The following relates to methods, systems, and devices for positioning and timing using networks of beacon transmitters, which can provide combinations of high precision, resilience to co-channel interference, especially due to beacons transmitting on the same time and frequency channel, and security to jamming and spoofing attacks.
High-precision, low-latency positioning, navigation, and timing (PNT) will be critical to the success of next-generation outdoor systems for management and navigation of sUAS's and autonomous vehicles, and for next-generation indoor systems to enable the Industrial Internet of Things (IIoT) and meet the ±3 meter 80th percentile Z-axis requirement (under review for reduction to ±2 meters) mandated by the Federal Communications Commission (FCC) for in-building E911 handset calls. In the nascent commercial drone industry, detection and avoidance of collisions between Class-1 (commercial class) small unmanned aerial systems (sUAS's), and between sUAS's and other objects, is already an issue as the popularity of sUAS's grow. Solving these issues will become critical as commercial ventures, such as Amazon and Google roll out their drone delivery services, creating both a dramatic increase in the density of such vehicles, and the need for beyond-visual-line-of-sight (BVLOS) command and control (C2) procedures to navigate them to their destinations. For this reason, fast, accurate, and cross-airspace shared PNT will be a critical component of next-generation UAS traffic management (UTM) systems operating below and outside conventional air traffic management (ATM) systems, such as the UTM pilot project (UPP) under development by NASA. Given the low altitudes and radar cross-section of class-1 sUAS's, which make them difficult to detect and localize using conventional ATM radars, the UTM concept relies on position reports from the sUAS's themselves, either on a regular basis during sUAS operations, or at request from UTM service suppliers (USS's) monitoring those operations. As the number and density of sUAS's grows, the timeliness and precision requirements for this positioning information will also grow.
Current PNT concepts provide this positioning information using signals received from global satellite navigation systems (GNSS), e.g., the Global Positioning System (GPS) operated and maintained by the United States, enabled by GNSS chipsets on-board the UAS's. With few exceptions (for example, B. Agee, “Blind Detection, Demodulation, and Separation of Civil GNSS Signals,” in Proc. 2016ION Joint Navigation Conference, June 2016, and B. Agee, “Blind Civil GNSS Despreading for Resilient PNT Applications,” U.S. Pat. No. 10,775,510, issued September 2020), these systems rely on “correlative” or “matched filter” methods that detect the GNSS signals and estimate their geo-observables, e.g., their time-of-arrival (TOA) and frequency-of-arrival (FOA) observed at the receiver, by correlating the received signals against replicas of the transmitted ranging codes, and searching over trial TOA's that compensate for the time-of-flight from the satellite vehicles (SV's) to the receiver, and trial FOA's that compensate for the Doppler shift between the satellite and receiver. In “cold start” scenarios where the specific ranging codes for satellites within the probable field of view (FoV) of the receiver are unknown, and where the receiver's internal clock is not synchronized to universal time coordinates (UTC), this requires further correlating the received signal against the entire library of possible ranging codes, e.g., 31 ranging codes for the 31 GPS satellites currently in orbit, and estimating the observed TOA's and FOA's between those signals and each of those replica codes, i.e., the additional unknown timing and carrier offset induced during the reception operation. The time-to-first-fix (TTFF) required to accomplish this search can take over 30 seconds in absence of any prior information about the satellite codes and timing/carrier offset relative to the receiver (cold-start TTFF), and can take 1-to-2 seconds if code lock has been lost for several hours (warm-start TTFF) or for a short time (hot-start TTFF), and is hugely power consumptive over that time period. Moreover, a full positioning and timing (P/T) solution requires knowledge of the ephemeris (trajectory over time) of the SV's, e.g., using the GPS satellite almanac transmitted over the GPS navigation signal, which takes 12.5 minutes to download in its entirety. Even then, acquisition of at least four GPS signals is needed to provide an initial P/T solution.
In addition, GNSS ranging signals have inherent low received incident power (RIP), due to propagation from satellites in medium-Earth orbit (MEO), or (for the Indian Navic and Japanese QZSS systems) geo-synchronous orbit (GSO). For example, GPS L1 C/A signals are mandated to have an RIP of at least −130 dBm at the ground, i.e., −20 dB signal-to-noise ratio (SNR) over the 2.046 MHz null-to-null bandwidth of that signal, assuming a 4 dB rolled-up receiver noise figure. These signals are easily suppressed by 10-to-20 dB in practice, e.g., due to attenuation by trees, foliage, and building walls, and can be lost entirely in valleys and urban canyons. At RIP's below −150 dBm (SNR's below −40 dB), acquisition can fail completely, e.g., due to suppression of the GPS signal down to or below the noise floor, even after despreading the signal down to the 50 bit-per-second (bps) GPS navigation signal rate (˜43 dB processing gain), or due to “false lock” caused by nonzero (−24 dB) cross-correlation between the 1,023-chip C/A replica codes and actual codes received from the GPS SV's (for example, A. Brown, P. Olsen, “Urban/Indoor Navigation Using Network Assisted GPS,” in Proc. ION 61st Annual Meeting, pp. 1-6, June 2006). GNSS solutions are also vulnerable to systematic (or systemic?) errors due to ionospheric propagation, satellite positioning and timing errors, and (esp. for low altitude aircraft or in urban environments) specular multipath.
In re UTM applications, stable sub-meter altitude accuracy needed for GPS-based commercial aircraft landing systems, and expected to be required for accurate UAS traffic management, can require minutes to hours to achieve, even using the wide area augmentation system (WAAS) to improve positioning precision. In addition, sUAS receivers are especially vulnerable to co-channel interference (CCI), e.g., intentional jamming of sUAS platforms, or inadvertent jamming due to so-called “personal privacy devices (PPD's)”, due to the large FoV of sUAS's at even modest altitudes, and typical line-of-sight (LOS) propagation between the interferers and the sUAS's. All of these issues can cause critical lapses in positioning capability at low altitude and in dense deployment scenarios, where errors of a few feet can inordinately increase the risk of sUAS's colliding with each other, or with buildings, ground vehicles, or even people.
Lastly, it is recognized that GPS based systems have difficulty providing centimeter-level horizontal precision accuracy and 10 millisecond tracking capability needed for autonomous vehicles. For this reason, Verizon recently announced rollout of a nation-wide network of reference stations to enable real-time kinematics (RTK), a method for enhancing reliability of GPS signals by using carrier phase, in addition TOA and FOA, as a positioning geo-observable. As described in I. Miller, C. Cohen, R. Brumley, W. Bencze, B. Ledvina, T. Holmes, M. Psiaki, “Systems, Methods, Devices and Subassemblies for Rapid-Acquisition Access to High-Precision Position, Navigation and/or Timing Solutions,” U.S. Pat. No. 9,360,557, issued June 2016, RTK has long been used to provide precise point positioning (PPP) and timing measurements in surveying and high-accuracy timing applications; however, it requires both careful calibration of system phase offset at the GPS transmitters and the user receivers, e.g., induced by the mixer local-oscillators (LO's), cabling, and filtering modules in both devices; and a means for resolving the cycle ambiguity in the carrier phase geo-observable; hence the need for a reference network, to perform both the system calibration, and at least partially reduce cycle ambiguity. Moreover, LO phase noise induced at either end of the link can require rapid tracking of this system phase, and/or expensive LO's and/or ancillary receiver hardware to precisely control or calibrate and compensate that phase noise. For this reason, stand-alone RTK-enabled systems can take as long as 30 minutes to achieve precise solutions. Moreover, the approach is inherently vulnerable to time-varying multipath, e.g., Jakes Law multipath caused by vehicle motion in vicinity of near-field scatterers, which can affect stability of RTK-based solutions even when using precise reference systems. Currently available RTK systems, such as Swift Navigations' Skylark Cloud-based reference station and Starling positioning engine, claim RTK convergence in as little as 20 seconds, and reacquisition time of 1 second, however, they can only provide an 80% circular error probability (CEP80) of >10 centimeters, and only for fixed users (tracking capability has not been provided for either product).
In response to these issues, a number of alternative navigation (AltNav) solutions have been advanced over the years. These include Locata's “LocataLite” beaconing system, as described in J. Cheong, X. Wei, N. Politi, A. Dempster, C. Rizos, “Characterizing the Signal Structure of Locata's Pseudolite-Based Position System,” in Proc. 2009IGNSS Symposium, December 2009, and C. Rizos, L. Yang, “Background and Recent Advances in the Locata Terrestrial Positioning and Timing Technology,” Sensors 2019, 19(8), 1821, April 2019, and NextNav's Metropolitan Beacon System (MBS), described in F. Van Grass, S. Meiyappan, “Terrestrial GPS Augmentation with a Metropolitan Beacon System,” presented to National Space-Based Positioning, Navigation, and Timing Advisory Board, December 2014, and J. Vogedes, G. Pittabiraman, A. Raghupathy, A. Sendonaris, N. Shaw, M. Shekhar, Metropolitan Beacon System (MBS) ICD (an Implementation of a Terrestrial Beacon System), v. G1.0, April 2014, which has been incorporated into LTE Release 13, both of which employ DSSS ranging signals and correlative despreading methods at the receiver; Satelles' Iridium-based system, e.g., D. Whelan, G. Gutt, “Cells Obtaining Timing and Positioning by Using Satellite Systems with High Power Signals for Improved Building Penetration,” U.S. Pat. No. 9,213,103, issued Dec. 15, 2015, which exploits narrowband (˜25 kHz) signals transmitted from low-Earth orbiting (LEO) Iridium SV's; and systems exploiting “signals of opportunity” (SOP's), e.g., M. Rabinowitz, J. Spilker, S. Furman, D. Rubin, H. Samra, D. Burgess, G. Opshaug, J. Omura, “Positioning and Timing Transfer Using Television Synchronization Signals,” U.S. Pat. No. 8,233,091, issued Jul. 31, 2012, which exploit cellular and broadcast television signals transmitted from known positions with known time-synchronized signal components. These solutions address some, but not all of GNSS vulnerabilities, and possess weaknesses of their own. In particular, the pseudolite, LocataLite, and NextNav systems are highly vulnerable to “near-far” interference caused by extreme differences in pathloss between transmit nodes. Mitigation of this issue requires either excessive integration time to separate co-channel signals using correlative methods, or transmission of signals over widely separated frequency channels or time slots to avoid it entirely. NextNav's system, for example, separates signals into ten 100 ms time slots separated by 1 second in time, which requires continuous reception over 5-6 seconds for a cold-start TTFF and 1 second for a warm-start TTFF, and even then provides an initial median horizontal positioning accuracy (CEP50) of 30 meters in outdoor environments (Van Grass, slides 13) and 4 meters in optimized “local” environments, e.g., campuses, malls, and warehouse-like areas (Van Grass, slides 16). Similarly, although Locata has reported centimeter-level accuracy for its 10.23 Mcps ranging system (Rizos), that accuracy requires time-hopping its signal by a factor of 10 (Cheong), yielding the same TTFF as GPS systems.
Although Satelles' system can exploit the much higher RIP and Doppler shift afforded by Iridium's network of LEO SV's, the Iridium signal requires at least one 4.32 second (48-frame) superframe, and typically two-to-three superframes (8.64-12.96 seconds), to acquire and obtain satellite ephemeres from the Iridium Ring Channel. Moreover, the 25 kHz×GPS signal bandwidth provides an inherently poor TOA geo-observable estimate on a per-slot basis, requiring many minutes to provide <100 ns timing synchronization, e.g., as SV's come into the receivers' FoV.
Other solutions use Bluetooth Low Energy (BLE) beacons, LTE position reference signals (PRS's), and 802.11-based positioning systems. None of these systems can provide the accuracy and latency required for next-generation 5GNR systems, e.g., 3 meter XYZ location accuracy, <1 second TTFF and 20 ms latency, and 0.5 meter/second XYZ velocity accuracy. Nor can they meet the FCC's 2024 goal of ±3 meter 80% Z-Axis handset positioning accuracy for E911 applications.
Aspects of the disclosure can overcome these issues, using resilient distributed positioning networks (RDPN), in which multiple network-provisioned co-channel navigation beacons are transmitted from a network of nodes (e.g., network nodes) to users on a common frequency channel; network-provisioned co-channel beacons are transmitted from users and received at network nodes; or navigation beacons transmitted from network notes, transponded through users, and received by network nodes. The disclosure describes aspects and features that overcome vulnerabilities of existing PNT systems. These aspects and features include (but are not limited to) the following:
The disclosed RDPN aspects can be implemented in at least three network topologies:
This approach can provide a number of benefits not shared by any competing GNSS or non-GNSS method, including (but not limited to) any of the following:
A first aspect relates to a method for transmitting beacon signals from network nodes to network users, transmitting beacon signals from the network users to the network nodes, and/or transponding beacon signals to and from the network nodes through the network users using bent-pipe transponders. The method comprises inducing at least one of spectral redundancy and temporal redundancy in the beacon signals; and exploiting the at least one of spectral redundancy and temporal redundancy to separate received beacon signals at the network users, the network nodes, or a central processing site.
The method of the first aspect may further comprise determining geo-observables from separated beacon transmissions. The method may further comprise determining positioning and/or timing from the geo-observables. The beacon signals may be separated with precision dictated by the power of the beacon signals above a receiver noise floor, and irrespective of other beacon signals received at the same time and frequency.
A second aspect relates to a method for transmitting beacon signals from network nodes to network users, transmitting beacon signals from the network users to the network nodes, or transponding beacon signals to and from the network nodes through the network users using bent-pipe transponders. The method comprises inducing at least one of spectral redundancy and temporal redundancy in each of the beacon signals, thereby enabling a receiver to exploit the at least one of spectral redundancy and temporal redundancy to separate multiples ones of the beacon signals in a snapshot of received signals.
A third aspect relates to a method, comprising generating a snapshot of a received plurality of beacon transmissions, each of the plurality of beacon transmissions having at least one of spectral redundancy and temporal redundancy; and exploiting the at least one of spectral redundancy and temporal redundancy to separate multiples ones of the beacon transmissions in the snapshot.
In the third aspect, the generating and the exploiting may be performed at a network user or a network node. The generating may be performed at the network user and the exploiting may be performed at a NOC. The generating may be performed at the network node and the exploiting may be performed at the NOC. The generating may be performed at the network user and the exploiting may be performed at the network node.
In a fourth aspect, a method comprises receiving a snapshot of a received plurality of beacon transmissions, each of the plurality of beacon transmissions having at least one of spectral redundancy and temporal redundancy; and exploiting the at least one of spectral redundancy and temporal redundancy to separate multiples ones of the beacon transmissions in the snapshot.
A NOC may be configured to perform the method of the third aspect, wherein the snapshot is generated by a network user and received by the NOC via a wireless network; or wherein the snapshot is generated by a network node and received by the NOC via a backhaul network.
A fifth aspect relates to a method, comprising receiving a plurality of beacon transmissions to produce a received signal, each of the plurality of beacon transmissions having at least one of spectral redundancy and temporal redundancy; and generating a snapshot of the received signal, wherein the snapshot retains the at least one of spectral redundancy and temporal redundancy; and wherein the at least one of spectral redundancy and temporal redundancy is exploitable for separating the plurality of beacon transmissions. A network user or a network node may be configured to perform the method of the fifth aspect.
A sixth aspect relates to a method comprising synthesizing multitone beacon signals, wherein subcarrier spacing and symbol duration of the multitone beacon signals are selected according to an expected range of time-of-arrival and frequency-of-arrival for network users; inducing at least one of spectral or temporal redundancy on the multitone beacon signals; and transmitting the multitone beacon signals to the network users.
A seventh aspect relates to a method comprising receiving multiple multitone beacon signals; and exploiting spectral redundancy in the multiple multitone beacon signals to use code nulling or Class-C linear minimum-mean-square error methods to separate the multiple multitone beacon signals.
Some aspects relate to an apparatus, comprising at least one processor and at least one memory in electronic communication with the at least one processor, and instructions stored in the at least one memory. The instructions executable by the at least one processor may perform the method of any of the above aspects.
Some aspects relate to a computer program product, comprising a computer readable hardware storage device (such as a non-transitory computer-readable memory) having computer-readable program code stored therein, wherein the program code contains instructions executable by one or more processors of a computer system for performing any of the methods of the above aspects.
Some aspects relate to an apparatus comprising a means for performing each step in any of the methods of the above aspects.
An eight aspect relates to an apparatus, comprising a means for transmitting beacon signals from network nodes to network users, a means for transmitting beacon signals from the network users to the network nodes, and/or a means for transponding beacon signals to and from the network nodes through the network users using bent-pipe transponders. The apparatus further includes a means for inducing at least one of spectral redundancy and temporal redundancy in beacon transmissions; and a means for exploiting the at least one of spectral redundancy and temporal redundancy to separate received beacon transmissions at the network users, the network nodes, or a central processing site. The apparatus may further comprise a means for determining geo-observables from separated beacon transmissions, and a means for determining positioning and/or timing from the geo-observables.
The means for transmitting beacon signals from network nodes to network users can include geographically distributed network nodes at calibrated locations, which can be communicatively coupled to a means for central processing. The means for transmitting beacon signals may include an RDPN or an RDTN. Exemplary network nodes include fixed outdoor transmitters co-located with cellular transmission towers or 802.11 access points; indoor transmitters coexisting with 802.11 WLAN or 802.15 Bluetooth or Zigbee networks; or standalone transmitters. The means for central processing can include a NOC, e.g., a 5GNR MEC or a USS, which provisions each of the network nodes with configuration data or time symbols over a means for communicating data between the network nodes and the means for central processing. The means for communicating data can include an Ethernet-based network, a PLC network, an 802.11 WLAN, an 802.15 Zigbee or Bluetooth network, and/or a 3G, 4G LTE, or 5G cellular network. The means for transmitting beacon signals can include computer processors and computer-readable memory that programs the processors to generate and/or transmit the beacon signals.
The means for transmitting beacon signals from the network users to the network nodes can comprise a wireless communications apparatus onboard a user device configured to receive navigation signals or beacon configuration information from the means for central processing over an ancillary wireless communication link, and transmit beacon signals in the FoV of network nodes configured to receive the beacon signals. Furthermore, the means for transmitting beacon signals can comprise means for generating the beacons signals. The means for transmitting beacon signals can include computer processors and computer-readable memory that programs the processors to generate and/or transmit the beacon signals.
The means for transponding beacon signals can comprise wireless communication transceivers that receive, condition, and retransmit the beacon signals without otherwise processing them. Network receivers (e.g., network nodes) in the FoV of the users then capture and backhaul snapshots of those retransmitted to the means for central processing, which can compute a P/T solution from the snapshots, and transmit the solution to the users over the ancillary wireless communication link. Thus, the means for transponding beacon signals can further comprise a wireless receiver for the ancillary wireless communication link. The means for transponding beacon signals can include computer processors and computer-readable memory that programs the processors to receive and transmit the beacon signals, and optionally, to receive the P/T solution. The means for transponding beacon signals may comprise an RDXN.
The means for inducing can include a modulator configured to perform subcarrier spreading modulation, such as SCSS modulation. In one example, an inner code is replicated over multiple clusters, each of which is modulated by one element of an outer code. Spectral redundancy can be achieved by spreading a narrowband signal with a wideband signal. The means for inducing can include a modulator configured to repeat a time symbol. Time symbols may be organized in slots, with multiple repetitions per slot. The means for inducing may include a computer processor and computer-readable memory that programs the processor to perform the spreading and/or repetition of symbols. A software-defined radio is one example of such a processor. The means for inducing may comprise a multitone modulator, which can employ a DFT, IDFT, FFT, IFFT, polyphase filter, and/or a discrete filter bank.
The means for exploiting can comprise any apparatus or computer program product having instructions that implement a resilient detection operation for excising CCI in a snapshot. The means for exploiting can comprise a subcarrier demodulator that eliminates inter-symbol interference and inter-subcarrier interference. The means for exploiting can perform code nulling or Class-C linear minimum-mean-square error (LMMSE) operations to separate co-channel received beacon signals with quality limited only by the received SNR of those signals, rather than the received SIR of those signals. The means for exploiting can further include spatial/polarization diverse antenna arrays at their transmitters or receivers, which allow for copy-aided DF methods to determine the DOA of the beacon signals, and copy-enhanced DF methods to determine the DOA of jammers. The means for exploiting may further comprise a means for channelizing.
The means for channelizing can comprise a DFT, such as a sparse DFT, a windowed DFT, or a combination thereof. Equivalent structure, such as filters configured for snapshot channelization, may be used. The means for channelizing can comprise any apparatus or computer program product having instructions that channelize a snapshot. In one aspect, the means for channelizing removes an estimated coarse (cold-start) or fine (warm/hot start) observed LO offset, and removes timing offset, if necessary. The means for channelizing may separate the snapshot into frequency subcarriers and time symbols using a windowed DFT.
A ninth aspect relates to an apparatus, comprising a means for generating a snapshot of a received plurality of beacon transmissions, each of the plurality of beacon transmissions having at least one of spectral redundancy and temporal redundancy; and means for exploiting the at least one of spectral redundancy and temporal redundancy to separate multiples ones of the beacon transmissions in the snapshot.
The means for generating the snapshot can comprise any apparatus or computer program product having instructions that, when directed to, collects a snapshot, e.g., based on prompts from the means for central processing, or at scheduled snapshot collection times. The means for generating can include a receiver front-end configured to receive beacon signals, a frequency down-converter, and an ADC, as well as other radio components. The means for generating may comprise an SDR.
A tenth aspect relates to an apparatus, comprising a means for receiving a snapshot of a received plurality of beacon transmissions, each of the plurality of beacon transmissions having at least one of spectral redundancy and temporal redundancy; and means for exploiting the at least one of spectral redundancy and temporal redundancy to separate multiples ones of the beacon transmissions in the snapshot.
The means for receiving the snapshot can comprise an ancillary wireless communication receiver configured to receive snapshots transmitted by network users on the ancillary wireless communication link. The ancillary wireless communication receiver may be an 802.11 WLAN, 802.15 Zigbee, Bluetooth, 3G, 4G LTE, or 5G cellular receiver. The means for receiving the snapshot can comprise a receiver coupled to a beacon communication bus, which connects the NOC with the network nodes, and the receiver may be an Ethernet, PLC, optical fiber, 802.11 WLAN, 802.15 Zigbee, Bluetooth, 3G, 4G LTE, or 5G cellular receiver.
An eleventh aspect relates to an apparatus, comprising a means for receiving a plurality of beacon transmissions to produce a received signal, each of the plurality of beacon transmissions having at least one of spectral redundancy and temporal redundancy; and means for generating a snapshot of the received signal, wherein the snapshot retains the at least one of spectral redundancy and temporal redundancy; and wherein the at least one of spectral redundancy and temporal redundancy is exploitable for separating the plurality of beacon transmissions.
The means for receiving the plurality of beacon transmissions can comprise a receiver front-end of a radio configured to receive transmitted beacon signals. The means for receiving can include a frequency down-converter and an ADC, as well as other radio components. In some aspects, the means for receiving comprises an SDR. The means for receiving may comprise a network user's beacon receiver configured to receive beacon transmissions, such as beacon signals transmitted from network nodes. The means for receiving may comprise network nodes configured to receive beacon transmissions from network users. The means for receiving may comprise network nodes in an RDRN and/or network users in an RDTN or an RDXN.
A twelfth aspect relates to an apparatus, comprising a means for synthesizing multitone beacon signals, wherein subcarrier spacing and symbol duration of the multitone beacon signals are selected according to an expected range of time-of-arrival and frequency-of-arrival for network users; means for inducing at least one of spectral or temporal redundancy on the multitone beacon signals; and means for transmitting the multitone beacon signals to the network users.
The means for synthesizing the multitone beacon signals can include a multitone modulator, which can employ a DFT, IDFT, FFT, IFFT, polyphase filter, and/or a discrete filter bank. The means for synthesizing may include at least one processor and at least one memory in electronic communication with the at least one processor, and instructions stored in the at least one memory to perform multitone signal generation. A software-defined radio is one example of such a processor.
A thirteenth aspect relates to an apparatus, comprising a means for receiving multiple multitone beacon signals; and a means for exploiting spectral redundancy in the multiple multitone beacon signals to use code nulling or Class-C linear minimum-mean-square error methods to separate the multiple multitone beacon signals.
The means for receiving multiple multitone beacon signals can include a multitone demodulator, which can employ a DFT, IDFT, FFT, IFFT, polyphase filter, and/or a discrete filter bank. The means for receiving may include at least one processor and at least one memory in electronic communication with the at least one processor, and instructions stored in the at least one memory to perform multitone demodulation. A software-defined radio is one example of such a processor.
A fourteenth aspect relates to an apparatus, comprising a means for transmitting beacon signals from network nodes to network users, a means for transmitting beacon signals from the network users to the network nodes, and/or a means for transponding beacon signals to and from the network nodes through the network users using bent-pipe transponders. The apparatus further includes a means for inducing at least one of spectral redundancy and temporal redundancy in the beacon signals, thereby enabling a receiver to exploit the at least one of spectral redundancy and temporal redundancy to separate multiples ones of the beacon signals in a snapshot of received signals.
The foregoing has outlined rather broadly the features and technical advantages of examples according to the disclosure in order that the detailed description that follows may be better understood. Additional features and advantages will be described hereinafter. The conception and specific examples disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. Such equivalent constructions do not depart from the scope of the appended claims. Characteristics of the concepts disclosed herein, both their organization and method of operation, together with associated advantages will be better understood from the following description when considered in connection with the accompanying figures. Each of the figures is provided for the purpose of illustration and description only, and not as a definition of the limits of the claims. All patent publications and non-patent publications mentioned in this disclosure are hereby incorporated by reference in their entireties.
A further understanding of the nature and advantages of the present disclosure may be realized by reference to the following drawings. In the appended figures, similar components or features may have the same reference label.
The detailed description set forth below in connection with the appended drawings is intended as a description of various configurations and is not intended to represent the configurations in which the concepts described herein may be practiced. The detailed description includes specific details for the purposes of providing a thorough understanding of various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In some instances, well-known structures and components are shown in block diagram form in order to avoid obscuring such concepts.
Exemplary Class-1 sUAS Deployment Scenarios
As these FIGS. show, the link TOA's are restricted to 3-229 μs in the LMS Scenario, and between 4-232 μs in the 2.4 GHz Ch. 13 Scenario, much lower than the 67-94 ms TOA range expected for GNSS signals transmitted from MEO. Similarly, the link FOA's range are restricted to ±135 Hz in the LMS Scenario and ±369 Hz in the 2.4 GHz Ch. 13 Scenario, much lower than the ±6 kHz FOA range expected for L-band GNSS signals transmitted from MEO. This is an exploitable feature of the RDPN for both scenarios. At the same, the RIP of the beacons range from −88 dBm to −40 dBm in the LMS Scenario, and from −105 dBm to −64 dBm in the 2.4 GHz Ch. 13 Scenario, much stronger than the nominal −130 dBm GPS L1 signal strength at the Earth surface. While this is also a clear advantage for any beacon-based positioning solution, it also shows that the beacons will likely be received at positive SNR and with significant near-far interference. That is, the performance of conventional “matched filter” receivers that correlate the received signal against replicas of the transmitted beacons will be limited by the interference observed relative to each beacon, despite their high receive SNR, due to self-interference between those received beacons.
This observation is borne out in
As these FIGS. show, the ADC output SINR ranges between −46 dB and +25 dB in the LMS Scenario, and between −39 dB and +8 dB in the 2.4 GHz Ch. 13 Scenario. In fact, while all of the links are above 0 dB SNR in the LMS Scenario, only 3.5% of the links are above a 0 dB SINR, and less than 18% of the links are above a −10 dB SINR. Similarly, 82% of the links are above 0 dB SNR in the 2.4 GHz Ch. 13 Scenario, but only 1.2% of the links are above 0 dB SINR, and 10% of the links are above a −10 dB SINR. Hence, the received beacons are clearly in an interference-limited environment. This is the reason that competing systems introduce time hopping and time slotting into their beacon transmitters—in order to avoid such interference.
These results motivate the use of beacons that can both exploit the much tighter range of TOA and FOA obtaining in a ground-to-low-altitude reception geometry, and allow the use of interference excision methods that can separate the received beacons with performance gated by their (high) receive SNR, rather than their (low) receive SINR.
),c1
, where the code indices 101 point to code libraries 102 containing inner and outer code vectors {θ(c0)}c
In one aspect, the phase vectors contained in the code libraries 102 are designed to yield library codebook signal
with low peak-to-average power ratio (PAPR), and low cross-correlation between other library codebook signals. The code libraries 102 can be designed to satisfy other system requirements as well.
The time symbol generator then performs an inner subcarrier construction operation 103 to generate K0×1 inner subcarrier vector 104=[
(k0)]k
=[
(k1)]k
Other aspects apply non-uniform amplitude weightings to either or both vectors, for example, to further reduce PAPR of the transmitted beacon, reduce interference to non-beacon networks caused by beacons in selected portions of the beacon transmission band, or reduce susceptibility to non-beacon interference at network receivers operating in the beacon transmission band.
The inner subcarrier vector 104 and outer subcarrier vector 106 are then combined 107 to form Ksub×1 full subcarrier vector 108=[
(ksub)]k
=
⊗
. In other aspects, this may be a more complex combining operation, for example, to improve robustness to LO frequency uncertainty at the transmitter or receiver, reduce interference to non-beacon networks caused by beacons in selected portions of the beacon transmission band, or reduce susceptibility to non-beacon interference at network receivers operating in the beacon transmission band.
The full subcarrier vector 108 is then passed through an optional subcarrier preemphasis 106 operation to generate preemphasized subcarrier vector =
, where “∘” denotes the element-wise (Shur or Hadamard) product operation, and
is a Ksub×1 preemphasis vector 110 that compensates for front-end digital-to-analog conversion (DAC), antialiasing lowpass filtering (LPF), and upconversion operations performed at network node 401
. The preemphasis vector 110 can be designed using analytic models for beacon transmission operations 213; or using calibration data obtained at each network node 401, for example, as described in G. Pattabiraman, S. Melyappan, A. Raghupathy, H. Sankar, “Wide Area Positioning System,”
U.S. Pat. No. 8,130,141, issued March 2012, and can be based on the magnitude or complex value of those beacon transmission operations 213.
The preemphasized subcarriers are then passed to a multitone modulator 111 that transforms the subcarriers to the time domain, and is optionally quantized 112, to provide an NDAC×1 time symbol vector 113=[
(nDAC)]n
Each time symbol vector 113 is then passed from the NOC 403 to the beacon transmitter over a beacon communication bus 114. Exemplary communication networks supporting a beacon communication bus 114 can include Ethernet-based networks, optical networks, power-line communication (PLC) networks, 802.11 WLAN's, 802.15 Zigbee or Bluetooth networks, or 3G, 4G LTE, or 5G cellular networks. In the networks shown in
and placed in local storage 212. For the networks shown in
The operations used to perform the beacon transmission operations 213 are analogous to an arbitrary waveform generator (AWG). In the aspect shown in
Typically, the DAC and LO employed in the beacon transmission operations 213 are locked to a system clock 214, which in general, has a clock rate and timing that is offset from a common time standard, e.g., UTC. As shown in is offset from UTC by rate offset
and timing offset
=
−tUTC(
), where
is the internal clock time at UTC time tUTC(
). In some aspects, the system clock 214 is synchronized to an external time and frequency standard using an external source, e.g., a GNSS receiver (Rx) 215. In some aspects, the system clock 214 is brought into a common time standard using network calibration methods computed at the NOC 403, e.g., by providing the system clock 214 with clock synchronization data 215, e.g., timing and rate offset estimates
and
. In the network shown in
In some aspects consistent with the networks shown in
For an exemplary subcarrier frequency layout assumed here, generated by the multitone modulator 107 then has complex baseband representation
at the PA input in the beacon transmission operations 213, where the subcarrier frequencies are given by
and where fsym=1/Tsym is the subcarrier spacing. Assuming the internal subcarrier structure shown here, then (t)=
(t)
, where
and where inner and outer subcarrier frequencies f0(k0) and f1(k1) are given by
respectively, such that Ksub=K0K1, f(K0k1+k0)=f0(k0)+f1(k1) and (K0k1+k0)=
(k0)=
(k1).
This beacon can be interpreted as a stacked-carrier spread spectrum (SCSS) signal, in which a narrowband signal (t) with bandwidth K0fsym and period 2(K
(t) with bandwidth Ksubfsym and period 2(K
over K1 independent clusters), and within clusters (replication of outer code
over K0 subcarriers within each cluster).
Exemplary Class-1 sUAS Compatible Beacon Generation and Transmission Parameters
Table 1 lists exemplary beacon generation and transmission parameters compatible with TOA and FOA ranges expected for Class-1 sUAS's, and for network geometries shown in
Assuming 12 bits per in-phase (I) and quadrature (Q) rail at the output of the quantizer 108, a single time symbol vector 113 requires transmission of 2,880 bytes (2.8125 KB) over the beacon communication bus 114 for the LMS Scenario, and 28.125 KB for the 2.4 GHz Ch. 13 Scenario. Assuming the time symbol vectors 113 are updated once per second, the NOC 403 requires the beacon communication bus 114 to support a 23.04 kbps link for the LMS scenario, and a 230.4 kbps link for the 2.4 GHz Ch. 13 Scenario. These rates are achievable in low-cost networks.
When needed at scheduled intervals, or given prompts from the NOC 403 over a wireless communication transceiver 402, the receiver system then performs a data snapshot collection 301 operation, which generates a snapshot 302 comprising the data provided by the reception operations 300 at a reception time and over a snapshot 302 time duration, shown in
In general, the receiver LO(s) and ADC samplers used in the reception operation 300 are locked to a system clock 214 with rate offset εR and timing offset τRref=tRref−tUTC(tRref), unique for each receiver, where tRref is the receiver time estimate at UTC time tUTC(tRref).
In some aspects of the disclosure, the NOC 403 also provides synchronization data 216 that can be used to bring the receiver system clock 214 into synchronization for subsequent time-stamped snapshots 302. In other aspects, the receiver obtains coarse synchronization information from the NOC 403 over a wireless communication transceiver 402. In additional aspects of the disclosure, the receiver performs coarse synchronization operations to determine the approximate center frequency and (for slotted beacon formats) slot transition time of the beacons, prior to the snapshot collection 301. The coarse frequency and timing information can then be used to adjust the timing carrier offset of the ADC output signal, or the receiver clock driving the LO and ADC; or simply conveyed to the NOC 403, along with time-stamped snapshot 302. In this last case, the frequency and timing offset is included in the time-stamped snapshot 302, for use by the P/T solution generator 303. The receiver may stream data to the P/T solution generator 303 (which may be remote or on the receiver platform itself), or may sparsely capture time-stamped snapshot 302 of frequency-and-timing aligned data, e.g., at the start of processing or as required/requested by the NOC 403.
The snapshot 303 is then frequency-shifted to remove the estimated FOA centroid 612, and if needed time-shifted to remove the estimated timing offset, and channelized into subcarriers and time symbols covering the active snapshot bandwidth and duration 502, creating a channelized snapshot 553, described in
The whitened snapshot matrix 604 is then passed through an FFT/IFFT mechanized resilient least-square (LS) search operation 507 to form a least-squares (LS) TOA-FOA surface 613, described in
The DoF and data dimensions, and the data dimension codes 506 and DoF dimension codes 509 are set based on the particular form of redundancy exploited in the FFT/IFFT mechanized resilient least-square (LS) search operation 507, as determined by the stacking operation performed in the data stacking and whitening operation 503. For example, in one aspect where the channelized snapshot is stacked over the inner-code dimension, data dimension Ndata=K1Nsym, and the data dimension codes 506 are the K1×1 outer subcarrier vector 106 phases ; and DoF dimension MDoF=K0 and the DoF dimension codes 509 are the K0×1 inner subcarrier vector 104 phases
. In a second aspect where the channelized snapshot is stacked over the outer-code dimension, data dimension Ndata=K0Nsym, and the data dimension codes 506 are the K0×1 inner subcarrier vector 104 phase
; and DoF dimension MDoF=K1 and the DoF dimension codes 509 are the K1×1 outer subcarrier vector 106 phases
.
The key components of this procedure are described in more detail in the next subsections.
The snapshot 303 is then separated into frequency subcarriers and time symbols 551 using a sparse, overlapped, optionally frequency-offset, windowed DFT with overlap time Tsym NADCTADC, sparsity factor Qsym, DFT length NDFT=QsymNADC, and channelizer window {wR(mADC)}m
where Nsym=Nrep−Qsym+1 is the number of time symbols in the channelized snapshot and
is the symbol nsym DFT time-center in the receiver's field of reference, and where GR(ksub,nsym;{circumflex over (α)}R) are snapshot channelizer equalizer 552 weights that remove effects caused by at least the carrier operation 552, and optionally filtering effects of the reception operations 300. Preferentially, the snapshot equalizer 552 weights are given by
where HR(f) is the aggregate frequency response of the reception operations 300, and where δR(ksub,nsym;{circumflex over (α)}R) removes dispersive effects of the FOA centroid 612 removal operation 502,
The aggregate frequency response term is optional, and can be based on modeling of the reception operations 300; or derived from calibration operations performed by the receiver or network, for example, as described in Pattabiraman 2012, and can be based on the magnitude or complex value of those reception operations 300.
Table 2 lists receiver and channelizer parameters compatible with the beacon generation and transmission parameters shown in Table 1. The receiver assumes a dual-ADC sampling rate of 3.84 million samples per second (Msps) for the LMS Scenario, and 30.72 Msps for the 2.4 GHz Ch. 13 Scenario, with sufficient antialiasing filtering to provide a 2 MHz and 20 MHz protected two-way passband, respectively, covering the active bandwidth of the beacons with ±40 kHz and ±400 kHz of guard band for LO uncertainty, respectively. A mixed-radix DFT with factor-of-four sparsity (Qsym=4) is assumed in both scenarios, and a separation of 250 μs between successive DFT's. The Table further assumes a 10 millisecond snapshot encompassing 16 symbol repetitions, 13 of which are used in subsequent geo-observable estimation operations, for both scenarios.
Assuming dual-ADC precision of 12 bits per I and Q rail, consistent with a low-cost receiver front-end, the size of each snapshot is 112.5 KB for the LMS Scenario, and 900 KB for the 2.4 GHz Ch. 13 Scenario. Assuming a snapshot is collected 303 once per second, backhaul 303 of ADC output data to the P/T solution generator requires a snapshot communication bus 304 that can support a 0.922 Mbps one-way data-rate for the LMS Scenario, and a 7.37 Mbps one-way data-rate for the 2.4 GHz Ch. 13 Scenario, well within capabilities of 4G cellular or 802.11 WLAN standards if the P/T solution generator 303 is in the NOC 403. Continuous backhaul of snapshots 302 to the P/T solution generator 303 over the snapshot communication bus 304 would require a factor of 100 higher data-rate, e.g., 92.2 Mbps and 737 Mbps, respectively, for the two scenarios, easily accomplished over Gbps Ethernet if the P/T solution generator 303 is on-board the user 400.
The FOA centroid 612 and optional timing estimate removal and channelization operations 502 can be performed in a number of different manners, for example, using polyphase filtering methods, discrete filter banks centered on each subcarrier frequency, mixtures of radix-2 and non-radix-2 fast Fourier transform (FFT) and inverse-FFT methods, and so on.
Assuming synchronized beacon transmitters in the network shown in (tUTC)≡tUTC and defining tUTCref
tUTC(tRref) as the actual UTC time (to be estimated in positioning/timing algorithms) at receiver reference time tRref, and further assuming short snapshots 302 are collected 301, then the channel link gain between the beacon transmitter deployed at network node 401
and a receiver deployed at a user 400 is approximated by
(tUTC)≈
(rUTCref), and the TOA and FOA of the beacon received at that user 400 is approximated by
are the TOA and differential TOA (DTOA) of beacon at time tUTCref, and where
(tUTC)=
−pR(tUTC) is the observed position of network node 401
at the user 400, and
(tUTC)=
(tUTC)/∥
(tUTC)∥2 is the observed line-of-bearing (LOB) from the user 400 to network node 401
. The TOA, DTOA, and FOA observed at the ADC sampler in the user 400 reception operations 300 are then given by
Further assuming accurate equalization of user 400 reception operations 300, and ideal suppression of inter-subcarrier interference by the channelizer window used in the FOA centroid 612 and optional timing estimate removal and channelization operations 502, channelized snapshot 553 xsub(ksub,nsym) is approximated by
where αsub() is the end-to-end beacon
channelizer output gain,
and where dsub(ksub,nsym;τ,α;) is the network node 401
beacon (“beacon
”) at candidate observed TOA τ and observed FOA α,
is the analytic discrete Fourier transform of the channelizer window. Assuming additive white Gaussian noise (AWGN) with noise density N0 at the LPF input and ideal LPF equalization, the background interference isub(ksub,nsym) has identical power Ri has identical SNR
≈|asub(
)|2/Ri
Using the channelized snapshot 553 model given in (Eq16)-(Eq20), the observed geo-observables {{tilde over (τ)}T()R(tRref),
(tRref)}
can in principle be estimated by correlating channelized snapshot 553 xsub(ksub,nsym) against {dsub(ksub,nsym;
)
. Moreover, if
then the second dispersive term in (Eq20) can be ignored, and this correlation can be efficiently mechanized using DFT and inverse-DFT (IDFT) methods. However, at high receive SNR this correlation will yield a poor result, or will require a high time-bandwidth product NsymKsub to remove cross-correlation between co-channel beacons. This problem can be overcome by exploiting the spectral or temporal redundancy imposed in this signal at the transmitter, to implement resilient TOA-FOA estimators. This procedure is described below.
K1−1 and Nsym time symbol indices nsym=0,
Nsym−1. Using (Eq16)-(Eq20), this signal can be modeled as
are the K0×1 inner-code stacked beacon signal vectors, respectively,
and where a0(τ;) and d1(k1,nsym;τ,α;
) is the K0×1 beacon
outer-code spectral signature at trial TOA τ and scalar inner-code signal at trial TOA τ and FOA α, respectively,
a
0(τ;)=asub(
)[exp{j(
(k0)−2πf0(k0)τ)}]k
d
1(k1,nsym;τ,α;=exp{j(
(k0)−2π(f1(k1)τ−(tR(nsym)−tRref)α))}, (Eq25)
and the dispersive terms δ0(nsym;α) and δ1(k1,nsym;α) are given by
respectively. If
then δ0(nsym;−{circumflex over (α)}R)≈1K
) is nondispersive over the inner-code dimension. Similarly, if
then δ1(k1,nsym;α)≈1 and (Eq23) holds closely. Assuming AWGN background noise and ideal LPF equalization, the K0×1 background interference vector i0(k1,nsym)=[isub(K0k1+k0,nsym)]k
This model is closely analogous to a multi-element antenna array with MDoF degrees-of-freedom (DoF's), where MDoF=K0 is the stacking or “DoF” dimension. Similar to an array, it allows the outer-code signals to be detected and separated with an output (despread) SINR approximated by ˜(MDoF−L+1
for in presence of strong interference from co-channel beacons (
1, where
′≠
),using well-known, mature linear signal separation methods, e.g., least-squares (LS) algorithms, referred to as code nulling in Agee 2000. The method sacrifices one despreader DoF to null each strong signal in the environment, and uses the despreader's remaining DoF's to improve the output SNR of the intended signal. It also admits superresolution geo-observable estimators with accuracy that scales with this output SINR.
The inner-code stacked signal is then formed into K1Nsym×K0 windowed data matrix 601 X0=[√{square root over (wTOA(k1)wFOA(nsym))}x0T(k1,nsym)], where tapering windows 602 {wTOA(k1)}k), by computing intermediate K0×1 FLS FOA vector 606
on each inner subcarrier channel using an DFT bank 605; computing K0×1 whitened FLS linear combiner vector
for each candidate FOA and data-dimension code 506, for this surface the outer-code, using an IDFT bank; and computing SINR-revealing FLS TOA-FOA surface 613
Optionally, the FLS FOA vector 606 also yields FLS FOA clutter spectrum 610 {circumflex over (γ)}FLS-clutter(α)={circumflex over (η)}FLS-clutter (α)/(1−{circumflex over (η)}FLS-clutter(α)), where
which can be used to compute FLS deflection statistic {circumflex over (d)}FLS(τ,α;)={circumflex over (γ)}FLS(τ,α;
)/{circumflex over (γ)}FLS-clutter(α), a particularly useful statistic in TOA-FOA spectra containing multiple significant peaks, e.g., due to specular multipath. In some aspects, the clutter statistic is also used to improve the FOA centroid 612, e.g., using formula
which can be used to regenerate the channelized snapshot 553.
In absence of substantive multipath, the TOA-FOA estimate is then given by
and the maximal TOA-FOA surface 613 value is a metric of the SINR of the FLS combiner output signal at the estimated TOA and FOA, {circumflex over (γ)}FLS()={circumflex over (γ)}FLS(
−{circumflex over (α)}R;
). The inner-stacked spectral signature is optionally estimated by â0(
)=(C0HûFLS(
,
−{circumflex over (α)}R;
)) where C0=R0−1. The TOA and FOA error variances are further optionally estimated by {circumflex over (σ)}(∘)2(
)/{circumflex over (γ)}FLS(
), where
and where the lower bounds in (Eq34)-(Eq35) are achieved for flat tapering windows 602. Moreover, the background TOA-FOA surface 613 values are a factor of 2∥wTOA(k1)∥22∥wFOA((nsym)∥22≥2/K1Nsym below {circumflex over (γ)}FLS(), where the lower bound is also achieved for flat tapering windows 602. For this reason, flat tapering windows 602 are recommended in absence of channel multipath, and shaped tapering windows 602 recommended if multiple TOA-FOA surface 613 peaks are expected, e.g., due to strong specular multipath.
The whitening operation 603 requires the DoF's of x0 (k1,nsym), MDoF=K0, be substantively larger than the number of inner-code stacked signal vectors, Ndata=K1Nsym. If the tapering windows 602 are rectangular, the SINR-revealing metric {circumflex over (γ)}FLS() can be optionally converted to unbiased SINR estimate
which holds closely if the interference is i.i.d. complex-Gaussian over the outer-code dimension.
Assuming uniform FOA spacing α(kFOA)=(kFOA/KFOA)fsym, (Eq28) can be computed using K0K1=Ksub Nsym:KFOA efficient DFT operations. Similarly, assuming uniform TOA spacing τ(nTOA)=(nFOA/NTOA)Tsym/K0, (Eq29) can be computed using K0KFOAL K1:MTOA efficient inverse-DFT (IDFT) operations. These operations are both highly regular and parallelizable, allowing their implementation using efficient FPGA or general-purpose GPU (GPGPU) computation modules.
The FLS TOA-FOA estimates given in (Eq33), and the FLS SINR, are further refined using local search methods in the vicinity of the maximizing FLS TOA-FOA surface value 508. Simple methods for accomplishing include polynomial fit to the surface peak, e.g., using two-dimensional quadratic fit over the nearest neighbors to the maximizing surface grid location. Optionally, parametric search operations that exploit the fully-dispersive form of d1(k1,nsym; τ, α; ) given in (Eq25) multiplied by δ1(k1,nsym;α) in (Eq27), can be used. In one aspect, Newton and Gauss-Newton recursions are defined over the symbol-normalized TOA-FOA vector
Defining 2×1 symbol-normalized frequency-time vector
and K1Nsym×2 symbol-normalized matrix G1=[g1T(k1,nsym)], the recursion is given by
The final TOA and FOA are then given =({circumflex over (υ)}1(
))1Tsym/K0 and
=({circumflex over (υ)}1(
))2fsym, and the FLS SINR estimate is given by {circumflex over (γ)}FLS(
)=∥uFLS(
)∥22/1−∥uFLS(
)∥22).
Equation (Eq33) shows that the FLS TOA-FOA spectrum 613 possesses TOA and FOA ambiguity Tsym/K0 and fsym, respectively. In some aspects, this ambiguity is resolved using copy-aided parameter estimation methods 510 that exploit the model of a0 (τ;) given in (Eq24). In one aspect, the copy-aided ambiguity resolution algorithm is given by
where uFLS() is given by (Eq40), and where {circumflex over (n)}zone(
) and {circumflex over (k)}tile(
) are the TOA zone and FOA tile containing the beacon
detection, respectively. The full TOA and FOA geo-observables are then given by
respectively. If {circumflex over (k)}tile()≠0 for any detected beacon, then the FOA centroid 612 {circumflex over (α)}R is optionally recomputed, e.g., using weighted estimate
and the channelized snapshot 553 is regenerated 505 and the subsequent FLS geo-observable estimation operations shown in
The copy-aided ambiguity estimator also provides complex gain estimate
which can be used to compute the beacon channelizer output power and phase offset. These parameters provide key inputs for channel calibration operations, e.g., to determine transmit and receive carrier phase, and true channel pathloss, for subsequent network calibration operations.
Table 3 lists FLS surface generation parameters usable in the exemplary UTM and IIoT scenarios described here. The degrees of freedom are large enough to separate all of the beacons in the users' FoV's for each scenario, which a roughly factor-of-two excess to account for multipath reflections. In each case, the number of data entries is a large enough multiple of the despreader DoF's to yield a stable QRD and FLS estimate.
Table 4 summarizes complexity of the channelization and FLS surface generation operations for the two scenarios, assuming one real multiply-and-add per operation, and assuming the whitening operation 603 is performed using a QRD instantiated using Modified Gram-Schmidt Orthogonalization (MGSO). Of these operations, the QRD uses than 23% of the total operations in each scenario. The complexity is well within the capabilities of modern DSP gear, even for the 2.4 GHz Ch. 13 Scenario. Moreover, the channelization and DFT/IDFT operations are easily implemented in FPGA (e.g., Xilinx 7K325T or higher devices) or using general-purpose GPU's (GPGPU's).
Table 5 summarizes memory requirements of the FLS surface generation procedure for the two scenarios. The memory requirements assuming 64-bit data precision at each stage of processing, and in-place QRD operations. The channelization operation imposes the bulk of memory requirements for each scenario, and is not particularly onerous in any case. The channelization memory is also well within capability of modern DSP, FPGA (e.g., Xilinx 7K325T or higher devices), or GPGPU's.
Other aspects of the disclosure employ similar operations using alternate stacking methods. These include outer-code stacking, which transforms xsub(ksub,nsym) into K1×1 outer-code stacked vector x1(k0,nsym)=[xsub(K0k1+k0,nsym)]k≈
mod(Tsym/K0), i.e., with range aliased between 0 and Tsym/K0, but with high precision within that range. For this reason it is referred to here as the fine least-squares (FLS) estimator. Conversely, outer-code stacking yields TOA estimate
≈
mod Tsym, i.e., with range aliased to full range between 0 and Tsym, but with precision that is a factor of K0 coarser. It is referred to here as the coarse least-squares (CLS) estimator. Both estimators provide full range and precision in FOA. The symbol-stacked estimator provides full range and precision in TOA, but no estimate of FOA estimate. In all cases, these issues are resolvable using copy-aided post-processing methods 508.
where FTOA (pR, τR) and FFOA (pR,vR,αR) are the TOA-only and FOA-only ML estimators, respectively,
and where λT=fT/c is the nominal signal-in-space wavelength, σTOA2 and σFOA2 are given in (Eq34) and (Eq35), respectively. In the aspect described here, the networks nodes 401 are assumed to be fixed and have known positions, such that network node 401 position (tUTC) ≡
and velocity
(tUTC)≡0. If the network nodes' 401 system clocks 214 are synchronized to UTC, then the user 400 system clock 214 and LO offsets in the reception operations 300 are given by τR=tRref−tUTC(tRref)=tRref−tUTCref and αR=−fTεR/(1+εR), respectively, allowing the UTC time at known receive reference time tRref and the clock rate offset εR to be derived from the observed estimates, and the user 400 position and velocity being estimated by the method are given by pR=pR(tUTCref) and vR=vR(tUTCref), respectively.
In some aspects, the network nodes' 401 system clocks 214 are not fully synchronized to UTC, but network node 401 timing offsets =
−tUTC
and rate offsets
from UTC have been estimated, e.g., using network calibration procedures. In this case, the detected TOA's and FOA's are adjusted to compensate for these offsets. In one aspect, this is performed by setting
←
−(
−(1+
){circumflex over (t)}UTC(
)), (Eq56)
←
+fT
, (Eq57)
prior to computation of the ML estimator. It should be noted that (Eq57) is not exact, as it fails to include division of the second term by 1+εR as shown in (Eq14). However, this effect is minor for user 400 system clocks 214 with <20 ppm rate offset, and can be removed in subsequent refinements.
Estimating and concentrating τR and αR estimates out of (Eq54)-(Eq55) yields
Introducing intermediate parameters
the velocity is further concentrated out of (Eq61), yielding
The concentrated TOA and FOA objective functions can then be used to find all of the user 400 positioning and timing parameters, by conducting a search over position pR alone.
Once the beacon geo-observables, and SINR's have been estimated, and the beacons have been detected or detection failure has been logged 605, a three-stage procedure is used to jointly geolocate the sUAS, and to determine its timing and carrier offset from the beacon network. In the first stage, a coarse areal search is carried out over the entire network geography 651, using the known position of the beacons and optional timing and rate offset estimates 652. Next, a fine areal search is carried out at the optimal search point determined during the coarse search 653. Lastly, a fine altitude search is carried out at the final fine-search location 654.
until {{circumflex over (n)}zone()
is stable at each candidate user 400 position coordinate. The TOA estimates are then updated using
←
+Tamb{circumflex over (n)}zone(
).
In some aspects, the optimal user position then found from the minimum of (Eq59). In other aspects, the FOA-only ML function given in (Eq63) is added to the TOA-only ML function, and the optimal position is found or refined using the combined TOA-FOA ML function. Optionally, the optimal position is further optimized using local search operations 708, e.g., polynomial fit to optimum ML function values or parametric Gauss-Newton method. The velocity and timing offset, and LO offset is then estimated from (Eq62), (Eq58), and (Eq60), respectively 709.
In some aspects, a “pruning” strategy is used to restrict the actual positions searched by the system.
The methods described above extend to specular multipath environments in a straightforward fashion. This aspect is also expected to be particularly important in IIoT applications, due to high degrees of multipath expected in warehouse and enterprise environments. However, it will also be important in urban outdoor environments due to reflections from large buildings and structures in the vicinity of users.
Multipath extensions include both multipath mitigation aspects, in which direct and reflection paths are individually identified and used to exclude reflection paths from subsequent positioning and timing solutions, or as part of those solutions; and multipath exploitation aspects, in which direct paths (if available) and reflection paths are identified and used in subsequent positioning and timing solutions. Multipath mitigation aspects usable by those of ordinary skill in the art include:
Additional aspects of the invention are shown Provisional Patent Application 62/969,264, entitled “Secure, low-latency, and high-precision interference-resilient navigation and timing using networks of spectrally/temporally redundant beacons,” specifically incorporated herein by reference; and in the text and drawings disclosed in the paper entitled “Resilient Distributed Positioning Networks: A New Approach to Extreme Low-Latency, High-Precision Positioning and Timing,” and the presentation with the same name, copies of which are attached to and specifically incorporated herein by reference, and in Provisional Patent Application 63/138,300, entitled “Distributed Resilient Positioning Networks” a copy of which is attached to and specifically incorporated herein by reference.
The description set forth herein, in connection with the appended drawings, describes example configurations and does not represent all the examples that may be implemented or that are within the scope of the claims. The term “exemplary” used herein means “serving as an example, instance, or illustration,” and not “preferred” or “advantageous over other examples.” The detailed description includes specific details for the purpose of providing an understanding of the described techniques. These techniques, however, may be practiced without these specific details. In some instances, well-known structures and devices are shown in block diagram form in order to avoid obscuring the concepts of the described examples.
In the appended figures, similar components or features may have the same reference label. Further, various components of the same type may be distinguished by following the reference label by a dash and a second label that distinguishes among the similar components. If just the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label.
Information and signals described herein may be represented using any of a variety of different technologies and techniques. For example, 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.
The various illustrative blocks and modules described in connection with the disclosure herein may be implemented or performed with a general-purpose processor, a digital signal processor (DSP), an ASIC, a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices (e.g., a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration).
The functions described herein may be implemented in hardware, software executed by a processor, firmware, or any combination thereof. If implemented in software executed by a processor, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Other examples and implementations are within the scope of the disclosure and appended claims. For example, due to the nature of software, functions described above can be implemented using software executed by a processor, hardware, firmware, hardwiring, or combinations of any of these. Features implementing functions may also be physically located at various positions, including being distributed such that portions of functions are implemented at different physical locations. Also, as used herein, including in the claims, “or” as used in a list of items (for example, a list of items prefaced by a phrase such as “at least one of” or “one or more of”) indicates an inclusive list such that, for example, a list of at least one of A, B, or C means A or B or C or AB or AC or BC or ABC (i.e., A and B and C).
Computer-readable media includes both non-transitory computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A non-transitory storage medium may be any available medium that can be accessed by a general purpose or special purpose computer. By way of example, and not limitation, non-transitory computer-readable media may comprise RAM, ROM, electrically erasable programmable read only memory (EEPROM), compact disk (CD) ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to carry or store desired program code means in the form of instructions or data structures and that can be accessed by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, include CD, laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above are also included within the scope of computer-readable media.
The description herein is provided to enable a person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the scope of the disclosure. Thus, the disclosure is not limited to the examples and designs described herein, but is to be accorded the broadest scope consistent with the principles and novel features disclosed herein.
All publications, patents, and patent applications disclosed herein are incorporated by reference in their entireties.
This application is a National Stage of PCT Appl. No. PCT/US21/16334, filed on Feb. 3, 2021, which claims the priority benefit of U.S. Patent Application Ser. No. 63/138,300, filed on Jan. 15, 2021, and claims the priority benefit of U.S. Patent Application Ser. No. 62/969,264, filed on Feb. 3, 2020, all of which are hereby incorporated by reference in their entireties.
Number | Date | Country | |
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63138300 | Jan 2021 | US | |
62969264 | Feb 2020 | US |
Number | Date | Country | |
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Parent | PCT/US21/16334 | Feb 2021 | US |
Child | 17875757 | US |