Patent Publication Number: US-2023152490-A1

Title: Mitigating Atmospheric Effects From Geographical Anomalies on Reference Pressure Estimates

Description:
RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Patent Application No. 63/264,203, filed Nov. 17, 2021, all of which is incorporated herein in its entirety. 
    
    
     BACKGROUND 
     A barometric altitude system for estimating an altitude of a mobile device often depends on having an accurate reference atmospheric pressure value for use in a barometric-based altitude equation. In some systems, the reference atmospheric pressure value is generated using a reference atmospheric pressure network that is made up of atmospheric sensors of varying stability and accuracy for measuring atmospheric pressure and/or temperature. Such sensors are often incorporated into atmospheric data measurement stations which include so-called stable pressure instruments (SPI) and/or weather stations. In general, a stable pressure instrument exhibits less sensor drift and produces more accurate atmospheric measurements as compared to a less stable pressure instrument of a so-called weather station. 
     A reference atmospheric pressure network is often designed such that weather stations are located in regions in which an ambient atmospheric pressure is an accurate representation of atmospheric pressure over a broad geographical region. However, geographical regions are often characterized by anomalous features such as ridges, valleys, waterbodies, and coastlines. These geographical anomalies create localized atmospheric effects such as localized deviations in atmospheric pressure, temperature, and/or humidity. Thus, a weather station or stable pressure instrument situated in the vicinity of geographical anomalies may produce atmospheric pressure measurements that are less representative of the broader geographical region. As a result, atmospheric pressure data from these instruments may lead to an inaccurate reference pressure for the broader geographical region. 
     SUMMARY 
     In some embodiments, a method involves determining, by one or more processors, an estimated position of a mobile device within a region. Multiple atmospheric data measurement stations are identified within the region by the one or more processors. A geographical anomaly within the region is identified, by the one or more processors, that physically intervenes between the estimated position of the mobile device and a position of a first atmospheric data measurement station of the atmospheric data measurement stations. Based on a positional relationship between the estimated position of the mobile device, the geographical anomaly, and the position of the first atmospheric data measurement station, it is determined, by the one or more processors, that atmospheric pressure measurements collected at the first atmospheric data measurement station should be conditionally used for determining a reference pressure estimate. The reference pressure estimate is determined, by the one or more processors, using a plurality of atmospheric pressure measurements collected at the multiple atmospheric data measurement stations and conditionally using the atmospheric pressure measurements collected at the first atmospheric data measurement station. An estimated altitude of the mobile device is determined, by the one or more processors, using a measurement of atmospheric pressure at the mobile device and the reference pressure estimate. 
     In some embodiments, a method involves determining, by one or more processors, a first position of a weather station within a region. Multiple respective second positions of multiple stable pressure instruments within the region are determined using the one or more processors. A geographical anomaly is identified within the region, by the one or more processors using a terrain database, that physically intervenes between the first position and one or more of the second positions. Atmospheric pressure measurements are collected, using the one or more processors, at the stable pressure instruments at the one or more of the second positions. Based on a positional relationship between the first position of the weather station, the geographical anomaly, and the one or more of the second positions, it is determined, using the one or more processors, that the atmospheric pressure measurements should be conditionally used for calibrating the weather station. A reference pressure estimate is conditionally determined, by the one or more processors, using the atmospheric pressure measurements collected by the stable pressure instruments at the one or more of the second positions. An atmospheric pressure sensor of the weather station is calibrated, by the one or more processors, using the reference pressure estimate. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    shows an example of a first region with a first geographical anomaly and a portion of a reference pressure network for calibrating a weather station, in accordance with some embodiments. 
         FIG.  2    shows an example of a second region with a second geographical anomaly and a portion of a reference pressure network for calibrating a weather station, in accordance with some embodiments. 
         FIG.  3    shows an example of the first region and a portion of a reference pressure network for determining an estimated altitude of a mobile device, in accordance with some embodiments. 
         FIG.  4    shows an example of the second region and a portion of a reference pressure network for estimated altitude of a mobile device, in accordance with some embodiments. 
         FIGS.  5 A-D  show first examples of exclusion zones that are determined to mitigate the effects of a geographical anomaly when determining a reference pressure, in accordance with some embodiments. 
         FIGS.  6 A-C  show second examples of exclusion zones that are determined to mitigate atmospheric effects of a geographical anomaly when determining a reference pressure, in accordance with some embodiments. 
         FIG.  7    shows a third example of an exclusion zone that is determined to mitigate atmospheric effects of a geographical anomaly when determining a reference pressure, in accordance with some embodiments. 
         FIG.  8    shows an example portion of a variogram model, in accordance with some embodiments. 
         FIG.  9    illustrates components of a transmitter, a mobile device, and a server, in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Geographical regions are often characterized by anomalous features such as ridges, mesas, valleys, water bodies, and coastlines. Atmospheric sensors situated in the vicinity of such features may produce atmospheric pressure measurements that are less representative of a broader geographical region. Systems and methods disclosed herein advantageously provide for an increased calibration accuracy of atmospheric sensors in geographical regions impacted by geographical anomalies. Such systems and methods may guide the design of a reference pressure network, as well as improve upon the accuracy of an altitude estimation of mobile devices in the vicinity of such anomalies. Additionally, the systems and methods disclosed herein are advantageously operable to guide the design of reference pressure networks across many regions which may have varying complexity and which would not be feasible to be designed manually by a person. For example, some regions may have so many changes in elevation and/or bodies of water that consideration of each geographic anomaly by a human is not feasible. Therefore, the systems and methods disclosed herein provide a substantial advantage as compared to prior art solutions which may require that a human manually identify geographical anomalies within a region and then manually design the reference network accordingly. 
     As is known in the art, altitude estimation of a mobile device may use a barometric equation that uses both an atmospheric pressure measurement made at the mobile device as well as a reference atmospheric pressure measurement associated with a geographical region that encompasses the mobile device. The reference atmospheric pressure measurement may be generated using a reference pressure network. In general, a reference pressure network may include weather stations and stable pressure instruments, among other components. Weather stations and stable pressure instruments are referred to generally as atmospheric data measurement stations herein. Weather stations and stable pressure instruments are each operable to provide (e.g., to a server and/or a mobile device) measurements of atmospheric conditions such as atmospheric pressure, temperature, wind speed, humidity, and other atmospheric conditions. A weather station is often less accurate and more prone to sensor drift as compared to a so-called stable pressure instrument. Because weather stations are often less expensive in both manufacturing costs and installation costs as compared to stable pressure instruments, weather stations may be more ubiquitous within the reference pressure network. Fortunately, the less stable weather stations may be calibrated using the stable pressure instruments to achieve an acceptable level of accuracy and stability. 
     As disclosed herein, consideration of geographical anomalies may advantageously guide the design of a reference atmospheric pressure network when determining where weather stations and/or stable pressure instruments are to be located within a geographical region. Some criteria used to optimize a topology of a reference atmospheric pressure network when adding or using stable pressure instruments or weather stations within the reference atmospheric pressure network are discussed with reference to  FIG.  1    and  FIG.  2   . 
       FIG.  1    includes an example of a first geographical region  100  that includes a portion of a reference atmospheric pressure network and geographical anomalies, in accordance with some embodiments. As shown, the first geographical region  100  includes a large lake  101  (i.e., a geographical anomaly), a coastline  130  (i.e., another geographical anomaly), and buildings/structures  102   a - e . The reference atmospheric pressure network includes weather stations  104   a - c , stable pressure instruments  110   a - b , and one or more servers  112 . Also shown are first signals  106   a - c  associated with the respective weather stations  104   a - c , second signals  112   a - b  associated with the respective stable pressure instruments  110   a - b , two-dimensional lines  120   a - b , and two-dimensional (e.g., horizontal) distance measurements  103   a - b.    
     The server  112  is operable to send and receive information via the signals  106   a - c  and  112   a - b  using a wired and/or wireless network. One or more of the weather stations  104   a - c  may include an atmospheric sensor that is less accurate and/or less stable (e.g., more prone to drift) than a corresponding atmospheric sensor of the stable pressure instruments  110   a - b . Thus, in some embodiments, the server  112  is configured to use information received from the stable pressure instruments  110   a - b  to calibrate the weather stations  104   a - c . An approach to calibrate a less stable atmospheric sensor using a stable pressure instrument is described in U.S. Pat. No. 10,514,258 B2, which issued on Dec. 24, 2019, all of which is incorporated herein by reference for all purposes. 
     A first criterion used to optimize a topology of a reference atmospheric pressure network when adding stable pressure instruments or weather stations includes ensuring that a distance over a waterbody that intervenes between a stable pressure instrument and a weather station that will be calibrated using the stable pressure instrument is less than a threshold distance (e.g., 1 km, 2 km, 5 km, etc.). In the example shown in  FIG.  1   , a distance measurement  103   a  of the line  120   a  that passes over the large lake  101  from the stable pressure instrument  110   a  to the weather station  104   a  is given to be less than a threshold distance (e.g., 1 km). As such, the weather station  104   a  could be calibrated using the stable pressure instrument  110   a . In contrast, a distance measurement  103   b  of the line  120   b  that passes over the large lake  101  from the stable pressure instrument  110   a  to the weather station  104   b  is given to be greater than the threshold distance. As such, the weather station  104   b  would not be calibrated using the stable pressure instrument  110   a . Instead, the stable pressure instrument  110   b  could be added to the reference atmospheric pressure network of the region  100  to accurately calibrate the weather station  104   b  (i.e., because a geographic anomaly does not intervene between the stable pressure instrument  110   b  and the weather station  104   b ). In this simplified example, only the large lake  101  is shown as a water body. However, in some regions there may be tens to hundreds of such water bodies and therefore the first example criterion used to optimize a topology of a reference atmospheric pressure network could not be feasibly determined by a human. 
     Additional criteria used to optimize a topology of a reference atmospheric pressure network when adding stable pressure instruments or weather stations to the reference atmospheric pressure network are discussed with reference to  FIG.  2   . 
       FIG.  2    includes an example of a second geographical region  200  that includes a portion of a reference atmospheric pressure network and a geographical anomaly, in addition to other features, in accordance with some embodiments. As shown, the second geographical region  200  includes a large mesa  201  (i.e., a geographical anomaly), and building/structure  202 . A reference atmospheric pressure network of the region  200  includes weather stations  204   a - b , stable pressure instruments  210   a - b , and one or more servers  212 . Also shown are first signals  206   a - b  associated with the respective weather stations  204   a - b , second signals  212   a - b  associated with the stable pressure instruments  210   a - b , and a height measurement  203 . The server  212  is the same as, or is similar to, to the server  112  shown in  FIG.  1   . 
     With reference to  FIG.  2   , a second criterion used to optimize a topology of a reference atmospheric pressure network when adding stable pressure instruments or weather stations to the reference atmospheric pressure network includes ensuring that a height difference between a stable pressure instrument and a weather station that will be calibrated using the stable pressure instrument does not exceed a threshold difference in height (e.g., 100 m, 150 m, 200 m, etc.). In the example shown in  FIG.  2   , an altitude difference, due to the mesa  201 , intervenes between the stable pressure instrument  210   a  and the weather station  204   b . The height measurement  203  of the mesa is given to be greater than the threshold height. Thus, the weather station  204   b  on top of the mesa  201  would not be calibrated using the stable pressure instrument  210   a  that is at the base of the mesa  201 . Instead, the stable pressure instrument  210   b  could be added to the reference atmospheric pressure network for the second geographical region  200  on top of the mesa  201  to calibrate the weather station  204   b  (i.e., because a geographic anomaly does not intervene between the stable pressure instrument  210   b  and the weather station  204   b ). Once again, in this simplified example, only the mesa  201  is shown as a geographical anomaly based on a height difference. However, in some regions there may be tens to hundreds of such height differences and therefore the second example criterion used to optimize a topology of a reference atmospheric pressure network could not be feasibly determined by a human (especially when also considering the first example criterion in conjunction with the second example criterion). 
     Despite adhering to such criteria for specifying a topology of the reference pressure network, in practice, it is likely that the pressure measurements will continue to be impacted by geographical anomalies such as waterbodies and changes in terrain. For example, referring back to  FIG.  1   , weather stations located near a coastline (e.g., the coastline  130 ) that has a dominant wind direction pointing from the waterbody to inland will experience a different pressure environment as compared to weather stations further inland (e.g., tens of km from the coastline). Thus, in some embodiments, weather stations located near a coastline are advantageously calibrated using a stable pressure instrument that is also situated near that coastline. Similarly, inland weather stations are calibrated using a stable pressure instrument that is also located inland. In the example shown in  FIG.  1   , the weather station  104   b  is located close to the coastline  130  and would therefore be calibrated using the stable pressure instrument  110   b  which is also located close to the coastline  130 . By contrast, the weather station  104   b  would not be calibrated using the stable pressure instrument  110   a  because the stable pressure instrument  110   a  is located far from the coastline  130 . Likewise, the weather station  104   c , which is located far from the coastline  130 , would be calibrated using the stable pressure instrument  110   a  which is also located far from the coastline  130 . By contrast, the weather station  104   c  would not be calibrated using the stable pressure instrument  110   b  which is located close to the coastline  130 . 
     Similar to how the first criterion was used to optimize a topology of a reference atmospheric pressure network, in some embodiments a distance over a waterbody between a stable pressure instrument and a weather station is considered when calibrating the weather station. In the example shown in  FIG.  1   , the distance measurement  103   a  of the line  120   a  that passes over the large lake  101  is given to be less than a threshold distance (e.g., 1 km, 2 km, 5 km, etc.) so the weather station  104   a  would be calibrated by the stable pressure instrument  110   a . In contrast, beyond considerations of the coastline  130 , the distance measurement  103   b  of the line  120   b  that passes from the stable pressure instrument  110   a  to the weather station  104   b  over the large lake  101  is given to be greater than the threshold distance. Therefore, the weather station  104   b  would not be calibrated by the stable pressure instrument  110   a . As mentioned above, though this is a simplified example, some regions include many geographical anomalies, making such considerations infeasible to be performed by a human. 
     Referring now to  FIG.  2   , similar to how the second criterion was used to optimize a topology of a reference atmospheric pressure network, a height difference between a stable pressure instrument and a weather station is considered when calibrating the weather station. In the example shown in  FIG.  2   , the height measurement  203  of the mesa  201  is given to be greater than a threshold height (e.g., 100 m, 150 m, 200 m, etc.). Thus, the weather station  204   b  on top of the mesa  201  would not be calibrated using the stable pressure instrument  210   a  that is at the base of the mesa  201 . Again, though this is a simplified example, many regions include many such geographical anomalies, making such considerations infeasible to be performed by a human. 
     In addition to considering local environmental effects when calibrating less stable atmospheric sensors such as those of the weather stations discussed above, atmospheric effects due to geographical anomalies may impact the accuracy of an altitude estimate determined using a barometric-based altitude equation for a mobile device. As described above, mobile devices may use a reference pressure generated by weather stations and stable pressure instruments as an input to a barometric-based altitude equation to generate an estimated altitude of the mobile device. The computation of a representative reference atmospheric pressure for use by a barometric altitude system is described in U.S. Pat. No. 10,386,448 B2, which issued on Aug. 20, 2019, all of which is incorporated herein by reference for all purposes. 
     In some embodiments, a reference pressure used by the mobile device for generating an estimated altitude is generated using all atmospheric data measurement stations, such as weather stations/stable pressure instruments, that are within a defined radius (e.g., 10 km) of the mobile device, but excluding any weather station/stable pressure instrument for which a two-dimensional distance over water along a line joining an estimated position of the mobile device and a position of the weather station/stable pressure instruments exceeds a threshold distance (e.g., 1 km, 2 km, 5 km, etc.).  FIG.  3    includes the elements of the first geographical region  100  described with reference to  FIG.  1   , with the addition of a mobile device  314 , in accordance with some embodiments. Also shown are lines  322   a - b  and distance measurements  303   a - b . The mobile device  314  may be a smartphone, a tablet computer, a laptop computer, a desktop computer, a surveying device, or other user equipment. In the example shown in  FIG.  3   , the distance measurement  303   a  of the line  322   a  that passes over the large lake  101  is given to be greater than a threshold distance (e.g., 1 km), so atmospheric pressure measurements from the weather station  104   a  would be “conditionally used” (see below) to generate a reference pressure for estimating an altitude of the mobile device  314 . In contrast, a distance measurement  303   b  of the line  322   b  that passes over the large lake  101  is given to be less than the threshold distance, so atmospheric pressure measurements from the weather station  104   b  could be “unconditionally used” (see below) to generate a reference pressure for the mobile device  314 . 
     In some embodiments, conditional use of an atmospheric pressure measurement involves wholly excluding that atmospheric pressure measurement for the determination of the reference pressure. In other embodiments, conditional use of the atmospheric pressure measurement involves attenuating the atmospheric pressure measurement (e.g., via weighting) such that the atmospheric pressure measurement does not contribute to the determined reference pressure as much as an unattenuated atmospheric pressure measurement. In some embodiments, unconditional use of an atmospheric pressure measurement involves wholly including that atmospheric pressure measurement for determination of the reference pressure. In other embodiments, unconditional use of the atmospheric pressure measurement involves weighting the atmospheric pressure measurement such that the atmospheric pressure measurement contributes to the determined reference pressure proportionally to some preferred criteria. 
     As shown in  FIG.  4   , in some embodiments, a reference pressure used by the mobile device for generating an estimated altitude is generated using all of the weather stations/stable pressure instruments within a defined radius (e.g., 10 km) of the mobile device but excluding any weather station/stable pressure instrument for which a change in height measurements along a line joining the mobile device and the weather station/stable pressure instrument exceeds a height threshold.  FIG.  4    includes the elements of the second geographical region  200  described with reference to  FIG.  2   , with the addition of a mobile device  414 , in accordance with some embodiments. Also shown are lines  422   a - b  and a height measurement  403 . The mobile device  414  may be a smartphone, a tablet computer, a laptop computer, a desktop computer, a surveying device, or other user equipment. In the example shown in  FIG.  4   , the height measurement  203  along the line  422   b  from the mobile device  414  to the weather station  204   b  is given to be greater than a height threshold (e.g., 150 m). As such, atmospheric pressure measurements from the weather station  204   b  would be conditionally used when determining a reference pressure used by the mobile device  414 . 
     In contrast, the height measurement  403  along the line  422   a  from the mobile device  414  to the weather station  204   a  is given to be not greater than a height threshold. As such, atmospheric pressure measurements from the weather station  204   a  could be unconditionally used when determining a reference pressure used by the mobile device  414 . 
     In other embodiments, a reference pressure used by the mobile device for generating an estimated altitude is generated by conditionally using weather stations that are associated with exclusion zones as described below and with reference to  FIGS.  5 A-D ,  FIGS.  6 A-C , and  FIG.  7   . That is, if the mobile device is located in an exclusion zone associated with a particular weather station, atmospheric pressure measurements from that weather station are conditionally used when determining a combined reference pressure computation.  FIG.  5 A  shows an orthoscopic view of a first portion of a geographical region  500  having a geographical anomaly  501  (e.g., a large lake). A reference pressure network of the geographical region  500  includes a weather station  502 . To determine a first exclusion zone associated with the weather station  502 , a region  504  that surrounds the weather station  502  is determined. In some embodiments, the region  504  is described by an outer perimeter (e.g., a circle, oval, or other shape) having a radius of about 10 km and quadrants  506   a - d . A bounding box (or other polygon)  504   a  having corners A, B, C, and D and that includes the geographical anomaly  501  is determined within a first section  507   a  of a first quadrant  506   a  of the region  504 . As shown in  FIG.  5 B , a sub-section  508   a  is determined for the bounding box  504   a  such that lines (i.e., “bounding edges”) of the sub-section  508   a  connect between the weather station  502  and opposite corners (e.g., ‘A’ and ‘D’) of the bounding box  504   a . An exclusion zone  510   a  is then determined by extending bounding edges of the sub-section  508   a  to an outer perimeter of the region  504 . If a mobile device is within the exclusion zone  510   a  such that the geographic anomaly intervenes between the mobile device and the weather station  502 , a reference pressure generated for altitude estimation of the mobile device will be generated conditionally using atmospheric pressure measurements from the weather station  502 . If the mobile device is not within the exclusion zone  510 , a reference pressure generated for altitude estimation of the mobile device could be generated unconditionally using atmospheric pressure measurements from the weather station  502 . Similar exclusion zones are determined for each section (e.g., an angular range) of each of the quadrants  506   a - d  of the region  504  depending on the presence of geographical anomalies in that section. Because some regions may have tens to hundreds of such geographical anomalies, determining exclusion zones which account for all of the geographical anomalies is not feasible for a human. 
       FIG.  5 C  shows a second portion of the geographical region  500  having a geographical anomaly  503  (e.g., another large lake) and the weather station  502 . To determine a second exclusion zone associated with the weather station  502 , a bounding box  504   b  having corners A, B, C, and D and that includes the geographical anomaly  503  is determined within a second section  507   b  of a second quadrant  506   b  the region  504 . As shown in  FIG.  5 D , a sub-section  508   b  is determined for the bounding box  504   b  such that lines of the sub-section  508   b  connect between the weather station  502  and opposite corners (‘B’ and ‘C’) of the bounding box  504   b . An exclusion zone  510   b  is then determined by extending lines of the sub-section  508   b  to an outer perimeter of the region  504 . If a mobile device is within the exclusion region  510   b , a reference pressure generated for altitude estimation of the mobile device would conditionally use atmospheric pressure measurements from the weather station  502 . In some embodiments, the sections  507   a - b  are defined by an angular range of the region  504 . In some embodiments, the angular range is about 30 degrees. 
     Another embodiment for determining an exclusion zone is shown and described with reference to  FIGS.  6 A-C .  FIG.  6 A  shows a first portion of a geographical region  600  having a geographical anomaly  603  (e.g., a large lake). A reference pressure network of the geographical region  600  includes a weather station  602 . To determine an exclusion zone associated with the weather station  602 , a region  604  that surrounds the weather station  602  is determined. In some embodiments, the region  604  is described by a circle having a radius of about 10 km and quadrants  606   a - d . Terrain polygons within the region  604  are then determined. An example portion of terrain polygons  605   a - g  within the region  604  are shown in  FIG.  6 A . A bounding box is determined for each of the terrain polygons within the region  604 . A first example bounding box  610   a  determined for the terrain polygon  605   a  is shown in  FIG.  6 B  and a second example bounding box  610   b  determined for the terrain polygon  605   b  is shown in  FIG.  6 C . Lines between the weather station and opposite corners of each of the bounding boxes are then determined. Example lines  608   a - b  between the weather station  602  and the bounding box  610   a  are shown in  FIG.  6 B  and example lines  608   c - d  between the weather station  602  and the bounding box  610   b  are shown in  FIG.  6 C . If a distance “over” (i.e., intersecting in two-dimensions) the large lake  603  (i.e., over water) from the weather station  602  along either of the lines  608   a - b  to the corners of the bounding box  610   a  exceeds a distance threshold (e.g., 1 km), then the terrain polygon  605   a  is added to an exclusion zone. Similarly, if a distance over the large lake  603  (i.e., over water) from the weather station  602  along either of the lines  608   c - d  to the corners of the bounding box  610   b  exceeds the distance threshold, then the terrain polygon  605   b  is added to an exclusion zone. This process is repeated for each terrain tile of the region  604 . In the example shown in  FIG.  6 B , a portion of the line  608   b  that passes over the large lake  603  is given to exceed a threshold distance, and as such, the terrain tile  605   a  is added to an exclusion zone. By contrast, in the example shown in  FIG.  6 C , neither of the lines  608   c - d  are given to have a portion over the large lake  603  that is given to exceed the threshold distance. As such, the terrain polygon  605   b  is not added to the exclusion zone. Because some regions may have tens to hundreds of such geographical anomalies, determining exclusion zones which account for all of the geographical anomalies is not feasible for a human. 
     Yet another embodiment for determining an exclusion zone is shown and described with reference to  FIG.  7   .  FIG.  7    shows a portion of a geographical region  700 . A reference pressure network of the geographical region  700  includes a weather station  702 . To determine an exclusion zone in the example shown, a bounding region  701  (e.g., a 20 km by 20 km square) that surrounds the weather station  702  is determined. Isolines (e.g.,  704 ,  706 , and  708 , among others) of constant elevations are then determined within the bounding region  701 . For a given location within the bounding region  701 , if an isoline that exceeds a threshold elevation (e.g., 150 m) intervenes between a location of a mobile device within the bounding region  701  and the weather station  702 , the pressure measurements from the weather station  702  would be conditionally used when determining a reference pressure for that mobile device. In the example shown, the isoline  704  is given to represent the threshold elevation and therefore constitutes an exclusion zone. That is, a mobile device outside of the perimeter of the isoline  704  would conditionally use a reference pressure determined using pressure measurements from the weather station  702 . In some embodiments, a mobile device inside the perimeter of the isoline  704  would unconditionally use a reference pressure determined using pressure measurements from the weather station  702 . 
     In other embodiments, as described below, rather than defining discrete exclusion zones, a continuous interpolated reference pressure surface using spatially correlated pressure data within a geographical region is determined. For example, a reference pressure for an unknown location (i.e., a location at which pressure is not measured) may be computed from a set of weather stations using multi-beacon average methods as described in U.S. Pat. No. 10,386,448 B2, which issued on Aug. 20, 2019, all of which is incorporated herein by reference for all purposes. 
     When computing a reference pressure for an unknown location, there are primarily three techniques to capture spatial correlation while interpolating the spatial data, i.e., spline interpolation, inverse distance weighted (IDW), and Kriging interpolation. Spline interpolation is a deterministic method that can be imagined as fitting a mathematical function to a given set of known points. Although simple in implementation, it is sensitive to outliers and does not provide an error estimate. Similar to spline interpolation, the IDW technique is also a deterministic technique. The IDW technique uses distance information between sampled points as weights while computing an average value (i.e., an interpolated value) for an unsampled location. In the IDW techniques, the weights are inversely proportional to the distance between sampled points and the unsampled location. As such, nearby points are assigned larger weights as compared to farther points. The IDW technique is simple to implement and understand but the technique is sensitive to outliers in the data and does not provide an error estimate. 
     For a set of weather stations that are equally spaced and around a user, the multi-beacon average described in U.S. Pat. No. 10,386,448 B2, incorporated above, is equivalent to a bi-linear spatial interpolation. However, such a bi-linear spatial interpolation is devoid of any parameters that explicitly represent the spatial correlation among the weather stations. 
     In some embodiments, an extension of the previous reference pressure computation using a bi-linear like spatial interpolation is through the use of a pressure surface fit (e.g., Kriging interpolation) that advantageously imposes a spatial correlation among the weather station measurements while yielding a spatially smooth pressure surface. Unlike spline interpolation and the IDW technique, Kriging interpolation is a stochastic technique that uses weighted linear combinations at locations having known values (e.g., pressure measurements of weather stations or stable pressure instruments) to estimate the value at unknown locations (i.e., locations at which there are no weather stations or stable pressure instruments to provide measurements). The weights in Kriging interpolation represent the spatial structure of the sampled data using a variogram model. Studies have reported that due to the use of a variogram model while estimating the Kriging weights, Kriging interpolation performs better than the IDW technique and spline interpolation (Kravchenko (2003), Lu and Wong (2008), Bekele et al., (2003), Chia-Yu et al., (2019)). 
     The Kriging interpolation method can advantageously be applied to instantaneous measurements from a set of weather stations and produce a set of pressure surface fits that vary over time. An example application of the Kriging method to fit a reference pressure surface, with the imposition of certain constraints in variogram model development and for estimating Kriging weights to mitigate geographical anomalies, is detailed below, in accordance with some embodiments. 
     Kriging interpolation is an approach that considers the spatial structure of correlation over a domain using a variogram model while constructing the interpolated surface. The formula for the interpolation is as follows: 
         {circumflex over (Z)} ( x   i   ,y   i )=Σλ j   Z   j ( x   j   ,y   j )  Equation 1,
 
     where i is the location at which a pressure value is to be predicted, j is a location at which a pressure value has been measured and goes from 1 to N for N measurements, λ j  is a coefficient (e.g., a weight) associated with each measurement location and represents the spatial correlation between measurements, Z j  is an observed characteristic property at location j, and {circumflex over (Z)} is a predicted characteristic property at location i. 
     The objective of Kriging interpolation is to minimize a prediction error variance while considering a particular spatial correlation structure in a spatial region. To achieve this, a variogram model is constructed (which represents the spatial correlation structure), followed by an estimation of λ j  using a Lagrange multiplier approach with a constraint of Σλ j =1. 
     The Lagrange multiplier approach involves introducing a new optimization function by adding weighted constraints to the original optimization function. 
     To estimate the values for λ of the optimization problem, the variance of error from Equation 1 is minimized, the minimization process being expressed as: 
     
       
         
           
             
               
                 
                   
                     
                       min 
                       λ 
                     
                     
                       Var 
                       ⁡ 
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                         ϵ 
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                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   2 
                 
               
             
           
         
       
     
     where ϵ(Z)={circumflex over (Z)}(x i , y i )−Z(x i , y j ), and Z(x i ,y i ) is the characteristic property (i.e., surface pressure) at location x i , yi. Additionally, in order to ensure unbiasedness, an additional constraint, Σλj=1, is imposed. As such, equation 2 becomes: 
     
       
         
           
             
               
                 
                   
                     
                       min 
                       λ 
                     
                     
                       Var 
                       ⁡ 
                       ( 
                       
                         ϵ 
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                         ) 
                       
                       ) 
                     
                   
                   ⁢ 
                   
 
                   
                     
                       
                         subject 
                         ⁢ 
                             
                         to 
                         ⁢ 
                             
                         
                           ∑ 
                           
                             λ 
                             ⁢ 
                             j 
                           
                         
                       
                       = 
                       1 
                     
                     , 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   3 
                 
               
             
           
         
       
     
     which can be rewritten in Lagrange multipliers as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         min 
                         
                           λ 
                           , 
                           μ 
                         
                       
                       
                         Var 
                         ⁡ 
                         ( 
                         
                           ϵ 
                           ⁡ 
                           ( 
                           Z 
                           ) 
                         
                         ) 
                       
                     
                     + 
                     
                       μ 
                       ⁢ 
                       
                         ∑ 
                         
                           λ 
                           j 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   4 
                 
               
             
           
         
       
     
     where μ is the Lagrange multiplier, and for Var(ϵ(Z)) a variogram model is used. 
     A variogram model is a quantitative descriptive statistic representing the spatial continuity of a data set with the assumption that nearby spatial locations behave similarly and as the distance between locations increases, the association between locations decreases. In some embodiments, a variogram model is selected, and drift and lag parameters are defined for the selected model. Optimal model parameters are obtained by a process of tuning, such that the average error with respect to the three nearest weather stations is minimized. The type of variogram model and associated parameters are described below. 
     The variogram model is used to calculate the covariance between observations, as well as between observations and locations at which predictions are to be made, as a function of distance. The semi-variance “Y” (half of the variogram to account for double counting of pairs) is defined as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             γ 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   Δ 
                                   ⁢ 
                                   x 
                                 
                                 , 
                                 
                                   Δ 
                                   ⁢ 
                                   y 
                                 
                               
                               ) 
                             
                           
                           = 
                           
                             
                               
                                 1 
                                 2 
                               
                               ⁢ 
                               
                                 E 
                                 ⁡ 
                                 ( 
                                 
                                   [ 
                                   
                                     
                                       x 
                                       + 
                                       
                                         Δ 
                                         ⁢ 
                                         x 
                                       
                                     
                                     , 
                                     
                                       y 
                                       + 
                                       
                                         Δ 
                                         ⁢ 
                                         y 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               Z 
                               ⁡ 
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                       2 
                     
                     ) 
                   
                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   5 
                 
               
             
           
         
       
     
     where Υ is the variogram, E is an expectation operator, x and y are positional arguments (i.e., longitude and latitude), and Z is the characteristic property (i.e., surface pressure). Several types of semi-variogram models may be chosen, ranging from Linear, Exponential, Gaussian, Power, and Spherical models. In some embodiments, a trial-and-error approach is used to determine which model yields the minimum error for many regions. 
     The model parameters associated with the different model types are: 
     
       
         
           
             
               
                 
                   i 
                   . 
                 
               
               
                  
               
             
             
               
                 
                   Linear 
                   , 
                   
                     i 
                     . 
                     e 
                     . 
                   
                   , 
                     
                   
                     
                       s 
                       × 
                       d 
                     
                     + 
                     n 
                   
                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   6 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   ii 
                   . 
                 
               
               
                  
               
             
             
               
                 
                   Exponential 
                   , 
                   
                     i 
                     . 
                     e 
                     . 
                   
                   , 
                   
                     
                       p 
                       × 
                       
                         ( 
                         
                           1 
                           - 
                           
                             exp 
                             ⁡ 
                             ( 
                             
                               
                                 - 
                                 d 
                               
                               
                                 ( 
                                 
                                   r 
                                   × 
                                   n 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     + 
                     n 
                   
                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   7 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   iii 
                   . 
                 
               
               
                  
               
             
             
               
                 
                   Gaussian 
                   , 
                   
                     i 
                     . 
                     e 
                     . 
                   
                   , 
                   
                     
                       p 
                       × 
                       
                         ( 
                         
                           1 
                           - 
                           
                             exp 
                             ⁡ 
                             ( 
                             
                               
                                 - 
                                 
                                   d 
                                   2 
                                 
                               
                               
                                 
                                   
                                     ( 
                                     
                                       4 
                                       
                                         7 
                                         ⁢ 
                                         r 
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     + 
                     n 
                   
                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   8 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   iv 
                   . 
                 
               
               
                  
               
             
             
               
                 
                   Power 
                   , 
                   
                     i 
                     . 
                     e 
                     . 
                   
                   , 
                   
                     
                       s 
                       × 
                       
                         d 
                         e 
                       
                     
                     + 
                     n 
                   
                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   9 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   v 
                   . 
                 
               
               
                  
               
             
             
               
                 
                   Spherical 
                   , 
                   
                     i 
                     . 
                     e 
                     . 
                   
                   , 
                   
                     
                       
                         
                           
                             
                               p 
                               × 
                               
                                 ( 
                                 
                                   
                                     
                                       3 
                                       ⁢ 
                                       d 
                                     
                                     
                                       2 
                                       ⁢ 
                                       r 
                                     
                                   
                                   - 
                                   
                                     
                                       d 
                                       3 
                                     
                                     
                                       2 
                                       ⁢ 
                                       
                                         r 
                                         3 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             n 
                           
                           , 
                           
                             d 
                             ≤ 
                             r 
                           
                         
                       
                     
                     
                       
                         
                           
                             p 
                             + 
                             n 
                           
                           , 
                           
                             d 
                             &gt; 
                             r 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   10 
                 
               
             
           
         
       
     
     where, as is known in the art, s is a scaling factor or slope of the model, n is a nugget of the model, d represents distance values at which to calculate the variogram, p is the partial sill (i.e., p=sill−nugget), r is the range parameter, and e is the exponent for the power model. The sill is the asymptotic maximum spatial variance at longest lags (distances). The range represents the distance at which the spatial variance has reached ˜95% of the sill variance. The nugget represents the random deviations from an overall smooth spatial data trend and effectively takes up ‘noise’ in measurements. For stationary variogram models (Gaussian, Exponential, and Spherical), the partial sill (p) is defined as the difference between the full sill and the nugget term. In some embodiments, the optimum set of parameters for the variogram model is found using a “soft” L1 norm minimization scheme. In some embodiments, the minimum error may be found for the ‘Linear’ and ‘Power’ semi-variogram models. 
     When using Kriging interpolation, spatial correlation is representative of an area and is mapped using the variogram model. A simple semi-variogram model along with some associated parameters (i.e., Range, Sill, and Nugget) is shown in  FIG.  8   . A legend  802  details observed and empirical data points of graph  800 . 
     In the variogram model, range parameters consider the change in correlation with distance. Thus, the range parameter r signifies the distance beyond which the correlation between pairs of weather stations becomes negligible and is customized depending upon the region being considered. For example, in some embodiments, for San Francisco (r=0.09 Km), Los Angeles (r=0.4 Km), Washington (r=0.3 Km), and Texas (r=1.9 Km). This means that in the San Francisco region, beyond a 90 m distance, the correlation between pairs of weather stations is considered negligible and beyond this distance, correlation remains almost constant. In the example shown in  FIG.  8   , the correlation remains almost constant after a range of about 35 km. 
     In some embodiments, no drift term for the variogram model is included. In other embodiments, a regional linear drift term for the variogram model is included. In such embodiments, the regional linear drift term may be an average or expected value of the regional variable. In some embodiments, the inclusion or exclusion of the drift term is guided by parameter tuning. Empirical results using embodiments disclosed herein indicate that the error of a variogram model that includes a drift term was lower as compared to that of a variogram model when excluding the “regional drift term.” 
     Lags or “nlags” represent the number of bins into which spatial points are to be grouped for averaging. For example, with nlags equal to six and a maximum distance equal to 30 km, there will be 5 bins grouping the variables covering the distance from 0-6 Km, 6-12 Km, 12-18 Km, 18-24 Km, and 24-30 Km. This is done to avoid a large number of possible combinations of pairs of weather stations. In some embodiments, the value of nlags is varied, e.g., between [2, 4, 6, 8, 10]. The use of specific values of nlags allows for an optimal approach that is computationally cheaper as compared to a brute force approach where all possible values of nlags are included. 
     In some embodiments, to find the optimum set of parameters, i.e., which variogram model to use, which drift terms to use, and what number of lags to use, each of the parameters is tuned with the objective of minimizing the average error with respect to three nearest weather stations. Empirical results using embodiments disclosed herein indicate that across a broad range of regions, 8 bins are found to provide the minimum errors. 
     As described above, the first step in Kriging interpolation is the construction of the variogram model and the second step is the estimation of coefficients (i.e., weights) (λ) such that the variance of prediction error is minimum. Once the coefficients (λ) are estimated, the value at a location can be predicted using Equation 1. Since the model can be constructed at any resolution in two dimensions, it allows the pressure surface to be a continuous surface. Moreover, this surface is “nudged” (i.e., adjusted) towards the observations, wherever available. This continuous surface captures the actual pressure variations. 
     To mitigate the effect of waterbodies when determining a reference pressure, the following two use cases with respect to the presence of waterbodies that intervene between weather stations are considered: mitigation of effects from large water bodies, and mitigation of effects from small waterbodies. 
     In the case of large waterbodies, the Kriging interpolation approach is sufficient to mitigate microclimate effects owing to a weak correlation arising from the large distance (greater than 1.5 km) between weather stations separated by the waterbody. For example, if a first group of weather stations is in San Francisco and another set of weather stations are in Oakland (with a large bay intervening between the two regions) a fitted pressure surface over San Francisco will be less influenced by measurements coming from the weather stations within the Oakland region. That is, the presence of a large waterbody between the two groups of weather stations leads to a weak correlation between the two groups of weather stations in the variogram model. The weak correlation yields smaller weights used in Equation 1 (i.e., the coefficients λ, in Equation 1). Thus, a reference pressure estimate from Equation 1 for a mobile device situated within San Francisco is less influenced by atmospheric pressure observations from Oakland. This approach can be applied to other regions with large waterbodies. Such regions include Chicago, Florida, Washington (Seattle), and Virginia. 
     To mitigate the effect of smaller waterbodies, weather stations within a first threshold distance (e.g., 30 km) of a mobile device&#39;s estimated location are identified. Weather stations that are within a second threshold distance from waterbodies (e.g., 1 km) are then identified. Dummy variables (e.g., having values of 1 or 0) are then selected to mitigate the effects of weather stations within the second threshold distance from the waterbody for use in either variogram construction and/or estimating weights for the weather stations. When estimating a correlation structure using the variogram model, zero weights are assigned to the weather stations that are within the second threshold distance from the waterbodies. Such weather stations may be identified with the help of water polygons (available from the National Hydrology Center, for example) that delineate water and land areas. This step will partially mitigate the effect of waterbodies. Further mitigation is achieved by imposing an additional constraint in Equation 1 such that weather stations within the second threshold distance from a waterbody are assigned a zero weight. That is, with reference to Equation 1, λ i =1 if not near a waterbody, and λ i =0 if a weather station is near a waterbody. In some embodiments, this approach may be applied to large waterbodies. 
     To mitigate the effect of large differences in terrain altitude, the following approach may be used, in accordance with some embodiments. Weather stations within a first threshold distance (e.g., 30 km) of a mobile device&#39;s estimated location are identified. Weather stations that are associated with a large difference in terrain altitude are then identified. For example, in some embodiments, a bounding region (e.g., a 20 km square) centered at each weather station is identified. Within the bounding region, an isoline of constant elevation (e.g., 150 m) is determined. Any weather station within the determined isoline is flagged as being associated with a large difference in terrain altitude. Dummy variables (e.g., having values of 1 or 0) are then selected to mitigate the effects of weather stations that are associated with a large difference in terrain altitude for use in either variogram construction and/or estimating weights for the weather stations. When estimating a correlation structure using the variogram model, zero weights are assigned to the weather stations that are flagged as being associated with a large difference in terrain altitude. This step will partially mitigate the effect of weather stations that are associated with a large difference in terrain altitude. Further mitigation is achieved by imposing an additional constraint in Equation 1 such that weather stations that are associated with a large difference in terrain altitude are assigned a zero weight. That is, with reference to Equation 1, λ i =1 if weather stations are not associated with a large difference in terrain altitude, and λi=0 if a weather station is associated with a large difference in terrain altitude. 
       FIG.  9    illustrates components of an example transmitter  901  (e.g., either a weather station  104  or a stable pressure instrument  110 ), an example mobile device  902  (e.g., the mobile device  314 / 414 ), and an example server  903  (e.g., the server  112 ). Examples of communication pathways are shown by arrows between components. 
     By way of example in  FIG.  9   , each of the transmitters  901  may include: a mobile device interface  11  for exchanging information with a mobile device (e.g., antenna(s) and RF front-end components known in the art or otherwise disclosed herein); one or more processor(s)  12 ; memory/data source  13  for providing storage and retrieval of information and/or program instructions; atmospheric sensor(s)  14  for measuring environmental conditions (e.g., pressure, temperature, humidity, other) at or near the transmitter; a server interface  15  for exchanging information with a server (e.g., an antenna, a network interface, or other); and any other components known to one of ordinary skill in the art. The memory/data source  13  may include memory storing software modules with executable instructions, and the processor(s)  12  may perform different actions by executing the instructions from the modules, including: (i) performance of a part or all of the methods as described herein or otherwise understood by one of skill in the art as being performable at the transmitter; (ii) generation of positioning signals for transmission using a selected time, frequency, code, and/or phase; (iii) processing of signals received from the mobile device or another source; or (iv) other processing as required by operations described in this disclosure. Signals generated and transmitted by a transmitter may carry different information that, once determined by a mobile device or a server, may identify the following: the transmitter; the transmitter&#39;s position; environmental conditions at or near the transmitter; and/or other information known in the art. The atmospheric sensor(s)  14  may be integral with the transmitter, or separate from the transmitter and either co-located with the transmitter or located in the vicinity of the transmitter (e.g., within a threshold amount of distance). 
     By way of example in  FIG.  9   , the mobile device  902  may include: a transmitter interface  21  for exchanging information with a transmitter (e.g., an antenna and RF front-end components known in the art or otherwise disclosed herein); one or more processor(s)  22 ; memory/data source  23  for providing storage and retrieval of information and/or program instructions; atmospheric sensor(s)  24  (such as barometers and temperature sensors) for measuring environmental conditions (e.g., pressure, temperature, other) at the mobile device; other sensor(s)  25  for measuring other conditions (e.g., inertial sensors for measuring movement and orientation); a user interface  26  (e.g., display, keyboard, microphone, speaker, other) for permitting a user to provide inputs and receive outputs; another interface  27  for exchanging information with the server or other devices external to the mobile device (e.g., an antenna, a network interface, or other); and any other components known to one of ordinary skill in the art. A GNSS interface and processing unit (not shown) are contemplated, which may be integrated with other components (e.g., the interface  21  and the processors  22 ) or a standalone antenna, RF front end, and processors dedicated to receiving and processing GNSS signaling. The memory/data source  23  may include memory storing software modules with executable instructions, and the processor(s)  22  may perform different actions by executing the instructions from the modules, including: (i) performance of a part or all of the methods as described herein or otherwise understood by one of ordinary skill in the art as being performable at the mobile device; (ii) estimation of an altitude of the mobile device based on measurements of pressure from the mobile device and transmitter(s), temperature measurement(s) from the transmitter(s) or another source, and any other information needed for the computation); (iii) processing of received signals to determine position information (e.g., times of arrival or travel time of the signals, pseudoranges between the mobile device and transmitters, transmitter atmospheric conditions, transmitter and/or locations or other transmitter information); (iv) use of position information to compute an estimated position of the mobile device; (v) determination of movement based on measurements from inertial sensors of the mobile device; (vi) GNSS signal processing; or (vii) other processing as required by operations described in this disclosure. 
     By way of example in  FIG.  9   , the server  903  may include: a mobile device interface  31  for exchanging information with a mobile device (e.g., an antenna, a network interface, or other); one or more processor(s)  32 ; memory/data source  33  for providing storage and retrieval of information and/or program instructions; a transmitter interface  34  for exchanging information with a transmitter (e.g., an antenna, a network interface, or other); and any other components known to one of ordinary skill in the art. The memory/data source  33  may include memory storing software modules with executable instructions, and the processor(s)  32  may perform different actions by executing instructions from the modules, including: (i) performance of a part or all of the methods as described herein or otherwise understood by one of ordinary skill in the art as being performable at the server; (ii) estimation of an altitude of the mobile device; (iii) computation of an estimated position of the mobile device; or (iv) other processing as required by operations described in this disclosure. Steps performed by servers as described herein may also be performed on other machines that are remote from a mobile device, including computers of enterprises or any other suitable machine. As disclosed herein, mobile devices, servers, and atmospheric data measurement stations may each include one or more processors that are operable to carry out steps of processes disclosed herein independently or in conjunction. 
     Certain aspects disclosed herein relate to estimating the positions of mobile devices—e.g., where the position is represented in terms of: latitude, longitude, and/or altitude coordinates; x, y, and/or z coordinates; angular coordinates; or other representations. Various techniques to estimate the position of a mobile device can be used, including trilateration, which is the process of using geometry to estimate the position of a mobile device using distances traveled by different “positioning” (or “ranging”) signals that are received by the mobile device from different beacons (e.g., terrestrial transmitters and/or satellites). If position information like the transmission time and reception time of a positioning signal from a beacon is known, then the difference between those times multiplied by the speed of light would provide an estimate of the distance traveled by that positioning signal from that beacon to the mobile device. Different estimated distances corresponding to different positioning signals from different beacons can be used along with position information like the locations of those beacons to estimate the position of the mobile device. Positioning systems and methods that estimate a position of a mobile device (in terms of latitude, longitude, and/or altitude) based on positioning signals from beacons (e.g., transmitters, and/or satellites) and/or atmospheric measurements are described in co-assigned U.S. Pat. No. 8,130,141, issued Mar. 6, 2012, and U.S. Pat. No. 9,057,606, issued Jun. 16, 2015, incorporated by reference herein in its entirety for all purposes. It is noted that the term “positioning system” may refer to satellite systems (e.g., Global Navigation Satellite Systems (GNSS) like GPS, GLONASS, Galileo, and Compass/Beidou), terrestrial transmitter systems, and hybrid satellite/terrestrial systems. 
     Reference has been made in detail to embodiments of the disclosed invention, one or more examples of which have been illustrated in the accompanying figures. Each example has been provided by way of explanation of the present technology, not as a limitation of the present technology. In fact, while the specification has been described in detail with respect to specific embodiments of the invention, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing, may readily conceive of alterations to, variations of, and equivalents to these embodiments. For instance, features illustrated or described as part of one embodiment may be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present subject matter covers all such modifications and variations within the scope of the appended claims and their equivalents. These and other modifications and variations to the present invention may be practiced by those of ordinary skill in the art, without departing from the scope of the present invention, which is more particularly set forth in the appended claims. Furthermore, those of ordinary skill in the art will appreciate that the foregoing description is by way of example only, and is not intended to limit the invention.