WO2024028342A1 - Procédés et appareil de positionnement d'un terminal mobile - Google Patents

Procédés et appareil de positionnement d'un terminal mobile Download PDF

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Publication number
WO2024028342A1
WO2024028342A1 PCT/EP2023/071321 EP2023071321W WO2024028342A1 WO 2024028342 A1 WO2024028342 A1 WO 2024028342A1 EP 2023071321 W EP2023071321 W EP 2023071321W WO 2024028342 A1 WO2024028342 A1 WO 2024028342A1
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Prior art keywords
mobile terminal
radio signal
airborne
spaceborne
transmission
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PCT/EP2023/071321
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English (en)
Inventor
Felix ABEL
Florin-Catalin GREC
Rigas Themistoklis IOANNIDIS
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European Space Agency
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Publication of WO2024028342A1 publication Critical patent/WO2024028342A1/fr

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/0009—Transmission of position information to remote stations
    • G01S5/0081—Transmission between base stations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/74—Systems using reradiation of radio waves, e.g. secondary radar systems; Analogous systems
    • G01S13/76—Systems using reradiation of radio waves, e.g. secondary radar systems; Analogous systems wherein pulse-type signals are transmitted
    • G01S13/765—Systems using reradiation of radio waves, e.g. secondary radar systems; Analogous systems wherein pulse-type signals are transmitted with exchange of information between interrogator and responder
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/0009—Transmission of position information to remote stations
    • G01S5/0018—Transmission from mobile station to base station
    • G01S5/0027—Transmission from mobile station to base station of actual mobile position, i.e. position determined on mobile
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0205—Details
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0205—Details
    • G01S5/0221—Receivers
    • G01S5/02213—Receivers arranged in a network for determining the position of a transmitter
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0249—Determining position using measurements made by a non-stationary device other than the device whose position is being determined
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/03—Protecting confidentiality, e.g. by encryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/10—Integrity
    • H04W12/104—Location integrity, e.g. secure geotagging
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/60—Context-dependent security
    • H04W12/63—Location-dependent; Proximity-dependent
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/025—Services making use of location information using location based information parameters
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/12—Detection or prevention of fraud
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/02—Hierarchically pre-organised networks, e.g. paging networks, cellular networks, WLAN [Wireless Local Area Network] or WLL [Wireless Local Loop]
    • H04W84/04—Large scale networks; Deep hierarchical networks
    • H04W84/06—Airborne or Satellite Networks

Definitions

  • This application relates to the field of air-based or space-based (e.g., satellite-based) positioning.
  • the application particularly relates to techniques for air-based or space-based positioning of a mobile terminal, and to constellations of satellites implementing such techniques.
  • the application further relates to such techniques that use two-way position validation and determination.
  • GNSS Global Navigation Satellite System
  • asset trackers are projected to be the fastest-growing GNSS device type.
  • the present disclosure proposes a method of air-based and/or space-based (e.g., satellite-based) positioning of a mobile terminal and a constellation of a plurality of satellites for positioning of a mobile terminal, having the features of the respective independent claims.
  • space-based e.g., satellite-based
  • An aspect of the disclosure relates to a method of air-based and/or space-based (e.g., satellite- based) positioning of a mobile terminal for determining or verifying a position of the mobile terminal.
  • the method may include, at an airborne or spaceborne transmitter, transmitting a first radio signal to the mobile terminal for prompting the mobile terminal to transmit a second radio signal.
  • the first radio signal may correspond to a first message.
  • the first radio signal may be repeatedly or periodically sent by the airborne or spaceborne transmitter.
  • the method may further include, at the mobile terminal, in response to receiving the first radio signal, transmitting the second radio signal.
  • the second radio signal may correspond to a second message.
  • the method may further include receiving the second radio signal at a plurality of airborne or spaceborne receivers.
  • the method may yet further include determining or verifying the position of the mobile terminal based on a time of transmission of the first radio signal at the airborne or spaceborne transmitter and times of reception of the second radio signal at respective ones of the plurality of airborne or spaceborne receivers. Determining or verifying the position of the mobile terminal may be performed at a processing node.
  • the processing node may be provided at one of the transmitter or the plurality of receivers, or separate therefrom, for example as a central node (e.g., ground station).
  • the mobile terminal can be reliably positioned (i.e., its position can be determined) even when it provides falsified data, or it can alternatively be verified whether the mobile terminal is indeed at a self-reported position. This can be achieved with marginal increase in complexity in the transmitter and receiver payloads.
  • the first message may include a first identifier that identifies the airborne or spaceborne transmitter.
  • the first identifier may include a transmitter number or a satellite number, for example.
  • the first identifier may include a pseudo-random bit sequence that is repeatedly updated at the airborne or spaceborne transmitter.
  • the random bit sequence may be updated periodically, at predefined time intervals, or at predefined timings. If the first radio signal is periodically transmitted, the pseudo-random bit sequence may be changed from one instance of the first radio signal to the next. In any case, the pseudo-random bit sequence may be updated so that it changes from one instance of the first radio signal to the next.
  • the second message may include a second identifier identifying the mobile terminal.
  • This the second identifier may include a portion that is generated, at the mobile terminal, based on the first identifier.
  • the method may further include measuring, at respective ones of the plurality of airborne or spaceborne receivers, frequencies of the second radio signal upon arrival. Then, determining or verifying the position of the mobile terminal may be further based on the frequencies of the second radio signal measured at respective ones of the plurality of airborne or spaceborne receivers.
  • the second message may further include an indication of a frequency of transmission (e.g., carrier frequency) of the second radio signal at the mobile terminal. Then, determining or verifying the position of the mobile terminal may be further based on the frequency of transmission of the second radio signal at the mobile terminal. In such cases, the method may further comprise determining a (radial) velocity of the mobile terminal, for example based on a determined Doppler frequency shift. Taking into account frequency measurements (and based thereon, Doppler frequency shifts) in determining or verifying the mobile terminal’s position can increase accuracy of determination and/or reduce the number of independent receivers that are required for the determination.
  • a frequency of transmission e.g., carrier frequency
  • the second message may include an indication of one or more parameters for assisting determination or verification of the position of the mobile terminal.
  • the one or more parameters for assisting determination or verification of the position of the mobile terminal may include at least one of: a transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal, and one or more components of a position of the mobile terminal. Then, determining or verifying the position of the mobile terminal may be further based on the one or more parameters for assisting determination or verification of the position of the mobile terminal.
  • the transmission delay may correspond to or include a processing delay at the mobile terminal.
  • the position of the mobile terminal may be a self-reported position, for example.
  • the cost function may be further based on the frequencies of the second radio signal measured at respective ones of the plurality of airborne or spaceborne receivers. Additionally or alternatively, the cost function may be further based on the frequency of transmission of the second radio signal. Additionally or alternatively, the cost function may be further based on the one or more parameters for assisting determination or verification of the position of the mobile terminal. For example, the cost function may be further based on the transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal.
  • determining the position of the mobile terminal based on the cost function may involve minimizing the cost function to estimate the position of the mobile terminal.
  • the cost function may be minimized using least-squares techniques, for example.
  • determining the position of the mobile terminal using the cost function may involve jointly determining a position of the mobile terminal and a transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal that minimize the cost function.
  • the second message may include an indication of a self-reported position of the mobile terminal.
  • the cost function may be further based on the self-reported position.
  • the self-reported position of the mobile terminal may be a Global Navigation Satellite System, GNSS, based position.
  • verifying the position of the mobile terminal may involve comparing the cost function to a threshold.
  • the threshold may be a predetermined threshold, for example.
  • the self-reported position of the mobile terminal may be considered verified if the cost function does not exceed the threshold (or is smaller than the threshold).
  • the first message may include an indication of a time of transmission of the first radio signal at the airborne or spaceborne transmitter.
  • the method may further include, at the airborne or spaceborne transmitter, encrypting information bits representing the first identifier. Additionally of alternatively, the method may further include, at the mobile terminal, encrypting information bits representing the second identifier.
  • the cost function may be given by
  • N may denote the number of airborne or spaceborne receivers
  • k 1, ...
  • N may denote a given one among the plurality of airborne or spaceborne receivers, p UE .
  • ⁇ t UE may denote the transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal
  • c may denote the speed of light.
  • the cost function may be given by
  • N may denote the number of airborne or spaceborne receivers
  • k 1, ...
  • N may denote a given one among the plurality of airborne or spaceborne receivers
  • p UE may denote the position of the mobile terminal
  • p sk may denote a position of the k-th airborne or spaceborne receiver
  • p s1 may denote a position of the airborne or spaceborne transmitter
  • t tx,S1 may denote the time of transmission of the first radio signal at the airborne or spaceborne transmitter
  • t rX,Sk,S1 may denote the time of reception of the second radio signal at the k-th airborne or spaceborne receiver
  • ⁇ t UE may denote the transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal
  • w may denote a weighting factor of unit [seconds]
  • v sk may denote a velocity of the k-th airborne or spaceborne receiver
  • f tX,UE
  • the weighting factor w may be given by the method may further include collecting, at a processing node, the time of transmission of the first radio signal at the airborne or spaceborne transmitter and the times of reception of the second radio signal at respective ones of the plurality of airborne or spaceborne receivers. Then, the method may further include determining the position of the mobile terminal at the processing node.
  • the processing node may be implemented by one or more of: a user terminal, the airborne or spaceborne transmitter, one or more of the airborne or spaceborne receivers, and a ground station.
  • the method may further include collecting, at the processing node, the frequency of transmission of the second radio signal at the mobile terminal and/or the frequencies of the second radio signal measured at the respective ones of the plurality of airborne or spaceborne receivers.
  • the airborne or spaceborne transmitter and the plurality of airborne or spaceborne receivers may be implemented by a plurality of satellite-based transceivers.
  • the satellites holding the transceivers may be LEO satellites, for example.
  • the plurality of satellites may include a first satellite comprising a transmitter for transmitting a first radio signal to the mobile terminal for prompting the mobile terminal to transmit a second radio signal.
  • the first radio signal may correspond to a first message.
  • the second radio signal may correspond to a second message.
  • the plurality of satellites i.e., constellation
  • the first satellite may be adapted to transmit an indication of a time of transmission of the first radio signal at the airborne or spaceborne transmitter to the mobile terminal (e.g., as part of the first message) or to a processing node.
  • Each of the second satellites may be adapted to transmit an indication of a time of reception of the second radio signal at the respective second satellite to the processing node.
  • the processing node may be implemented by one or more of: a user terminal, the first satellite, one or more of the second satellites, and a ground station.
  • the second message may include an indication of a frequency of transmission of the second radio signal at the mobile terminal.
  • Each of the second satellites may be further adapted to transmit the indication of the frequency of transmission of the second radio signal at the mobile terminal and/or an indication of a frequency of the second radio signal measured at the respective second satellite to the processing node.
  • the second message may include an indication of one or more parameters for assisting determination or verification of the position of the mobile terminal.
  • the one or more parameters for assisting determination or verification of the position of the mobile terminal may include at least one of: a transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal and one or more components of a position of the mobile terminal.
  • each of the second satellites may be further adapted to transmit the indication of the one or more parameters for assisting determination or verification of the position of the mobile terminal to the processing node.
  • the first message may include a first identifier that identifies the first satellite. Then, the first satellite may be further adapted to transmit the first identifier to the processing node. Additionally or alternatively, the second message may include a second identifier that identifies the mobile terminal. Then, each of the second satellites may be further adapted to transmit the second identifier to the processing node.
  • Fig. 1 schematically illustrates an example of an overall framework for employing methods according to embodiments of the disclosure
  • Fig. 2 is a flowchart illustrating an example of a method accordingto embodiments of the disclosure
  • Fig. 3 schematically illustrates an example of a message exchange scheme for methods according to embodiments of the disclosure
  • Fig. 4 schematically illustrates an example of message content of a downlink message (first message) in methods according to embodiments of the disclosure
  • Fig. 5 schematically illustrates an example of message content of an uplink message (second message) in methods according to embodiments of the disclosure
  • Fig. 6 includes diagrams showing examples of mean RMS distance error as function of orbit height and user masking angle, respectively, for methods according to embodiments of the disclosure
  • Fig. 7 includes diagrams showing examples of mean RMS distance error as function of error standard deviation for honest users and fraudulent users, respectively, for methods according to embodiments of the disclosure,
  • Fig. 8 includes diagrams showing further examples of mean RMS distance error as function of orbit height and user masking angle, respectively, for methods according to embodiments of the disclosure,
  • Fig. 9 is a diagram showing another example of mean RMS distance error as function of error standard deviation for honest users and fraudulent users, for methods according to embodiments of the disclosure.
  • Fig. 10 includes diagrams showing examples of probability distributions of mean RMS distance error for varying orbit height and varying user masking angle, respectively, for methods according to embodiments of the disclosure, and
  • Fig. 11 is a diagram showing an example of a probability distributions of mean RMS distance error for varying error standard deviation, for methods according to embodiments of the disclosure.
  • Uplink TDOA positioning methods as described for example in References [2], [3] use at least four synchronized receivers to timestamp an uplink message from the user, further combining these measurements into three independent TDOA equations allowing to position the user in 3D.
  • Current TDOA approaches rely only on the uplink message.
  • Other existing methods employing two-way round-trip time (RTT) measurements are dependent on the user to report correct timestamping.
  • satellite-based geoiocation services can be used to locate an emitter/user.
  • SAR search and rescue
  • users are fully cooperative.
  • operational systems like Galileo MEOSAR (Reference [4]) and other projected systems (Reference [5]).
  • the aforementioned methods rely either on uplink TDOA or on the user obtaining its own position via GNSS and supplying it through the uplink message.
  • Access policing for satellite services Reference [6]
  • AIS-based ship tracking Reference [7]
  • the terms “partly cooperative user” and “non-trusted user” may be used interchangeably for a user for which it can be assumed that it will transmit uplink signals, either for an intrinsic incentive (e.g. , being allowed to use a service) or to avoid regulatory/legal repercussions (e.g., in the case of AIS). It is further assumed that the user might have an incentive to tamper with its uplink signals and the information therein for their own benefit (e.g., self-spoof to cover up illegal fishing activities).
  • Non-cooperative users by contrast might not have any incentive to conform to a certain pattern or message format for uplink signals.
  • the geolocation of such non-cooperative users may have its main application in a military and law enforcement context, but may also relate to tailoring communication services to a user’s location, for example.
  • Operational services are offered for example by Atos (Reference [8]) and Spire (Reference [9]), where the latter can be employed for GNSS interference monitoring.
  • Atos Reference [8]
  • Spire Reference [9]
  • Working with non-cooperative users these methods rely by definition on one-way uplink signals.
  • partly cooperative or non- trusted users are the main targeted group for techniques according to the present disclosure.
  • the present disclosure relates to methods for two-way position validation or position determination of user elements (mobile terminals) by means of a set of airborne or spaceborne nodes (e.g., satellites in low Earth orbit (LEO), other spacecraft, high-altitude platforms, airplanes, balloons, etc.) that can determine the position of a non-trusted user.
  • airborne or spaceborne nodes e.g., satellites in low Earth orbit (LEO), other spacecraft, high-altitude platforms, airplanes, balloons, etc.
  • satellites in particular, LEO satellites
  • transmitters and/or receivers e.g., transceivers
  • present disclosure is not so limited and likewise applies to other airborne or spaceborne transceivers (transceiver platforms), such as high-altitude platforms.
  • present disclosure further relates to techniques employing combinations of different receivers (receiver platforms), including systems comprising satellites and high-altitude platforms. Unless indicated otherwise, it is understood that statements made with regard to satellites likewise apply to other receiver platforms, such as high-altitude platforms.
  • a downlink signal (first radio signal) is sent from one LEO satellite at time t tx,S1 (time of transmission) to the mobile terminal (user element (UE)).
  • the transmitting LEO satellite is a non-limiting example of an airborne or spaceborne transmitter.
  • the mobile terminal then uplinks a signal (second radio signal) that is received by multiple LEO satellites at times t rX,Sk,S1 (times of reception).
  • the multiple LEO satellites are non-limiting examples of airborne or spaceborne receivers.
  • the delay between reception and transmission, ⁇ t UE and the three coordinates of the user position p UE can be computed independently of position and timing and information by the UE, for example as described in Eq. (l)-Eq. (4) given below.
  • the transmitting LEO satellite may be among the multiple receiving LEO satellites. Detail of geometric and/or temporal aspects of these methods, optional features, message composition, and details of the position computation procedure will be described below.
  • Fig. 1 schematically illustrates an example of a framework (or geometry) 100 for employing techniques according to the present disclosure.
  • the framework comprises an optional set of GNSS satellites 190, for example in medium Earth orbit (MEO), a mobile terminal (user element) 150 for example located on earth surface or in earth atmosphere, a set (e.g., constellation, or part thereof) of satellites (SI, S2, S3,...) 110, 120, for example in low Earth orbit (LEO), and optionally, a ground station (GS) 180.
  • MEO medium Earth orbit
  • SI, S2, S3,...) 110, 120 for example located on earth surface or in earth atmosphere
  • LEO low Earth orbit
  • GS ground station
  • Fig. 1 further schematically shows the different stages or steps of methods according to embodiments of the disclosure.
  • GNSS satellites 190 transmit navigation signals (GNSS signals) 195 that are received by the mobile terminal 150, which in turn subsequently computes its position based on the GNSS signals 195.
  • GNSS signals navigation signals
  • one LEO satellite 110 among the LEO satellites transmits a signal (downlink signal, first radio signal) 115 to the mobile terminal 150.
  • This signal 115 includes a unique identifier (first identifier) of the LEO satellite 110 and the time of transmission of the signal at the LEO satellite 110,
  • the mobile terminal 150 transmits an uplink signal (second radio signal) 155.
  • the uplink signal 155 includes a unique identifier (second identifier) of the mobile terminal 150.
  • the uplink signal may optionally further include the carrier frequency of the uplink signal, f tX,UE .
  • the uplink signal may optionally further include the time elapsed between receiving the signaling from the LEO satellite 110 and transmitting the uplink signal 155, ⁇ t UE and/or the reported position of the mobile terminal 150 determined by means of the GNSS, p UE .
  • the uplink signal 155 from the mobile terminal 150 is received at LEO satellites 120 among the LEO satellites.
  • the receiving LEO satellites 120 may or may not include the transmitting LEO satellite 110.
  • the receiving LEO satellites 120 measure (or record) respective times of arrival t rX,Sk,S1 of the uplink signal 155. Further, optionally, also frequencies of arrival f rx,sk,s1 of the uplink signal 155 are measured by respective LEO satellites 120. 4)
  • all measurements are downlinked to the ground station 180 (alternatively, to one of the LEO satellites, a separate user terminal, or even the mobile terminal 150, depending on the implementation). In any case, the measurements are transmitted to a processing node (i.e. , a node having processing capability).
  • the ground station 180 (or processing node in general) then determines or validates the position of the mobile terminal 150 based on the collected data.
  • the position of the transmitter (e.g., satellite) and each receiver (e.g., satellite) at the relevant times are assumed to be known, for example through orbit determination techniques, orbit propagation, ground based ranging, or other solutions.
  • the mobile terminal 150 and the LEO satellites 110, 120 are strictly required.
  • the set of GNSS satellites 190 in MEO is only required if the UE should determine its position a priori and transmit its position (and possibly retransmission delay ⁇ t UE ) to the LEO satellites 110, 120 via the uplink message 155.
  • This provision permits the LEO satellites 110, 120 to confirm or reject the mobile terminal’s 150 reported position, for example based on the RMSE using Eq. (2) and Eq. (6) given below, rather than computing it ab initio, for example using Eq. (4) and Eq. (8) given below, thereby saving computational resources.
  • the ground station 180 is only required if the processing is to be performed on ground.
  • the proposed method only requires the measurements/recordings by the transmitting satellite and all receiving satellites to be collected (e.g., fused) in an arbitrary place or at an arbitrary processing node to perform the computation.
  • This processing node could be one of the satellites, or other spaceborne, airborne, or ground-based elements, depending on use cases and implementations.
  • Fig. 2 is a flowchart illustrating an example of a method 200 of air-based and/or space-based positioning of a mobile terminal for determining or verifying a position of the mobile terminal according to embodiments of the disclosure. This method may proceed, for example, in the framework 100 described above.
  • a first radio signal is transmitted, at an airborne or spaceborne transmitter (e.g., the LEO satellite 110 in the example of Fig. 1), to the mobile terminal (e.g., the mobile terminal 150 in the example of Fig. 1). This is done for prompting the mobile terminal to in turn transmit a second radio signal.
  • the first radio signal is understood to correspond to (e.g., comprise, implement) a first message. Further, the first radio signal may be repeatedly or periodically sent by the airborne or spaceborne transmitter.
  • the first message includes a first identifier (unique downlink identifier) that identifies the airborne or spaceborne transmitter.
  • the first identifier may include a (unique) transmitter number or a satellite number, for example.
  • the unique downlink identifier may fulfil requirements concerning expiration time, non-predictability and/or encryption/privacy.
  • the second radio signal in response to receiving the first radio signal, is transmitted at the mobile terminal. It is understood that the second radio signal corresponds to (e.g. , comprises, implements) a second message.
  • the second message includes a second identifier (unique uplink identifier) identifying the mobile terminal.
  • the second identifier includes at least a portion that is generated, at the mobile terminal, based on the first identifier. This may be done by simply copying the first identifier, or by hashing the first identifier, for example.
  • the unique uplink identifier may fulfil requirements concerning unique identifiability of the mobile terminal, unique identifiability of the downlink satellite and message, and/or encryption/privacy.
  • the second radio signal is received at a plurality of (e.g., N) airborne or spaceborne receivers (e.g., the LEO satellites 120 in the example of Fig. 1).
  • a plurality of airborne or spaceborne receivers e.g., the LEO satellites 120 in the example of Fig. 1).
  • Each of the receivers measures/records the time of arrival (time of reception) of the second radio signal at the respective receiver.
  • the position of the mobile terminal is determined or verified based on a time of transmission of the first radio signal at the airborne or spaceborne transmitter and times of reception of the second radio signal at respective ones of the plurality of airborne or spaceborne receivers.
  • Determining or verifying the position of the mobile terminal at this step may be performed at a processing node.
  • This processing node may be provided at one of the transmitter or the plurality of receivers, or separate therefrom, for example as a central node (e.g., ground station).
  • the processing node may be implemented by one or more of: a user terminal, the airborne or spaceborne transmitter, one or more of the airborne or spaceborne receivers, and a ground station.
  • method 200 may further comprise a step (not shown in Fig. 2) before step S240 of collecting (or aggregating), at the processing node, the time of transmission of the first radio signal at the airborne or spaceborne transmitter and the times of reception of the second radio signal at respective ones of the plurality of airborne or spaceborne receivers. It is understood that further information as needed at step S240 (e.g., information as described below) may be collected as well at the processing node.
  • Method 200 may further comprise an optional step (not shown in Fig. 2) of determining whether the mobile terminal is at an allowed position, based on the position determined or verified at step S240. If so, the user of the mobile terminal may be regarded as a legitimate user, otherwise, as a malicious or non-legitimate user. Limits of what is considered an allowable position may be determined by a service agreement between the user of the mobile terminal and a service provider, for example.
  • the airborne or spaceborne transmitter and the plurality of airborne or spaceborne receivers may be implemented, without intended limitation, by a plurality of satellite-based transceivers, for example.
  • the satellites holding the transceivers may be LEO satellites (e.g., LEO-PNT satellites), for example.
  • Fig. 3 schematically illustrates an example 300 of message composition and temporal sequence of message transmission for methods according to embodiments of the disclosure.
  • Time is shown on the horizontal axis.
  • the vertical axis shows the different transmitting or receiving entities as defined above.
  • at least some elements of message content and at least some interactions are optional in the sense that they are only required for certain optional features of the proposed methods.
  • boxes denote messages and arrows denote their transmission.
  • the mobile terminal 150 may determine Its position p UE based on one or more GNSS messages 195 transmitted by the GNSS satellites.
  • the airborne or spaceborne transmitter transmits the first radio signal 115, corresponding to the first message (downlink message) to the mobile terminal 150.
  • the first message includes the first identifier (unique downlink identifier) and can optionally further include the time of transmission t tx,S1 .
  • the mobile terminal 150 Prompted by the first radio signal, a time interval ⁇ t UE after reception of the first message, the mobile terminal 150 transmits the second radio signal 155, corresponding to the second message (uplink message), which is then received by the multiple airborne or spaceborne receivers 120 (or receivers for short) at respective times t rX,Sk,S1 , with index k indicating the respective receiver.
  • the second message includes the second identifier (unique uplink identifier).
  • the second message can further include any, some, or all of an indication of the time interval ⁇ t UE , an indication of a carrier frequency f tX,UE of the second radio signal 155, and the self-reported position of the mobile terminal 150 for example determined based on the one or more GNSS messages 195.
  • the receivers 120 then each send a downlink to ground station message 160 (or in general, downlink to processing node message) to the ground station 180 (or in general, to the processing node).
  • the downlink to ground station message 160 includes an identification of the respective receiver, a copy or digest (e.g., hash) of the uplink message, the time of transmission of the first radio signal 115 at the transmitter (unless this information is provided to the ground station 180 via alternative channels, for example directly by the transmitter 110), the time of reception t rX,Sk,S1 at the respective receiver 120, and optionally the frequency of the second radio signal f rx,sk,s1 measured at the respective receiver 120.
  • a copy or digest e.g., hash
  • the optional frequency measurements and message content of the second messages relating to the carrier frequency of the second radio signal may be used for joint time- frequency domain positioning.
  • step S230 of method 200 may comprise measuring, at respective ones of the plurality of airborne or spaceborne receivers, frequencies f rx,sk,s1 of the second radio signal upon arrival. Accordingly, determining or verifying the position of the mobile terminal at step S240 may then further be based on the frequencies f rx,sk,s1 of the second radio signal measured at respective ones of the plurality of airborne or spaceborne receivers 120. Additionally or alternatively, the second message transmitted at step S220 may include an indication of a frequency f tx,US of transmission (e.g., carrier frequency) of the second radio signal at the mobile terminal. Accordingly, determining or verifying the position of the mobile terminal at step S240 may be further based on the frequency of transmission f tX,UE of the second radio signal at the mobile terminal.
  • f tx,US e.g., carrier frequency
  • time-domain only positioning can be employed. This may require data from more receivers 120 (e.g., require more satellites).
  • the information may be further used for determining a (radial) velocity of the mobile terminal, for example based on a determined Doppler frequency shift.
  • elements and message content for self-reported (e.g., GNSS-based) position can be used for position validation.
  • the second message transmitted at step S220 of method 200 may include an indication of one or more components of the (self-reported) position of the mobile terminal. Accordingly, determining or verifying the position of the mobile terminal at step S240 may be further based on the one or more components of the position p UE of the mobile terminal.
  • the position of the mobile terminal may be determined ab initio (i.e. , from scratch), which may be computationally more expensive.
  • the second message transmitted at step S220 of method 200 may include an indication of the transmission delay (retransmission delay) ⁇ t UE between reception of the first radio signal and transmission of the second radio signal at the mobile terminal. Accordingly, determining or verifying the position of the mobile terminal at step S240 may be further based on the transmission delay.
  • This transmission delay ⁇ t UE may correspond to or include a processing delay at the mobile terminal.
  • the second message transmitted at step S220 of method 200 may include one or more parameters for assisting determination or verification of the position of the mobile terminal. These parameters may be said to include the aforementioned one or more components of the position p UE . of the mobile terminal and/or the transmission delay ⁇ t UE , but may also include additional information.
  • determining or verifying the position of the mobile terminal may be based on a cost function.
  • methods according to embodiments of the disclosure may further foresee determining such cost function.
  • the cost function may be for example based on the time of transmission t tx,S1 of the first radio signal at the airborne or spaceborne transmitter and the times of reception t rX,Sk,S1 of the second radio signal at the respective ones of the plurality of airborne or spaceborne receivers.
  • the cost function may be further based on one or more parameters for assisting determination or verification of the position of the mobile terminal. These may include, as described above, at least one of the transmission delay ⁇ t UE between reception of the first radio signal and transmission of the second radio signal at the mobile terminal, and one or more (e.g., all) components of the position p UE of the mobile terminal.
  • the cost function may be based on, in addition to the time of transmission t tx,S1 of the first radio signal at the airborne or spaceborne transmitter and the times of reception t rX,Sk,S1 of the second radio signal at the respective ones of the plurality of airborne or spaceborne receivers, the transmission delay ⁇ t UE at the mobile terminal and/or the self-reported position p UE of the mobile terminal.
  • the self-reported position may be GNSS-based, for example.
  • the distance based on the satellite and user positions can be compared to the measured two-way propagation time of the signal. This may be done using a cost function, as noted above.
  • the cost function in meters for each receiving satellite k may be given by where N denotes the number of airborne or spaceborne receivers, k - 1, N denotes a given one among the plurality of airborne or spaceborne receivers, p UE denotes the position of the mobile terminal, p sk denotes the position of the fc-th receiver (e.g., LEO satellite), p s1 denotes a position of the airborne or spaceborne transmitter, t tx,S1 denotes the transmission time at the transmitter (e.g., the one transmitting LEO satellite), t rX,Sk,S1 denotes the reception time at the fc-th receiver, and c is the speed of light.
  • N denotes the number of airborne or spaceborne receivers
  • k - 1 denotes a given one among the plurality of airborne or spaceborne receivers
  • p UE denotes the position of the mobile terminal
  • p sk denotes the position
  • the quantities p UE and ⁇ t UE represent the position of the user element and the time delay (retransmission delay) at the user element, respectively, and are to be validated if available (and otherwise, are to be determined, as described below). For example, if the mobile terminal (user element) provides its position p UE and delay ⁇ t UE , the root mean square (RMS) error using measurements from all N satellites can be computed as
  • the results for the RMS error can then be compared against a threshold
  • the user's reported position can be judged as validated, otherwise it is judged to be false.
  • the acceptable threshold may depend on application needs and/or user element and satellites capabilities.
  • the threshold may be a predetermined threshold.
  • verifying the position of the mobile terminal at step S240 of method 200 may involve comparing the cost function to a threshold.
  • the unknowns can be estimated by minimizing RMSE as
  • determining the position of the mobile terminal based on the cost function at step S240 of method 200 may involve minimizing the cost function to estimate the position of the mobile terminal. This may be done using least-squares techniques, for example. Further, determining the position of the mobile terminal using the cost function at step S240 may involve jointly determining a position of the mobile terminal and a transmission delay between reception of the first radio signal and transmission of the second radio signaI at the mobile terminal that minimize the cost function.
  • N 4 receivers (e.g., satellites) are required. More generally, N ⁇ N D + 1, where N D is the dimension of the space.
  • any information entering the cost functions defined throughout the present disclosure may be (jointly) determined by minimizing the error function, for example using least squares techniques. It is understood that the number N of independent receivers required for the task may then depend on the number of parameters that are to be jointly determined.
  • the cost function may be further based on the frequencies of the second radio signal measured at respective ones of the plurality of airborne or spaceborne receivers and/or the frequency of transmission of the second radio signal.
  • an additional contribution to the cost function in frequency domain may be defined that compares the Doppler frequency to the expected Doppler frequency based on the positions of satellites k and the mobile terminal (user element), and the (known) velocity v sk of the satellite k, with weighting factor w.
  • the weighting factor w (of unit [seconds]) is necessary for achieving the same units for contributions and to the cost function, and/or for adjusting the relative importance of each contribution in the overall cost function, depending on expected accuracies of (or confidence in) measurements entering the contributions, for example.
  • the weighting factor w may be given for example by to ensure that ⁇ F,k has the unit [meters]. This particular example of the weighting factor w may be said to scale the velocity error by the uplink signal propagation time.
  • N denotes the number of airborne or spaceborne receivers
  • k 1, ,.., N denotes a given one among the plurality of airborne or spaceborne receivers
  • p UE denotes the position of the mobile terminal
  • p sk denotes a position of the fc-th airborne or spaceborne receiver
  • p s1 denotes a position of the airborne or spaceborne transmittetr t
  • x,S1 denotes the time of transmission of the first radio signal at the airborne or spaceborne transmitter
  • t rX,Sk,S1 denotes the time of reception of the second radio signal at the fc-th airborne or spaceborne receiver
  • ⁇ t UE denotes the transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal
  • v s denotes the transmission delay between reception of the first radio signal and transmission of the second radio signal at the mobile terminal
  • v s denotes the transmission delay between reception of the
  • the frequency information is available, it is understood that it may be collected at the processing node along with the time information for determining or verifying the position of the mobile terminal.
  • the position validation or computation equations can be obtained by extending Eq. (3), (4) to the frequency domain as
  • Fig. 4 schematically illustrates an example of the structure of a downlink message (first message)
  • Fig. 5 schematically illustrates an example of the structure of an uplink message (second message.)
  • the downlink message (first message) transmits as core part a downlink identifier (DL ID; first identifier), together with the time of transmission t tx,S1 of the downlink message at the transmitter.
  • the downlink identifier may include a satellite number (e.g., “01”).
  • It may further include a (pseudo-)random, non-predictable bit sequence (e.g., “1a8fe”, “04c2”, “e804”, “d33a”) that is repeatedly updated at the transmitter.
  • the random bit sequence may be renewed after an expiration time t exp . That is, the random bit sequence may be updated periodically, at predefined time intervals, or at predefined timings. If the first radio signal is periodically transmitted, the (pseudo-)random bit sequence may be changed from one instance of the first radio signal to the next. In any case, the pseudo-random bit sequence may be updated such that it changes from one instance of the first radio signal to the next, to increase robustness of the system against spoofing.
  • a (pseudo-)random, non-predictable bit sequence e.g., “1a8fe”, “04c2”, “e804”, “d33a”
  • the random bit sequence may be renewed after an expiration time t
  • multiple satellites would downlink simultaneously.
  • the messages would be sent repeatedly either in a continuous or periodical mode, hence the random bit sequence to distinguish individual messages by the same satellites.
  • the non-predictability requirement serves the purpose of preventing delay attacks and other sophisticated spoofing attacks creating artificial messages.
  • method 200 described above may further comprise an optional step of, at the airborne or spaceborne transmitter, encrypting information bits representing the first identifier (downlink identifier).
  • the downlink message could contain additional information on flow control, uplink access, cryptography and/or other contents typical for a navigation message.
  • the uplink message contains as core element an uplink identifier (second identifier).
  • the uplink identifier may comprise a user number (e.g., “AA”), a copy of the downlink identifier (e.g., “2a8fe”), or any combination or hash thereof.
  • the purpose of the uplink message is the identification of the mobile terminal (e.g., user element) to the receiving satellites, the identification of the downlink satellite, and random sequence received by the UE.
  • the message may optionally be encrypted to preserve the privacy of the user and prevent identity theft.
  • method 200 described above may further comprise an optional step of, at the mobile terminal, encrypting information bits representing the second identifier.
  • frequency measurements could be used as an optional feature in addition to time domain measurements, to reduce the number of satellites required for position validation.
  • Time domain only measurements may be assumed to be default. The advantages of joint-time frequency positioning compared to this default are
  • the mobile terminal optionally can report its own position based on ME0- GNSS measurements and report the user delay ((re)transmission delay).
  • One advantage of reporting the GNSS position and the user delay is that the position can be validated by computing Eqs. (2) and (6) instead of solving the inverse problem of Eqs. (4) and (8) for computing the position from scratch. Additional implementation efforts and complexity may result from the increased time required for the GNSS fix and the higher number of bits in the uplink message to transmit the GNSS position. In some implementations, it might depend on the application or service offered to the user of the mobile terminal whether the mobile terminal should be required to report its GNSS position.
  • the constellation may include a first satellite comprising a transmitter as described above, i.e., a transmitter for transmitting a first radio signal to the mobile terminal for prompting the mobile terminal to transmit a second radio signal, wherein the first radio signal corresponds to a first message (downlink message) and the second radio signal corresponds to a second message (uplink message).
  • the constellation may further include a plurality of second satellites, each comprising a receiver for receiving the second radio signal.
  • the first and second satellites may be configured to perform respective functionalities described above, including in particular transmission of first and reception of second messages, respectively, as described above, and downlinking of the information required for position determination or verification to a processing node (e.g., ground station).
  • LEO-PNT constellation in LEO (Reference [15]).
  • the LEO-PNT constellation is envisioned to be deployed either as a dedicated constellation or hosted as secondary payload on another constellation in LEO.
  • the payload will embark an onboard GNSS receiver to obtain time and position from MEO GNSS signals using state of the art Precise On-board Orbit Determination (P2OD) algorithms achieving decimeter accuracy or better.
  • P2OD Precise On-board Orbit Determination
  • the Payload would further feature two-way links, thereby enabling methods according to embodiments of the disclosure.
  • the mean RMSE is defined as the average RMSE over all N rep runs of the simulation.
  • the mean RMSE over all runs is shown as a solid line in the diagrams discussed below, whereas the transparent region around it illustrates the 1 ⁇ confidence interval.
  • the RMS error should be zero assuming no noise and no modeling errors.
  • the two diagrams of Fig. 6 show the RMS distance for the time-only determination method (dark grey curve; upper curve) and the time-frequency determination method (light grey curve; lower curve).
  • the left diagram shows the RMS distance as a function of orbit height h Q
  • the right diagram shows the RMS distance as function of user masking angle UMA. 1 ⁇ regions are Indicated by shaded areas.
  • the mean RMSE is constant in orbit height and user masking angle for both methods.
  • the expected errors can be computed for the time domain method as since total variance is the sum of the individual variances and the stochastic noise applies twice because of the RTT measurement.
  • the variance of time domain measurements and the frequency measurements can be averaged as
  • the proposed method is further verified in Fig. 7, where the mean RMSE is shown as a function of the noise standard deviation ⁇ D .
  • the left diagram shows honest users, while the right diagram shows fraudulent users that manipulate their position.
  • the orbit height is set constant at 600km and the user masking angle at 20 degrees. Again, lo regions are indicated by shaded areas.
  • the mean RMSE of both methods follow the linear relation shown in Eqs. (9) and 10, respectively.
  • the results in the right diagram of Fig. 7 show the RMSE of a fraudulent user that reports a position 100m away from its true position, the direction of the offset is randomly generated from a uniform distribution of azimuth and elevation angles. It can be seen that fraudulent users lead to significantly higher RMSE values, which is expected and desired as it is intended to use this metric to detect fraudulent users. It should be noted that the fraudulent user only manipulates its position, however, it does not tamper with its reported user element processing delay and transmitted frequency in this simulation.
  • Fig. 8 shows the RMSE of the joint time-frequency method for honest users (dark grey curve; iower curve) and fraudulent users (light grey curve; upper curve) against orbit height in the left diagram and user masking angle in the right diagram, where lo regions are indicated by shaded areas.
  • ⁇ D 50m even the lo regions overlap.
  • Fig. 10 The probability distributions of the RMSE for honest and fraudulent users are shown in Fig. 10 for varying orbit height in the left diagram and varying user masking angle in the right diagram.
  • the distributions seem invariant to orbit height in line with Fig. 8, while the distribution curve of the fraudulent users widening with its mean shifting slightly to the right for increasing UMA. As speculated earlier, this is likely due to worse GDOP conditions.
  • RMSEs are Gaussian-distributed both for fraudulent and honest users.
  • the overlap of the PDFs is small, meaning it would allow detection of fraudulent users with good confidence for low ⁇ D .
  • Fig. 11 shows the probability distribution of the RMS distance error for varying error standard deviation ⁇ D using time-frequency linear method on honest and fraudulent user data.
  • noise standard deviations of 10m or lower one can with very high confidence detect fraudulent users.
  • ⁇ D gives the maximum allowed noise on time and frequency measurements. System accuracy requirements and subsequently hardware requirements can be derived from the maximum allowed noise.
  • the uplink capacity is a technical challenge not to the concept of the present disclosure per se, but rather to specific implementations, such as for example in a LEO-PNT satellite system that is aimed at supporting a large number of users. Furthermore, the challenge of uplink capacity and multiple access applies to all two-way satellite communication and navigation systems.
  • Appendix C a simple calculation is made to establish a rough order of magnitude for the number of instantaneous users that can be supported by a single satellite in the uplink, coming to the conclusion that with CDMA DS-SS between 27k - 500k instantaneous users could be supported.
  • two-way positioning adds the following security improvements:
  • the function of providing the position of a non-trusted user in a secure manner i.e. , employing two-way positioning with uplink to multiple satellites
  • space is not present in conventional technologies. Additional value can arise for example from atmospheric measurements (e.g., by radio occultation methods) as by-product of the two-way ranging.
  • the present disclosure provides techniques in the field of air-based or space-based (e.g., satellite- ased) positioning.
  • the present disclosure provides positioning methods and satellite constellations for positioning.
  • the present disclosure mitigates this vulnerability by employing two-way position validation. Its core aspects include a two-way message exchange procedure, the message composition, and content and the position computation algorithm in combination with exploitation of joint time- frequency for two-way satellite-based positioning of non-trusted users.
  • the proposed techniques overcome the weakness to several classes of meaconing, spoofing, and cyber-attacks of current GNSS-based asset tracking solutions.
  • the unique property of these techniques compared to legacy solutions is that the position of the asset is validated by the satellite constellation and therefore inherently trustable.
  • the present disclosure thereby offers increased robustness to added-delay attacks, uplink meaconing, user identity theft, and increases the cost of all classes of spoofing attacks using frequency information.
  • better user identification, privacy and secrecy can be achieved using spread-spectrum codes and message encryption and the option to encrypt the downlink ranging signal to avoid its use by unauthorized users.
  • the additional downlink required by techniques according to the present disclosure when embarked on a LEO-PNT system can be integrated into the navigation message of said system, thereby requiring only little additional effort for the downlink.
  • the present disclosure offers a satellite-validated position that is robust to spoofing attacks and not reliant on terrestrial infrastructure or the internet for communicating the position.
  • modules, units, or blocks described above may be implemented by a computer processor or respective computer processors, or the like. Modules, units or blocks described above may further be implemented in a cloud-based manner.
  • LEO satellites in LEO transmitting downlink signaling where said signaling includes: a
  • EEE 2 The method of EEE 1, wherein the uplink signal further includes the carrier frequency of said uplink signal; the LEO satellites of the constellation of satellites in LEO further measure the frequencies of arrival of the uplink signal; and the method further comprises determining the position of the user further based on said frequencies of arrival measured at the LEO satellites.
  • EEE 3 The method of EEE 1 or 2, wherein the uplink signal further includes the reported position of the user element determined based on signaling from a set of non-LEO navigation satellites; and the method further include determining the position of the user further based on said reported position of the user element.
  • EEE 4 The method of any one of EEE 1 to EEE 3, wherein the uplink signal further includes the time elapsed between receiving the signaling from the at least one LEO satellite and transmitting the uplink signal.
  • EEE 5 The method of any one of EEE 1 to EEE 4, wherein the method further comprises encryption of the uplink signal; and/or the unique identifier of the uplink signal comprises an identifier of the user element transmitting said signal and a unique identifier of the downlink signaling.
  • EEE 6 The method of any one of EEE 1 to EEE 5, wherein the downlink signaling by the at least one LEO satellite comprises at least one of: encryption of said downlink signal; the unique identifier including an identifier of said LEO satellite; and the unique identifier including a randomly generated bit sequence that is non-predictable by the user element or other outside parties; and wherein the downlink signaling is renewed after reaching a pre-defined expiration time.
  • EEE 7 The method of any one of EEE 1 to EEE 6, wherein the constellation of satellites in LEO is able to simultaneously service multiple users, employing at least one of: time division multiple access (TDMA); frequency division multiple access (FDMA); and code division multiple access (CDMA).
  • TDMA time division multiple access
  • FDMA frequency division multiple access
  • CDMA code division multiple access
  • PEW trusts “Use of Electronic Offender-Tracking Devices Expands Sharply - Number of monitored individuals more than doubled in 10 years," https://www.pewtrusts.org/en/research-and-analysis/issue-briefs/2017/03/use-of- electronic-offender-tracking-devices-expands-sharply, 7 September 2016. [Online].
  • This appendix contains the derivation of ranging equations in the time domain (Eq. (1)) and frequency domain (Eq. (5)).
  • f D,Sk is the Doppler frequency shift between satellite k and the user element
  • f tx,UE and f rx,sk,s1 are the frequency transmitted by the UE and the frequency received by the receiving satellite k, respectively.
  • the Doppler velocities f D,Sk can be expressed as a function of the positions and velocities as where v r,UE,Sk is the radial velocity between satellite k and user element.
  • Vector v sk is the relative velocity of the UE and satellite k. Equating Eq.
  • the satellites’ kinematics p sk , v sk and the measured frequencies f tX,UE and f rX,Sk,S1 are known, for example to the satellites.
  • the user position and transmit frequency need to be validated or computed.
  • the RMSE time domain cost function to be minimized can be also expressed as an L2 norm where To solve the optimization in Eq. (4), it is required to find the argument to minimize ⁇ T,rms(x) .
  • the optimal x minimizes not only the norm but also the norm squared as shown in Reference [21, p. 131]. This allows to formulate the equivalent problem of minimizing the norm squared as
  • a CDMA uplink scheme is proposed using Direct Sequence Spread Spectrum (DS-SS) techniques.
  • DS-SS Direct Sequence Spread Spectrum
  • the goal is to obtain a first estimate about how many users could be served simultaneously on a single satellite, following an approach from Goldsmith (Reference [22, pp. 424-436]).
  • K be the number of users in view of a single satellite and r b be the required bitrate per single user.
  • the required symbol rate per user and corresponding information bandwidth are then given by where M is the order of modulation.
  • the bandwidth of the chipped DS-SS signal is where T c is the chip time, i.e., the duration of one spreading signal code.
  • the processing gain or spreading factor of a DS-SS system is where is the symbol time.
  • bit error rate using BPSK modulation as function of the Signal to Noise Ratio (SNR) at the demodulation threshold is given by with Q(.) being the tail distribution function of the standard normal distribution.
  • SIR Signal to Interference Ratio
  • a synchronized system with orthogonal codes for example using Walsh-Hadamard codes, will have zero cross-correlation and thus no interference.

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Abstract

La présente demande concerne un procédé de positionnement basé sur l'air et/ou basé sur l'espace d'un terminal mobile pour déterminer ou vérifier une position du terminal mobile. Le procédé comprend les étapes suivantes : au niveau d'un émetteur aéroporté ou spatial, transmettre un premier signal radio au terminal mobile pour inviter le terminal mobile à transmettre un second signal radio, le premier signal radio correspondant à un premier message ; au niveau du terminal mobile, en réponse à la réception du premier signal radio, transmettre le second signal radio, le second signal radio correspondant à un second message ; recevoir le second signal radio au niveau d'une pluralité de récepteurs aériens ou spatiaux ; et déterminer ou vérifier la position du terminal mobile sur la base d'un temps de transmission du premier signal radio au niveau de l'émetteur et des temps de réception du second signal radio au niveau de récepteurs respectifs de la pluralité de récepteurs. L'invention concerne en outre une constellation de satellites pour le positionnement spatial d'un terminal mobile.
PCT/EP2023/071321 2022-08-01 2023-08-01 Procédés et appareil de positionnement d'un terminal mobile WO2024028342A1 (fr)

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