Coarse geolocation of remote terminals

Abstract

To provide a method for coarsely estimating (with an accuracy of approximately 100 km) the position of a terminal in a satellite communication system. The terminal uses multiple transmissions from one or more LEO satellites and estimates the footprint of each transmission using the time of transmission and satellite ephemeris. A coarse location is then determined by estimating the intersection area of ​​each estimated footprint. This location may be determined in various manners, such as using optimization methods using centroids, midpoints, and error functions. The intersection area may be approximated as a polygon and may be implemented using a circular buffer to maintain the most recent estimate. Additionally, the method may be performed remotely by a satellite or core network to estimate the location of transmitters, including non-system transmitters, and may be used as an initial input for computationally more complex signal-based location estimation.

Description

[Technical field]

[0001] Priority document This application claims priority to Australian Provisional Patent Application No. 2022900611, entitled "COARSE GEOLOCATION OF REMOTE TERMINALS", filed on March 14, 2022, the contents of which are incorporated herein by reference in their entirety.

[0002] FIELD OF THE DISCLOSURE The present disclosure relates to estimating the position of a terrestrial terminal in a satellite communication system. In a particular aspect, the disclosure relates to a system in which the estimation is performed either at the terminal or remotely from the terminal.

[0003] Incorporation by Reference The following patent applications are referenced in this application: PCT / AU2013 / 000895 entitled “CHANNEL ALLOCATION IN A COMMUNICATION SYSTEM”, filed on 14 August 2013, claiming priority to Australian Provisional Patent Application No. 2012903489, filed on 14 August 2012; PCT / AU2013 / 001078 entitled “COMMUNICATION SYSTEM AND METHOD”, filed on 20 September 2013, claiming priority to Australian Provisional Patent Application No. 2012904130, filed on 21 September 2012; PCT / AU2013 / 001079 entitled “MULTI-ACCESS COMMUNICATION SYSTEM”, filed on 20 September 2013, claiming priority to Australian Provisional Patent Application No. 2012904145, filed on 21 September 2012; PCT / AU2014 / 000826 entitled “A MULTIUSER COMMUNICATIONS SYSTEM”, filed on 21 August 2014, claiming priority to Australian Provisional Patent Application No. 2013903163, filed on 21 August 2013; PCT / AU2015 / 000743 entitled “MULTICARRIER COMMUNICATIONS SYSTEM”, filed on December 9, 2015, claiming priority to Australian Provisional Patent Application No. 2014904976, filed on December 9, 2014; PCT / AU2017 / 000058, entitled “TERMINAL SCHEDULING METHOD IN SATELLITE COMMUNICATION SYSTEM”, filed on 24 February 2017, claiming priority to Australian Provisional Patent Application No. 2016900685, filed on 25 February 2016; PCT / AU2017 / 000108, entitled “POSITION ESTIMATION IN A LOW EARTH ORBIT SATELLITE COMMUNICATIONS SYSTEM”, filed on May 16, 2017, claiming priority to Australian Provisional Patent Application No. 2016901913, filed on May 20, 2016; PCT / AU2017 / 000286, entitled “SYSTEM AND METHOD FOR GENERATING EXTENDED SATELLITE EPHEMERIS DATA”, filed on December 21, 2017, claiming priority to Australian Provisional Patent Application No. 2016905314, filed on December 22, 2016; and PCT / AU2018 / 000151, entitled “SYSTEM AND METHOD FOR PREDICTION OF COMMUNICATIONS LINK QUALITY”, filed on 28 August 2018, which claims priority to Australian Provisional Patent Application No. 2017903470, filed on 28 August 2017.

[0004] The contents of each of these applications are incorporated herein by reference in their entirety. [Background technology]

[0005] This application is directed to a satellite communication system 1 consisting of a terrestrial transceiver, referred to as a terminal 10, that transmits data 12 using radio signals to one or more low-earth-orbiting (LEO) satellites 20. Those satellites transmit signals 22 to relay the terminal's radio signals to a gateway, such as a ground station 30, where the received signals 22 are delivered to a core network and end users (e.g., those monitoring their own remote assets). Those LEO satellites also transmit data using radio signals to the terrestrial transceivers. The data transmitted from the satellites to the terminals may be data relayed from the core network and end users, or it may be network information transmitted for purposes of network control, configuration, and optimization. The terminals may be associated with remote assets or sensors to which they are attached or have a local connection to provide remote Internet of Things (IoT) connectivity, such as for monitoring or control of the remote assets and sensors. These remote assets may be stationary or may move (typically at much slower speeds than satellites), such as livestock, personnel, vehicles, industrial machinery, shipping containers, and environmental sensors. Such systems may be used to monitor a large number of remotely located assets and sensors operated by a large number of users (through associated terminals).

[0006] There are several cases in which it is useful for a terminal to know its location (e.g., latitude, longitude) or location. For example, a terminal may want to determine its own location in order to optimize the timing of transmissions to reduce energy usage or improve performance. For example, a terminal may want to schedule wake-up times to transmit to orbiting LEO satellites based on their ephemeris and knowledge of its own location. Because a typical satellite footprint (the area of ​​the Earth that can be seen by a satellite) is several thousand kilometers in size, even a very rough estimate with an accuracy on the order of 100 km may be useful. A coarse estimate may also serve usefully as an initial estimate for more refined location estimation methods.

[0007] In other cases, it is not the terminal or transmitter that needs to know its own location, but rather the end user or core network that is interested in knowing the location of a remote terminal or transmitter (or a sensor or asset associated with a remote terminal). This is the case in many IoT tracking applications, or in the case of third-party or interfering transmitters (i.e., not part of the IoT communication system).

[0008] In such systems, it is often desirable to keep the cost, complexity, and power requirements of the terminal as low as possible to enable widespread and long-term use (e.g., potentially tens of months to years). The terminal 10 can be equipped with a Global Navigation Satellite System (GNSS) receiver, such as a GPS receiver, that can be used to transmit the terminal's position (via LEO satellites 20) to a ground station 30, but the addition of a GNSS / GPS receiver module increases both cost and power requirements. The GNSS module requires significant computational resources to estimate the position, and in addition the GNSS module needs to have up-to-date satellite ephemeris data for the GNSS satellites. This typically requires the GNSS module to wake up periodically to obtain an updated almanac every few hours. For example, GPS ephemeris is updated every four hours, and in cold start mode it takes the GPS receiver 12 minutes to download the full almanac, placing a significant strain on the power requirements of the terminal. Measurements of a remote IoT device equipped with a GNSS module in a typical use case show that GNSS operations represent almost 50% of the energy usage. This can have a significant impact on the battery life (and therefore operational life) of the remote device, which may be left idle for months or years.

[0009] The assisted GPS system can be used to reduce the computational or power load on the terminal by transmitting new almanac information to the terminal and / or by allowing the terminal to sample the GPS signal and transmit the samples to a more powerful processing device. However, this requires that the terminal be able to establish a communication link with sufficient capacity to transmit the samples over a communication channel between the terminal and the more powerful processing device. In applications using the remote terminal 10 for IoT applications such as those described above, this requirement can add significant cost and power requirements to the terminal 10. Summary of the Invention [Problem to be solved by the invention]

[0010] There is therefore a need to provide a system and method for estimating the position of a remote ground terminal or other transmitter in a satellite communication system that avoids the need for a GNSS module in the terminal, or at least provides a useful alternative to existing systems and methods. [Means for solving the problem]

[0011] According to a first aspect, there is provided a method for estimating a position of a terminal in a satellite communication system comprising a plurality of LEO satellites and a plurality of terminals, the method comprising: receiving a plurality of transmissions from each of one or more LEO satellites; obtaining an estimate of current time and ephemeris for each of one or more LEO satellites; estimating at least one footprint for each of a plurality of LEO satellites from the plurality of transmissions; and determining a location of the terminal by estimating an intersection area of ​​each of the estimated footprints.

[0012] In one form, the method further includes estimating a position within the intersection region.

[0013] In one form, estimating the location includes estimating a centroid location of the intersection region or a geometric midpoint of the intersection region.

[0014] In one form, the footprint of the LEO satellite is estimated as a convex region. In a further form, the convex region may be obtained by estimating a set of points on a reference surface that have a direct line of sight to the LEO satellite above a predetermined threshold elevation angle.

[0015] In one form, determining a location of the terminal by estimating an intersection area of ​​each estimated footprint includes: defining an error function that is a measure of the error between an estimate of the location obtained from the estimated footprint and an estimate of the true location; optimizing the error function using an optimization method to obtain an optimized estimate of the true position of the terminal.

[0016] In one form, the intersection region is approximated as a polygon.

[0017] In one form, determining the location includes determining a centroid of the polygon.

[0018] In one form, the method further includes storing the vertices of the polygon and updating estimates of the vertices of the polygon with each new received transmission from one of the one or more LEO satellites.

[0019] In one form, the method further includes, updating the polygon estimate includes receiving a new transmission from one of the one or more LEO satellites, estimating a footprint of the new transmission, calculating intersections of the new footprint with each line segment defining the polygon, and discarding any vertices in the expanded set that lie outside the new footprint.

[0020] In one form, the method further includes storing a circular buffer of n footprints of the n previously received transmissions and updating the polygon estimate with each new transmission from one of the one or more LEO satellites using the footprints stored in the circular buffer.

[0021] In one form, the method further includes obtaining at least an estimate of a Doppler frequency for each received transmission, and refining an estimate of the terminal's position using a non-linear optimization algorithm configured to use the terminal's position obtained by the method of any one of claims 1 to 10 as an initial position, and to refine the position by minimizing an error function that is based on at least the estimated Doppler frequency. In a further form, the non-linear optimization algorithm is further configured to use a cost function that is based on the error function at each position obtained using at least the estimated Doppler frequency.

[0022] According to a second aspect, there is provided a method for estimating a position of a transmitter in a satellite communications system comprising a plurality of LEO satellites, the method comprising: receiving, by one or more LEO satellites, a plurality of transmissions from a transmitter; obtaining an estimate of a time of transmission of each transmission and an ephemeris for each of a plurality of LEO satellites at that time of transmission; estimating at least one footprint for each of a plurality of LEO satellites from the plurality of transmissions; determining a location of the transmitter at a location remote from the transmitter by estimating an intersection area of ​​each of the estimated footprints.

[0023] In one form, the method further includes estimating a position within the intersection region.

[0024] In one form, estimating the location includes estimating a centroid location of the intersection region or a geometric midpoint of the intersection region.

[0025] In one form, the footprint of the LEO satellite is estimated as a convex region. In a further form, the convex region may be obtained by estimating a set of points on a reference surface that have a direct line of sight to the LEO satellite above a predetermined threshold elevation angle.

[0026] In one form, determining a location of the transmitter by estimating an intersection area of ​​each estimated footprint, comprising: defining an error function that is a measure of the error between an estimate of the location obtained from the estimated footprint and an estimate of the true location; optimizing the error function using an optimization method to obtain an optimized estimate of the true position of the transmitter.

[0027] In one form, the intersection region is approximated as a polygon.

[0028] In one form, determining the location includes determining a centroid of the polygon.

[0029] In one form, the method further includes storing the vertices of the polygon and updating estimates of the vertices of the polygon with each new received transmission from one of the one or more LEO satellites.

[0030] In one form, the method further includes, updating the polygon estimate includes receiving a new transmission from one of the one or more LEO satellites, estimating a footprint of the new transmission, calculating intersections of the new footprint with each line segment defining the polygon, and discarding any vertices in the expanded set that lie outside the new footprint.

[0031] In one form, the method further includes storing a circular buffer of n footprints of the n previously received transmissions and updating the polygon estimate with each new transmission from one of the one or more LEO satellites using the footprints stored in the circular buffer.

[0032] In one form, the method further includes identifying the transmitter by determining one or more signal characteristics of the received transmission and determining whether the signal characteristics match signal characteristics of a previously received transmission from the transmitter, and if there is a match, updating an estimate of the location of the transmitter using the received transmission.

[0033] In one aspect, the transmitter is a terminal and the method further includes obtaining an estimate of at least a Doppler frequency for each received transmission and refining an estimate of a position of the terminal using a nonlinear optimization algorithm configured to use a position of the terminal obtained by the method of the first aspect (if provided to a satellite or core network) or the second aspect as an initial position and to refine the position by minimizing an error function based on at least the estimated Doppler frequency. In a further aspect, the nonlinear optimization algorithm is further configured to use a cost function based on the error function at each position obtained using at least the estimated Doppler frequency.

[0034] According to a third aspect, there is provided a terminal for use in a satellite communications system comprising a plurality of LEO satellites, the method comprising: a receiver for receiving one or more transmissions from one or more of the plurality of LEO satellites; At least one processor and at least one memory, the memory configured to store ephemeris data for a plurality of LEO satellites and instructions for configuring the at least one processor to perform the method of the first aspect.

[0035] According to a fourth aspect, there is provided a computing device in a LEO satellite or a network entity of a satellite communications system comprising a plurality of LEO satellites and a plurality of terminals, the computing device comprising: The system comprises at least one processor and at least one memory, the at least one memory configured to store ephemeris data for a plurality of LEO satellites and to store instructions for performing the method of the second aspect.

[0036] According to a fifth aspect, there is provided a computer readable medium comprising instructions for configuring one or more processors to perform the method of either the first or second aspects.

[0037] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. [Brief description of the drawings]

[0038] [Figure 1A] 1 is a schematic diagram of a low earth orbit satellite communications system, according to one embodiment;

[0039] [Figure 1B] 1 is a schematic diagram illustrating overlapping low earth orbit satellite footprints according to one embodiment;

[0040] [Figure 1C] FIG. 2 is a schematic diagram of a terminal device according to one embodiment.

[0041] [Figure 2A] 1 is a flowchart of a method for estimating a terminal's position in a satellite communications system comprising multiple LEO satellites and multiple terminals, according to one embodiment.

[0042] [Figure 2B] 1 is a flowchart of a method for estimating a transmitter position in a satellite communications system comprising multiple LEO satellites, according to one embodiment.

[0043] [Figure 3A] 1 is a schematic diagram illustrating overlapping low earth orbit satellite footprints according to one embodiment;

[0044] [Figure 3B] 1 is a plot of distance error as a function of number of observations for a first simulation, according to one embodiment.

[0045] [Figure 3C] 11 is a plot of distance error as a function of number of observations for a second simulation, according to one embodiment.

[0046] [Figure 4A] A plot of the measured footprint centers of multiple transmissions received by a terminal over a 10 day test period, along with the true (known) terminal location and estimated average location, and associated polygon intersection areas, in accordance with one embodiment.

[0047] [Figure 4B] 1 is a histogram plot showing the estimation error of the location of the mean (horizontal line) and the location of the median (vertical line) for a test including 540 sets of measurements in which the terminal location was known, according to one embodiment.

[0048] [Figure 4C] 1 is a plot of measured Doppler frequency of packets received from a terminal at a satellite over a 10 day test period, according to one embodiment.

[0049] [Figure 4D] FIG. 13 is a diagram of a heat map cost function for use in a signal-based optimization algorithm, according to one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0050] In the following description, like reference characters refer to like or corresponding parts throughout the drawings.

[0051] Referring now to FIG. 1, a schematic diagram of a low earth orbit (LEO) satellite communication system 1 according to one embodiment is shown. The system 1 may be used to provide Internet of Things (IoT) connectivity to remotely located sensors and assets 12 for multiple users 42. The satellite communication system 1 is comprised of multiple terminals 10, multiple low earth orbit (LEO) satellites 20 that serve as access nodes for the terminals in the system, and multiple geographically distributed gateways 30, such as ground stations, that communicate with a core network infrastructure 40. The terminals 10, which may be ground transceivers, communicate with the LEO satellites 20 using radio frequency signals and are connected to, attached to, or in communication with the sensors or assets 12. Similarly, the LEO satellites 20 communicate with the multiple geographically distributed gateways 30 using radio frequency signals. The core network infrastructure 40 may include a cloud based server that manages the system, may decode and process received signals, and provides application interfaces to forward data from the terminals to multiple users 42 or provide interfaces allowing users to access data provided by the terminals 10. Multiple users may be supported, each user communicating with a different terminal 10. The satellite communication system may be an embodiment of the satellite communication system described in PCT / AU2013 / 000895, filed August 14, 2013, and entitled "CHANNEL ALLOCATION IN A COMMUNICATION SYSTEM," the contents of which are incorporated herein by reference.The satellites, terminals, and operation of the communications system may also be described in PCT / AU2013 / 001079, filed September 20, 2013, and entitled "MULTI-ACCESS COMMUNICATION SYSTEM," PCT / AU2014 / 000826, filed August 21, 2014, and entitled "A MULTIUSER COMMUNICATIONS SYSTEM," and / or PCT / AU2015 / 000743, filed December 9, 2015, and entitled "MULTICARRIER COMMUNICATIONS SYSTEM," the contents of each of which are incorporated herein by reference.

[0052] FIG. 1A shows a first LEO satellite 20a traveling along an orbital path 22a and transmitting a signal 23a that is received by the terminal 10, and a second LEO satellite 20b traveling along an orbital path 22b and transmitting a signal 23b that is received by the terminal 10. The terminal may also transmit signals to the LEO satellites 20a, 20b, such as data collected from sensors, for use by the user 42. Also shown is a terrestrial transmitter 50, which is not part of the communication system, transmitting signals 51a, 51b, which are received by the LEO satellites 20a, 20b and act as interfering signals. The first and second LEO satellites 20a, 20b communicate with the gateway 30 via signals 24a, 24b. Depending on the location, the terminal 10 may also communicate directly with the gateway node 30 and may receive broadcast signals from the gateway node 30.

[0053] 1C is a schematic diagram of a terminal 10 according to one embodiment. The terminal comprises a communications module 110 having an RF front end with one or more antennas 112 and associated hardware for preparing data for transmission, including encoding and modulation, and transmitting data to the satellite 20 over a radio frequency uplink, and receiving and decoding data from the satellite 20 (or other transmission source) over a downlink. The satellite 20 comprises a communications module with an RF front end with one or more antennas for communicating with terminals and earth stations, transmitter and receiver modules, each of which may comprise encoding / decoding and modulation / demodulation components, and a processor and associated memory for storing data (e.g., ephemeris, configuration and performance data) and for controlling satellite operation and signal transmission / reception, including signal decoding, generating acknowledgements, performing system optimization and other support operations. In some embodiments, satellite 20 operates in a bent pipe mode or a digital sampling with store-and-forward mode, performing minimal or no signal processing of received transmissions and redirecting received transmissions or packets to gateways and core network infrastructure for further processing, including remote decoding by a cloud-based processor.

[0054] The terminal also includes a processor module 120 and a memory 130. The memory includes software instructions or modules that cause the processor to perform the methods described herein. The memory may also be used to store satellite ephemeris, satellite footprints, measured and estimated signal parameters, and any data, parameters, or indicators used to generate or update such estimates. The memory may include one or more databases, circular buffers, or other storage structures. The memory may also be used to store modules for other functions. Other components, such as a power supply, a clock, a sensor platform, etc., may also be included in the terminal. Upon startup, the terminal may determine a system time or obtain a system time by listening to one or more satellites. The terminal may also listen for ephemeris data or updates broadcast by system satellites or read ephemeris data from a storage device into the memory. For example, the ephemeris may be an extended ephemeris stored in memory and may be obtained using the method described in PCT / AU2017 / 000286, entitled "SYSTEM AND METHOD FOR GENERATING EXTENDED SATELLITE EPHEMERIS DATA," filed on December 21, 2017, the contents of which are incorporated herein by reference.

[0055] During use, data may be exchanged with other local devices 12 via the local communication module 140, for example through a short-range wireless connection using a protocol based on Bluetooth or Wi-Fi, or through a wired interface such as a USB interface or direct connection. In addition, the terminal equipment may receive timing information via the communication module 110, or the terminal equipment may include a stable built-in clock that is periodically synchronized with UTC, for example during service or maintenance.

[0056] The core network infrastructure is in communication with the gateway node 30 and may include an authentication broker, a scheduler, and an app gateway. The broker may exchange data with user applications through the app gateway and may exchange control information directly with user applications. The components of the core network infrastructure may be distributed and communicate through communication links. Some components may be cloud-based. The terminal or satellite may provide information to the core network to perform location estimates of terminals or non-system transmitters 50 (e.g., interference sources) and provide feedback information to the terminals.

[0057] In one embodiment, system 1 uses a publisher / subscriber model and includes the following system entities: Terminal 10: A communication module within the terminal provides core network connectivity to the access nodes. The terminal 10 may have both devices 102 and sensors 104 attached to it, which may be physically attached or embedded or operatively connected to the terminal through a local wired or local wireless link. Device 12: These entities receive the data to which they subscribe via an authentication broker. Sensors 12: These entities publish data without other network nodes being aware of it. Sensors may be capable of receiving ephemeral control data, publishing ACK messages, etc. Access Node 20: A number of access nodes provide wireless communication with a number of terminals. Most access nodes are satellite access nodes, but the system may also include terrestrial base stations. The satellite access nodes provide access to the core network 40. Access Gateways 30: These act as gateways between the access nodes and the authentication brokers. The gateways may be combined with the access nodes 20 (e.g., on-board a satellite). Authentication Broker: A broker between publishers and subscribers that authenticates that received messages come from registered devices. App Gateway: A data gateway between user applications and the broker that implements multiple interfaces, which may be cloud-based interfaces, including a Message Queuing Telemetry Transport (MQTT) interface that routes to customer-controlled or customer-accessible endpoints. User Applications: These communicate with an App Gateway, e.g. a cloud-based App Gateway, through wired and wireless links.

[0058] There are several cases where a terminal may be interested in estimating its coarse position (on-board geolocation). For example, if the terminal knows its own position and the ephemeris of orbiting LEO satellites, the terminal may optimize the timing of transmissions to reduce energy usage or improve performance. Even very coarse estimates on the order of 100 km or better may be useful in early stages of operation to serve as initial estimates for more refined position estimation methods. For example, optimization-based signal-based estimation techniques such as those described in PCT application PCT / AU2017 / 000108 (WO2017197433), entitled “POSITION ESTIMATION IN A LOW EARTH ORBIT SATELLITE COMMUNICATIONS SYSTEM,” filed May 16, 2017, the contents of which are incorporated herein by reference.

[0059] An embodiment of a method for estimating a position of a terminal 10 in a satellite communication system 1 will now be described. The position may also be referred to as a geographic location or a location. A flowchart of the method 100 is further shown in FIG. 2A. In general terms, the method includes receiving a plurality of transmissions from each of one or more LEO satellites 110. The terminal then obtains 120 an estimate of the current time and an ephemeris of each of the one or more LEO satellites. The terminal estimates 130 at least one footprint on each of the plurality of LEO satellites from the plurality of transmissions, and then determines the terminal's position, i.e., geolocation, by estimating 140 an intersection area of ​​each estimated footprint. In this embodiment, the position is a coarse position defined by the intersection area. In a further embodiment, the position may be a position within the intersection area as described below.

[0060] This is further illustrated in Figures 1A and 1B. Figure 1A shows a first LEO satellite 20a traveling along an orbital path 22a and transmitting a signal 23a that is received by the terminal 10. A second LEO satellite 20b travels along an orbital path 22b and also transmits a signal 23b that is received by the terminal 10. That is, the terminal is receiving several transmissions from one or more LEO satellites. The terminal has a clock (or oscillator) so that it can determine the time of receipt of each received transmission 23a, 23b. Furthermore, the terminal can identify transmissions from the same satellite, for example, by decoding a unique satellite identifier included in each transmission by one satellite, or by otherwise determining a transmission characteristic or parameter that uniquely identifies transmissions from the same satellite, for example, upon decoding or other signal analysis of the transmission.

[0061] In one embodiment, the satellites periodically broadcast beacon signals including their satellite identifiers as they move along their orbital paths. They may be broadcast every second, or at the beginning of a frame of fixed duration, or at some other fixed time interval determined by the system 1. Using the satellite identifier, the terminal can look up (in memory or on-board database) the stored ephemeris of the satellite that sent the received transmission. It is noted that the terminal may receive multiple transmissions from the same satellite, each at different times, or the terminal may receive multiple transmissions from multiple satellites over some time. The terminal may listen continuously for a fixed time (e.g., 10 seconds), or may listen periodically, for example, for 1 second every 60 seconds over 10 minutes (e.g., 10 observations), or for 1 second every 5 minutes over 12 or 24 hours. The length of time to listen for a transmission may be on the order of milliseconds to a few seconds. Spacing out observations (e.g., every 5, 10, 15, or 60 minutes) also increases the chances of capturing different satellites on different orbital paths. Determination of the duration and frequency of listens may be based on parameters of the satellite communication system, such as the typical path length (the time a satellite is overhead for a given point on the Earth's surface) and the frequency of the beacon signal. In one embodiment, LEO satellites have a path length of approximately 5 minutes.

[0062] From the received transmissions, the terminal can estimate the satellite footprint for each transmission using the time of transmission and the ephemeris of each satellite. The satellite footprint is defined as the set of possible locations to which transmission from that satellite is possible. This is the area where the satellite can be "seen" at the time of transmission. In one embodiment, the locations are locations on the surface of the Earth, and may be locations on a reference surface such as a geodetic system, including global systems such as WGS84 or the International Terrestrial Coordinate System (e.g., ITRF2014, ITRF2020, etc.), or regional systems such as NAD83, OSGB36, ETRS89, GDA94, etc.

[0063] For a terminal to receive a transmission, it must, by definition, be within the intersection of their footprints, so an initial rough estimate of the location may be the entire intersection area of ​​the footprints.

[0064] More preferably, the coarse estimate is a point or location within the intersection region. In the absence of any other information, each point within the intersection is equally likely to be the location of the terminal. Thus, in one embodiment, the coarse estimate of the terminal's location is the geometric midpoint of this intersection region. This point has the property (by definition) of minimizing the average position error (averaged over all equally likely points within the region). Similarly, the coarse estimate of location can be the centroid location of the intersection region, or another center estimator, such as an average or weighted average. In one embodiment, the center of each footprint can be estimated and used to define the intersection region, such as a polygon that encompasses all centers (i.e., with the farthest center forming a vertex). In one embodiment, the coarse estimate is calculated as the average of all centers. In one embodiment, the footprint centers are estimated by first converting the satellite positions (obtained from ephemeris data) to Earth-centred, Earth fixed (ECEF) coordinates for each transmission, and then calculating the average of those points (centers) to obtain an estimate of the center of the intersection region. Another central estimator may be used, such as the median or weighted average. The weighting may be determined using a metric obtained when decoding the transmission, such as the SNR or SINR or Doppler.

[0065] In practice, the footprint may have an irregular shape due to terrain and other radio propagation characteristics, but as a simplifying assumption, the footprint may be defined here as a set of points that have a direct line of sight to the satellite above some threshold elevation angle (e.g., 5°, 10°, 15°, or 20°). These points may be estimated using (or on) a reference surface such as a geodetic system (e.g., WGS84) and may be estimated using geometric methods (e.g., cone intersection with the surface) and / or coordinate transformations. In another example, an ellipse, for example in ECEF, may be selected with the property that each point has a direct line of sight to the satellite at least above the threshold elevation angle. These regions have the important property that they are convex. Furthermore, the intersection set maintains convexity, and thus the intersection of the convex footprints defines a convex intersection region. Other numerical, mathematical, or geometric methods may be used to define a convex region to each satellite. For example, the footprint may be estimated on a reference surface and a convex shape is fitted within the boundary. Similar to the elevation threshold approach, a buffer zone can be defined (e.g., 10 km, 20 km, 50 km, etc.) and a convex shape is fitted to the inner boundary of the buffer zone.

[0066] Suppose there are n received transmissions. F i Let x, i=1, 2, ..., n be the footprints corresponding to transmission i. To estimate the location, an optimization method can be used whose objective function is an error function d(y), which is a measure of the error between the location estimate (x) obtained from the footprint estimation and the true location estimate (y). In one embodiment, the error function can be defined as

number

number

[0067] Since we are optimizing a convex function over a convex set, standard gradient-based optimization methods such as Newton's method will converge. The optimum point is, by definition, ∩F i That is, solving the optimization problem defined in Equation 1 returns an estimate of the location that is the geometric midpoint of the intersection region.

[0068] In another embodiment, the error function is chosen as the squared distance:

number

number

[0069] The performance of such an estimator is ultimately determined by ∩F iis governed by the magnitude of n. Thus, the estimate is made using multiple transmissions, and the accuracy improves as more transmissions are received. Typically, the accuracy improves rapidly with the first few transmissions (n<10) and then stabilizes. The rate at which the accuracy improves depends on the number of different satellites observed and the time interval over which the transmissions are obtained. For example, in some embodiments, a single satellite may be seen for the duration of one pass (e.g., 5 minutes). In this case, the intersection region becomes lens-shaped, and the estimates at the beginning and end of the pass act to constrain the intersection region to the direction of the satellite's motion (or pass). Each additional satellite that is observed acts to significantly constrain the size of the intersection region, since each satellite typically has a different (and misaligned) orbital path. Having two satellites with orthogonal orbital paths acts to tightly constrain the orbital path. Listening to the same satellite over multiple satellite passes can also help to more tightly constrain the intersection region. Various error functions may be defined, for example weighted error functions based on signal strength, number of transmissions, or geometry may be used. For example, it may be beneficial to weight observations from more distant or newly detected satellites for which only a few transmissions have been received so far.

[0070] As mentioned above, in many embodiments the terminals are remote terminals located outside the coverage of terrestrial communication systems and are required to provide low bandwidth connectivity to remote assets over periods of months to years (e.g., for basic monitoring). To enable more widespread use, the terminals are often low-cost devices with limited processing power, storage, and battery life, and it is of interest to formulate easily computable estimates to minimize power consumption to maximize battery life.

[0071] Feasible region ∩F iA simplification can be obtained for any of the above estimators by approximating by a polygon defined by the subset of footprint intersections that lie within every footprint. The centroid of the polygon can then be used as an estimate of position.

[0072] This is illustrated in Figure IB, which is a schematic diagram showing an overlap 60 of footprints of four low Earth orbit satellites according to one embodiment. In this example, each of the four satellites has an associated footprint 20a, 20b, 20c, 20d (shown as dashed circles in Figure IB). The four footprints define an intersection region 62. A polygon 64, shown by a thick solid black line in Figure IB, is defined by vertices shown as solid points 62a, 62b, 62c, 62d, which are intersection points between two footprints. For example, vertex 64a is defined by the intersection of footprints 20a and 20b, vertex 64b is defined by the intersection of footprints 20b and 20c, vertex 64c is defined by the intersection of footprints 20c and 20d, and vertex 64d is defined by the intersection of footprints 20b and 20d. A centroid 66 of polygon 64 is indicated by a "+" in Figure IB.

[0073] This polygon 62 is the inner boundary of the intersection region 62 and the resulting estimate is an approximation. This has the advantage that the calculation of the polygon centroid is of low complexity (i.e., simple).

[0074] A set of points (x i ,y i Consider a two-dimensional non-self-intersecting polygon defined by , i = 1, 2, …, n, where the points are arranged in counterclockwise order. The area of ​​the polygon is given by:

number

[0075] If the points were instead arranged in clockwise order, the area would be the same size but negative, so A is called the signed area.

number

number

number

[0076] In this manner, the center of gravity 66 can be quickly and efficiently estimated from the vertices of the polygon.

[0077] Another advantage of using polygon 64 to approximate intersection region 62 is that only the vertices of this polygon need to be stored and updated with each new received transmission. Thus, in one embodiment, the vertices are stored by a memory that is updated with each new received transmission from one of the LEO satellites.

[0078] The polygon can also be iteratively updated by computing the intersections of the new footprint with the line segments that define the polygon, and discarding any vertices in the expanded set that lie outside the new footprint. That is, when a new transmission is received from one of the LEO satellites, the footprint of the new transmission is estimated, and the intersections of the new footprint with each line segment that defines the polygon are computed. Any vertices in the expanded set that lie outside the new footprint are discarded.

[0079] In another embodiment, only the footprint centers are stored by the memory and the polygon can be recalculated when necessary. This approach facilitates time windowing, whereby a circular buffer of only the most recent footprint centers is stored. That is, a circular buffer of the most recent n footprints (i.e., of the n previously received transmissions) is stored, and each time a new transmission is received from one of the LEO satellites, the footprints stored in the circular buffer are used to update the polygon estimate. This provides an efficient implementation for maintaining an up-to-date estimate of the terminal position.

[0080] In some embodiments, the terminal may be within range of a gateway 30 that broadcasts beacons, and these transmissions may also be used (in conjunction with satellite transmissions). This requires knowledge of the location and transmission range (e.g., footprint) of the gateway. The location and transmission range may be stored by the terminal or retrieved from the beacon signal (if included).

[0081] The coarse estimates produced by the above methods may then be used by the terminal as initial estimates for use by a more complex position estimator, such as the signal-based estimator described below.

[0082] The above method was simulated using actual orbital parameters of a constellation of 15 LEO satellites. FIG. 3A is a schematic diagram showing the overlapping footprints 300 of eight low Earth orbit satellites captured during one simulation, showing the resulting polygon 62 and estimated centroid 66. Each pass over a location was 5 minutes before and after. In this embodiment, the terminal was placed at a known location, and every 5 minutes an observation was made by the terminal to determine if the terminal was within the footprint of any satellite at that time (based on the actual orbit). If a satellite was observed, the latest footprint and all previous footprints up to that time (i.e., all accumulated observations) were used to estimate the updated location of the terminal (centroid of the polygon). An error (difference between actual centroid location and estimated centroid location) was then determined for each observation.

[0083] FIG. 3B is a plot of distance error 310 as a function of observation number for a first simulation in which the terminal is in a first location, according to one embodiment. This simulation was conducted over a 12-hour period (tracking 15 satellites), and the distance error 310 started around 1400 km, dropped to around 400 km after 10 observations, plateaued around 250 km, and finally dropped to 7 km at the end of the 12 hours. FIG. 3C is a plot of distance error 320 as a function of observation number for a second simulation in which the terminal is in a second location, according to one embodiment. This simulation was conducted over a 24-hour period (again tracking 15 satellites), and the distance error 320 started around 2500 km, dropped quickly to around 800 km, then dropped to around 200 km after 10 observations, and plateaued around 70 km by the end of the 24 hours.

[0084] These simulations show that for LEO satellites, accuracies on the order of a few hundred kilometers can be obtained with as few as 10 observations, and that these can be further reduced to less than 100 kilometers with 20 or more transmissions. These simulations also show that accuracies on the order of 10 kilometers can be obtained using embodiments of the methods described above.

[0085] In another example, a 10-day test was conducted in the Adelaide area of ​​South Australia, where the terminal collected a set of 302 packets from several satellites over the 10-day period. The average path length for each satellite was approximately 5 minutes, and a total of four satellites were observed. The footprint centers were estimated by taking the satellite's position at the time of the transmission from each satellite ephemeris and converting it to Earth Centered Earth Fixed (ECEF) coordinates. The terminal's location was then estimated by calculating the average of those footprint centers and comparing it to the known true location. In this test, the estimation error was 37.9 km. FIG. 4A is a plot of the measured footprint centers 402 for each of the 302 transmissions, with the polygon intersection area 64 including all the measurements (footprint centers) 402 along with the true (known) location 404 and the estimated average location 406. This process was then repeated 540 times, resulting in 540 sets of measurements / footprint centers (each defining an intersection region), and for each set, we estimated the mean of that set and the median of that set, respectively, and compared them to the known true location to construct a histogram of the estimation error. Figure 4B is a histogram plot showing the estimation error for the location of the mean (horizontal line) and the location of the median (vertical line). As can be seen in Figure 4B, the mean and median produce similar results (see overlapping regions), both generally estimating the location to within 100 km of the true device location, although the median estimator has a somewhat improved distribution and precision (i.e., it is shifted to the left), likely due to a reduced influence of outliers.

[0086] The method can also be performed in the reverse direction, for example by a satellite or core network, to remotely estimate the location of a transmitter in view of a satellite or multiple satellites. The transmitter may be a terminal in the communication system, but need not be a system entity, and may be a potential interferer. Figure 2B is a flow chart of a method 150 for a satellite communication system with multiple LEO satellites to estimate a transmitter's location, according to one embodiment.

[0087] Generally, the method 150 includes receiving 160 a plurality of transmissions from a transmitter by one or more LEO satellites. An estimate of a transmission time of each transmission and an ephemeris for each of the plurality of LEO satellites that received the transmission at that transmission time are then obtained 170. From the plurality of transmissions, at least one footprint for each of the plurality of LEO satellites is then estimated 180, and a location of the transmitter is determined 190 at a location remote from the transmitter by estimating an intersection area of ​​each of the estimated footprints.

[0088] This method may be performed by a single satellite in the case of receiving multiple transmissions from the transmitter, or by satellites in the network when they receive messages from other satellites that they received the same transmission (at the same time), assuming the satellite has knowledge of the ephemeris of those other satellites. Alternatively, the satellite receiving the transmission may transmit the time of transmission to a gateway, and a computing device in the core network infrastructure may perform an estimate of the transmitter's location. Variations including the use of convex intersection regions, polygons, and optimizations discussed above may be used with this method.

[0089] In some embodiments, the transmitter includes a unique identifier in the transmission to facilitate identification of transmissions from the same transmitter. However, in some embodiments, the satellite (or core network infrastructure) may not be able to decode the identifier, or the identifier may not exist. In those cases, the method may further include identifying the transmitter by determining one or more signal characteristics of the received transmission and determining whether the signal characteristics match signal characteristics of a previously received transmission from that transmitter. If there is a match, the received transmission may be used to update an estimate of the transmitter's location. The signal characteristics may be obtained from signal analysis on the received signal or from an attempt to decode the received signal.

[0090] The coarse estimates generated by the above methods can also be used as initial estimates for use by more computationally complex position estimators, such as the signal-based estimator described in PCT / AU2017 / 000108, entitled "POSITION ESTIMATION IN A LOW EARTH ORBIT SATELLITE COMMUNICATIONS SYSTEM," filed May 16, 2017, the contents of which are incorporated herein by reference. As the satellite passes over the terminal, the Doppler shift and related parameters such as time offset and rate of change of Doppler frequency change because they depend on the terminal's position (relative to the satellite). This is illustrated in FIG. 4C, which shows a plot of the measured Doppler frequency of packets received from the terminal at the satellite over the 10 days of the test referred to above. An optimization algorithm is then used to find the terminal's position that best fits the observed Doppler shift measurements using the coarse position as a starting point.

number

number

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number

[0091] The estimation of the Doppler frequency may be further aided by using beacon signals or received packets. The beacon signals may be non-system transmitters including other terminals and / or non-system satellites that transmit beacons or known signals to announce their presence. By measuring the frequency offset of the beacon signals, an improved estimate of the channel effects can be obtained, which in turn allows for an improved estimate of the Doppler frequency to be obtained, which is then used in the optimization algorithm.

[0092] Table 1 below presents results from yet another four-day test, where four devices were distributed across two locations, with two devices at each location. The two locations were within the Adelaide area and were 17 km apart observing the same set of four satellites over the four days. A set of packets was received from each terminal and used to estimate a coarse location. In addition, Doppler shift was also measured by the satellites as explained above, and an optimization method was used to refine the location estimate. Table 1 shows the total number of packets received from each terminal, along with the accuracy obtained by estimating the coarse location using the footprint-based method, and the accuracy using the Doppler-based method to refine the coarse estimate. [Table 1]

[0093] As can be seen in Table 1, the coarsest estimates were well below 100 km, and these position estimates were further refined significantly by updating refined estimates using Doppler-based methods with errors on the order of 5 km.

[0094] In the embodiments described above, the refined estimation is performed remotely from the terminal, such as by a satellite or a core network, both of which are less power constrained than the terminal. However, it should be understood that the method can also be performed by the terminal using packets received from one or more satellites. In those embodiments, the Doppler measurements (or time delay and / or rate of change of Doppler) may be measured by the terminal and obtained from decoding packets received from the satellites or by processing the received signals. The Doppler measurements may be obtained from beacon satellites or other beacon transmitters. Since this signal-based estimation method is computationally intensive, this embodiment may be used sparingly and only on demand for specific requirements or applications where greater accuracy is required. The terminal may be configured to use a coarse location estimate by default for tasks such as scheduling and to reserve (e.g., only on demand) the more power-intensive signal-based estimation for specific high priority applications. For example, the terminal may be configured to provide communication services to co-located sensors, for example to report the sensor measurements or status to the core network (e.g., for use by the sensor owner). In case of sensor error conditions or certain use cases, a precise estimate of the location may be required, and thus the sensor's control software may request a precise estimate of the location from the terminal, which may then be used by the sensor and / or included in the transmission by the terminal. A hybrid approach may be performed, where a coarse estimate is performed by the terminal, which transmits it to the satellite and / or core network, which uses it as an input location to the signal-based estimation methods performed by the satellite or core network.

[0095] The embodiments of the methods (and systems implementing those methods) described above provide an improved method for coarsely estimating the position of a remote terrestrial terminal in a LEO satellite communication system that avoids the need for a power-demanding GNSS module in the terminal. The embodiments of the methods described herein define an intersection region of footprints from multiple transmissions. The use of an elevation threshold can be used to ensure convexity, which further enables the use of optimization techniques. Of note, since the region is convex, the geometric midpoint is an optimal location within the intersection region. Convexity also allows for the estimation of the centroid using optimization to an error function, including a weighted error function, to further refine the estimate. An efficient implementation can be achieved by approximating the intersection region as a polygon, which has the advantage that the calculation of the centroid is of low complexity. Additionally, a circular buffer may be used to maintain an up-to-date estimate of the terminal's position.

[0096] Thus, the embodiments can be advantageously implemented in low-cost terminals with limited processing power, storage, and battery life (and lacking a GNNS module), resulting in significant power savings. The terminal uses a coarse estimate of the terminal's location to enable the terminal to optimize the timing (scheduling) of transmissions to reduce energy usage, or to otherwise improve performance, such as by scheduling transmissions to increase the probability of successful transmission. The embodiments have low computational complexity and low storage requirements, and thus can be computed efficiently by the terminal, thereby minimizing power consumption. In particular, they may be used by remotely located low-cost terminals with limited processing power, storage, and battery life that may be left unattended for months or years, where lower power consumption is crucial.

[0097] Additionally, method embodiments may be performed remotely from the terminal by satellite or core network and used to estimate the location of transmitters such as non-system transmitters acting as interference sources. In the remote case, the coarse estimate may serve as an initial estimate for computationally more complex (and power intensive) optimization-based signal-based estimation techniques that provide more accurate or refined location estimates (e.g., 5 km vs. 100 kms). These may use Doppler frequency estimates and related parameters that vary based on the terminal's location. These signal-based estimation methods described above that use the coarse estimate as an initial location can also be implemented by the terminal when a more accurate estimate of location is required. This gives the remote terminal flexibility to control power consumption. The terminal may be configured to use the coarse location estimate by default for tasks such as scheduling and reserve the more power intensive signal-based estimates for certain high priority applications (e.g., used only on request).

[0098] Those skilled in the art will appreciate that information and signals may be represented using any of a variety of technologies. For example, the data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

[0099] Those skilled in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithmic steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software or instructions, or a combination of both. To clearly illustrate this interchangeability of hardware and software, the various illustrative components, blocks, modules, circuits, and steps have been described generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the particular application and design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in a variety of different ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the invention.

[0100] The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, as a software module executed by a processor, or as a combination of both. In a hardware implementation, processing may be implemented within one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processors (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, or other electronic units designed to perform the functions described herein, or a combination thereof.

[0101] In some embodiments, the processor module comprises one or more central processing units (CPUs) configured to perform some of the steps of the method. The computing unit may also comprise one or more graphic processing units (GPUs), tensor processing units (TPUs), input devices and output devices. The CPU may comprise an input / output interface, an arithmetic logic unit (ALU), and a control unit and program counter element that communicates with the input devices and output devices through the input / output interface. The input / output interface may comprise a network interface and / or a communication module for communicating with a comparable communication module in another device using a predefined communication protocol (e.g., Bluetooth, Zigbee, IEEE 802.15, IEEE 802.11, TCP / IP, UDP, etc.). The computing or terminal device may comprise a single CPU (core) or multiple CPUs (multiple cores), or multiple processors, as well as GPUs and TPUs. The computing or terminal device may use parallel processors, vector processors, or may be a distributed computing device, including cloud-based computing devices and resources. The memory is operatively coupled to the processor and may include RAM and ROM components and may be provided within or external to the device or processor module. The memory may be used to store an operating system and other software modules or instructions. The processor may be configured to load and execute the software modules or instructions stored in the memory.

[0102] A software module, also referred to as a computer program, computer code, or instructions, may include a number of source code or object code segments or instructions and may reside in any computer readable medium, such as RAM memory, flash memory, ROM memory, EPROM memory, registers, a hard disk, a removable disk, a CD-ROM, a DVD-ROM, a Blu-ray® disk, or any other form of computer readable medium. In some aspects, the computer readable medium may comprise a non-transitory computer readable medium (e.g., a tangible medium). Additionally, in other aspects, the computer readable medium may comprise a transitory computer readable medium (e.g., a signal). Combinations of the above should also be included within the scope of computer readable media. In another aspect, the computer readable medium may be integral to the processor. The processor and the computer readable medium may reside in an ASIC or related device. The software code may be stored in a memory unit and the processor may be configured to execute it. The memory unit may be implemented within the processor or external to the processor, and if external, it may be communicatively coupled to the processor via various means known in the art. The computer program may be written, for example, in a general-purpose programming language (e.g., Python, Java, C++, C, C#, etc.) or some specialized, application-specific language, and may utilize or invoke software libraries or packages, for example, to implement a data interface (e.g., JSON) or utilize machine learning (e.g., TensorFlow, CUDA) or numerical optimization.

[0103] Further, it should be understood that modules and / or other suitable means for performing the methods and techniques described herein may be downloaded and / or otherwise obtained by a computing device. For example, such a device may be coupled to a server to facilitate the transfer of means for performing the methods described herein. Alternatively, the various methods described herein may be provided via a storage means (e.g., a physical storage medium such as a flash disk, RAM, ROM, a compact disk (CD) or a floppy disk, etc.), and a computing device may acquire the various methods upon coupling to or providing the storage means to the device. Furthermore, any suitable technique for providing the methods and techniques described herein to a device may be utilized.

[0104] The methods disclosed herein include one or more steps or actions for achieving the described method. The steps and / or actions of the methods may be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of steps or actions is specified, the order and / or use of specific steps and / or actions may be modified without departing from the scope of the claims.

[0105] As used herein, the terms "estimating" or "determining" encompass a wide range of actions. For example, "estimating" or "determining" may include calculating, computing, processing, deriving, investigating, referencing (e.g., referencing a table, database, or another data structure), ascertaining, and the like. Also, "estimating" or "determining" may include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory), and the like. Also, "determining" may include solving, selecting, choosing, establishing, and the like.

[0106] The reference to prior art in this specification is not, and should not be construed as, an admission or any form of suggestion that such prior art forms part of the common general knowledge.

[0107] It will be understood that, as used in this specification and the following claims, the terms "comprise" and "include" and their derivatives (e.g., comprises, comprising, includes, including) are to be interpreted as inclusive of the features referred to by the word and are not intended to exclude the presence of additional features unless specifically stated or indicated.

[0108] In some cases, a single embodiment may combine multiple features for brevity and / or to aid in understanding the scope of the disclosure. In such cases, it should be understood that those multiple features may be provided separately (in separate embodiments) or in any other suitable combination. Alternatively, when separate features are described in separate embodiments, those separate features may be combined into a single embodiment, unless otherwise stated or indicated. This also applies to the claims, which may be recombined in any combination. That is, the claims may be amended to include features defined in other claims. Furthermore, phrases referring to "at least one" of a list of items refer to any combination of those items, including single elements. As an example, "at least one of a, b, or c" is intended to encompass a, b, c, ab, ac, bc, and abc.

[0109] Those skilled in the art will recognize that the use of the present disclosure is not limited to the specific applications described. Nor is the present disclosure limited to its preferred embodiments with respect to the specific elements and / or features described or illustrated herein. It will be recognized that the present disclosure is not limited to the disclosed embodiment or embodiments, but is capable of numerous rearrangements, modifications, and substitutions without departing from the scope as set forth and defined by the following claims.

Claims

1. 1. A method for estimating a position of a terminal in a satellite communication system comprising a plurality of LEO satellites and a plurality of terminals, comprising: receiving a plurality of transmissions from each of one or more LEO satellites; obtaining an estimate of a current time and an ephemeris for each of the one or more LEO satellites; estimating at least one footprint for each of the plurality of LEO satellites from the plurality of transmissions; determining a location of the terminal by estimating an intersection area of ​​each of the estimated footprints.

2. The method of claim 1 , further comprising estimating a position within the intersection region.

3. The method of claim 2 , wherein estimating a location includes estimating a centroid location of the intersection region or a geometric midpoint of the intersection region.

4. The method of claim 1 , 2 or 3, wherein the footprint of the LEO satellite is estimated as a convex area.

5. The method of claim 4 , wherein the convex region is estimated as a set of points on a reference surface that have a direct line of sight to the LEO satellite above a predetermined threshold elevation angle.

6. determining a location of the terminal by estimating an intersection area of ​​each of the estimated footprints; defining an error function that is a measure of the error between said estimate of location obtained from the estimated footprint and an estimate of true location; optimizing the error function using an optimization method to obtain an optimized estimate of the true position of the terminal; The method of any one of claims 1 to 5, comprising:

7. The method of claim 1 , wherein the intersection region is approximated as a polygon.

8. The method of claim 7 , wherein determining a location comprises determining a centroid of the polygon.

9. 9. The method of claim 7 or 8, further comprising storing vertices of the polygon and updating estimates of the vertices of the polygon with each new received transmission from one of the one or more LEO satellites.

10. 9. The method of claim 7 or 8, further comprising: updating the polygon estimate includes receiving a new transmission from one of the one or more LEO satellites, estimating a footprint of the new transmission, calculating intersections of the new footprint with each line segment that defines the polygon, and discarding any vertices in the expanded set that lie outside the new footprint.

11. 11. The method of claim 7, further comprising: storing a circular buffer of n footprints of n previously received transmissions; and updating the polygon estimate for each new transmission from one of the one or more LEO satellites using the footprints stored in the circular buffer.

12. 12. The method of claim 1, further comprising obtaining an estimate of at least a Doppler frequency for each of the received transmissions, and obtaining a refined estimate of the position of the terminal by using a non-linear optimization algorithm configured to use the position of the terminal as an initial position and to refine the estimate of the position by minimizing an error function that is based on at least the estimated Doppler frequency.

13. The method of claim 12 , wherein the nonlinear optimization algorithm is further configured to use a cost function based on the error function at each position obtained using at least the estimated Doppler frequency.

14. 1. A method for estimating a transmitter position by a satellite communication system comprising a plurality of LEO satellites, comprising: receiving, by one or more LEO satellites, a plurality of transmissions from a transmitter; obtaining an estimate of a time of transmission of each transmission and an ephemeris for each of the plurality of LEO satellites at the time of transmission; estimating at least one footprint for each of the plurality of LEO satellites from the plurality of transmissions; determining a location of the transmitter at a location remote from the transmitter by estimating an intersection area of ​​each of the estimated footprints.

15. The method of claim 14 , further comprising estimating a position within the intersection region.

16. The method of claim 15 , wherein estimating a location includes estimating a centroid location of the intersection region or a geometric midpoint of the intersection region.

17. 17. The method of claim 14, 15, or 16, wherein the footprint of the LEO satellite is estimated as a convex area.

18. The method of claim 17 , wherein the convex region is estimated as a set of points on a reference surface that have a direct line of sight to the LEO satellite above a predetermined threshold elevation angle.

19. determining a location of the transmitter by estimating an intersection area of ​​each of the estimated footprints; defining an error function that is a measure of the error between said estimate of location obtained from the estimated footprint and an estimate of true location; optimizing the error function using an optimization method to obtain an optimized estimate of the true position of the transmitter; 19. The method of any one of claims 14 to 18, comprising:

20. The method of claim 14 , wherein the intersection region is approximated as a polygon.

21. The method of claim 20 , wherein determining a location includes determining a centroid of the polygon.

22. 22. The method of claim 20 or 21, further comprising storing vertices of the polygon and updating estimates of the vertices of the polygon with each new received transmission from one of the one or more LEO satellites.

23. 22. The method of claim 20 or 21, further comprising: updating the polygon estimate includes receiving a new transmission from one of the one or more LEO satellites, estimating a footprint of the new transmission, calculating intersections of the new footprint with each line segment that defines the polygon, and discarding any vertices in the expanded set that lie outside the new footprint.

24. 24. The method of claim 20, further comprising: storing a circular buffer of n footprints of n previously received transmissions; and updating the polygon estimate for each new transmission from one of the one or more LEO satellites using the footprints stored in the circular buffer.

25. 25. The method of claim 14, further comprising identifying a transmitter by determining one or more signal characteristics of a received transmission and determining whether the signal characteristics match signal characteristics of a previously received transmission from the transmitter, and if there is a match, updating the estimate of the location of the transmitter using the received transmission.

26. 25. The method of claim 14, wherein the transmitters are terminals, the method further comprising obtaining an estimate of at least a Doppler frequency for each of the received transmissions, and obtaining a refined estimate of the terminal's position by using a non-linear optimization algorithm configured to use the position of the terminal obtained by the method of claim 1 as an initial position, and to refine the estimate of the position by minimizing an error function that is based on at least the estimated Doppler frequency.

27. 27. The method of claim 26, wherein the non-linear optimization algorithm is further configured to use a cost function based on the error function at each position obtained using at least the estimated Doppler frequency.

28. 1. A terminal for use in a satellite communications system comprising a plurality of LEO satellites, the method comprising: a receiver for receiving one or more transmissions from one or more of the plurality of LEO satellites; 15. A terminal comprising at least one processor and at least one memory, the memory configured to store ephemeris data of the plurality of LEO satellites and instructions for configuring the at least one processor to perform the method of any one of claims 1 to 14.

29. 1. A computing device in a LEO satellite or network entity of a satellite communications system comprising a plurality of LEO satellites and a plurality of terminals, comprising: At least one processor and at least one memory, the at least one memory configured to store instructions for configuring the at least one processor to store ephemeris data for the plurality of LEO satellites and to perform the method of any one of claims 14 to 27. A computing device comprising:

30. 28. A computer readable medium comprising instructions for configuring one or more processors to perform the method of any one of claims 1 to 27.

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