and in the accompanying figures, the adjacency graph is used in the temporal analysis of wireless terminal  201 &#39;s movements. It will be clear to those skilled in the art, after reading this disclosure, how to make the adjacency graph for any partitioning of geographic region  220 . 
     In accordance with the illustrative embodiment, the staying and moving probabilities P S (b, T, N, W) and P M (b, T, N, W, c) for all b are generated based on a model of the movement of wireless terminal W that considers:
         i. the topology of the adjacency graph; and   ii. the calendrical time T; and   iii. the environmental conditions N; and   iv. the natural and man-made physical attributes that affect the location and movement of wireless terminals and the entities that carry them (e.g., buildings, sidewalks, roads, tunnels, bridges, hills, walls, water, cliffs, rivers, etc.); and   v. the legal laws governing the location and movement of wireless terminals and the entities that carry them (e.g., one-way streets, etc.); and   vi. the past data for the movement of all wireless terminals; and   vii. the past data for the movement of wireless terminal W.
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use any subcombination of i, ii, iii, iv, v, vi, and vii to generate the staying and moving probabilities for each location b.
       

     The moving probabilities P M (b, T, N, W, c) associated with a location b can be considered to be either isotropic or non-isotropic. For the purposes of this specification, “isotropic moving probabilities” are defined as those which reflect a uniform likelihood of direction of movement and “non-isotropic moving probabilities” are defined as those which reflect a non-uniform likelihood of direction of movement. For example, for locations arranged in a two-dimensional regular hexagonal grid the values of P M (b, T, N, W, c) of location b are isotropic if and only if they are all equal (e.g., P M (b, T, N, W, c)=⅙ for each adjacent location c). Conversely, the values of P M (b, T, N, W, c) are non-isotropic if there are at least two probabilities with different values. As another example, for locations arranged in a two-dimensional “checkerboard” grid, the values of P M (b, T, N, W, c) are isotropic if and only if:
         (i) the north, south, east, and west moving probabilities out of location b all equal p,   (ii) the northeast, northwest, southeast, and southwest moving probabilities out of location b all equal p/√{square root over (2)}, and   (iii) 4p(1+1/√{square root over (2)})+P S (b, T, N, W)=1.       

     Isotropic moving probabilities are simple to generate, but are considerably less accurate than non-isotropic moving probabilities that are generated in consideration of the above criteria. Therefore, in accordance with the illustrative embodiment, the moving probabilities are non-isotropic, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use isotropic moving probabilities. 
     Populating Trait-Correction Database  313 — FIG. 7  depicts a flowchart of the salient processes performed as part of process  402 : populating Trait-Correction Database  313 . 
     In general, the ability of location server  214  to estimate the location of wireless terminal  201  is limited by the accuracy with which the traits are measured by wireless terminal  201  and by base stations  202 - 1 ,  202 - 2 , and  202 - 3 . When the nature or magnitude of the measurement errors is unpredictably inaccurate, there is little that can be done to overcome them. 
     In contrast, when the nature and magnitude of the measurement errors are predictable, they can be corrected, and the nature and magnitude of some measurement errors are, in fact, predictable. For example, one make and model of wireless terminal is known to erroneously measure and report the signal strength of signals by −2 dB. If the measurements from this model of wireless terminal are left uncorrected, this −2 dB error could cause location server  214  to erroneously estimate the location of the wireless terminal. In contrast, if location server  214  adds 2 dB to the measurements from that make and model of wireless terminal, the likelihood that location server  214  would erroneously estimate the location of the wireless terminal would be reduced. 
     Trait-Correction Database  313  comprises the information needed by location server  214  to be aware of systemic measurement errors and to correct them. A technique for eliminating some situational errors in the measurements is described below and in the accompanying figures. 
     In accordance with process  701 , a distortion function is generated for every radio that might provide measurements to location server  214  and for every trait whose measurements can be erroneous. 
     In general, the distortion function D(A,K,Q) relates the reported measurement R for a trait Q to the actual value A for that trait and the defining characteristic K of the radio making the measurement:
 
 R=D ( A,K,Q ).  (Eq. 1)
 
     In accordance with the illustrative embodiment, the distortion function D(A,K,Q) is provided to the owner/operator of location server  214  by the radio manufacturer. It will be clear to those skilled in the art, however, after reading this disclosure, how to generate the distortion function D(A,K,Q) for any radio without the assistance of the radio manufacturer. 
     An ideal radio perfectly measures and reports the value of the traits it receives and the distortion function D(A,K,Q) for one trait and for an ideal radio is depicted in  FIG. 8   a . As can be seen from the graph in  FIG. 8   a , the salient characteristic of an ideal radio is that the reported value of the measurement, R, is exactly equal to the actual value of the trait A at the radio (i.e., there is no measurement or reporting error). 
     In contrast, most real-world radios do not perfectly measure the traits of the signals they receive. This is particularly true for measurements of signal-strength where the errors can be large. For example,  FIG. 8   b  depicts a graph of the distortion function of an illustrative real-world radio. In this case, the reported measurement is too high for some values, too low for others, and correct for only one value. 
     The nature and magnitude of each of the errors in the reported measurements is inherent in the distortion function D(A,K,Q), and, therefore, knowledge of the distortion function enables the measurement errors to be compensated for. In other words, when location server  214  knows exactly how a radio distorts a measurement, it can correct—or calibrate—the reported measurement with a calibration function to derive the actual value of the trait. The calibration function, denoted C(R,K,Q), is generated in process  1102 . 
     In accordance with the illustrative embodiment, the distortion function D(A,K,Q) for all measurements is represented in tabular form. For example, the distortion function for one type of signal-strength measurement for various radios is shown in Table 1. It will be clear to those skilled in the art, after reading this disclosure, however, how to make and use alternative embodiments of the present invention in which the distortion function for some or all measurements is not represented in tabular form. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that comprise distortion functions for any type of measurement of any type of trait and for any radio. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 The Distortion function D(A, K, Q) in Tabular Form 
               
            
           
           
               
               
            
               
                   
                 R = D(A, K, Q) 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 K = Motorola 
                   
                 K = Samsung 
               
               
                   
                   
                 Model A008; Q = 
                   
                 Model A800; Q = 
               
               
                   
                 A 
                 Signal Strength 
                 . . . 
                 Signal Strength 
               
               
                   
                   
               
               
                   
                 −110 
                 −115 
                 . . . 
                 −107 
               
               
                   
                 −109 
                 −114 
                 . . . 
                 −106 
               
               
                   
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                   
                  −48 
                  −38 
                 . . . 
                  −50 
               
               
                   
                  −47 
                  −37 
                 . . . 
                  −49 
               
               
                   
                   
               
            
           
         
       
     
     The purpose of the characteristic, K, is to identify which calibration function should be used in calibrating the reported measurements from wireless terminal  201 , and, therefore, the characteristic, K, should be as indicative of the actual distortion function for wireless terminal  201  as is economically reasonable. 
     For example, the characteristic, K, can be, but is not limited to:
         i. the unique identity of wireless terminal  201  (e.g., its electronic serial number (“ESN”), its international mobile station identifier (“IMSI”), its temporary international mobile station identifier (“TIMSI”), mobile station identification (“MSID”), its directory number (“DN”), etc.); or   ii. the model of wireless terminal  201  (e.g., Timeport  210   c , etc.); or   iii. the make (i.e., manufacturer) of wireless terminal  201  (e.g., Motorola, Samsung, Nokia, etc.); or   iv. the identity of the radio-frequency circuitry of wireless terminal  201  (e.g., Motorola RF circuit design  465 B, etc.); or   v. the identity of one or more components of wireless terminal  201  (e.g., the part number of the antenna, the part number of the measuring component, etc.); or   viii. any combination of i, ii, iii, iv, v, vi, and vii.       

     The most accurate characteristic is the unique identity of wireless terminal  201  because that would enable location server  214  to use the calibration function generated for that very wireless terminal. It is unlikely, however, that this is economically feasible because it would require that every wireless terminal be tested to determine its own unique distortion function. 
     On the other hand, using only the make of wireless terminal  201  as the characteristic, K, is economically reasonable, but it is unlikely that a single calibration function for all of a manufacturer&#39;s wireless terminals would provide very accurate calibrated signal-strength measurements. 
     As a compromise, the illustrative embodiment uses the combination of make and model of wireless terminal  201  as the characteristic, K, because it is believed that the amount of variation between wireless terminals of the same make and model will be small enough that a single calibration function for that model should provide acceptably accurate calibrated measurements for every wireless terminal of that make and model. 
     It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the characteristic, K, is based on something else. 
     In accordance with process  502 , the calibration function C(R,K,Q) is generated for every radio that might provide measurements to location server  214  and for every trait whose measurements can be distorted. 
     In general, the calibration function C(R,K,Q) relates the calibrated measurement S of a trait Q, to the reported measurement R of trait Q and the defining characteristic K of the radio making the measurement:
 
 S=D ( R,K,Q )  (Eq. 2)
 
     The calibration function C(R,K,Q) is the inverse of the distortion function D(A,K,Q). In other words, the salient characteristic of the calibration function C(R,K,Q) is that it satisfies the equation 3:
 
 S=A=C ( D ( A,K,Q ), K,Q )  (Eq. 3)
 
so that the calibrated measurement, S, is what the reported measurement, R, would have been had the radio making and reporting the measurement been ideal. It will be clear to those skilled in the art, after reading this disclosure, how to derive C(R,K,Q) from D(A,K,Q).  FIG. 8   c  depicts a graph of the calibration function C(R,K,Q) for the distortion function D(A,K,Q) depicted in  FIG. 8   b.  
 
     In accordance with the illustrative embodiment, the function C(R,K,Q) is represented in tabular form, such as that shown in Table 2. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 The Calibration Function C(R, C, N) in Tabular Form 
               
            
           
           
               
               
            
               
                   
                 S = C(R, C, N) 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 C = Motorola 
                   
                 C = Samsung 
               
               
                   
                   
                 Model A008; Q = 
                   
                 Model A800; Q = 
               
               
                   
                 R 
                 Signal Strength 
                 . . . 
                 Signal Strength 
               
               
                   
                   
               
               
                   
                 −110 
                 −115 
                 . . . 
                 −107 
               
               
                   
                 −109 
                 −114 
                 . . . 
                 −106 
               
               
                   
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                   
                  −48 
                  −38 
                 . . . 
                  −50 
               
               
                   
                  −47 
                  −37 
                 . . . 
                  −49 
               
               
                   
                   
               
            
           
         
       
     
     In accordance with process  402 , the calibration functions C(R,K,Q) are stored in Trait-Corrections Database  313 . 
     Maintaining Location-Trait Database  313 — FIG. 9  depicts a flowchart of the salient processes performed in process  403 : maintaining Location-Trait Database  313  and Trait-Corrections Database  314 . The ability of the illustrative embodiment to function is based on—and limited by—the accuracy, freshness, and completeness of the information contained in Location-Trait Database  313  and Trait-Corrections Database  314 . 
     In accordance with process  901 , a drive-test regimen is developed that periodically makes empirical measurements throughout geographic region  220  with highly-accurate equipment to ensure the accuracy, freshness, and completeness of the information contained in Location-Trait Database  313  and Trait-Corrections Database  314 . 
     In accordance with process  902 , the drive-test regimen is implemented. 
     In accordance with process  903 , Location-Trait Database  313  and Trait-Corrections Database  314  are updated, as necessary. 
     Estimating the Location of Wireless Terminal  201 — FIG. 10  depicts a flowchart of the salient processes performed in process  403 : estimating the location of wireless terminal  201 . In accordance with the illustrative embodiment, process  403  is initiated by a request from location client  213  for the location of wireless terminal  201 . It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which process  403  is initiated periodically, sporadically, or in response to some other event. 
     In accordance with process  1001 , Y probability distributions for the location of wireless terminal  201  are generated for each of instants H 1  through H Y  in the temporal interval ΔT, wherein Y is a positive integer, based on comparing the measurements of traits associated with wireless terminal  201  at each of instants H 1  through H Y  to expected values for those traits at those times. Each of the Y probability distributions provides a first estimate of the probability that wireless terminal  201  is in each location at each of instants H 1  through H Y . The details of process  1001  are described below and in the accompanying figures. 
     In accordance with process  1002 , Z probability distributions for the location of wireless terminal  201  are generated for each of instants A 1  though A Z  in the temporal interval ΔT, wherein Z is a positive integer, based on Assisted GPS measurements at wireless terminal  201  at each of instants A 1  though A Z . Each of the Z probability distributions provides a first estimate of the probability that wireless terminal  201  is in each location at each of instants A 1  though A Z . The details of process  1002  are described below and in the accompanying figures. 
     In accordance with process  1003 , the Y probability distributions generated in process  1001  and the Z probability distributions generated in process  1002  are combined, taking into account their temporal order, to generate a second estimate of the location of wireless terminal  201 . The details of process  1003  are described below and in the accompanying figures. 
     Generating the Probability Distributions for the Location of Wireless Terminal  201  Based on Pattern Matching of Traits— FIG. 11   a  depicts a flowchart of the salient processes performed in process  1001 —generating the Y probability distributions for the location of wireless terminal  201  based on comparing the measurements of traits associated with wireless terminal  201  at each of instants H 1  through H Y  to expected values for those traits at those times. In accordance with the illustrative embodiment, location server  214  performs each of processes  1101  through  1105  as soon as the data necessary for performing the process becomes available to it. 
     In accordance with process  1101 , location server  214  receives Y non-empty sets of measurements of the traits, M 1  though M Y , associated with wireless terminal  201 . Each set of measurements is made at one of instants H 1  through H Y . 
     In accordance with the illustrative embodiment, each set of measurements comprises:
         i. the pathloss of all of the signals received by wireless terminal  201  from all transmitters (e.g., base stations  202 - 1 ,  202 - 2 , and  202 - 3 , commercial television, commercial radio, navigation, ground-based aviation, etc.); and   ii. the pathloss of all of the signals transmitted by wireless terminal  201  as received at base stations  202 - 1 ,  202 - 2 , and  202 - 3 ; and   iii. the received signal strength of all of the signals received by wireless terminal  201  from all transmitters; and   iv. the received signal strength of all of the signals transmitted by wireless terminal  201  as received at base stations  202 - 1 ,  202 - 2 , and  202 - 3 ; and   v. the received signal-to-impairment ratio of all of the signals received by wireless terminal  201  from all transmitters; and   vi. the received signal-to-impairment ratio of all of the signals transmitted by wireless terminal  201  as received at base stations  202 - 1 ,  202 - 2 , and  202 - 3 ; and   vii. the received temporal difference of each pair of multipath components of all of the signals received by wireless terminal  201  from all transmitters; and   viii. the received temporal difference of each pair of multipath components of all of the signals transmitted by wireless terminal  201  as received at base stations  202 - 1 ,  202 - 2 , and  202 - 3 ; and   ix. the received delay spread of all of the signals received by wireless terminal  201  from all transmitters; and   x. the received delay spread of all of the signals transmitted by wireless terminal  201  as received at base stations  202 - 1 ,  202 - 2 , and  202 - 3 ; and   xi. the received relative arrival times of two or more multipath components of all of the signals received by wireless terminal  201  from all transmitters; and   xii. the received relative arrival times of two or more multipath components of all of the signals transmitted by wireless terminal  201  as received at base stations  202 - 1 ,  202 - 2 , and  202 - 3 ; and   xiii. the round-trip time of all of the signals transmitted and received by wireless terminal  201  through base stations  202 - 1 ,  202 - 2 , and  202 - 3 ; and   xiv. the round-trip time of all of the signals transmitted as received at base stations  202 - 1 ,  202 - 2 , and  202 - 3  through wireless terminal  201 ; and   xv. the identity of the base stations that provide telecommunications service to wireless terminal  201 ; and   xvi. the identities of the neighboring base stations that can provide telecommunications service to wireless terminal  201 ; and   xvii. the handover state (e.g., soft, softer, 1×, 2×, etc.) of wireless terminal  201  and wireless telecommunication system  200 ; and   xviii. an indication of the calendrical time, T; and   xix. an indication of the environmental conditions, N.       

     In accordance with the illustrative embodiment, wireless terminal  201  provides its measurements directly to location server  214  via the user plane and in response to a request from location server  214  to do so. This is advantageous because the quality of the estimate of the location of wireless terminal  201  is enhanced when there are no limitations on the nature, number, or dynamic range of the measurements—as might occur when measurements are required to be made in accordance with the air-interface standard. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which wireless terminal  201  provides its measurements periodically, sporadically, or in response to some other event. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which wireless terminal  201  provides its measurements to location server  214  via the UMTS protocol. 
     In accordance with the illustrative embodiment, base stations  202 - 1 ,  202 - 2 , and  202 - 3  provide their measurements to location server  214  via wireless switching center  211  and in response to a request from location server  214  to do so. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which base stations  202 - 1 ,  202 - 2 , and  202 - 3  provide their measurements to location server  214  periodically, sporadically, or in response to some other event. 
     As part of process  1101 , location server  214  also receives from wireless terminal  201 :
         i. the identities of the base stations that provided service to wireless terminal  201  at each of instants H 1  through H Y , and   ii. the identities of the neighboring base stations that provided service to the location of wireless terminal  201  at each of instants H 1  through H Y .
 
This information is used by location server  214  in performing search area reduction, which is described in detail below.
       

     In accordance with process  1102 , location server  214  uses the calibration functions C(R,K,Q) in the Trait-Corrections Database  314  to correct the systemic errors in the measurements received in process  1001 . 
     In accordance with process  1103 , location server  214  computes the differentials, in those cases that are appropriate, of the measurements to correct the situational errors in the measurements received in process  1001 . Many factors, including the condition of wireless terminal  201 &#39;s antenna, the state of its battery, and whether or not the terminal is inside a vehicle can introduce situational measurement errors. This is particularly true for measurements of pathloss and signal strength. 
     The illustrative embodiment ameliorates the effects of these factors by pattern matching not the measurements themselves—whether corrected in process  1102  or not—to the expected values for those traits, but by pattern matching the pair-wise differentials of those measurements to the pair-wise differentials of the expected values for those traits. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which different measurements are corrected for situational errors by the use of pair-wise differentials. 
     A simple example involving signal strengths illustrates this approach. A first radio station, Radio Station A, can be received at −56 dBm at Location  1 , −42 dBm at Location  2 , −63 dBm at Location  3 , and −61 dBm at Location  4 , and a second radio station, Radio Station B, can be received at −63 dBm at Location  1 , −56 dBm at Location  2 , −65 dBm at Location  3 , and −52 dBm at Location  4 . This information is summarized in the table below and forms the basis for a map or database that correlates location to signal strength. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Illustrative Location-Trait Database (Differential Reception) 
               
            
           
           
               
               
               
               
            
               
                   
                 Radio 
                 Radio 
                   
               
               
                   
                 Station A 
                 Station B 
                 Difference 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Location 1 
                 −56 dBm 
                 −63 dBm 
                 −7 dB 
               
               
                   
                 Location 2 
                 −42 dBm 
                 −56 dBm 
                 −14 dB  
               
               
                   
                 Location 3 
                 −63 dBm 
                 −65 dBm 
                 −2 dB 
               
               
                   
                 Location 4 
                 −61 dBm 
                 −52 dBm 
                   9 dB 
               
               
                   
                   
               
            
           
         
       
     
     If a given wireless terminal with a broken antenna and at an unknown location receives Radio Station A at −47 dBm and Radio Station B at −61 dBm, then it registers Radio Station A as 14 dBm stronger than Radio Station B. This suggests that the wireless terminal is more likely to be at Location  2  than it is at Location  1 ,  3 , or  4 . If the measured signal strengths themselves were pattern matched into Location-Trait Database  313 , the resulting probability distribution for the location of wireless terminal  201  might not be as accurate. 
     A disadvantage of this approach is that the situational bias is eliminated at the expense of (1) doubling the variance of the random measurement noise, and (b) reducing the number of data points to pattern match by one. Furthermore, the pair-wise subtraction introduces correlation into the relative signal strength measurement errors (i.e., all of the data points to be matched are statistically correlated). It will be clear to those skilled in the art how to account for this correlation in calculating the likelihood of the measurement report. 
     In accordance with process  1104 , location server  214  performs a technique called “search area reduction” in preparation for process  1105 . To understand what search area reduction is and why it is advantageous, a brief discussion of process  1105  is helpful. In process  1105  location server  214  estimates the probability that wireless terminal  201  is in each location at each of instants H 1  through H Y . This requires generating Y multi-dimensional probability distributions, one for each of instants H 1  through H Y . 
     The process for generating each multi-dimensional probability distribution can be computationally intensive and the intensity depends on the number of locations that must be considered as possible locations for wireless terminal  201 . When the number of locations that must be considered is small, the process can be performed quickly enough for many “real-time” applications. In contrast, when the number of locations that must be considered is large, the process can often take too long. 
     Nominally, all of the locations in geographic region  220  must be considered because, prior to process  1104 , wireless terminal  201  could be in any location. In accordance with the illustrative embodiment, geographic region  220  comprises only 28 locations. In many alternative embodiments of the present invention, however, geographic region  220  comprises thousands, millions, or billions of locations. The consideration of thousands, millions, or billions of locations for each instant by location server  214  might take too long for many real-time applications. 
     Therefore, to expedite the performance of process  1105 , location server  214  performs some computationally-efficient tests that quickly and summarily eliminate many possible locations for wireless terminal  201  from consideration, and, therefore, summarily set to zero the probability that wireless terminal  201  is at those locations. This reduces the number of locations that must be fully considered in process  1105  and generally improves the speed with which process  1001  is performed. 
     In accordance with search area reduction, for each of instants Ha through H Y  location server  214  uses six computationally efficient tests in an attempt to designate one or more locations as improbable locations for wireless terminal  201 . A location that is designated as improbable by one or more of the six tests at instant H i  is designated as improbable by process  1104  at instant H i . To the extent that a location is designated as improbable at instant H i , the computational burden on location server  214  of generating the probability distribution for that instant is reduced. 
     There are two types of errors that can be made by process  1104 . The first type of error—a Type I error—occurs when process  1104  designates a location as improbable when, in fact, it is not improbable for wireless terminal  201  to be in that location. The second type of error—a Type II error—occurs when process  1104  fails to designate a location as improbable when, in fact, it is improbable that wireless terminal  201  is in that location. 
     In general, a Type I error affects the accuracy with which the illustrative embodiment can estimate the location of wireless terminal  201 , and a Type II error affects the speed with which processor  1104  can generate the probability distributions. In accordance with the illustrative embodiment, the tests and their parameters are chosen to balance the number of Type I and Type II errors with the computational complexity and value of process  1104 . For example, when there are too many Type II errors, the value of process  1104  is undermined by the computational burden of process  1104 . It will be clear those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that have any number of Type I and Type II errors. 
       FIG. 11   b  depicts a flowchart of the salient processes performed in accordance with process  1104 : search area reduction. 
     In accordance with process  1111 , location server  214  designates a location as improbable when the difference between a measured value of a trait and the expected value of that trait at that location exceeds a threshold. The theory underlying this test is that a major discrepancy between a measurement of a trait and the expected value of a trait at a location suggests that the measurement was not made when wireless terminal  201  was in that location. In accordance with the illustrative embodiment, location engine  214  performs process  1111  on each measured value of each trait for each signal for each of instants H 1  through H Y . It will be clear to those skilled in the art, after reading this disclosure, how to choose the traits and signals and thresholds to achieve the desired number of Type I and Type II errors. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that omit process  1111  or that omit testing one or more traits and/or one or more signals in process  1111 . 
     In accordance with process  1112 , when the magnitude of two measurements of a trait at one instant exceed a first threshold and the magnitude of the expected values for that trait at a location exceed a second threshold, location server  214  designates that location as improbable when a ranking of the two measurements differs from a ranking of the expected values. The theory underlying this test is that a major discrepancy between the ranking of the measurements of a trait and the ranking of the expected values of that trait in the location suggests that the measurements were not made when wireless terminal  201  was in that location. In accordance with the illustrative embodiment, location engine  214  performs process  1112  on each pair of measurements of each trait for each of instants H 1  through H Y . It will be clear to those skilled in the art, after reading this disclosure, how to choose the traits and signals and thresholds to achieve the desired number of Type I and Type II errors. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that omit process  1112  or that omit testing one or more traits and/or one or more signals in process  1112 . 
     In accordance with process  1113 , location server  214  designates a location as improbable when a measurement of traits of a signal is not received when it is expected if wireless terminal  201  were, in fact, in that location. In accordance with the illustrative embodiment, location engine  214  performs process  1113  on each trait of each expected signal for each of instants H 1  through H Y . This test is highly prone to Type I errors and should be used judiciously. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that omit process  1113  or that omit testing one or more traits and/or one or more signals in process  1113 . 
     In accordance with process  1114 , location sever  214  designates a location as improbable when a measurement of a trait of a signal is received when it is not expected if wireless terminal  201  were, in fact, in that location. In accordance with the illustrative embodiment, location engine  214  performs process  1114  on each trait of each signal for each of instants H 1  through H Y . In general, this test is less prone to Type I errors than the test in process  1113 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that omit process  1114  or that omit testing one or more traits and/or one or more signals in process  1114 . 
     In accordance with process  1115 , location server  214  designates a location as improbable when the location is not provided wireless telecommunications service by a base station that is known to be providing service to wireless terminal  201  at that instant. The theory underlying this test is that if a base station that provided telecommunications service to wireless terminal  201  at that instant does not provide service to the location, then it suggests that wireless terminal  201  is not in that location at that instant. In general, this test is highly accurate and has a low number of both Type I and Type II errors. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that omit process  1115 . 
     In accordance with process  1116 , location server  214  designates a location as improbable designating a possible location as improbable when the location is not within the neighboring coverage area of a base station that is known to be a neighboring base station of wireless terminal  201 . The theory underlying this test is that if a location is not within the neighboring coverage area of a base station that is a neighbor of wireless terminal  201  at that instant, then it suggests that wireless terminal  201  is not in the location at that instant. In general, this test is highly accurate and has a low number of both Type I and Type II errors. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that omit process  1116 . 
     A location that that is designated as improbable at instant H i  by one or more of processes  1111  through  1116  is designated as improbable by process  1104  at instant H i . 
     In accordance with process  1105 , location server  214  generates each of the Y probability distribution for that wireless terminal  201  at each of instants H 1  through H Y . To accomplish this, location server  214  performs the processes described below and in  FIG. 11   c.    
       FIG. 11   c  depicts a flowchart of the salient processes performed in accordance with process  1105 : generating the Y probability distribution for that wireless terminal  201  at each of instants H 1  through H Y . 
     In accordance with process  1121 , location server  214  sets the probability of wireless terminal  201  being at a location at instant H i  to zero (0) if the location was designated as improbable at instant H i  by process  1104 . 
     In accordance with process  1122 , location server  214  generates the Euclidean norm between the measurements of a trait and the expected values for that trait at all instants and for all locations not designated as improbable by process  1104 . To accomplish this, the Euclidean norm is generated between the measurements (as corrected in process  1102 , if necessary and/or the differentials of measurements as the case may be) of the expected values for those traits in Location-Trait Database  313 . To accomplish this, the Euclidean norm is generated as described in Equation 4:
 
 V ( b,H   i )=√{square root over (Σ(( E ( b,H   i   ,N,W,Q )− M ( b,H   i   ,N,W,Q ))·ω( Q )) 2 )}{square root over (Σ(( E ( b,H   i   ,N,W,Q )− M ( b,H   i   ,N,W,Q ))·ω( Q )) 2 )}{square root over (Σ(( E ( b,H   i   ,N,W,Q )− M ( b,H   i   ,N,W,Q ))·ω( Q )) 2 )}  (Eq. 4)
 
wherein V(b,H i ) is the Euclidean norm for Location b at instant H i  based on the square root of the sum of the square of the differences between each (corrected and differential, where appropriate) trait measurement M(b, H i , N, W, Q) minus the expected value E(b, H i , N, W, Q) for that trait, where ω(Q) is a weighting factor that indicates the relative weight to be given discrepancies in one trait versus discrepancies in the other traits.
 
     At accordance with process  1123 , the un-normalized probabilities of the location of wireless terminal  201  at each location are generated based on the Euclidean norms generated in process  1122  as shown in Equation 5. 
                     UP   ⁡     (     b   ,     H   i       )       =     ⅇ     (       -       V   2     ⁡     (     b   ,     H   i       )           δ   2       )               (     Eq   .           ⁢   5     )               
wherein UP(b,H i ) represents the un-normalized probability that wireless terminal  201  is in Location b at instant H i , and wherein δ 2  equals:
 
                     δ   2     =       δ   E   2     +     δ   M   2               (     Eq   .           ⁢   6     )               
wherein δ E   2  is the square of the uncertainty in the error in Location-Trait Database and δ M   2  is the square of the uncertainty in the calibrated measurements. It will be clear to those skilled in the art, after reading this disclosure, how to generate δ 2 .
 
     At process  1124 , the probabilities generated in process  1123  are normalized as described in Equation 7. 
                     NP   ⁡     (     b   ,     H   i       )       =       UP   ⁡     (     b   ,     H   i       )         ∑     UP   ⁡     (     b   ,     H   i       )                   (     Eq   .           ⁢   7     )               
wherein NP(b,H i ) represents the normalized probability that wireless terminal  201  is in Location b.
 
     As part of process  1124 , location server  214  generates a preliminary estimate of the location of wireless terminal  201  at instant H 1  based on the maximum likelihood function of the normalized probability distribution at instant H i . 
     Generating the Probability Distributions for the Location of Wireless Terminal  201  Based on Assisted GPS— FIG. 12  depicts a flowchart of the salient processes performed in process  1002 : generating the Z probability distributions for the location of wireless terminal  201  based on GPS-derived information (i.e., information from GPS constellation  221 ). 
     In accordance with processes  1124  and  1201 , location server  214  transmits, and assistance server  212  receives, the preliminary estimate of the location of wireless terminal  201  at instant H 1  as generated in process  1105 . 
     In accordance with process  1202 , assistance server  212  generates assistance data for wireless terminal  201  based on the preliminary estimate of the location of wireless terminal  201  at instant H 1 . In accordance with the illustrative embodiment, assistance server  212  generates “fully-custom” assistance data based on the estimate of the location of wireless terminal  201  at instant H 1 . The assistance data is “fully-custom” because it is specifically tailored to the estimated location of wireless terminal  201  at instant H 1 . It will be clear to those skilled in the art how to generate fully-custom assistance data for wireless terminal  201  based on the estimated location of wireless terminal  201  at instant H 1 . As part of process  1202 , assistance server  212  transmits the assistance data to wireless terminal  201  via wireless switching center  212  in well-known fashion. 
     In accordance with some alternative embodiments of process  1202 , assistance server  212  pre-computes assistance data for a plurality of diverse locations within geographic region  220  and selects that pre-computed assistance data for wireless terminal  201  based on the estimated location of wireless terminal  201  at instant H 1 . Because the assistance data selected for wireless terminal  201  is not specifically tailored to the estimated location of wireless terminal  201  at instant H 1 , nor generic to all of geographic region  220  or to the cell or sector of the base station serving wireless terminal  201 , it is deemed “semi-custom” assistance data. In general, semi-custom assistance data is less accurate than fully-custom assistance data, but more accurate, on average, than generic assistance data, which is chosen based on cell ID alone and that is based on one location within geographic region  220 . It will be clear to those skilled in the art, after reading this disclosure, how to generate the fully-custom and semi-custom assistance data for wireless terminal  201 . 
     In accordance with process  1203 , wireless terminal  201  (a) receives the assistance data from assistance server  212 , in well-known fashion, (b) uses it to facilitate the acquisition and processing of one or more GPS satellite signals in well-known fashion, and (c) transmits Z non-empty sets of GPS-derived information to location server  214  for readings at instants G 1  through G Z , where Z is a positive integer. In accordance with the illustrative embodiment of the present invention, each set of GPS-derived information comprises:
         i. a GPS-derived estimate of the location of wireless terminal  201  (e.g., a latitude, longitude, and altitude coordinate, etc.), or   ii. ranging data (e.g., PRN code phase, etc.) from one or more GPS satellites, or   iii. partially-processed ranging signals (e.g., signals from which the ranging data has not yet been extracted, etc.) from one or more GPS satellites, or   iv. any combination of i, ii, and iii.       

     In accordance with process  1204 , location server  214  receives Z non-empty sets of GPS-derived information to location server  214  for readings at instants G 1  through G Z  and generates a probability distribution that indicates the likelihood that wireless terminal  201  is in each location at each of instants G 1  through G Z . It will be clear to those skilled in the art how to perform process  1204 . 
       FIG. 13  depicts a flowchart of the salient processes performed in process  1003 —combining the Y non-GPS-based probability distributions with the Z GPS-based probability distributions to derive F refined multi-dimensional probability distributions for the location of wireless terminal  201  at each of instants J 1  through J F , where each J i  corresponds to one of:
         i. a particular instant H Y , where 1≦y≦Y, or   ii. a particular instant G Z , where 1≦z≦Z, or   iii. a concurrence of both a particular instant H Y , and a particular instant G Z , where 1≦y≦Y and 1≦z≦Z.
 
In other words, each “composite” instant J i  corresponds to either an instant associated with a non-GPS-based probability distribution, or an instant associated with a GPS-based probability distribution, or an instant associated with both a non-GPS probability distribution and a GPS-based probability distribution.
       

     In accordance with process  1003 , the Y non-GPS-based probability distributions with the Z GPS-based probability distributions are intelligently combined, taking into consideration their relative temporal occurrence to derive a refined multi-dimensional probability distribution for the location of wireless terminal  201  at instants J 1  through J F . 
     To generate the refined probability distribution for the location of wireless terminal  201  at instant J i , the probability distributions that occur before instant J i  are temporally-extrapolated progressively to instant J i , the probability distributions that occur after instant J i  are temporally-extrapolated regressively to instant J i , and they all are combined with the un-temporally-extrapolated probability distribution for the location of wireless terminal  201  at instant J i . In this way, the accuracy of all of the refined probability distributions for each instant J i  are enhanced by the empirical data at other instants. 
       FIG. 14  depicts a first example of determining each of instants J 1  through J F  based on non-GPS-based instants H 1  through H Y , where Y=4, and GPS-based instants G 1  through G Z , where Z=6. As can be seen in  FIG. 14 , the number of composite instants F is at most Y plus Z, and is at least the maximum of Y and Z—the former occurring when there are no coincident GPS/non-GPS probability distributions, and the latter when there are as many as possible coincident GPS/non-GPS probability distributions. 
       FIG. 15  depicts a second example of determining each of instants J 1  through J F  based on non-GPS-based instants and GPS-based instants. This second example illustrates that even when the non-GPS-based instants are uniformly spaced in time and the GPS-based instants are uniformly spaced in time, the composite instants are not necessarily uniformly spaced in time. 
     In accordance with the present invention, the time step Δt is defined as the minimum time interval between any two instants. The time step is atomic in that the time difference between any two instants is an integral multiple of time steps. (Note that two consecutive instants—whether they are non-GPS-based instants, GPS-based instants, or composite instants—might be more than a single time step apart.) The time step of the present invention is therefore similar to the time step employed in clock-driven discrete event simulations. 
     As will be appreciated by those skilled in the art, selecting an appropriate value for the time step Δt typically will depend on the particular application, and involves a tradeoff between (1) temporal precision and (2) available memory and processing power. As will be further appreciated by those skilled in the art, after reading this disclosure, the selected time step can affect the definition of locations, the moving and staying probabilities, and consequently the graphs that are derived from them (e.g., the adjacency graph, etc.). 
     In accordance with process  1301 , location server  214  determines instants J 1  through J F , as described above. 
     In accordance with process  1302 , location server  214  constructs unrefined probability distributions V 1  through V F  for instants J 1  through J F  as follows:
         i. if J i  corresponds to a particular H j  only, then V i  equals the non-GPS probability distribution at instant H j ,   ii. if J i  corresponds to a particular G k  only, then V i  equals the GPS probability distribution at instant G k , and   iii. otherwise (C i  corresponds to both a particular H j  and a particular G k ), V i  equals a probability distribution that equals the normalized product of the non-GPS and GPS probability distributions at instant J i .       

     In accordance with process  1303 , location server  214  determines for each instant J i , temporally-extrapolated probability distributions D i,j  for all j≠i, 1≦j≦F, which are based on (i) the unrefined probability distribution V j  at instant J j , (ii) P S (b, T, N, W), and (iii) P M (b, T, N, W, c). The extrapolated probability distribution D i,j  is therefore a predictive probability distribution at instant J i  that is based on empirical data at instant J j —but not on any empirical data at other instants, including J i .
         i. the past data for the movement of all wireless terminals; and   ii. the past data for the movement of wireless terminal W; and   iii. the location, speed, and acceleration of wireless terminal W at calendrical time T; and   iv. the state of traffic signals that can affect the movement of wireless terminals in location b.       

     A temporally-extrapolated probability distribution can be progressed (i.e., projected into the future based on a past probability distribution). For example, if instant J 3  is one time step after instant J 2 , then extrapolated probability distribution D 3,2  is derived by a single application of P S (b, T, N, W) and P M (b, T, N, W, c) to unrefined probability distribution V 2 . In other words, for any location b: 
                       D     3   ,   2       ⁡     [   b   ]       =           V   2     ⁡     [   b   ]       ·       P   S     ⁡     (     b   ,     J   2     ,   N   ,   W     )         +       ∑         (     c   ,   b     )     ∈     i   ⁢           ⁢     n   ⁡     (   b   )           ⁢               ⁢         V   2     ⁡     [   c   ]       ·       P   M     ⁡     (     c   ,     J   2     ,   N   ,   W   ,   b     )                     (     Eq   .           ⁢   8     )               
where in(b) is the set of arcs into location b from other locations in the adjacency graph. Similarly, a temporally-extrapolated probability distribution can be regressed (i.e., projected into the past based on a future unrefined probability distribution) based on the equation:
 
                       V   3     ⁡     [   b   ]       =           D     2   ,   3       ⁡     [   b   ]       ·       P   S     ⁡     (     b   ,     J   2     ,   N   ,   W     )         +       ∑         (     c   ,   b     )     ∈     i   ⁢           ⁢     n   ⁡     (   b   )           ⁢               ⁢         D     2   ,   3       ⁡     [   c   ]       ·       P   M     ⁡     (     c   ,     J   2     ,   N   ,   W   ,   b     )                     (     Eq   .           ⁢   9     )               
by setting up a system of equations (9) for a plurality of locations {b 1 , b 2 , . . . , b η } and solving for {D 2,3 [b 1 ], D 2,3 [b 2 ], . . . , D 2,3 [b η ]} via matrix algebra.
 
     As will be well-understood by those skilled in the art, after reading this disclosure, when consecutive instants are two or more time steps apart, then Equation 8 can be applied iteratively in well-known fashion. (Because the time step is atomic the number of iterations is always integral.) As will be further appreciated by those skilled in the art, after reading this disclosure, the extrapolated probability distributions for non-consecutive time instants (e.g., D 2,4 , D 5,1 , etc.) can be efficiently computed in a bottom-up fashion from the extrapolated probability distributions for consecutive time instants via dynamic programming. 
     In accordance with process  1304 , location server  214  computes each refined probability distribution L i , corresponding to each instant J i , 1≦i≦F, as a weighted average of:
         i. the corresponding unrefined probability distribution V i , and   ii. all available temporally-extrapolated probability distributions D i,j , j≠i:       

                     L   i     =         V   i     +       ∑     j   ≠   i       ⁢     [       α          j   -   i            ·     D     i   ,   j         ]           1   +       ∑     j   ≠   i       ⁢     α          j   -   i                          (     Eq   .           ⁢   10     )               
wherein α is a constant, 0&lt;α&lt;1, that acts as an “aging factor” that weights less temporally-extrapolated probability distributions more heavily that more temporally-extrapolated probability distributions because of the more temporally-extrapolated probabilities distributions are less likely to be correct than the less temporally-extrapolated probability distributions. For example, when i=4 and F=5, Equation 10 in expanded form yields:
 
     
       
         
           
             
               
                 
                   
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     In accordance with process  1305 , location server  214  generates an estimate of the location of wireless terminal  201  at one or more instants J i  based on the maximum likelihood function of L i . (As will be appreciated by those skilled in the art, after reading this disclosure, in some other embodiments of the present invention an estimate might be generated from probability distribution L i  using another function or method.) 
     In accordance with process  1306 , location server  214  provides the estimate(s) of the location of wireless terminal  201  generated in process  1305  to location client  213 , in well-known fashion. 
     It is to be understood that the above-described embodiments are merely illustrative of the present invention and that many variations of the above-described embodiments can be devised by those skilled in the art without departing from the scope of the invention. It is therefore intended that such variations be included within the scope of the following claims and their equivalents.