Patent Publication Number: US-10324161-B2

Title: Balloon-based positioning system and method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation application of U.S. patent application Ser. No. 14/018,153, filed Sep. 4, 2013, which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Unless otherwise indicated herein, the materials described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section. 
     Many positioning systems exist that help determine a position of a device. One of the most commonly used positioning systems is the Global Positioning System (GPS), which is maintained by the United States government. The GPS is a satellite-based system that provides positioning information to ground-based receivers located throughout the world. The GPS include a fleet of thirty-two atomic clock satellites. Each satellite orbits the earth and broadcasts a signal containing satellite-positioning data for the respective satellite. A given receiver then receives signals from different satellites, and processes the collective satellite-positioning data contained therein as a basis for determining the receiver&#39;s position. However, for a variety of reasons, the receiver may be unable to receive one or more of these signals, or it may receive signals that have been distorted. As a result, receivers are often unable to accurately determine their position. Accordingly, improved positioning systems are desired. 
     SUMMARY 
     An example balloon-based positioning system may include a group of at least three balloons and a control system. Generally, the control system may be configured to determine a position of each balloon in the group relative to the earth. The control system may make these determinations based on one or more spatial relationships, including for example a distance between two balloons or a distance between a balloon and a reference point that has a known position relative to the earth. The control system may then transmit the determined positions to the respective balloons, which in turn may broadcast the determined positions such that they may be received and processed by a ground-based receiver. This may allow the ground-based receiver to determine its position relative to the earth. 
     In one aspect, a system includes a group of at least three balloons deployed in the stratosphere and a control system. The control system is configured for: determining a first set of spatial relationships relating to the group; determining a second set of spatial relationships relating to at least a portion of the group and to a reference point; determining a position of the reference point relative to the earth; using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth; and transmitting the determined position of the target balloon relative to the earth. 
     In another aspect, a computer-readable medium has stored thereon program instructions that upon execution by a processor, cause performance of a set of functions. The set of functions include: determining a first set of spatial relationships relating to a group of at least three balloons deployed in the stratosphere; determining a second set of spatial relationships relating to at least a portion of the group and to a reference point; determining a position of the reference point relative to the earth; using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth; and transmitting the determined position of the target balloon relative to the earth. 
     In yet another aspect, a method involves: determining, by a computing device, a first set of spatial relationships relating to a group of at least three balloons deployed in the stratosphere, wherein determining the first set comprises (i) determining, by the computing device, a distance between a balloon in the group and another balloon in the group, and (ii) determining, by the computing device, an angle between a first vector and a second vector, wherein the first vector extends from a first balloon in the group towards a second balloon in the group, and wherein the second vector extends from the first balloon towards a third balloon in the group; determining a second set of spatial relationships relating to at least a portion of the group and to a reference point; determining, by a computing device, a position of the reference point relative to the earth; using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth; and transmitting the determined position of the target balloon relative to the earth. 
     In yet another aspect, disclosed are means for: determining a first set of spatial relationships relating to a group of at least three balloons deployed in the stratosphere; determining a second set of spatial relationships relating to at least a portion of the group and to a reference point; determining a position of the reference point relative to the earth; using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth; and transmitting the determined position of the target balloon relative to the earth. 
     In yet another aspect, disclosed are means for: determining a first set of spatial relationships relating to a group of at least three balloons deployed in the stratosphere, wherein determining the first set comprises (i) determining a distance between a balloon in the group and another balloon in the group, and (ii) determining an angle between a first vector and a second vector, wherein the first vector extends from a first balloon in the group towards a second balloon in the group, and wherein the second vector extends from the first balloon towards a third balloon in the group; determining a second set of spatial relationships relating to at least a portion of the group and to a reference point; determining a position of the reference point relative to the earth; using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth; and transmitting the determined position of the target balloon relative to the earth. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is a simplified block diagram illustrating a balloon network, according to an example embodiment. 
         FIG. 2  is a simplified block diagram illustrating a balloon-network control system, according to an example embodiment. 
         FIG. 3  is a simplified block diagram illustrating a high-altitude balloon, according to an example embodiment. 
         FIG. 4  is a simplified block diagram illustrating a balloon network that includes super-nodes and sub-nodes, according to an example embodiment. 
         FIG. 5  is a simplified block diagram of a balloon-based positioning system, according to an example embodiment. 
         FIG. 6  is a flow chart showing functions of a method, according to an example embodiment. 
         FIG. 7  is an alternate depiction of a portion of the system of  FIG. 5 . 
         FIG. 8  is another alternate depiction of a portion of the system of  FIG. 5 . 
         FIG. 9  is again another alternate depiction of a portion of the system of  FIG. 5 . 
         FIG. 10  is still another alternate depiction of a portion of the system of  FIG. 5 . 
         FIG. 11  is yet another alternate depiction of a portion of the system of  FIG. 5 . 
         FIG. 12  is even another alternate depiction of a portion of the system of  FIG. 5 . 
     
    
    
     DETAILED DESCRIPTION 
     Throughout this disclosure, unless otherwise specified and/or unless the particular context clearly dictates otherwise: any usage of “a” or “an” means “at least one,” and any usage of “the” means “the at least one.” 
     Illustrative embodiments of a balloon-based positioning system are described herein and are not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented herein. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, may be arranged, substituted, combined, separated, and designed in a wide variety of different configurations, all of which are contemplated herein. 
     1. Overview 
     Embodiments of a balloon-based positioning system may be integrated with a balloon data network that includes a plurality of balloons; for example, a mesh network formed by high-altitude balloons deployed in the stratosphere. Since winds in the stratosphere may affect the positions of the balloons in a differential manner, each balloon in a network may be configured to change its horizontal position by adjusting its vertical position (i.e., altitude). For instance, by adjusting its altitude, a balloon may be able find winds that will carry it horizontally (e.g., latitudinally and/or longitudinally) to a desired horizontal location. 
     In one balloon network, balloons may move latitudinally and/or longitudinally relative to one another so as to form a desired topology. However, keeping an individual balloon at a specific location may be difficult due to winds, and possibly for other reasons as well. Accordingly, the desired topology may define a relative framework and/or rules for positioning of balloons relative to one another, such that balloons can move with respect to the ground, while maintaining the desired topology. Thus, at a given location on earth, the particular balloon or balloons that provide service may change over time. 
     In one example, a balloon-based positioning system may include a group of at least three balloons and a control system. Generally, the control system may be configured to perform one or more functions related to determining a position of each balloon in the group relative to the earth. The control system may then transmit the determined positions to the respective balloons, which in turn may broadcast the determined positions such that they may be received and processed by a ground-based receiver. This may allow the ground-based receiver to determine its position relative to the earth. 
     In one example, the control system may determine the position of each balloon in the group relative to the earth by determining the position of each balloon in the group relative to each other balloon in the group and then determining the position of the group relative to the earth. The control system may make these determinations based on one or more spatial relationships. 
     A spatial relationship in this context may take a variety of forms. For example, a spatial relationship may be a distance between two objects. An object may be a balloon or a reference point that has a known position relative to the earth. Such a reference point may be, for example, a ground-based station, a celestial object, a satellite, or perhaps the earth itself. As another example, a spatial relationship may be an angle between a first vector and a second vector, where the first vector extends from a first object towards a second object, and where the second vector extends from the first object towards a third object. 
     In one example, the control system may then use the determined spatial relationships as constraint-optimization conditions in connection with an optimization function to determine (as an estimate) the position of each balloon in the group relative to the earth. The control system may also use balloon properties, environmental conditions, and/or other data as constraint-optimization conditions in this respect. Notably, as the control system considers more observed data, the control system may determine the position of each balloon relative to the earth with a greater level of accuracy. 
     As noted above, once the control system transmits the determined positions to the respective balloons, the balloons may broadcast their respective positions. In one example, each balloon may include a position-broadcasting module (PBM) configured for broadcasting a balloon signal containing balloon-positioning data. The balloon-positioning data may include the position of the respective balloon and a corresponding time of broadcast (i.e., indicating when the balloon signal was broadcast). These balloon signals may then be used by a ground-based receiver as a basis for determining its position relative to the earth. As such, the ground-based receiver may be configured to receive these balloon signals and determine its position based on the collective balloon-positioning data contained therein, such as by employing a triangulation technique. 
     Embodiments of a balloon-based positioning system may provide several advantages. As one example, the typical distance from a balloon to a ground-based receiver is relatively short, as compared to for example, the typical distance from a GPS satellite to a ground-based receiver. As a result, balloon signals are likely to be stronger, and are more likely to reach ground-based receivers, as compared to in a parallel GPS scenario. 
     As another example advantage, the balloons are positioned beneath the ionosphere. As a result, the balloon signals need not traverse the ionosphere to reach ground-based receivers, and therefore they may avoid refraction-based interference that is caused by the ionosphere. Again, this means that balloon signals are likely to be stronger, and are more likely to reach ground-based receivers, as compared to in a parallel GPS scenario where satellite signals traverse the ionosphere. 
     Notably, to minimize the effects of refraction-based interference, satellite signals are typically broadcast simultaneously on two different channel frequencies. Since balloon signals avoid this type of interference, they may be broadcast on a single channel frequency. Among other things, this may allow ground-based receivers to be less complex, as compared to those used in the GPS that must be configured to receive signals on multiple channels. 
     While not necessary, some embodiments of a balloon-based positioning system may include a large number of balloons, including thousands, tens of thousands, or more. In addition to providing additional data for determining more spatial relationships, these embodiments provide a further advantage of increasing the likelihood that a given ground-based receiver will have a direct line-of-sight with one or more of the balloons. Accordingly, balloon signals are more likely to reach ground-based receivers, as compared to in a parallel GPS scenario where the GPS is limited by its fleet of thirty-two satellites. 
     It should be appreciated that the possible benefits and advantages described above are merely examples and are non-limiting. Embodiments of a balloon-based positioning system may provide additional advantages, such as those described in greater detail throughout this disclosure, and/or those that would be apparent to one of ordinary skill in the art. Further, the possible benefits and advantages described are not necessarily required, and should not be construed as limiting the claims. 
     2. Example Balloon Networks 
     In some embodiments, a high-altitude-balloon network may be homogenous. That is, the balloons in a high-altitude-balloon network could be substantially similar to each other in one or more ways. More specifically, in a homogenous high-altitude-balloon network, each balloon is configured to communicate with nearby balloons via free-space optical links. Further, some or all of the balloons in such a network, may also be configured to communicate with ground-based station(s) using RF communications. (Note that in some embodiments, the balloons may be homogenous in so far as each balloon is configured for free-space optical communication with other balloons, but heterogeneous with regard to RF communications with ground-based stations.) 
     In other embodiments, a high-altitude-balloon network may be heterogeneous, and thus may include two or more different types of balloons. For example, some balloons may be configured as super-nodes, while other balloons may be configured as sub-nodes. Some balloons may be configured to function as both a super-node and a sub-node. Such balloons may function as either a super-node or a sub-node at a particular time, or, alternatively, act as both simultaneously depending on the context. For instance, an example balloon could aggregate search requests of a first type to transmit to a ground-based station. The example balloon could also send search requests of a second type to another balloon, which could act as a super-node in that context. 
     In such a configuration, the super-node balloons may be configured to communicate with nearby super-node balloons via free-space optical links. However, the sub-node balloons may not be configured for free-space optical communication, and may instead be configured for some other type of communication, such as RF communications. In that case, a super-node may be further configured to communicate with sub-nodes using RF communications. Thus, the sub-nodes may relay communications between the super-nodes and one or more ground-based stations using RF communications. In this way, the super-nodes may collectively function as backhaul for the balloon network, while the sub-nodes function to relay communications from the super-nodes to ground-based stations. Other differences could be present between balloons in a heterogeneous balloon network. 
       FIG. 1  is a simplified block diagram illustrating a balloon network  100 , according to an example embodiment. As shown, balloon network  100  includes balloons  102 A to  102 F, which are configured to communicate with one another via free-space optical links  104 . Balloons  102 A to  102 F could additionally or alternatively be configured to communicate with one another via RF links  114 . Balloons  102 A to  102 F may collectively function as a mesh network for packet-data communications. Further, balloons  102 A to  102 F may be configured for RF communications with ground-based stations  106  and  112  via RF links  108 . In another example embodiment, balloons  102 A to  102 F could be configured to communicate via optical link  110  with ground-based station  112 . 
     In an example embodiment, balloons  102 A to  102 F are high-altitude balloons, which are deployed in the stratosphere. At moderate latitudes, the stratosphere includes altitudes between approximately 10 kilometers (km) and 50 km altitude above the surface. At the poles, the stratosphere starts at an altitude of approximately 8 km. In an example embodiment, high-altitude balloons may be generally configured to operate in an altitude range within the stratosphere that has lower winds (e.g., between 5 and 20 miles per hour (mph)). 
     More specifically, in a high-altitude-balloon network, balloons  102 A to  102 F may generally be configured to operate at altitudes between 17 km and 25 km (although other altitudes are possible). This altitude range may be advantageous for several reasons. In particular, this layer of the stratosphere generally has mild wind and turbulence (e.g., winds between 5 and 20 miles per hour (mph)). Further, while the winds between 17 km and 25 km may vary with latitude and by season, the variations can be modeled in a reasonably accurate manner. Additionally, altitudes above 17 km are typically above the maximum flight level designated for commercial air traffic. Therefore, interference with commercial flights is not a concern when balloons are deployed between 17 km and 25 km. Additional advantages relating to this altitude range, particularly in connection with positioning-related features, are discussed in greater detail below. 
     To transmit data to another balloon, a given balloon  102 A to  102 F may be configured to transmit an optical signal via an optical link  104 . In an example embodiment, a given balloon  102 A to  102 F may use one or more high-power light-emitting diodes (LEDs) to transmit an optical signal. Alternatively, some or all of balloons  102 A to  102 F may include laser systems for free-space optical communications over optical links  104 . Other types of free-space optical communication are possible. Further, in order to receive an optical signal from another balloon via an optical link  104 , a given balloon  102 A to  102 F may include one or more optical receivers. Additional details of example balloons are discussed in greater detail below, with reference to  FIG. 3 . 
     In a further aspect, balloons  102 A to  102 F may utilize one or more of various different RF air-interface protocols for communication with ground-based stations  106  and  112  via RF links  108 . For instance, some or all of balloons  102 A to  102 F may be configured to communicate with ground-based stations  106  and  112  using protocols described in IEEE 802.11 (including any of the IEEE 802.11 revisions), various cellular protocols such as GSM, CDMA, UMTS, EV-DO, WiMAX, and/or LTE, and/or one or more propriety protocols developed for balloon-to-ground RF communication, among other possibilities. 
     In a further aspect, there may be scenarios where RF links  108  do not provide a desired link capacity for balloon-to-ground communications. For instance, increased capacity may be desirable to provide backhaul links from a ground-based gateway, and in other scenarios as well. Accordingly, an example network may also include downlink balloons, which could provide a high-capacity air-ground link. 
     For example, in balloon network  100 , balloon  102 F could be configured as a downlink balloon. Like other balloons in an example network, a downlink balloon  102 F may be operable for optical communication with other balloons via optical links  104 . However, downlink balloon  102 F may also be configured for free-space optical communication with a ground-based station  112  via an optical link  110 . Optical link  110  may therefore serve as a high-capacity link (as compared to an RF link  108 ) between the balloon network  100  and a ground-based station  112 . 
     Note that in some implementations, a downlink balloon  102 F may additionally be operable for RF communication with ground-based stations  106 . In other cases, a downlink balloon  102 F may only use an optical link for balloon-to-ground communications. Further, while the arrangement shown in  FIG. 1  includes just one downlink balloon  102 F, an example balloon network can also include multiple downlink balloons. On the other hand, a balloon network can also be implemented without any downlink balloons. 
     In other implementations, a downlink balloon may be equipped with a specialized, high-bandwidth RF communication system for balloon-to-ground communications, instead of, or in addition to, a free-space optical communication system. The high-bandwidth RF communication system may take the form of an ultra-wideband system, which provides an RF link with substantially the same capacity as the optical links  104 . Other forms are also possible. 
     Balloons could be configured to establish a communication link with space-based satellites in addition to, or as an alternative to, a ground-based communication link. 
     Ground-based stations, such as ground-based stations  106  and/or  112 , may take various forms. Generally, a ground-based station may include components such as transceivers, transmitters, and/or receivers for communication via RF links and/or optical links with a balloon network. Further, a ground-based station may use various air-interface protocols in order communicate with a balloon  102 A to  102 F over an RF link  108 . As such, ground-based stations  106  and  112  may be configured as an access point with which various devices can connect to balloon network  100 . Ground-based stations  106  and  112  may have other configurations and/or serve other purposes without departing from the scope of the invention. 
     Further, some ground-based stations, such as ground-based stations  106  and  112 , may be configured as gateways between balloon network  100  and one or more other networks. Such ground-based stations  106  and  112  may thus serve as an interface between the balloon network and the Internet, a cellular service provider&#39;s network, and/or other types of networks. Variations on this configuration and other configurations of ground-based stations  106  and  112  are also possible. 
     2a) Mesh Network Functionality 
     As noted, balloons  102 A to  102 F may collectively function as a mesh network. More specifically, since balloons  102 A to  102 F may communicate with one another using free-space optical links, the balloons may collectively function as a free-space optical mesh network. 
     In a mesh-network configuration, each balloon  102 A to  102 F may function as a node of the mesh network, which is operable to receive data directed to it and to route data to other balloons. As such, data may be routed from a source balloon to a destination balloon by determining an appropriate sequence of optical links between the source balloon and the destination balloon. These optical links may be collectively referred to as a “lightpath” for the connection between the source and destination balloons. Further, each of the optical links may be referred to as a “hop” on the lightpath. 
     To operate as a mesh network, balloons  102 A to  102 F may employ various routing techniques and self-healing algorithms. In some embodiments, a balloon network  100  may employ adaptive or dynamic routing, where a lightpath between a source and destination balloon is determined and set-up when the connection is needed, and released at a later time. Further, when adaptive routing is used, the lightpath may be determined dynamically depending upon the current state, past state, and/or predicted state of the balloon network. 
     In addition, the network topology may change as the balloons  102 A to  102 F move relative to one another and/or relative to the ground. Accordingly, an example balloon network  100  may apply a mesh protocol to update the state of the network as the topology of the network changes. For example, to address the mobility of the balloons  102 A to  102 F, balloon network  100  may employ and/or adapt various techniques that are employed in mobile ad hoc networks (MANETs). Other examples are possible as well. 
     In some implementations, a balloon network  100  may be configured as a transparent mesh network. More specifically, in a transparent balloon network, the balloons may include components for physical switching that is entirely optical, without any electrical operations involved in physical routing of optical signals. Thus, in a transparent configuration with optical switching, signals travel through a multi-hop lightpath that is entirely optical. 
     In other implementations, the balloon network  100  may implement a free-space optical mesh network that is opaque. In an opaque configuration, some or all balloons  102 A to  102 F may implement optical-electrical-optical (OEO) switching. For example, some or all balloons may include optical cross-connects (OXCs) for OEO conversion of optical signals. Other opaque configurations are also possible. Additionally, network configurations are possible that include routing paths with both transparent and opaque sections. 
     In a further aspect, balloons in an example balloon network  100  may implement wavelength division multiplexing (WDM), which may help to increase link capacity. When WDM is implemented with transparent switching, physical lightpaths through the balloon network may be subject to the “wavelength continuity constraint.” More specifically, because the switching in a transparent network is entirely optical, it may be necessary to assign the same wavelength for all optical links on a given lightpath. 
     An opaque configuration, on the other hand, may avoid the wavelength continuity constraint. In particular, balloons in an opaque balloon network may include the OEO switching systems operable for wavelength conversion. As a result, balloons can convert the wavelength of an optical signal at each hop along a lightpath. Alternatively, optical wavelength conversion could take place at only selected hops along the lightpath. 
     Further, various routing algorithms may be employed in an opaque configuration. For example, to determine a primary lightpath and/or one or more diverse backup lightpaths for a given connection, example balloons may apply or consider shortest-path routing techniques such as Dijkstra&#39;s algorithm and k-shortest path, and/or edge and node-diverse or disjoint routing such as Suurballe&#39;s algorithm, among others. Additionally or alternatively, techniques for maintaining a particular Quality of Service (QoS) may be employed when determining a lightpath. Other techniques are also possible. 
     2b) Station-Keeping Functionality 
     In one embodiment, a balloon network  100  may implement station-keeping functions to help provide a desired network topology. For example, station-keeping may involve each balloon  102 A to  102 F maintaining and/or moving into a certain position relative to one or more other balloons in the network (and possibly in a certain position relative to the ground). As part of this process, each balloon  102 A to  102 F may implement station-keeping functions to determine its desired positioning within the desired topology, and if necessary, to determine how to move to the desired position. 
     The desired topology may vary depending upon the particular implementation. In some cases, balloons may implement station-keeping to provide a substantially uniform topology. In such cases, a given balloon  102 A to  102 F may implement station-keeping functions to position itself at substantially the same distance (or within a certain range of distances) from adjacent balloons in the balloon network  100 . 
     In other cases, a balloon network  100  may have a non-uniform topology. For instance, example embodiments may involve topologies where balloons are distributed more or less densely in certain areas, for various reasons. As an example, to help meet the higher bandwidth demands that are typical in urban areas, balloons may be clustered more densely over urban areas. For similar reasons, the distribution of balloons may be denser over land than over large bodies of water. Many other examples of non-uniform topologies are possible. 
     In a further aspect, the topology of an example balloon network may be adaptable. In particular, station-keeping functionality of example balloons may allow the balloons to adjust their respective positioning in accordance with a change in the desired topology of the network. For example, one or more balloons could move to new positions to increase or decrease the density of balloons in a given area. Other examples are possible. 
     In some embodiments, a balloon network  100  may employ an energy function to determine if and/or how balloons should move to provide a desired topology. In particular, the state of a given balloon and the states of some or all nearby balloons may be input to an energy function. The energy function may apply the current states of the given balloon and the nearby balloons to a desired network state (e.g., a state corresponding to the desired topology). A vector indicating a desired movement of the given balloon may then be determined by determining the gradient of the energy function. The given balloon may then determine appropriate actions to take in order to effectuate the desired movement. For example, a balloon may determine an altitude adjustment or adjustments such that winds will move the balloon in the desired manner. 
     2c) Control of Balloons in a Balloon Network 
     In some embodiments, mesh networking and/or station-keeping functions may be centralized. For example,  FIG. 2  is a block diagram illustrating a balloon-network control system, according to an example embodiment. In particular,  FIG. 2  shows a distributed control system, which includes a central control system  200  and a number of regional control-systems  202 A to  202 B. Such a control system may be configured to coordinate certain functionality for balloon network  204 , and as such, may be configured to control and/or coordinate certain functions for balloons  206 A to  206 I. 
     In the illustrated embodiment, central control system  200  may be configured to communicate with balloons  206 A to  206 I via a number of regional control systems  202 A to  202 C. These regional control systems  202 A to  202 C may be configured to receive communications and/or aggregate data from balloons in the respective geographic areas that they cover, and to relay the communications and/or data to central control system  200 . Further, regional control systems  202 A to  202 C may be configured to route communications from central control system  200  to the balloons in their respective geographic areas. For instance, as shown in  FIG. 2 , regional control system  202 A may relay communications and/or data between balloons  206 A to  206 C and central control system  200 , regional control system  202 B may relay communications and/or data between balloons  206 D to  206 F and central control system  200 , and regional control system  202 C may relay communications and/or data between balloons  206 G to  206 I and central control system  200 . 
     In order to facilitate communications between the central control system  200  and balloons  206 A to  206 I, certain balloons may be configured as downlink balloons, which are operable to communicate with regional control systems  202 A to  202 C. Accordingly, each regional control system  202 A to  202 C may be configured to communicate with the downlink balloon or balloons in the respective geographic area it covers. For example, in the illustrated embodiment, balloons  206 A,  206 F, and  206 I are configured as downlink balloons. As such, regional control systems  202 A to  202 C may respectively communicate with balloons  206 A,  206 F, and  206 I via optical links  208 ,  210 , and  212 , respectively. 
     In the illustrated configuration, where only some of balloons  206 A to  206 I are configured as downlink balloons, the balloons  206 A,  206 F, and  206 I that are configured as downlink balloons may function to relay communications from central control system  200  to other balloons in the balloon network, such as balloons  206 B to  206 E,  206 G, and  206 H. However, it should be understood that it in some implementations, it is possible that all balloons may function as downlink balloons. Further, while  FIG. 2  shows multiple balloons configured as downlink balloons, it is also possible for a balloon network to include only one downlink balloon. 
     Note that a regional control system  202 A to  202 C may in fact just be a particular type of ground-based station that is configured to communicate with downlink balloons (e.g. the ground-based station  112  of  FIG. 1 ). Thus, while not shown in  FIG. 2 , a control system may be implemented in conjunction with other types of ground-based stations (e.g., access points, gateways, etc.). 
     In a centralized control arrangement, such as that shown in  FIG. 2 , the central control system  200  (and possibly regional control systems  202 A to  202 C as well) may coordinate certain mesh-networking functions for balloon network  204 . For example, balloons  206 A to  206 I may send the central control system  200  certain state information, which the central control system  200  may utilize to determine the state of balloon network  204 . The state information from a given balloon may include position data, optical-link information (e.g., the identity of other balloons with which the balloon has established an optical link, the bandwidth of the link, wavelength usage and/or availability on a link, etc.), wind data collected by the balloon, and/or other types of information. Accordingly, the central control system  200  may aggregate state information from some or all the balloons  206 A to  206 I in order to determine an overall state of the network. 
     The overall state of the network may then be used to coordinate and/or facilitate certain mesh-networking functions such as determining lightpaths for connections. For example, the central control system  200  may determine a current topology based on the aggregate state information from some or all the balloons  206 A to  206 I. The topology may provide a picture of the current optical links that are available in the balloon network and/or the wavelength availability on the links. This topology may then be sent to some or all of the balloons so that a routing technique may be employed to select appropriate lightpaths (and possibly backup lightpaths) for communications through the balloon network  204 . 
     In a further aspect, the central control system  200  (and possibly regional control systems  202 A to  202 C as well) may also coordinate certain station-keeping functions for balloon network  204 . For example, the central control system  200  may input state information that is received from balloons  206 A to  206 I to an energy function, which may effectively compare the current topology of the network to a desired topology, and provide a vector indicating a direction of movement (if any) for each balloon, such that the balloons can move towards the desired topology. Further, the central control system  200  may use altitudinal wind data to determine respective altitude adjustments that may be initiated to achieve the movement towards the desired topology. The central control system  200  may provide and/or support other station-keeping functions as well. 
       FIG. 2  shows a distributed arrangement that provides centralized control, with regional control systems  202 A to  202 C coordinating communications between a central control system  200  and a balloon network  204 . Such an arrangement may be useful to provide centralized control for a balloon network that covers a large geographic area. In some embodiments, a distributed arrangement may even support a global balloon network that provides coverage everywhere on earth. A distributed-control arrangement may be useful in other scenarios as well. 
     Further, it should be understood that other control-system arrangements are possible. For instance, some implementations may involve a centralized control system with additional layers (e.g., sub-region systems within the regional control systems, and so on). Alternatively, control functions may be provided by a single, centralized, control system, which communicates directly with one or more downlink balloons. 
     In some embodiments, control and coordination of a balloon network may be shared between a ground-based control system and a balloon network to varying degrees, depending upon the implementation. In fact, in some embodiments, there may be no ground-based control systems. In such an embodiment, all network control and coordination functions may be implemented by the balloon network itself. For example, certain balloons may be configured to provide the same or similar functions as central control system  200  and/or regional control systems  202 A to  202 C. Other examples are also possible. 
     Furthermore, control and/or coordination of a balloon network may be de-centralized. For example, each balloon may relay state information to, and receive state information from, some or all nearby balloons. Further, each balloon may relay state information that it receives from a nearby balloon to some or all nearby balloons. When all balloons do so, each balloon may be able to individually determine the state of the network. Alternatively, certain balloons may be designated to aggregate state information for a given portion of the network. These balloons may then coordinate with one another to determine the overall state of the network. 
     Further, in some aspects, control of a balloon network may be partially or entirely localized, such that it is not dependent on the overall state of the network. For example, individual balloons may implement station-keeping functions that only consider nearby balloons. In particular, each balloon may implement an energy function that takes into account its own state and the states of nearby balloons. The energy function may be used to maintain and/or move to a desired position with respect to the nearby balloons, without necessarily considering the desired topology of the network as a whole. However, when each balloon implements such an energy function for station-keeping, the balloon network as a whole may maintain and/or move towards the desired topology. 
     As an example, each balloon A may receive distance information d 1  to d k  with respect to each of its k closest neighbors. Each balloon A may treat the distance to each of the k balloons as a virtual spring with a vector representing a force direction from the first nearest neighbor balloon i toward balloon A and with force magnitude proportional to d i . The balloon A may sum each of the k vectors and the summed vector is the vector of desired movement for balloon A. Balloon A may attempt to achieve the desired movement by controlling its altitude. 
     Alternatively, this process could assign the force magnitude of each of these virtual forces equal to d i ×d I , wherein d I  is proportional to the distance to the second nearest neighbor balloon, for instance. 
     In another embodiment, a similar process could be carried out for each of the k balloons and each balloon could transmit its planned movement vector to its local neighbors. Further rounds of refinement to each balloon&#39;s planned movement vector can be made based on the corresponding planned movement vectors of its neighbors. It will be evident to those skilled in the art that other algorithms could be implemented in a balloon network in an effort to maintain a set of balloon spacings and/or a specific network capacity level over a given geographic location. 
     2d) Example Balloon Configuration 
     Various types of balloons may be incorporated in an example balloon network. As noted above, an example embodiment may utilize high-altitude balloons, which could typically operate in an altitude range between 17 km and 25 km.  FIG. 3  shows a high-altitude balloon  300 , according to an example embodiment. As shown, the balloon  300  includes an envelope  302 , a skirt  304 , a payload  306 , and a cut-down system  308 , which is attached between the balloon  302  and payload  304 . 
     The envelope  302  and skirt  304  may take various forms, which may be currently well-known or yet to be developed. For instance, the envelope  302  and/or skirt  304  may be made of a highly-flexible latex material or may be made of a rubber material such as chloroprene. In one example embodiment, the envelope and/or skirt could be made of metalized Mylar or BoPet. Other materials are also possible. Further, the shape and size of the envelope  302  and skirt  304  may vary depending upon the particular implementation. Additionally, the envelope  302  may be filled with various different types of gases, such as helium and/or hydrogen. Other types of gases are possible as well. 
     The payload  306  of balloon  300  may include a processor  312  and on-board data storage, such as memory  314 . The memory  314  may take the form of or include a non-transitory computer-readable medium. The non-transitory computer-readable medium may have instructions stored thereon, which can be accessed and executed by the processor  312  in order to carry out the balloon functions described herein. 
     The payload  306  of balloon  300  may also include various other types of equipment and systems to provide a number of different functions. For example, payload  306  may include optical communication system  316 , which may transmit optical signals via an optical signal transmitter (e.g., an ultra-bright LED transmitter)  320 , and which may receive optical signals via an optical signal receiver  322  (e.g., a photodiode receiver). In one example, the optical signal transmitter  320  may be configured to transmit optical signals (using a modulation technique) in a multidirectional or omnidirectional manner. Similarly, the optical signal receiver  322  may be configured to receive optical signals from a variety of different directions at a given time. 
     In some instances, the optical signal transmitter may take the form of a steerable optical signal transmitter (referred to herein as a “steerable transmitter”) and the optical signal receiver may take the form of a steerable optical signal receiver (referred to herein as a “steerable receiver”). In one example, the steerable transmitter and steerable receiver may be integrated together as a steerable transmitter/receiver  344 . The steerable transmitter may be configured to transmit optical signals in a relatively focused manner, as compared to the multidirectional or omnidirectional manners discussed above. Similarly, the steerable receiver may be configured to receive optical signals from a relatively focused direction, as compared to from a variety of different directions as discussed above. 
     The steerable transmitter/receiver  344  (or the steerable transmitter and/or the steerable receiver individually) may be configured to rotate about one or more axes (e.g., defining yaw and pitch Euler angle offsets). This may allow two balloons to steer their respective steerable transmitter/receiver towards each other such that the respective balloons may communicate using free-space optical links. In some instances, alignment techniques may be used to properly orient each steerable transmitter/receiver. Further, the combined use of a steerable transmitter on one balloon and an optical signal receiver on another balloon may aid in determining a particular angle-based spatial relationship as described in greater detail below. 
     Notably, the optical communication system  316  may be implemented in various ways (e.g., with mechanical systems and/or with hardware, firmware, and/or software) depending upon the particular application. 
     The payload  306  may also include a reflector (sometimes called a retro-reflector)  346  that is configured to reflect (in one or more directions) an optical signal directed at it. The combined use of a steerable transmitter on one balloon and a reflector on another balloon may also aid in determining a particular angle-based spatial relationship as described in greater detail below. 
     Payload  306  may also include an RF communication system  318 , which may transmit and/or receive RF communications via an antenna system  340 . The optical communication system  316  and/or the RF communication system  318  are examples of communication systems that may include communication interfaces for communications between a balloon and other nodes in a balloon network. It should be understood that other types of communication systems that provide other types of communication interfaces are also possible, and may vary depending upon the particular network implementation. 
     The payload  306  may also include a power supply  326  to supply power to the various components of balloon  300 . The power supply  326  could include a rechargeable battery. In other embodiments, the power supply  326  may additionally or alternatively represent other means known in the art for producing power. In addition, the balloon  300  may include a solar power generation system  327 . The solar power generation system  327  may include solar panels and could be used to generate power that charges and/or is distributed by power supply  326 . 
     Further, payload  306  may include various types of other systems and sensors  328  managed by a sensor system  330 . For example, payload  306  may include various motion sensors (e.g., accelerometers, magnetometers, gyroscopes, and/or compasses), altimeters (e.g., pressure, sonic, or radar-based), and/or various sensors for capturing environmental data. Further, some or all of the components within payload  306  may be implemented in a radiosonde or other probe, which may be operable to measure, e.g., pressure, altitude, geographical position (latitude and longitude), temperature, relative humidity, and/or wind speed and/or wind direction, among other information. 
     The balloon may further include a GPS (or other positioning system) receiver  342  that may process satellite or other types of signals received via the antenna system  340 . The antenna system  340  may also be used to broadcast various types of signals. Further discussion relating to receiving and broadcasting signals, particularly in connection with positioning-related features, is provided in greater detail below. 
     In a further aspect, balloon  300  may be configured for altitude control. For instance, balloon  300  may include a variable buoyancy system, which is configured to change the altitude of the balloon  300  by adjusting the volume and/or density of the gas in the balloon  300 . A variable buoyancy system may take various forms, and may generally be any system that can change the volume and/or density of gas in the envelope  302 . 
     In an example embodiment, a variable buoyancy system may include a bladder  310  that is located inside of envelope  302 . The bladder  310  could be an elastic chamber configured to hold liquid and/or gas. Alternatively, the bladder  310  need not be inside the envelope  302 . For instance, the bladder  310  could be a ridged bladder that could be pressurized well beyond neutral pressure. The buoyancy of the balloon  300  may therefore be adjusted by changing the density and/or volume of the gas in bladder  310 . To change the density in bladder  310 , balloon  300  may be configured with systems and/or mechanisms for heating and/or cooling the gas in bladder  310 . Further, to change the volume, balloon  300  may include pumps or other features for adding gas to and/or removing gas from bladder  310 . Additionally or alternatively, to change the volume of bladder  310 , balloon  300  may include release valves or other features that are controllable to allow gas to escape from bladder  310 . Multiple bladders  310  could be implemented within the scope of this disclosure. For instance, multiple bladders could be used to improve balloon stability. 
     In an example embodiment, the envelope  302  could be filled with helium, hydrogen or other lighter-than-air material. The envelope  302  could thus have an associated upward buoyancy force. In such an embodiment, air in the bladder  310  could be considered a ballast tank that may have an associated downward ballast force. In another example embodiment, the amount of air in the bladder  310  could be changed by pumping air (e.g., with an air compressor) into and out of the bladder  310 . By adjusting the amount of air in the bladder  310 , the ballast force may be controlled. In some embodiments, the ballast force may be used, in part, to counteract the buoyancy force and/or to provide altitude stability. 
     In another embodiment, a portion of the envelope  302  could be a first color (e.g., black) and/or a first material from the rest of envelope  302 , which may have a second color (e.g., white) and/or a second material. For instance, the first color and/or first material could be configured to absorb a relatively larger amount of solar energy than the second color and/or second material. Thus, rotating the balloon such that the first material is facing the sun may act to heat the envelope  302  as well as the gas inside the envelope  302 . In this way, the buoyancy force of the envelope  302  may increase. By rotating the balloon such that the second material is facing the sun, the temperature of gas inside the envelope  302  may decrease. Accordingly, the buoyancy force may decrease. In this manner, the buoyancy force of the balloon could be adjusted by changing the temperature/volume of gas inside the envelope  302  using solar energy. In such embodiments, it is possible that a bladder  310  may not be a necessary element of balloon  300 . Thus, various contemplated embodiments, altitude control of balloon  300  could be achieved, at least in part, by adjusting the rotation of the balloon with respect to the sun. 
     Further, a balloon  306  may include a navigation system (not shown). The navigation system may implement station-keeping functions to maintain position within and/or move to a position in accordance with a desired topology. In particular, the navigation system may use altitudinal wind data to determine altitudinal adjustments that result in the wind carrying the balloon in a desired direction and/or to a desired location. The altitude-control system may then make adjustments to the density of the balloon chamber in order to effectuate the determined altitudinal adjustments and cause the balloon to move laterally to the desired direction and/or to the desired location. Alternatively, the altitudinal adjustments may be computed by a ground-based or satellite-based control system and communicated to the high-altitude balloon. In other embodiments, specific balloons in a heterogeneous balloon network may be configured to compute altitudinal adjustments for other balloons and transmit the adjustment commands to those other balloons. 
     As shown, the balloon  300  also includes a cut-down system  308 . The cut-down system  308  may be activated to separate the payload  306  from the rest of balloon  300 . The cut-down system  308  could include at least a connector, such as a balloon cord, connecting the payload  306  to the envelope  302  and a means for severing the connector (e.g., a shearing mechanism or an explosive bolt). In an example embodiment, the balloon cord, which may be nylon, is wrapped with a nichrome wire. A current could be passed through the nichrome wire to heat it and melt the cord, cutting the payload  306  away from the envelope  302 . 
     The cut-down functionality may be utilized anytime the payload needs to be accessed on the ground, such as when it is time to remove balloon  300  from a balloon network, when maintenance is due on systems within payload  306 , and/or when power supply  326  needs to be recharged or replaced. 
     In an alternative arrangement, a balloon may not include a cut-down system. In such an arrangement, the navigation system may be operable to navigate the balloon to a landing location, in the event the balloon needs to be removed from the network and/or accessed on the ground. Further, it is possible that a balloon may be self-sustaining, such that it does not need to be accessed on the ground. In other embodiments, in-flight balloons may be serviced by specific service balloons or another type of aerostat or aircraft. 
     3. Balloon Network with Optical and RF Links Between Balloons 
     In some embodiments, a high-altitude-balloon network may include super-node balloons, which communicate with one another via optical links, as well as sub-node balloons, which communicate with super-node balloons via RF links. Generally, the optical links between super-node balloons may be configured to have more bandwidth than the RF links between super-node and sub-node balloons. As such, the super-node balloons may function as the backbone of the balloon network, while the sub-nodes may provide sub-networks providing access to the balloon network and/or connecting the balloon network to other networks. 
       FIG. 4  is a simplified block diagram illustrating a balloon network that includes super-nodes and sub-nodes, according to an example embodiment. More specifically,  FIG. 4  illustrates a portion of a balloon network  400  that includes super-node balloons  410 A to  410 C (which may also be referred to as “super-nodes”) and sub-node balloons  420  (which may also be referred to as “sub-nodes”). 
     Each super-node balloon  410 A to  410 C may include a free-space optical communication system that is operable for packet-data communication with other super-node balloons. As such, super-nodes may communicate with one another over optical links. For example, in the illustrated embodiment, super-node  410 A and super-node  401 B may communicate with one another over optical link  402 , and super-node  410 A and super-node  401 C may communicate with one another over optical link  404 . 
     Each of the sub-node balloons  420  may include a radio-frequency (RF) communication system that is operable for packet-data communication over one or more RF air interfaces. Accordingly, each super-node balloon  410 A to  410 C may include an RF communication system that is operable to route packet data to one or more nearby sub-node balloons  420 . When a sub-node  420  receives packet data from a super-node  410 , the sub-node  420  may use its RF communication system to route the packet data to a ground-based station  430  via an RF air interface. Additionally or alternatively, the sub-node may use its optical communication system to route the packet data to a ground-based station such as via a free-space optical link or via RF transmission. Notably, the ground-based station  430  may include one or more of the components described above in connection with the payload  306  of the balloon  300 . 
     As noted above, the super-nodes  410 A to  410 C may be configured for both longer-range optical communication with other super-nodes and shorter-range RF communications with nearby sub-nodes  420 . For example, super-nodes  410 A to  410 C may use using high-power or ultra-bright LEDs to transmit optical signals over optical links  402 ,  404 , which may extend for as much as 100 miles, or possibly more. Configured as such, the super-nodes  410 A to  410 C may be capable of optical communications at speeds of 10 to 50 GB/sec or more. 
     A larger number of balloons may be configured as sub-nodes, which may communicate with ground-based Internet nodes at speeds on the order of approximately 10 MB/sec. Configured as such, the sub-nodes  420  may be configured to connect the super-nodes  410  to other networks and/or to client devices. 
     Note that the data speeds and link distances described in the above example and elsewhere herein are provided for illustrative purposes and should not be considered limiting; other data speeds and link distances are possible. 
     In some embodiments, the super-nodes  410 A to  410 C may function as a core network, while the sub-nodes  420  function as one or more access networks to the core network. In such an embodiment, some or all of the sub-nodes  420  may also function as gateways to the balloon network  400 . Additionally or alternatively, some or all of ground-based stations  430  may function as gateways to the balloon network  400 . 
     4. Example Structure of a Balloon-Based Positioning System 
       FIG. 5  is a simplified block diagram illustrating a balloon-based positioning system  500 , according to an example embodiment. System  500  includes control system  502 , ground-based station  504 , a group of balloons  506 A to  506 C (the group is generally designated  506 ), celestial object  508 , and ground-based receiver  510 . 
     Control system  502  may include a processor and data storage, such as memory. And the memory may take the form of or include a non-transitory computer-readable medium having stored thereon, instructions which can be accessed and executed by the processor in order to carry out the functions described herein. Control system  502  may also have a communication system to allow it to communicate with one or more devices such as ground-based station  504 . In some examples, control system  502  may be integrated with or may communicate with one or more other devices such as balloons  506 A to  506 C. 
     Ground-based station  504  may include one or more components from payload  302  of balloon  300  and may provide functionality as described above. Ground-based receiver  510  may also include one or more components from payload  302  of balloon  300  as described above. Ground-based station  510  may take a variety of forms, including for example, a mobile phone, a tablet or laptop computer, or a navigation system. 
     Throughout this disclosure, the term “ground-based” refers to any location on or proximate the earth&#39;s ground or surface. As such, the term is not limited to locations that are literally on the earth&#39;s ground, but may also refer to locations in buildings or even on commercial aircrafts. As shown in  FIG. 5 , in one example ground-based station  504  and ground-based receiver  510  may be located on the surface of earth  512 . 
     Each balloon  506 A to  506 C may include one or more components from balloon  300  as described above. Finally, celestial object  508  may take various forms, including for example a planet, a moon, or a star (e.g., the sun). 
     Notably, system  500  has been provided for illustration purposes only and is not meant to be limiting. Indeed, while not necessary, some embodiments of a balloon-based positioning system may include a large number of balloons, including thousands, tens of thousands, or more, perhaps spanning around the entire earth Likewise, such a system may include a large number of control stations, ground-based stations, celestial objects, and/or ground-based receivers. 
     5. Example Operation of a Balloon-Based Positioning System 
       FIG. 6  is a flow chart illustrating example functions of a method, according to an example embodiment. Generally, at block  602 , the method may involve determining, by a computing device, a first set of spatial relationships relating to a group of at least three balloons deployed in the stratosphere. At block  604 , the method may involve determining, by the computing device, a second set of spatial relationships relating to at least a portion of the group and to a reference point. Further, at block  606 , the method may involve determining, by the computing device, a position of the reference point relative to the earth. Still further, at block  608 , the method may involve using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth. And at block  610 , the method may involve transmitting the determined position of the target balloon relative to the earth. Additional details relating to these functions are provided below. For illustration purposes, the functions are described in connection with system  500 . However, the functions may also be implemented in other systems (e.g., balloon-based positioning systems of a larger scale). 
     5a) Determining a First Set of Spatial Relationships Relating to the Group 
     As noted above, at block  602 , the method may involve determining, by a computing device, a first set of spatial relationships relating to a group of at least three balloons deployed in the stratosphere. This may involve control system  502  determining a first set of spatial relationships relating to group  506 . Generally, this first set of spatial relationships defines the geometry of group  506 . 
     The spatial relationships in the first set may take various forms. For example, the spatial relationships may be distance-based. As such, control system  502  determining the first set of spatial relationships may involve control system  502  determining a distance between a balloon in group  506  and another balloon in group  506 . As shown in  FIG. 5 , this may involve control system  502  determining distance D 1  between balloons  506 A and  506 B, distance D 2  between balloons  506 A and  506 C, and/or distance D 3  between balloons  506 B and  506 C. 
     Control system  502  may determine such distances in a variety of ways. For example, control system  502  may determine distance D 1  based on the “time of flight” of a signal traveling from balloon  506 A to balloon  506 B. This may involve several functions. A first function may involve control system  502  determining a transmission time of a signal sent by balloon  506 A and received by balloon  506 B. In one example, balloon  506 A may encode the transmission time in the signal. Balloon  506 B may then extract the transmission time from the signal and provide it to control system  502 . A second function may involve control system  502  determining a receipt time of the signal by balloon  506 B. In one example, balloon  506 B may record the time at which it receives the signal, and provide it to control system  502 . A third function may involve control system  502  determining a travel speed of the signal (e.g., via a look-up table). And a fourth function may involve control system  502  using the determined transmission time, the determined receipt time, and the determined travel speed as a basis for determining the distance between balloon  506 A and balloon  506 B, such as by solving for distance as a function of time and speed. For example, control system  502  may determine distance D 1  by determining the difference between the determined transmission time and the determined receipt time, and multiplying the determined difference by the determined travel speed of the signal. 
     As another example, control system  502  may determine distance D 1  based on other distances and/or angles as shown in connection with  FIG. 7 . This may involve several functions. A first function may involve control system  506 A determining distance D 4  between balloon  506 A and earth  512  (i.e., the center of earth  512 ). In one example, balloon  506 A may use an altimeter to determine its altitude and provide it to control system  502 . Control system  502  may then determine the distance from the surface of earth  512  (under balloon  506 A) to the center of earth  512  (e.g., via a look-up table) and add that distance to the altitude to determine distance D 4 . A second function may involve control system  502  determining angle A 1  between a first vector and a second vector, where the first vector extends from balloon  506 A towards earth  512 , and where the second vector extends from balloon  506 A towards balloon  506 B. A third function may involve determining angle A 2  between the second vector and a third vector, where the third vector extends from balloon  506 B towards earth  512 . Example ways in which such angles may be determined are described in greater detail below. 
     A fourth function may involve control system  502  using the determined distance D 4 , the determined angle A 1 , and the determined angle A 2  as a basis for determining the distance D 1 , such as by solving a sine function. Additionally or alternatively, control system  502  may determine distance D 5  between balloon  506 B and earth  512 . And control system  502  may use the determined distance D 4 , the determined distance D 5 , the determined angle A 1 , and the determined angle A 2  as a basis for determining distance D 1 , such as by solving a cosine function. 
     As yet another example, control system  502  may determine distance D 1  based on a change of an RF signal&#39;s strength between when it is received by a first antenna and when it is received by a second antenna, where the RF signal is broadcast from balloon  506 A, and where both antennas extend from different portions of balloon  506 B. 
     Additionally or alternatively to determining distance D 1 , control system  502  may determine other distances in similar manners. For example, control system  502  may determine distance D 2  and/or distance D 3 , and therefore the first set of spatial relationships may include distances D 1 , D 2 , and/or D 3 . 
     In some instances, a distance-based spatial relationship may specify a distance range between two objects. For example, if balloon  506 A determines that it is within RF communication range of balloon  506 B, balloon  506 A may determine that distance D 1  is within a distance range having an upper limit equal to the maximum distance that an RF signal may travel. A similar technique may also be used for balloons that communicate using optical signals. Further, balloon  506 A may use the received strength of a signal send from balloon  506 B to further narrow the range of distance D 1 . 
     Additionally or alternatively to determining a range of distance D 1 , control system  502  may determine other distance ranges in similar manners. For example, control system  502  may determine a range of distance D 2  and/or a range of distance D 3 , and therefore the first set of spatial relationships may include ranges of distances D 1 , D 2 , and/or D 3 . 
     The spatial relationships may also be angle-based. In one example, control system  502  determining the first set of spatial relationships may involve control system  502  determining an angle between a first vector and a second vector, where the first vector extends from a first balloon in the group  500  towards a second balloon in the group  500 , and where the second vector extends from the first balloon towards a third balloon in the group  500 . As shown in  FIG. 8 , this may involve control system  502  determining angle A 3  between vectors V 1  and V 2 . 
     Control system  502  determining angle A 3  may involve several functions. A first function may involve control system  502  determining angle A 4  between vector V 1  and a reference vector V 3 , where vector V 3  extends from balloon  506 A. A second function may involve control system  502  determining angle A 5  between vector V 2  and vector V 3 . A third function may involve control system  502  using the determined angle A 4  and the determined angle A 5 , as a basis for determining angle A 3 . For example, where the angles A 4  and A 5  have different signs (relative to the vector V 3 ), control system  502  may determine angle A 3  to be the sum of the magnitude of the angles A 4  and A 5 . Alternatively, where the angles A 4  and A 5  have the same signs (relative to the vector V 3 ), control system  502  may determine angle A 3  to be the difference of the magnitudes of the angles A 4  and A 5 . 
     Control system  502  may determine angles A 4  and A 5  in a variety of ways. In one example, balloon  506 A may determine angle A 4  and provide it to control system  502 . This may involve several functions. A first function may involve balloon  506 A emitting an optical signal via a steerable transmitter in a first position. A second function may involve balloon  506 A detecting a reflection of the emitted optical signal (e.g., using an imaging system). A third function may involve responsive to detecting the reflection of the emitted optical signal, balloon  506 A determining an offset between the first position and a second position of the steerable transmitter, where in the second position, the steerable transmitter is aligned with vector V 3 . And a fourth function may involve balloon  506 A determining angle A 4  using the determined offset (e.g., via a lookup table that maps offsets to angles). 
     Additionally or alternatively, balloon  506 A may determine angle A 4  based on the receipt of a confirmation message from balloon  506 B, and balloon  506 A may then provide angle A 4  to control system  502 . This may involve several functions. A first function may involve balloon  506 A scanning the sky while emitting an optical signal that encodes the current position of the steerable transmitter. As such, balloon  506 A may transmit an optical signal via a steerable optical signal transmitter in a first position, where the optical signal includes the first position, and where the optical signal is directed at balloon  506 B. In response to receiving this signal, balloon  506 B may send to balloon  506 A a message indicating that when the steerable transmitter was in the first position balloon  506 B received the optical signal. A second function may therefore involve balloon  506 A receiving the message from balloon  506 B. A third function may involve responsive to balloon  506 A receiving the message, balloon  506 A determining an offset between the first position and a second position of the steerable transmitter, where in the second position, the steerable transmitter is aligned with the vector V 3 . A fourth function may involve balloon  506 A determining angle A 4  using the determined offset. 
     Additionally or alternatively, balloon  506 A may determine angle A 4  by analyzing an image including balloon  506 B. This may involve several functions. A first function may involve balloon  506 A using an imaging system to take an image of the sky. A second function may involve balloon  506 A determining that balloon  506 B is in the image at a first position. A third function may involve responsive to determining that balloon  506 B is in the image at a first position, balloon  506 A determining an offset between the first position and a second position, where the second position represents a position in the image of reference vector V 3 . A fourth function may involve balloon  506 A determining angle A 4  using the determined offset. 
     Notably, control system  502  may also determine angle A 5  using one or more of the techniques described above in connection with determining angle A 4 . Then, after determining angles A 4  and A 5 , control system  502  may determine angle A 3  as described above. 
     Additionally or alternatively to determining angle A 3 , control system  502  may determine other angles related to the group  506  in similar manners. For example, control system  502  may determine an angle between a first vector extending from balloon  506 B towards balloon  506 A and a second vector extending from balloon  506 B towards balloon  506 C. Likewise, control system  502  may determine an angle between a first vector extending from balloon  506 C towards balloon  506 B and a second vector extending from balloon  506 C towards balloon  506 A. Accordingly, the first set of spatial relationships may include one or more of such angles. 
     5b) Determining a Second Set of Spatial Relationships Relating to at Least a Portion of the Group and to a Reference Point 
     As noted above, at block  604 , the method may involve determining, by the computing device, a second set of spatial relationships relating to at least a portion of the group and to a reference point. This may involve control system  502  determining a second set of spatial relationships relating to at least a portion of the group  506  and to a reference point such as ground-based station  504  or celestial object  508 . Generally, the second set of spatial relationships defines the orientation of the group  506  relative to earth  512 . 
     As with those in the first set, the spatial relationships in the second set may take various forms and may be distance-based. For example, as shown in  FIG. 5 , spatial relationships in the second set may include distance D 6  between balloon  506 A and ground-based station  504 , distance D 7  between balloon  506 B and ground-based station  504 , and/or distance D 8  between balloon  506 C and ground-based station  504 . 
     As noted above, ground-based station  504  may include one or more of the components of payload  300  of balloon  300 . Accordingly, control system  502  may determine such distances using the similar techniques to those described above in connection with the first set of spatial relationships. For example, control system  502  may determine the time of flight of a signal traveling from one of the balloons  506 A to  506 C to ground-based station  504  and visa-versa. Additionally or alternatively, control system  502  may determine such distances based on a change of an RF signal&#39;s strength as described above. Also as with those in the first set, the spatial relationships in the second set may specify a distance range. Also, in some examples, one of balloons  506 A to  502 C or ground-based station  504 , may determine a distance or distance range and provide it to control system  502 . 
     Further as with those in the first set, the spatial relationships in the second set may be angle-based. For example, the second set may include an angle between a first vector and a second vector, where the first vector extends from balloon  506 A towards earth  512 , and where the second vector extends from balloon  506 A towards celestial object  508 . As shown in  FIG. 9 , this may involve control system  502  determining angle A 6  between vectors V 4  and V 5 . In one example, balloon  506 A may determine angle A 6  using techniques similar to those described above in connection with balloon  506 A determining angle A 4 , and provide it to control system  502 . 
     As another example, the second set may include an angle between a first vector and a second vector, where the first vector extends from ground-based station  504  towards earth  512 , and where the second vector extends from ground-based station  504  towards balloon  506 A. As shown in  FIG. 10 , this may involve control system  502  determining angle A 7  between vectors V 6  and V 7 . In one example, ground-based station  504  may determine angle A 7  using techniques similar to those described above in connection with balloon  506 A determining angle A 4 , and provide it to control system  502 . 
     As yet another example, the second set may include an angle between a first vector and a second vector, where the first vector extends from balloon  506 A towards earth  512 , and where the second vector extends from balloon  506 A towards ground-based station  504 . As shown in  FIG. 11 , this may involve control system  502  determining angle A 8  between vectors V 8  and V 9 . In one example, balloon  506 A may determine such an angle using one or more of the techniques described above in connection with balloon  506 A determining angle A 4 , and provide it to control system  502 . 
     5c) Determining a Position of the Reference Point Relative to the Earth 
     As noted above, at block  606 , the method may involve determining, by the computing device, a position of the reference point relative to the earth. This may involve control system  502  determining a position of ground-based station  504 , celestial object  508 , or another object relative to earth  512 . In one example, control system  502  may make this determination by identifying the reference point and retrieving the position of the identified reference point from a lookup table. In one example, balloon  506 A may identify a reference point and provide it to control system  502 . Balloon  506 A may identify a reference point in a variety of ways. For instance, where the reference point is celestial object  508 , balloon  506 A may identify celestial object  508  using an imaging system (e.g., that uses “star tracker” technology). Where the reference point is ground-based station  504 , balloon  506 A may identify the ground-based station  504  using an imaging system and/or based on a reference point identifier broadcast by ground-based station  504 . 
     5d) Determining a Position of a Target Balloon Relative to the Earth 
     As noted above, at block  608 , the method may involve using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth. This may involve control system  502  using the determined first set, the determined second set, and the determined position of ground-based station  504  and/or celestial object  508  as a basis for determining a position of balloon  506 A. 
     Since the determined spatial relationships inherently have at least some degree of measurement uncertainty, in one example control system  502  may use the spatial relationships in the determined first set and the determined second set as constraint-optimization conditions in connection with an optimization function. The optimization function may employ any of a variety of optimization techniques to determine (i.e., optimize) the position of balloon  506 A. Such techniques may include minimum mean square error (MMSE), simultaneous localization and mapping (SLAM) (although without the mapping component), partially-observable Markov design, linear quadratic estimation, dynamic Bayesian network estimation, and/or convex optimization. In some instances, temporal-based optimization functions may also be used (i.e., that take into account a change in spatial relationships over time). 
     By using one or more of these optimization functions, control system  502  may determine the most likely position of balloon  506 A relative to earth  512  in view of the determined first and second sets of spatial relationships. In practice, control system  502  may determine the position of each balloon (or at least multiple balloons) in group  506  relative to earth  512  using a similar process. As such, control system  502  may determine the position of balloons  506 B and  506 C relative to earth  512 . 
     Control system  502  may also use balloon properties, environmental conditions, and/or other data as constraint-optimization conditions in this respect. For instance, in a balloon-based positioning system that extends around the earth, the continuous or “closed-loop” nature of the group of balloons may be used as such a condition. This may provide a benefit that is not available in other environments in which measurement errors may accumulate over long distances. Indeed, in such a closed-loop system, control system  502  may self-correct errors that would otherwise accumulate over such distances. 
     In one example, control system  502  may separately determine the position of each balloon in group  506  relative to each other balloon in group  506 , and the position of group  506  relative to earth  512 . As such, the function at block  608  may involve control system  502  using the determined first set as a basis for determining for each balloon in group  506  a position relative to the remaining balloons in group  506 , and control system  502  using the determined positions relative to the remaining balloons, the determined second set, and the determined position of the reference point relative to earth  512  as a basis for determining the position of the target balloon relative to earth  512 . 
     In some instances, control system  502  may use a first optimization function to determine for each balloon in the group  506  the position relative to the remaining balloons in the group, and a second optimization function to determine the position of the target balloon relative to the earth  512 . 
     5e) Transmitting the Determined Position of the Target Balloon Relative to the Earth 
     As noted above, at block  610 , the method may involve transmitting the determined position of the target balloon relative to the earth. This may involve control system  502  transmitting the determined position of balloon  506 A relative to earth  512  to balloon  506 A. In another example, control system  502  may provide the determined position to ground-based station  504 , and ground-based station  504  may transmit the determined position to balloon  506 A. Balloon  506 A may then broadcast or otherwise transmit the determined position and other relevant data for use by ground-based receiver  510 . These functions may also be performed with respect to other balloons in the group, including for example, balloons  506 B and  506 C. 
     As shown in  FIG. 12 , each balloon  506 A to  506 C may include a respective PBM  514 A to  514 C configured for broadcasting (e.g., via an antenna) a respective balloon signal  516 A to  516 C containing balloon-positioning data. The balloon-positioning data includes the determined position of the respective balloon and a corresponding time of broadcast (i.e., indicating when the balloon signal was broadcast). Ground-based receiver  510  may be configured to receive one or more of balloon signals  516 A to  516 C and determine its position relative to earth  512  based on the collective balloon-positioning data contained therein. 
     As used in this disclosure, a PBM is a functional module that refers to one or a group of components contained in the respective balloon, such as those described in connection with  FIG. 3 , that may carry out the described functions. For example, the PBM may include a particular set of instructions stored in the memory  314  that relate to the function of broadcasting a position of the respective balloon relative to the earth, together with the processor  312  for executing those instructions, and any communication systems or other associated components. However, a PBM is not limited to any particular set of components. 
     Notably, in some embodiments, each PBM may broadcast the respective balloon signal on a single channel frequency. This provides a particular advantage over traditional positioning systems, such as the GPS, where satellite signals are typically broadcast simultaneously on two different channel frequencies (typically L1 at 1575.42 Mhz and L2 at 1227.6 Mhz) for the purpose of attempting to detect and remove delay caused by refraction-based interference. Due to the altitude of GPS satellites, satellite signals sent directly to ground-based receivers traverse the ionosphere, and therefore are subject to this type of interference. 
     Since GPS satellites broadcast signals on two channel frequencies, traditional GPS receivers must be configured to receive both channel frequencies. On the other hand, in embodiments of the balloon-based positioning system where balloon signals are transmitted on a single channel frequency, the corresponding ground-based receiver need only be configured to receive a single channel frequency. Among other things, this allows ground-based receivers to be less complex, and therefore, typically less expensive to produce. Notably, the single channel frequency that is used may be any particular frequency, although in select embodiments, it may differ from the frequencies of the L1 and L2 or other commonly used frequencies to reduce or avoid potential interference. 
     Further, due to the relatively slow speed at which the balloons are likely to travel (i.e., as compared to GPS satellites), ground-based receivers do not need to compensate for Doppler shifts as is the case with GPS receivers. Again, this reduces the complexity and the production cost of ground-based receivers. 
     5f) Variations 
     While one or more functions of the disclosed methods have been described as being performed by the certain entities (e.g., control system  502 ), the functions may be performed by any entity or combination of entities, such as those included in system  500  described above. 
     Also, as noted above, the disclosed system need not be limited to the configuration of system  500 . Indeed, in practice the disclosed system may include thousands, tens of thousands, or even more balloons, control systems, ground-based stations, celestial objects, ground-based receivers, and/or other entities. Likewise, the method may involve determining thousands, tens of thousands, or even more spatial relationships such as in the example manners described above. Notably, as more spatial relationships are determined, the control system may be able to determine the position of a target balloon with greater accuracy and with less calculation time. As such, in some embodiments, a large-scale balloon-based positioning system may be desired. 
     Further, the described steps throughout this application need not be performed in the disclosed order, although in some examples, an order may be preferred. Also, not all steps need to be performed to achieve the desired advantages of the disclosed systems and methods, and therefore not all steps are required. Further, the variations described throughout this disclose may be applied to any of the disclosed examples and perhaps in other environments. 
     Still further, the various techniques described throughout this application may be utilized in environments other than a balloon-based positioning system. For example, the described techniques for determining a distance between two balloons may be used to determine the distance between two other objects. Likewise, the described techniques for determining an angle between two vectors need not be utilized in the context of a balloon-based positioning system. Indeed, the first vector may extend from a first object to a second object and the second vector may extend from the first object to a reference point (e.g., a third object). As such, it is contemplated that a control system (or other device) may determine spatial relationships between other (non-balloon) objects. Notably, these objects may include one or more of the balloon components described above, and such components may be used, at least in part, in determining such spatial relationships. Then, based on these spatial relationships, a control system (or other device) may determine the position of each object relative to one or more other objects and/or relative to a reference point such as the earth in a manner similar to that described above in connection with the example balloon-based positioning systems. 
     6. Additional Example Advantages 
     In the context of the GPS, a receiver is often unable to determine its position because it cannot receive the signals being broadcast by one or more of the GPS satellites. These signals may have difficulty reaching GPS receivers for a number of reasons, such as due to weak signal strength and signal interference due to reflection, refraction, and/or multipath propagation. In an attempt to minimize issues concerning weak signal strength, the GPS employs a digital-sequence spread spectrum (DSSS) encoding technique that improves signal strength by utilizing an increased amount of bandwidth. However, this technique only marginally improves signal strength. 
     As noted, GPS satellites typically orbit the earth at an altitude of approximately 20,000 km. As a result of the satellite signals traveling such a long distance, signal attenuation is often substantial, even with DSSS encoding. On the other hand, in the balloon-based positioning system, balloon signals sent from a balloon to a ground-based receiver travel a substantially shorter distance. In one embodiment, balloon signals travel a distance in the range of approximately 17 km to 25 km. Further, balloon signals destined for a receiver originate beneath the ionosphere, and therefore are not subject to refraction-based interference as discussed above. For these reasons, balloon signals are likely to be stronger, and are more likely to reach receivers, as compared to in a parallel GPS scenario. 
     Finally, when a given GPS receiver is in certain environments such as cities, tall buildings or other objects may block or interfere with the signals. As discussed, some embodiments of the balloon-based positioning system may include a large number of balloons deployed across the stratosphere. Some embodiments may include thousands, tens of thousands, or even more balloons. As a result, any given ground-based receiver is likely to have a line-of-sight to many balloons, in some embodiments, as many as 50-100 at a time. As a result, a receiver has a much greater likelihood of being able to receive balloon signals, as compared to for example, a GPS receiver that may have lines-of-sight with a maximum of approximately eleven or twelve GPS satellites. 
     While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.