Method and apparatus for cognitive opportunistic navigation with reference signals

Abstract

A method of navigating user equipment in motion relies upon local signals of opportunity for mapping landmarks. The signals of opportunity include synchronization signals and reference signals used to identify sources of the received signals, the respective carrier phases, the respective code phases, and the Doppler frequency for each received signal. A reference signal locked loop, a phase locked loop, and a delay locked loop utilize inherent channel gain from an acquisition step to provide navigation observable data.

Description

METHOD AND APPARATUS FOR COGNITIVE OPPORTUNISTICNAVIGATION WITH REFERENCE SIGNALSREFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and incorporates by reference Provisional Patent Application Serial No. 63 / 457,372 filed on April 5, 2023, entitled Cognitive Opportunistic Navigation with Starlink LEO Satellites: On-Demand and Always-On OFDM Reference Signals.STATEMENT OF GOVERNMENT INTEREST

[0002] This invention was made with government support under contract number FA9550-22-1-0476 awarded by the Air Force Office of Scientific Research, contract number 69A3552047138 awarded by the U.S. Department of Transportation, contract number N00014-19-1-2511 awarded by the Office of Naval Research, and contract number N00014- 22-1-2242 awarded by the Office of Naval Research. The United States government has certain rights in the invention.BACKGROUND OF THE DISCLOSURE

[0003] Navigation receivers typically rely on known references signals transmitted by the sources (such as satellites) to draw time of arrival (TOA), direction of arrival (DOA), and frequency of arrival (FOA) measurements [9] to use for navigating user equipment.Conventional opportunistic navigation receivers (i.e., those only utilizing the downlink signals) will either fail to operate or will be unable to exploit the entire available bandwidth in situations where reference signals are unknown and / or dynamic, which is the case in 5G new radio and private networks, such as broadband low Earth orbit signals. A need exists in the art of signal transmission and mapped navigation for more reliable navigation tools using signals of opportunity already in the environment as landmarks.SUMMARY OF THE DISCLOSURE

[0004] In one embodiment, a computer implemented method of navigating user equipment according to received signals proximate the user equipment includes using a receiver connected to the user equipment to process the received signals with a computer having a processor and computer memory storing software implementing steps of acquiring, at the user equipment, respective received signals having reference signals and synchronization signals within the received signals; autocorrelating the synchronization signals to form a train of periodic impulse waveforms corresponding to an autocorrelation function of the received signals; estimating baseband data for the received signals, wherein the baseband data comprises a frame length of the received signals as a distance between two of the periodic impulse waveforms; using sequential matched subspace detection to identify a number of sources of the received signals, wherein the subspace domain is defined as a set of chirp parameters corresponding to each source; utilizing a general linear detector method to sequentially test the received signals at the user equipment and using a likelihood function with the general linear detector to rank a corresponding signal source according to a respective power level of the corresponding signal source; iteratively evaluating the received signals with the computer and calculating a maximum of the likelihood function to estimate, for each received signal, an estimated coherent processing interval (CPI), estimated chirp parameters including initial Doppler frequency (fo) and Doppler rate (P), and estimated sample data for a corresponding reference signal; providing initial estimated sample data of the corresponding reference signal, estimated chirp parameters, the likelihood function and the estimated coherent processing interval for each received signal to a reference signal locked loop; iteratively tracking the corresponding reference signals for each source with the reference signal locked loop (RSLL), iteratively tracking phases and delays of the received signals with respective phase lock loops and delay lock loops; and calculating, for each received signal, a carrier phase, a code phase, and a Doppler frequency as navigation data for the user equipment.

[0005] In another embodiment, the Doppler frequency is equal to a sum of an initial Doppler frequency and a Doppler rate of change.

[0006] In another embodiment, the method includes using the frame length to determine a sampling period of at least one reference signal.

[0007] In another embodiment, the method includes iteratively evaluating the received signals with the computer in an order of the rank of the corresponding signal source.

[0008] In another embodiment, the method includes estimating the baseband data by sampling the received signals at a time instant and for the received signals, using the computer to perform steps of estimating a code delay at the time instant; estimating a carrier phase at the time instant; and estimating a code phase at the time instant.

[0009] In another embodiment, the method includes estimating a complex channel gain between the user equipment and a corresponding signal source at the time instant.

[0010] In another embodiment, the method includes utilizing the likelihood function as an indicator of performance of signal acquisition and adjusting a gain of the reference signal locked loop according to the performance.

[0011] In another embodiment, the method includes maximizing a contribution of a particular received signal in the calculating of the carrier phase, code phase, and Doppler inputs when the likelihood function is above a threshold for the particular received signal and minimizing contributions from other received signals.

[0012] In another embodiment, the method includes modeling the received signal with the computer as an equivalent summation of the reference signals totaling a baseband signal with a complex channel gain alpha (a) between a satellite source of the received signal and the user equipment.

[0013] In another embodiment, the method includes estimating a Doppler rate of respective received signals as the Doppler rate that results in the autocorrelation function exhibiting signal pulses of constant amplitude.

[0014] In another embodiment, the method includes comparing the likelihood function to a threshold to determine the corresponding source and the power level.

[0015] In another embodiment, the method includes calculating a matrix of samples of periodic reference signals within the received signals; calculating a scalar value, lambda (X), as a function of Doppler frequency differences between respective corresponding sources; and modeling the likelihood function as a function of lambda (X).

[0016] In another embodiment, the method includes estimating corresponding reference signals by estimating at least one of demodulation reference signals, phase tracking reference signals, sounding reference signals, and channel state information reference signals.

[0017] In another embodiment, the method includes identifying a number of sources of the received signals comprises evaluating the received signals when the estimated Doppler rate is wiped off of the received signal.

[0018] In another embodiment, the method includes autocorrelating the synchronization signals by acquiring the received signals for a time period that is longer than an estimated period of the received signals.

[0019] In another embodiment, the method includes iteratively updating the initial estimated sample data of the corresponding reference signal by attenuating a code delay and the Doppler frequency of the estimated sample data of the reference signal; and accumulating measurements of a next sample.

[0020] In another embodiment, the method includes setting a loop gain of the reference signal locked loop (RSLL) according to the likelihood function value and applying the loop gain to the next sample before accumulating the estimated sample data.

[0021] In another embodiment, the method includes iteratively updating the Doppler frequency of the reference signals by dividing a rate of change of carrier phase error in radians per second by 2K.

[0022] In another embodiment, the method includes iteratively updating a carrier phase of the reference signals by adding a product of a rate of change of carrier phase error and a time length of coherent accumulation.

[0023] In another embodiment, the method includes tracking a delay of each time length of coherent accumulation; and calculating a change of the code phase of the received signal.

[0024] In another implementation, a receiver for navigating user equipment according to received signals proximate the user equipment includes at least one data connection to a computer having a processor and computer memory in data communication with the receiver; a correlator hardware assembly configured to receive inputs from the computer wherein the inputs comprise, for a respectively received signal, initial estimated sample data of at least one corresponding reference signal, an estimated initial Doppler frequency for the respectively received signal, and baseband data comprising at least an estimated frame length of the respectively received signal; a reference signal locked loop assembly iteratively updating the initial estimated sample data of the at least one corresponding reference signal with a coherent accumulation of sequential reference signal sample data; a phase locked loop assembly tracking updated phases of the received signals; and a delay locked loop assembly trackingdelays over a time length of the coherent accumulation, wherein the computer is configured to calculate, for each received signal, a carrier phase, a code phase, and a Doppler frequency as navigation data for the user equipment.

[0025] In another embodiment, the receiver includes software stored in the memory performing a computer implemented method comprising steps of acquiring, at the user equipment, respective received signals having reference signals and synchronization signals within the received signals; autocorrelating the synchronization signals to form a train of periodic impulse waveforms corresponding to an autocorrelation function of the received signals; estimating baseband data for the received signals, wherein the baseband data comprises a frame length of the received signals as a distance between two of the periodic impulse waveforms; using sequential matched subspace detection to identify a number of sources of the received signals, wherein the subspace domain is defined as a set of chirp parameters corresponding to each source; utilizing a general linear detector method to sequentially test the received signals at the user equipment and using a likelihood function with the general linear detector to rank a corresponding signal source according to a respective power level of the corresponding signal source; iteratively evaluating the received signals with the computer and calculating a maximum of the likelihood function to estimate, for each received signal, an estimated coherent processing interval (CPI), estimated chirp parameters including initial Doppler frequency (fo) and Doppler rate (P), and estimated sample data for a corresponding reference signal; providing initial estimated sample data of the corresponding reference signal, estimated chirp parameters, the likelihood function and the estimated coherent processing interval for each received signal to a reference signal locked loop; iteratively tracking the corresponding reference signals for each source with the reference signal locked loop (RSLL), and iteratively tracking phases and delays of the received signals with respective phase lock loops and delay lock loops.

[0026] In another embodiment, the receiver includes a carrier phase discriminator hardware assembly receiving a sample of the received signal for carrier phase determination.

[0027] In another embodiment, the receiver includes a code phase discriminator hardware assembly utilizing the delay lock loop to track a rate of change of delay during a time length of coherent accumulation of the sequential reference signal sample data.BRIEF DESCRIPTION OF FIGURES

[0028] The components in the drawings are not necessarily to scale relative to each other. Like reference numerals designate corresponding parts throughout the several views.

[0029] FIG. 1 A illustrates autocorrelation impulses of the recorded signal after Doppler wipe-off with autocorrelation of the 100 ms of Starlink Downlink signal and shows a frame length (between the impulses) of 1.33331 ms.

[0030] FIG. IB illustrates autocorrelation of the recorded signal after Doppler wipe-off with autocorrelation of the 40 ms of 5G new radio (NR) downlink signal which shows the frame length (between the impulses) of 10 ms (5GNR standard frame length).

[0031] FIG. 2 illustrates orthogonal frequency-division multiplexing (OFDM) frame structure (always-on subcarriers) with synchronization signals on a physical broadcast channel (SS / PBCH) block and corresponding OFDM symbols and subcarriers are indicated in the inset box.

[0032] FIG. 3 A illustrates theoretical and experimental autocorrelation functions of a time segment of 150 ms for a value of the Doppler rate P of 1323 Hz / sec.

[0033] FIG. 3B illustrates theoretical and experimental autocorrelation functions of a time segment of 150 ms for a value of the Doppler rate P of 523 Hz / sec.

[0034] FIG. 3C illustrates theoretical and experimental autocorrelation functions of a time segment of 150 ms for a value of the Doppler rate 323 Hz / sec.

[0035] FIG. 3D illustrates theoretical and experimental autocorrelation functions of a time segment of 150 ms for a value of the Doppler rate a P of 0 Hz / sec.

[0036] FIG. 4A illustrates hardware for tracking loops. One difference between the proposed tracking loop and conventional tracking loops

[0042] is the local reference signal (RS) generator with adaptive gains as described in this disclosure.

[0037] FIG. 4B illustrates an example computer environment used with the tracking loops of FIG. 4 A.

[0038] FIG. 4C illustrates an example flow chart of one computerized method that can be implemented with this disclosure.

[0039] FIG. 5 illustrates one experimental environment for the 5G new radio (NR) scenario showing UAV trajectory and the two base station gNodeB structures (gNBs).

[0040] FIG. 6A shows an acquisition and tracking of 5G gNBs with two base stations transmitting next generation node B data (gNodeB further abbreviated gNBs) that are detected although their Doppler frequencies are almost right on the top of each other. The likelihood inthe first stage curve exceeds the threshold which means that the first gNB is detected. In the likelihood of the second stage curve, the first gNB is nulled, and the second gNB is detected.

[0041] FIG. 6B shows the carrier-phase error in the tracking loops for the two gNBs. The carrier-phase errors of both detected sources are converging which means that the tracking loops are locked for both detected sources.

[0042] FIG. 7A illustrates the reconstructed frame structure for reference signals (RS) and shows post-acquisition stage.

[0043] FIG. 7B shows post-tracking stage. The noted subcarriers correspond to non-active subcarriers or the subcarriers which do not correspond to the RS waveform. Ideally these subcarriers should have zero energy in the detected RS. The non-active subcarriers in FIG. 7B have less energy in the detected RS which means that the post-tracking version of the estimated RS is less noisy.

[0044] FIG. 8 shows the effect of the loop gain on the navigation root mean square error RMSE. The minimum RMSE is obtained when G1 = 1 / K1 x 1 / L*1 and G2 = 1 / K2 x 1 / L*2.

[0045] FIG. 9A illustrates the navigation solution for different values of coherent processing intervals (CPIs) and demonstrates a region where the solution does not converge.

[0046] FIG. 9B illustrates the estimated trajectories via the proposed receiver and the receiver in Ref.

[0046] which only uses the synchronization signal on the physical broadcast channel (SS / PBCH) block, and the ground truth trajectory.

[0047] FIG. 10 illustrates an environment layout, vehicle trajectory, and hardware setup according to aspects of this disclosure. The true location and a photo of the location of the blindly detected gNB are shown.

[0048] FIG. 11 illustrates acquisition results for five (5) sources that are detected in the acquisition stage. The dashed horizontal line is the detection threshold and the light colored vertical dashed line corresponds to the detected source at each stage. The dark colored vertical dashed lines are the previously detected sources at each stage.

[0049] FIG. 12 shows delay tracking results of the detected sources versus the true delay corresponding to the source base station (gNB). The delay of one of the sources matches the true delay.

[0050] FIG. 13 illustrates example cognitive sensing results of this disclosure: The True position of the gNB and the blindly estimated position are plotted. The 2D error was found to be 5.83 m.

[0051] FIG. 14A illustrates autocorrelation of the estimated reference signal (RS) in comparison with the autocorrelation of always-on signals.

[0052] FIG. 14B illustrates the estimated Doppler using the proposed method which exploits the always-on and on-demand components versus the method in Ref.

[0046] ,

[0053] FIG. 15A illustrates acquisition stages in the proposed receiver for Starlink downlink signals showing the likelihood function of Ref.

[0048] at each stage and the detected and nulled source. In the first stage, a source is detected at 200 Hz (dashed line).

[0054] FIG. 15B shows the second stage when the first detected source is nulled.

[0055] FIG. 16 illustrates carrier-phase error for arbitrary selected CPI (K’ 1) of 40, and the maximized likelihood function (ML) estimated CPI of 300.

[0056] FIG. 17A shows Starlink SV trajectories.

[0057] FIG. 17B shows ground truth position and initial position estimate.

[0058] FIG. 17C shows ground truth position and estimated position.

[0059] FIG. 18 depicts Table 1 of this disclosure as discussed herein.

[0060] FIG. 19A shows a table of the formulas and equations used in this disclosure and referenced therein according to the number of the row as shown.

[0061] FIG. 19B shows a table of the formulas and equations used in this disclosure and referenced therein according to the number of the row as shown.

[0062] FIG. 19C shows a table of the formulas and equations used in this disclosure and referenced therein according to the number of the row as shown.

[0063] FIG. 20 illustrates a proof referenced in this disclosure as Appendix A.

[0064] FIG. 21 illustrates a proof referenced in this disclosure as Appendix B. DETAILED DESCRIPTION

[0065] Technical terms in this disclosure are intended to have their broadest plain meaning that the context allows.

[0066] All aspects of the system embodiment are amenable to be described as computer implemented methods that may be incorporated into a computer program product or operated as a part of a system.

[0067] Figure 4B illustrates an example computing device 400 upon which the methods described herein may be implemented in conjunction with the receiver example of FIG. 4A. It should be understood that the example computing device 400 is only one example of a suitable computing environment upon which the methods, apparatuses and systems described herein may be implemented. Optionally, the computing device 400 can be a well-known computingsystem including, but not limited to, personal computers, servers, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, network personal computers (PCs), minicomputers, mainframe computers, embedded systems, and / or distributed computing environments including a plurality of any of the above systems or devices. Distributed computing environments enable remote computing devices, which are connected to a communication network or other data transmission medium, to perform various tasks. In the distributed computing environment, the program modules, applications, and other data may be stored on local and / or remote computer storage media.

[0068] In its most basic configuration, computing device 400 typically includes at least one processing unit 406 and system memory 404. Depending on the exact configuration and type of computing device, system memory 404 may be volatile (such as random access memory (RAM)), non-volatile (such as read-only memory (ROM), flash memory, etc.), or some combination of the two. This most basic configuration is illustrated in Figure 4B by dashed line 402. The processing unit 406 may be a standard programmable processor that performs arithmetic and logic operations necessary for the operation of the computing device 400. The computing device 400 may also include a bus or other communication mechanism for communicating information among various components of the computing device 400.

[0069] Computing device 400 may have additional features / functionality. For example, computing device 400 may include additional storage such as removable storage 408 and nonremovable storage 410, including, but not limited to, magnetic or optical disks or tapes. Computing device 400 may also contain network connect! on(s) 416 that allow the device to communicate with other devices. Computing device 400 may also have input device(s) 414 such as a keyboard, mouse, touch screen, etc. Output device(s) 412, such as a display, speakers, printer, etc., may also be included. The additional devices may be connected to the bus in order to facilitate the communication of data among the components of the computing device 400. All these devices are well-known in the art and need not be discussed at length here.

[0070] The processing unit 406 may be configured to execute program code encoded in tangible, computer-readable media. Tangible, computer-readable media refers to any media that is capable of providing data that causes the computing device 400 (i.e., a machine) to operate in a particular fashion. Various computer-readable media may be utilized to provide instructions to the processing unit 406 for execution. Example of tangible, computer-readable media may include, but is not limited to, volatile media, non-volatile media, removable media,and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. System memory 404, removable storage 408, and non-removable storage 410 are all examples of tangible, computer storage media. Examples of tangible, computer-readable recording media include, but are not limited to, an integrated circuit (e.g., field-programmable gate array or application-specific IC), a hard disk, an optical disk, a magneto-optical disk, a floppy disk, a magnetic tape, a holographic storage medium, a solid-state device, RAM, ROM, electrically erasable program read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices.

[0071] In an example implementation, the processing unit 406 may execute program code stored in the system memory 404. For example, the bus may carry data to the system memory 404, from which the processing unit 406 receives and executes instructions. The data received by the system memory 404 may optionally be stored on the removable storage 408 or the nonremovable storage 410 before or after execution by the processing unit 406.

[0072] It should be understood that the various techniques described herein may be implemented in connection with hardware or software or, where appropriate, with a combination thereof. Thus, the methods and apparatuses of the presently disclosed subject matter, or certain aspects or portions thereof, may take the form of program code (i.e., instructions) embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium where, when the program code is loaded into and executed by a machine, such as a computing device, the machine becomes an apparatus for practicing the presently disclosed subject matter. In the case of program code execution on programmable computers, the computing device generally includes a processor, a storage medium readable by the processor (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device. One or more programs may implement or utilize the processes described in connection with the presently disclosed subject matter, e.g., through the use of an application programming interface (API), reusable controls, or the like. Such programs may be implemented in a high-level procedural or object-oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language, and it may be combined with hardware implementations.

[0073] Machine learning and Al methods may be employed.

[0074] Machine Learning. In addition to the machine learning features described above, the system can be implemented using one or more artificial intelligence and machine learning operations. The term “artificial intelligence” can include any technique that enables one or more computing devices or comping systems (i.e., a machine) to mimic human intelligence. Artificial intelligence (Al) includes but is not limited to knowledge bases, machine learning, representation learning, and deep learning. The term “machine learning” is defined herein to be a subset of Al that enables a machine to acquire knowledge by extracting patterns from raw data. Machine learning techniques include, but are not limited to, logistic regression, support vector machines (SVMs), decision trees, Naive Bayes classifiers, and artificial neural networks. The term “representation learning” is defined herein to be a subset of machine learning that enables a machine to automatically discover representations needed for feature detection, prediction, or classification from raw data. Representation learning techniques include, but are not limited to, autoencoders and embeddings. The term “deep learning” is defined herein to be a subset of machine learning that enables a machine to automatically discover representations needed for feature detection, prediction, classification, etc., using layers of processing. Deep learning techniques include but are not limited to artificial neural networks or multilayer perceptron (MLP).

[0075] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. Methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure. As used in the specification, and in the appended claims, the singular forms “a,” “an,” “the” include plural referents unless the context clearly dictates otherwise. The term “comprising” and variations thereof as used herein is used synonymously with the term “including” and variations thereof and are open, non-limiting terms. While implementations will be described for steering wheel hand detection systems, it will become evident to those skilled in the art that the implementations are not limited thereto.

[0076] As utilized herein, the terms “approximately,” “about,” “substantially,” and similar terms are intended to have a broad meaning in harmony with the common and accepted usage by those of ordinary skill in the art to which the subject matter of this disclosure pertains. It should be understood by those of skill in the art who review this disclosure that these terms are intended to allow a description of certain features described and claimed without restricting the scope of these features to the precise numerical ranges provided. Accordingly, these termsshould be interpreted as indicating that insubstantial or inconsequential modifications or alterations of the subject matter described and claimed are considered to be within the scope of the invention as recited in the appended claims.

[0077] It should be noted that the term “exemplary” as used herein to describe various embodiments is intended to indicate that such embodiments are possible examples, representations, and / or illustrations of possible embodiments (and such term is not intended to connote that such embodiments are necessarily extraordinary or superlative examples).

[0078] The terms “coupled,” “connected,” and the like as used herein mean the joining of two members directly or indirectly to one another. Such joining may be stationary (e.g., permanent) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another.

[0079] References herein to the positions of elements (e.g., “top,” “bottom, ” “above, ” “below, ” etc.) are merely used to describe the orientation of various elements in the figures. It should be noted that the orientation of various elements may differ according to other exemplary embodiments, and that such variations are intended to be encompassed by the present disclosure.

[0080] Section I

[0081] Section I of this disclosure includes this introduction. Due to significant advancements in cellular technologies and dense deployment of cellular infrastructure, fifth generation (5G), and beyond, cellular networks will be adopted by intelligent transportation systems to enable reliable and safe autonomous operations [1], Several features in 5G cellular networks (and more technologies further beyond 5G) depend on the ability to localize the user equipment (UE) to a high degree of accuracy [2], The localization allows for mapping an environment and allowing the user equipment to navigate landmarks defined for third party signals and beacons in the environment, i.e., local “signals of opportunity” for enhanced mapping. The signals of opportunity that are detectable by user equipment can use any signal’s estimations for time-of-arrival (TOA), directi on-of-arrival (DOA), and / or frequency - of-arrival (FOA) to assist in navigating the user equipment in proper, or desired, directions of movement. These and other reference signals (RS) of multiple users / targets may be present in an inseparable block of some 5G, and beyond, technologies, such as joint sensing and communication [3],

[0082] Similar to 4G long-term evolution (LTE) transmission, 5G new radio (NR) transmission adopts orthogonal frequency division multiplexing (OFDM) [4], In addition, new constellations of broadband low Earth orbit (LEO) space vehicles (SVs) will transmit OFDM- type signals [5], In OFDM-based systems, a part of the transmitted power is dedicated to periodic synchronization signals, and other reference signals (RSs), which are transmitted for synchronization purposes. RSs are designed (or selected) based on their distinctive bandwidth and correlation properties and the physical channel type [6], While the RSs allocated to a single LTE channel have a predetermined bandwidth of up to 20 MHz, the allocated bandwidth for the RSs in a single 5G channel is dynamic, i.e., it adaptively changes based on the transmission mode, and can go up to 100 MHz and 400 MHz for frequency ranges 1 and 2 (FR1 and FR2), respectively [7], On the other hand, Starlink downlink signals occupy 250 MHz bandwidth of the Ku-band to provide high-rate broadband connectivity, but the allocated bandwidth (and other signal characteristics) of the RSs are unknown [8],

[0083] Reference

[0010] explains that navigation receivers typically rely on known RSs transmitted by the sources to draw time of arrival (TOA), direction of arrival (DOA), and frequency of arrival (FOA) measurements. Conventional opportunistic navigation receivers (i.e., those only utilizing the downlink signals) will either fail to operate or will be unable to exploit the entire available bandwidth in situations where RSs are unknown and / or dynamic, which is the case in 5GNR and private networks, such as broadband Low Earth Orbit (LEO) satellites. Cognitive opportunistic navigation has been recently introduced to address the following challenges of navigation with signals of unknown and dynamic nature. First, unlike public networks where the broadcast RSs are known at the UE and are universal across network operators, in private networks, the signal specifications of some RSs may not be available to the public or are subject to change. Second, in cellular long term evolution (LTE) networks, several RSs (e.g., cell-specific reference signals (CRSs)) are broadcast at regular and known time intervals, regardless of the number of UEs in the environments. Ultra-lean design refers to minimizing these always-on transmissions. 5G NR transmits some of the RSs only when necessary or on-demand. As such, designing cognitive receivers that can cognitively acquire partially known, unknown, or dynamic beacon signals (periodic synchronization signals) is an emerging need for the future of navigation receivers.

[0084] Opportunistic navigation frameworks usually rely on the broadcast reference signals (RSs), which are used to derive direction-of-arrival (DOA) and time-of-arrival (TOA). These signals are known at the UE and are universal across network operators. Hence, theycan be exploited for positioning without the need for the UE to be a network subscriber. In cellular long-term evolution (LTE) networks, several RSs, such as the cell-specific reference signal (CRS), are broadcast at regular and known time intervals, regardless of the number of UEs in the environments. This always-on type of transmitted RSs reduces the network’s energy efficiency and increases operational expenses and interference. One of the main features of 5G signals is ultra-lean transmission, which minimizes the transmission of always- on signals. For instance, CRS which used to be an always-onRS in LTE, is not necessarily being continuously transmitted in 5G signals. Up until now, 5G opportunistic navigation methods relied on the always-on signals, e.g., the primary and secondary synchronization signals (PSS and SSS, respectively) and the physical broadcast channel (SB / PBCH) block, none of which use the entire signal bandwidth.

[0085] This paper presents a cognitive opportunistic navigation framework (CON) by developing a 5G receiver architecture to simultaneously detect the active gNBs in the environment, estimate the number of gNBs and their unknown RSs which are not necessarily always-on, and exploit them to derive navigation observables in a cognitive fashion. There are four main reference signals (RSs) in 5G signals: demodulation RSs, phase tracking RSs, sounding RSs, and channel state information (CSI) RSs. These RSs are only transmitted on demand, which limits the efficacy of conventional opportunistic navigation frameworks which rely on always-on RSs. For instance, the first 5G-based opportunistic navigation receiver relied on the always-on SB / PBCH block. The downside of relying only on the SB / PBCH block is the limited bandwidth. Higher signal bandwidth translates to more accurate TOA estimates. In order to exploit the full ranging accuracy achievable with 5G signals, the proposed CON receiver is designed to cognitively estimate the RSs present in the entire bandwidth and exploit them to obtain navigation observables (pseudoranges and carrier phase). Not only is the proposed receiver is capable of exploiting RSs which are not always- on, but the cognitive nature of the proposed receiver enables opportunistic navigation with future communication standards with unknown or partially known signal specifications. The proposed receiver architecture relies solely on the periodicity of the RSs and requires very limited information about the 5G signal.

[0086] The problem of cognitively exploiting on-demand and always-on 5GNR signals has been previously studied in

[0010] ,

[0014] , and

[0015] , These methods rely on the difference between the Doppler frequencies of received signals to acquire and track the unknown sources. However, the acquisition and tracking of unknown sources may fail in the followingextreme scenarios: (i) an almost static scenario that may lead to a Doppler subspace overlap and (ii) a high dynamic scenario where the receiver or the transmitter are moving with high dynamics which results in an intensive Doppler rate. These two extreme scenarios introduce the following challenges in the acquisition and tracking of the unknown sources:

[0087] The almost static scenario: When the receiver and transmitter are almost static, the Doppler frequencies of the transmitting sources will be very close to each other. This event is referred to as the Doppler subspace overlap. Distinguishing between the sources with Doppler subspace overlap becomes very challenging for the cognitive navigation framework.

[0088] Intensive Doppler rate scenario: In cognitive navigation frameworks, the unknown and dynamic parameters of the RSs are estimated via a coherent accumulation of the received samples over time. High values of Doppler rate limits the coherence time, i.e., the time interval that the channel between the transmitter and the receiver is static. A limited coherence time affects the unknown source acquisition and tracking performance. Therefore, considering the effect of the doppler rate in the signal model and selecting a proper coherent processing interval (CPI) play a key role in intensive Doppler rate scenarios.

[0089] This paper addresses the two challenges by: (i) presenting a maximum likelihood (ML)-based detection method to estimate the coherent processing interval (CPI) jointly with the initial Doppler frequency and the Doppler rate of change of a base station, (ii) presenting a sequential matched subspace detector based on a chirp Doppler model to distinguish between the sources with Doppler subspace overlap, and (iii) designing tracking loops with adaptive loop gains which enable RS tracking in challenging scenarios. Additional contributions of this work include the following aspects.

[0090] A full receiver architecture is presented which could jointly estimate the unknown RSs of multiple sources in almost static and intensive Doppler rate scenarios. The cognitive nature of the proposed receiver enables estimating both always-on and on-demand RSs, the latter of which are not necessarily always-on. Both components were shown to be detected and refined in post-acquisition and tracking stages via properly designed adaptive gains. The adaptive gains are provided by the acquisition stage and are designed based on the source detection performance.

[0091] Feeding this information to the tracking loops establishes a link between the acquisition and tracking loops which is necessary in challenging scenarios and distinguishes the proposed architecture from conventional navigation algorithms. This link between the acquisition and tracking stages has not been considered in either classic global navigationsatellite system (GNSS) receivers, e.g.,

[0016] and

[0017] , and the state-of-the-art joint detection and tracking techniques, e.g.,

[0010] , One of the non-limiting contributions of this disclosure is demonstration of the importance of reporting the detection performance to the tracking loops by experimentally showing that the state-of-the art receiver architectures will fail to track the signals in challenging scenarios without the proposed link between the acquisition and tracking loops.

[0092] The effect of Doppler rate estimation error on the autocorrelation function is presented analytically. A closed-form solution for the autocorrelation attenuation is presented which matches the experimental results. The analysis of the effect of Doppler rate estimation error on the autocorrelation function is one significant factor in navigation with LEO satellites. In non-limiting embodiments, this analysis enables a novel blind Doppler rate estimation technique for LEO satellite signals.

[0093] Experimental results are presented showing an application of the proposed receiver architecture by (i) enabling an unmanned aerial vehicle (UAV) to detect and exploit terrestrial 5G NR cellular signals for navigation purposes, achieving a position root mean-squared error (RMSE) of 4.2 m over a total trajectory of 416 m; (ii) enabling a ground vehicle to cognitively sense (detect and track) an unknown 5G gNB in the environment, estimating the position of the gNB with a two-dimensional (2D) error of 5.83 m in a blind fashion; and (iii) exploiting Starlink downlink OFDM signals to localize a stationary receiver, showing that starting from an initial estimate of 179 km away, the final 2D error converges to 6.5 m. Portions of this disclosure are organized as follows. Section II surveys relevant related work. Section III presents the received baseband signal model. Section IV presents different stages of the proposed receiver. Section V presents experimental results for the utilization of the adaptive cognitive receiver in UAV navigation. Section VI gives concluding remarks.

[0094] This Section II overviews related work in positioning with 5G NR, unknown signals, and LEO SV signals.

[0095] 1) Positioning With 5G NR: Positioning with 5G signals has been studied in the literature

[0018] ,

[0019] ,

[0020] ,

[0021] ,

[0022] ,

[0023] , High data rate in 5G signals necessitates a higher transmission bandwidth and more advanced spatial and time domain-based multiplexing techniques. However, since the unlicensed spectrum in lower frequencies is scarce, millimeter waves (mm Waves) have been adopted for 5G FR2

[0024] , To mitigate the high pathloss of propagated mm Wave signals different beamforming techniques and massive multiple-input, multiple-output (mMIMO) antenna structures are proposed for the 5G protocol

[0025] , Sincebeamforming in 5G requires the knowledge of the user’s location, 5G-based positioning is essential for resource allocation

[0026] , The signal characteristics of mm Wave for positioning were studied in

[0027] , Reference [2] focuses on the integrated positioning methodology of GNSS and device-to-device (D2D) measurements in 5G communication networks. In

[0020] , a tensor-based method for channel estimation in mm Wave systems was presented, which enables positioning and mapping using diffuse multipath in 5G mmWave communication systems. Experimental results in

[0028] showed meter-level navigation using TOA estimates from 5G signals. All the aforementioned methods relied on the knowledge of the beacon signals. The proposed cognitive framework in this paper is capable of detecting and tracking unknown on-demand and always-on beacons. This feature of the proposed receiver architecture enables navigation with systems with ultra-lean design, where dynamic and on- demand beacons are adopted.

[0096] 2) Positioning With Unknown Signals: The detection problem of an unknown source in the presence of other interfering signals falls into the paradigm of matched subspace detectors, which has been widely studied in the classic detection theory literature

[0029] ,

[0030] ,

[0031] ,

[0032] , In the navigation literature, detection of unknown signals has been studied to design frameworks, which are capable of navigating with unknown or partially known signals

[0033] ,

[0034] , Preliminary results for navigation with partially known signals from low and medium Earth orbit satellites were conducted in

[0012] ,

[0013] , and

[0035] , In particular, a chirp parameter estimator was used in

[0035] to blindly estimate the GPS pseudorandom noise (PRN) codes. In

[0010] and

[0014] , a cognitive opportunistic navigation framework was developed to navigate with LTE and 5GNR signals.

[0097] None of the aforementioned methods have considered the optimal selection of the coherent processing interval (CPI), which dramatically affects the performance. Such selection is addressed in the proposed receiver in this paper, which is capable of jointly detecting and tracking both always-on and on-demand RSs in a challenging acquisition scenarios. Moreover, unlike conventional signal acquisition and tracking methods, the proposed receiver utilizes information about acquisition performance into the tracking loops, which enables tracking weak signals in challenging environments. Such a connection between the acquisition and tracking stages is crucial for navigation with unknown signals (whether terrestrial 5GNR or Starlink LEO SV) in challenging scenarios, such as intensive Doppler.

[0098] 3) Navigation With Starlink LEO SV Signals: The first positioning results withStarlink SV signals were presented in

[0036] ,

[0037] , and

[0038] , These papers exploited a train ofpure tones in the downlink of Starlink SV signals to obtain carrier-phase and Doppler measurements. Starlink downlink signals occupy 250 MHz bandwidth of the Ku-band to provide a high-rate broadband connectivity [8], In this paper, the Starlink OFDM-based RSs are detected cognitively. It is shown that the RSs of Starlink downlink signals have an ultralean like behavior, in which some of the RSs are not always-on. The RSs of multiple Starlink SVs are estimated and the whole available signal bandwidth is exploited and employed in tracking loops to provide code-phase and carrier-phase observables.

[0099] III. SIGNAL MODEL

[0100] A. Overview of OFDM Frame

[0101] In OFDM-based transmission, the symbols are mapped onto multiple carrier frequencies, referred to as subcarriers, with a particular spacing known as subcarrier spacing. The subcarrier spacing is either fixed, e.g., LTE standard, or selected based on the carrier frequency, and / or other requirements and scenarios, e.g., 5G new radio (NR). Once the subcarrier spacing is configured, using a higher-level signaling, the frame structure is identified. One of the challenges that should be addressed in the proposed receiver design is the estimation of the frame length of the OFDM signals. 5G NR frame has a duration of 10 ms and consists of 10 subframes with durations of 1 ms [7], Due to the high Doppler dynamics in LEO satellites, a smaller frame length should be elected to avoid Doppler spread

[0039] , It should be pointed out that the frame length is equal to the period of the synchronization signals.

[0102] The autocorrelation of a large enough time segment of the received signal will result in a train of an impulse-like function whose shape depends on the autocorrelation properties of the synchronization signals. The distance between two consecutive impulses is equal to the OFDM frame length. FIG. 1(a) demonstrates the autocorrelation of a 100 ms time segment of the Starlink downlink signal after Doppler rate wipe-off The details of the Doppler rate wipe-off process will be discussed later. It can be seen that the distance between the impulses of the resulting train is estimated to be 1.33331 ms. Also, as a reference, FIG. IB shows the same processing on a 40 ms time segment of a 5G NR signal which results in a frame length estimation of 10 ms which corroborates the standard frame length of 5GNR downlink signals. More details about frame length estimation and the effect of Doppler rate on the autocorrelation function will be discussed below. In the frequency domain, each subframe is divided into numerous resource grids, each of which has multiple resource blocks with 12 subcarriers. The number of resource grids in the frame is provided to the UE fromhigher-level signal transmissions. A resource element is the smallest element of a resource grid that is defined by its symbol and subcarrier number [7], To provide frame timing to the UE, a base station (gNB) broadcasts synchronization signals (SS) on pre-specified symbol numbers. An SS includes a primary synchronization signal (PSS) and a secondary synchronization signal (SSS), which provide symbol and frame timing, respectively. The PSS and SSS are transmitted along with the PBCH signal and its associated demodulation reference signal (DM-RS) on a block called SS / PBCH block. The SS / PBCH block consists of four consecutive OFDM symbols and 240 consecutive subcarriers. The SS / PBCH block is transmitted numerous times on one of the half frames, which is also known as SS / PBCH burst.

[0103] FIG. 2 demonstrates the SS / PBCH subcarriers and non-active subcarriers which are illustrated therein. A non-active subcarrier can be a subcarrier that is allocated to data or on- demand RSs.

[0104] B. Baseband Signal Model

[0105] The common feature of always-on and on-demand reference signals (RSs) is periodicity. If a subcarrier is being periodically transmitted, it will be detected by the receiver, estimated, and used to derive navigation observables. The channel between the ithsource and the user equipment (UE) is considered to have a single tap with the complex channel gain ai. The received baseband signal samples can be modeled as Formula 1 in FIG. 19A , where r[n] is the received signal at the nth time instant; ai[n] is the complex channel gain between the UE and the ith source at the nth time instant; and rr[n] = rn-tsi [n], where tsi [n] is the code-delay corresponding to the UE and the ithsource at the nth time instant, and in is the sample time expressed in the receiver time. Moreover, N is the number of unknown sources; ci[n] represents the samples of the continuous-time waveform ci(t) of the periodic reference signals (RS) corresponding to the ithsource with a period of L samples; 9i[n] = 27tfDi [n]Tsn is the carrier-phase in radians, where fDi [n] is the Doppler frequency at the nth time instant and Ts is the sampling time; di[n] represents the samples of some data transmitted from the ithsource; and w[n] is a zero-mean independent and identically distributed noise with E{w[m]w*[n]} = c2w 5[m - n], where 5[n] is the Kronecker delta function, and w*[n] denotes the complex conjugate of random variable w[n]. The received signals can be expressed in terms of equivalent RS from the ithsource, denoted by si[n], and the equivalent noise, denoted by weqi, which are defined as Formulas 2 and 3 of FIG. 19 A. Hence the baseband samples can be rewritten as Formula 4 of FIG. 19 A.

[0106] Remark 1 : In this paper, the Doppler frequency is modeled as a linear chirp, i.e., fDi [n] = fDiO [n] + pi[n]Tsn, where fDiO [n] is the initial Doppler frequency, and pi[n] is the Doppler rate.

[0107] Definition 1 : The CPI is defined as the number of periods of an RS in a time interval during which the Doppler fDiO [n], Doppler rate pi[n], delay tsi [n], and channel gains ai are considered to be constant.

[0108] IV. RECEIVER ARCHITECTURE

[0109] This section describes the proposed receiver.

[0110] A. Frame Length Estimation

[0111] Detection and tracking of unknown sources rely on two fundamental features of theRS: (i) periodicity and (ii) correlation properties in the time- and frequency-domains. In broadband communication systems, the RS waveform is designed based on the correlation properties of the so-called synchronization sequences. Different sequences have distinct correlation behaviors and can be adopted in a particular system based on the physical considerations. For instance, Zadoff-Chu sequences are known for their low autocorrelation sidelobes at zero Doppler shift, and Bjorck sequences can more effectively decouple the effect of time and frequency shifts [6], The correlation properties of a sequence are usually characterized using the so-called ambiguity function.

[0112] Definition 2: Let p[n] be a sequence of numbers of length L, where n = 0, . . . ,L-1. Define the periodic sequence c[n] as the periodic extension of p[n], i.e., c[m] = p[k], for m E Z, where 0 < k < L - 1 and k = (m mod L). The discrete ambiguity function of periodic code c[m] is defined as Formula 5 of FIG. 19A. [6],

[0113] In order for the acquisition stage to be able to detect always-on and on-demand RSs, having an estimate (or the exact value) of the RS period is necessary. While the frame length is known for public networks (e.g., 5GNR), in private networks, the frame length might be unknown or dynamically change based on the transmission mode [7], The first stage of the proposed receiver involves frame length estimation. The autocorrelation of a large enough time segment of the received signal results in a periodic train of ambiguity functions in the time-domain.

[0114] If the transmitted sequences have good correlation properties, the ambiguity functions will have an impulse-like shape. Good autocorrelation means that the RS waveform of the RS is nearly uncorrelated with its own time-shifted versions, while good crosscorrelation indicates that the RSs of different satellites’ waveforms are nearly uncorrelated.The following Lemma gives a closed-form solution for the autocorrelation function in the presence of Doppler rate.

[0115] Lemma 1 : Denoting the autocorrelation function of a large enough and arbitrary time segment of length L' of the received signal by Rrr[m] = (1 / L') x Summation from k=0 to L’, r[m + k]r*[k], where L' » L, the following equality holds according to Formula 6 of FIG. 19A, where |ai bar | = 1, Aci bar (m, 0) = E{Aci (m, 0)} is the expected value of the periodic ambiguity function of the RS corresponding to the ith satellite and Rww[m] is the autocorrelation function of noise.

[0116] Proof: See Appendix A of FIG. 20.

[0117] Note that the term sin(27tPTs2mL') / sin(27tPTs2m) in (6) has a sine function-like behavior in terms of m for a nonzero Doppler rate. Assuming that the RS has good correlation properties, the term Aci (m, 0) contains a periodic train of impulse-like functions with a period of L samples (the RS period). For a non-zero Doppler rate, due to sinc-like behavior of the term sin(27tPTs2mL') / sin(27tPTs2m) , the autocorrelation function Rrr[m] is not periodic as the periodic impulse-like functions are attenuated by the effect of the sine.

[0118] To validate Lemma 1 practically, real Starlink LEO SV signals are analyzed to demonstrate the effect of the Doppler rate on the autocorrelation function. The details of the hardware setup which is used to record Starlink LEO SV signals is presented in Section V-C. FIG. 3 demonstrates the autocorrelation function of 150 ms of real Starlink downlink signal for different values of the Doppler rate: (a) P = 1323, (b) P = 523, (c) P = 323, and (d) P = 0 Hz / s. To achieve these Doppler rate values in Fig. 3, the actual Doppler rates of the Starlink LEO SV was estimated using the receiver that will be described in Section IV. The estimated Doppler rate is partially wiped-off to obtain the different P values in Fig. 3. The large impulse in the center of the autocorrelation function contains the summation of the autocorrelation function, the RS ambiguity function, and noise autocorrelation at m = 0, Formula 7 at FIG. 19A. Assuming white Gaussian noise, i.e., Rww[m] = 0 for m / = 0, Formula 7 can be used to estimate the carrier-to-noise ratio (CNR) of the received signal. For the white Gaussian noise case, the amplitude of the impulses for m / = 0 correspond to the term Aci bar (m, 0) x sin(27tPTs2mL') / sin(27tPTs2m) in Formula 6 of FIG. 19 A.

[0119] The train of the impulse-like functions, i.e., |A ci (m, 0)|, is associated with the ambiguity function of the always-on and on-demand RSs which have good correlation properties. The period of |Aci bar (m, 0)| is approximately 1.33 ms. It can be seen in FIG. 3that the amplitude of the impulse train follows the sine function-like behavior of sin(27tPTs2mL') / sin(27tPTs2m) which matches the results of Lemma 1. It should be pointed out that for large Doppler rate values, the term sin(27tPTs2mL') / sin(27tPTs2m) approaches a Kronecker delta. Therefore, large values of Doppler rate will attenuate the impulses. On the other hand, Formula 8 of FIG. 19A, which is the case of FIG. 3(d).

[0120] Remark 2: Lemma 1 shows that when the Doppler rate is perfectly wiped-off, the autocorrelation function is almost constant as the impulses will have equal amplitudes.Therefore, Lemma 1 can be used to obtain a rough estimate of the Doppler rate by searching over different values of the Doppler rate to find the one that results in a constant autocorrelation function. Assume that the estimated Doppler rate is denoted by P = P+eP, where P is the actual Doppler rate of the satellite and eP is the estimation error for the Doppler rate. P* denotes an arbitrarily guessed Doppler rate value. The received signal at the nth time instant when the Doppler rate is wiped off by P* is denoted by r'[n] and Formula 9 of FIG. 19A. The r'[n] contains a residual Doppler rate denoted by P ~ = P - P*. Note that if P* = P, the Doppler rate is wiped off perfectly and, since lim P^O sin(27tPTs2mL') / sin(27tPTs2m) = L', it is expected from Lemma 2 Formula 10 of FIG. 19A for B* = B.

[0121] B. AcquisitionThis disclosure notes that si[n] is the received signal at the nth time instant when the Doppler rate is wiped-off according to Formula 11 of FIG. 19A. This disclosure noted that ci[n] represents the samples of the continuous-time waveform ci(t) of the periodic reference signals (RS), and in is the sample time expressed in the receiver time. Due to the periodicity of sampled reference signals, c(rn), si[n] has the following properties of Formula 11 of FIG. 19 A, where coi = 27tfDiO Ts is the normalized Doppler corresponding to the ithtransmitting source, and ~7t < coi < 7t. A vector of L observation samples corresponding to the mth period of the signal is formed as zm = [r'[mL], r'[mL+l], . . . , r'[(m+l)L-l]]T. The CPI vector is constructed by concatenating K aggregates of zmvectors to form the KL x 1 vector. FIG. 12 of FIG. 19A shows where the received signal si = [si

[0001] , . . . , si[L]]T; the KL x L Doppler matrix is defined as Hi = [IL, exp (jcoiL) IL, . . . , exp (jcoi(M - 1)L) IL]T, where IL denotes an L x L identity matrix; and w is the noise vector.

[0122] Similar to

[0010] , the concept of sequential matched subspace detection is used to provide an initial estimate for the unknown parameters which are: (i) number of unknown sources, (ii) corresponding RSs, (iii) chirp parameters, and (iv) CPI. A hypothesis testingproblem is solved sequentially in multiple stages to detect the active sources in the environment. Unlike

[0010] , where a constant Doppler subspace was used to distinguish between different sources. In this, paper the matched subspace is defined based on the chirp parameters of each source. At each stage, a test is performed to detect the most powerful source, while the chirp subspace of the previously detected sources are nulled.

[0123] The so-called general linear detector

[0040] is used at each stage of the sequential detection algorithm. In the first stage of the sequential algorithm, the presence of a single source is tested, and if the null hypothesis is accepted, then N = 0, which means that no source is detected to be present in the environment. If the test rejects the null hypothesis, the algorithm asserts the presence of at least one source and performs the test to detect the presence of other sources in the presence of the previously detected source. The unknown chirp parameters, the RSs of each sources, and the corresponding CPIs are estimated at each stage.

[0124] In general, if the null hypothesis at the ithlevel of the sequential algorithm is accepted, the algorithm is terminated and the estimated number of sources will be "N = i - 1. The detection problem of ithRS is defined as a binary hypothesis test of Formulas 13 and 14 of FIG. 19A, where Bi-1 A [H1,H2, . . . ,Hi-l] and Oi-1 A [sTl, sT2. , . . . , sTi — 1]T stores the chirp parameters and estimated RS in the previous steps.

[0125] The decision criteria for the source detection is developed based on the generalized likelihood ratio (GLR). A matched subspace detector for a generic form of (13) is derived in

[0029] , Based on the specific characteristics of the Doppler subspace matrix in (12), an alternative derivation of the matched subspace detector is presented in Appendix B of FIG. 21 .

[0126] The likelihood (FIG. 4, Ref. 490) of the GLR detector is set forth in Formula 15 for a given normalized Doppler frequency coi, Doppler rate pi, and CPI Ki. Vector yH is the Hermitian transpose of y, PX A X(XHX)-1XH denotes the projection matrix to the column space of X, and Pl X A I-PX denotes the projection matrix onto the space orthogonal to the column space of X. Also, Si A Pl Bi-lHi. It should be pointed out that HHi Pl Bi-lHi = il, where the scalar i is the Schur complement of block Ci-1, i.e., the upper (i— l)x(i— 1) block of the matrix Ci, whose ijth element is (see Appendix B of FIG. 21) and Formula 16. It can be seen from (16) that the elements of the matrix Ci, and consequently the scalar Xi, are scalar functions of the Doppler frequency difference between ith source and the previously detected sources.

[0127] Remark 3 : Similar calculation to Theorem 9.1 in

[0040] has been used to derive the probability of detection results in Formula 17 of FIG. 19B, where Pdi is the probability of detection of the ith source and pi is set forth in Formula 18, which is the effective SNR of ithsource. The probability of detection is a monotonically increasing function of the scalar Xi. In other words, Xi provides a measure for the reliability of detection of the ith source. When the Doppler frequencies of the ith source and other sources are very close, Xi the becomes small which result in a poor detection performance, i.e., lim Xi— >0 Pdi = 0.

[0128] The simplified likelihood can be written as (Appendix B of FIG. 21) in Formula 19 of FIG. 19B.

[0129] The likelihood should be compared with predetermined threshold qi which is designed based on a particular probability of false alarm. For known subspaces and the corresponding projection matrices, the probability of false alarm for the ith stage of the likelihood in Formula 15 of FIG. 19A asymptotically tends to (cf. Theorem 7.1 in

[0040] ) Formula 20 of FIG. 19B for a large number of observation samples. In the experimental results presented in Section V, Formula 20 is used to determine the threshold. The maximum likelihood (ML) estimates of the coherent processing interval CPI, denoted by "Ki 495 in FIG. 4A, and the chirp parameters, ( TDi , [3i ) can be obtained by maximizing Li(y) 490.Accordingly, the least squares (LS) estimate of the ith source, i.e., si, is given by Formula 21 of FIG. 19B.

[0130] The conventional and the proposed cognitive methods use tracking loops which involve the same computational complexity. The main difference between the computational complexity of the proposed cognitive receiver and a conventional receiver stems from the acquisition stage. The number of complex operations is considered as a metric for computational complexity. In the likelihood function (15), the size of the projection matrices increases with the detection stage, i.e., i. However, in

[0041] (Appendix 8B), a recursive formula is provided to calculate the projection matrix at the ith stage based on the already calculated projection matrix at (i - l)th stage. Using the recursive formula presented in this appendix, the complexity of the projection matrix is O (K2) where O( • ) denotes the rate of growth of a function, i.e., its order. Consequently, the number of complex operations to calculate the matched subspace detector is O((5(KL)2 + KL)N).

[0131] C. Tracking

[0132] The initial estimate of the chirp parameters fDi and ~[3i, the estimated CPI (’Ki) 495, and the associated likelihood functions Li-to-* 490 are fed to the tracking stage 450 along with the estimated RS. By employing a phase-locked loop (PLL) 470 and a delay-locked loop (DLL) 465 the delay and the Doppler are tracked over time. One major difference between the proposed tracking loops and the conventional tracking loops is the RS-locked loop (RSLL) 460. The tracked Doppler and the delay are used to lock the estimated RS signal along with the code and carrier phase. The details of the tracking loops are discussed next.

[0133] 1) RS-Locked Loop (RSLL): The reference signals (RS) in the tracking loop for the ith source is initialized with the RS estimated in the acquisition stage ’sacqi. Therefore, ’sOi = "sacqi . Assuming that the ith source is being tracked, in this subsection the subscript i is dropped for convenience of notation. Let ’tsk and ’fok be the code-phase and the Doppler estimates at time-step k in the tracking loop, respectively. In the kth time-step of the tracking loop, the estimated RS is updated by coherently accumulating the measurement at the kth step of the tracking loop when the delay and Doppler are wiped-off If the subspace spanned by the columns of Si = Pl Bi-lHi is viewed as the ith source’s signal subspace, and the orthogonal subspace as the noise subspace, then the likelihood L*i in (19) can be interpreted as an estimated SNR corresponding to the ith gNB. The reader is referred to

[0029] for further interpretations of matched subspace detectors. The gain loop of the RSLL is designed based on the performance of the acquisition. If the estimated SNR of the ith source, i.e., L*i , is large, the tracking loop relies more on the acquisition by diluting the contribution of the new measurements in the estimation of the RS.

[0134] Hence, the metric L*i informs the performance of the detection of the ith source to the tracking loops. It will be shown that this link between the acquisition and the tracking results in a dramatic effect on the navigation performance. The nth sample of the updated RS at kth time-step of tracking loop is calculated as shown in Formula 22 in FIG. 19A.

[0135] 2) PLL and DLL: To track the phase of the received signals, a PLL, consisting of a phase discriminator, a loop filter, and a numerically-controlled oscillator (NCO) with a second-order PLL with a loop filter transfer function is employed. The estimate of the Doppler frequency at each time-step k is deduced by dividing the rate of change of the carrier-phase error vPLL,k in rad / s by 2K. Assuming a zero initial carrier phase, the estimate of the carrierphase estimate at time-step k is updated according to ’0k = ’0k- l+vPLL • Tsub, where Tsub is the time length of coherent accumulation in the tracking loop. Subsequently, a carrier-aidedDLL, consisting of an early-minus-late discriminator and a simple gain loop filter is used to follow the delay of each Tsub of the measured signals. The rate of change of the code-phase vDLL is used to update code-phase of the received signals, assuming low-side mixing at the radio frequency front-end, according to Formula 23 of FIG. 19A.

[0136] Fig. 4A illustrates the proposed tracking loops. One difference between the proposed tracking loop and conventional tracking loops is shown in the reference signal locked loop 460. Traditional carrier and code-phase tracking architectures are discussed for background in Ref.

[0042] , In order to track the time-variations of the carrier-phase, a traditional phase locked loop (PLL) 470 is composed of three basic constituent blocks: (i) a code phase discriminator 465 and carrier-phase discriminator 470, which is in charge of providing output measurements that, on average, are proportional to the code-phase and carrier-phase error to be compensated; (ii) a loop filter 475A, 475B, which is a very narrow low-pass filter that smooths the variability caused by thermal noise at the phase detector output; and (iii) a numerically-controlled oscillator (NCO) 480 for generating the local carrier replica based on the corrections imposed by the loop filter output. One non-limiting difference between the proposed tracking loop and conventional tracking loops is the local RS generator 460 with adaptive gains as described in Section IV-C.l.

[0137] In one embodiment, a computer implemented method of navigating user equipment according to received signals proximate the user equipment includes using a receiver 450 connected to the user equipment to process the received signals with a computer 400 having a processor 406 and computer memory 404 storing software implementing steps of acquiring, at the user equipment, respective received signals 405 having reference signals and synchronization signals within the received signals; autocorrelating the synchronization signals 410 to form a train of periodic impulse waveforms corresponding to an autocorrelation function of the received signals; estimating baseband data for the received signals, wherein the baseband data comprises a frame length 415 of the received signals as a distance between two of the periodic impulse waveforms; using sequential matched subspace detection to identify a number of sources 420 of the received signals, wherein the subspace domain is defined as a set of chirp parameters corresponding to each source; utilizing a general linear detector method to sequentially test the received signals at the user equipment and using a likelihood function with the general linear detector to rank a corresponding signal source according to a respective power level of the corresponding signal source; iteratively evaluating the received signals with the computer and calculating a maximum of the likelihood function to estimate, for eachreceived signal, an estimated coherent processing interval (CPI) 435, estimated chirp parameters including initial Doppler frequency (fo) and Doppler rate (P) 435, and estimated sample data 425 for a corresponding reference signal; providing initial estimated sample data of the corresponding reference signal, estimated chirp parameters, the likelihood function and the estimated coherent processing interval for each received signal to a reference signal locked loop; iteratively tracking the corresponding reference signals for each source with the reference signal locked loop (RSLL) 440, iteratively tracking phases and delays of the received signals with respective phase lock loops 440 and delay lock loops 440; and calculating, for each received signal, a carrier phase, a code phase, and a Doppler frequency as navigation data for the user equipment 450. In another embodiment, the Doppler frequency is equal to a sum of an initial Doppler frequency and a Doppler rate of change. In another embodiment, the method includes using the frame length to determine a sampling period of at least one reference signal. In another embodiment, the method includes iteratively evaluating the received signals with the computer in an order of the rank of the corresponding signal source. In another embodiment, the method includes estimating the baseband data by sampling the received signals at a time instant and for the received signals, using the computer to perform steps of estimating a code delay at the time instant; estimating a carrier phase at the time instant; and estimating a code phase at the time instant.

[0138] In another embodiment, the method includes estimating a complex channel gain between the user equipment and a corresponding signal source at the time instant. In another embodiment, the method includes utilizing the likelihood function as an indicator of performance of signal acquisition and adjusting a gain of the reference signal locked loop according to the performance. In another embodiment, the method includes maximizing a contribution of a particular received signal in the calculating of the carrier phase, code phase, and Doppler inputs when the likelihood function is above a threshold for the particular received signal and minimizing contributions from other received signals. In another embodiment, the method includes modeling the received signal with the computer as an equivalent summation of the reference signals totaling a baseband signal with a complex channel gain alpha (a) between a satellite source of the received signal and the user equipment. In another embodiment, the method includes estimating a Doppler rate of respective received signals as the Doppler rate that results in the autocorrelation function exhibiting signal pulses of constant amplitude. In another embodiment, the method includes comparing the likelihood function to a threshold to determine the corresponding source andthe power level. In another embodiment, the method includes calculating a matrix of samples of periodic reference signals within the received signals; calculating a scalar value, lambda (X), as a function of Doppler frequency differences between respective corresponding sources; and modeling the likelihood function as a function of lambda ( ). In another embodiment, the method includes estimating corresponding reference signals by estimating at least one of demodulation reference signals, phase tracking reference signals, sounding reference signals, and channel state information reference signals. In another embodiment, the method includes identifying a number of sources of the received signals comprises evaluating the received signals when the estimated Doppler rate is wiped off of the received signal. In another embodiment, the method includes autocorrelating the synchronization signals by acquiring the received signals for a time period that is longer than an estimated period of the received signals. In another embodiment, the method includes iteratively updating the initial estimated sample data of the corresponding reference signal by attenuating a code delay and the Doppler frequency of the estimated sample data of the reference signal; and accumulating measurements of a next sample. In another embodiment, the method includes setting a loop gain of the reference signal locked loop (RSLL) according to the likelihood function value and applying the loop gain to the next sample before accumulating the estimated sample data.

[0139] In another embodiment, the method includes iteratively updating the Doppler frequency of the reference signals by dividing a rate of change of carrier phase error in radians per second by 2K. In another embodiment, the method includes iteratively updating a carrier phase of the reference signals by adding a product of a rate of change of carrier phase error and a time length of coherent accumulation. In another embodiment, the method includes tracking a delay of each time length of coherent accumulation; and calculating a change of the code phase of the received signal.

[0140] In another implementation, a receiver 450 for navigating user equipment according to received signals proximate the user equipment includes at least one data connection to a computer 400 having a processor 406 and computer memory 404 in data communication with the receiver. A correlator hardware assembly 450 is configured to receive inputs from the computer wherein the inputs comprise, for a respectively received signal, initial estimated sample data of at least one corresponding reference signal (sOi), an estimated initial Doppler frequency (fDi(0) for the respectively received signal, and baseband data comprising at least an estimated frame length of the respectively received signal; a reference signal locked loop 460 assembly iteratively updating the initial estimated sample data of the at least onecorresponding reference signal with a coherent accumulation of sequential reference signal sample data; a phase locked loop 470 assembly tracking updated phases of the received signals; and a delay locked loop 465 assembly tracking delays over a time length of the coherent accumulation, wherein the computer 400 is configured to calculate, for each received signal, a carrier phase, a code phase, and a Doppler frequency as navigation data for the user equipment.

[0141] In another embodiment, the receiver includes software stored in the memory performing a computer implemented method comprising steps of acquiring, at the user equipment, respective received signals having reference signals and synchronization signals within the received signals; autocorrelating the synchronization signals to form a train of periodic impulse waveforms corresponding to an autocorrelation function of the received signals; estimating baseband data for the received signals, wherein the baseband data comprises a frame length of the received signals as a distance between two of the periodic impulse waveforms; using sequential matched subspace detection to identify a number of sources of the received signals, wherein the subspace domain is defined as a set of chirp parameters corresponding to each source; utilizing a general linear detector method to sequentially test the received signals at the user equipment and using a likelihood function with the general linear detector to rank a corresponding signal source according to a respective power level of the corresponding signal source; iteratively evaluating the received signals with the computer and calculating a maximum of the likelihood function to estimate, for each received signal, an estimated coherent processing interval (CPI), estimated chirp parameters including initial Doppler frequency (fo) and Doppler rate (P), and estimated sample data for a corresponding reference signal; providing initial estimated sample data of the corresponding reference signal, estimated chirp parameters, the likelihood function and the estimated coherent processing interval for each received signal to a reference signal locked loop; iteratively tracking the corresponding reference signals for each source with the reference signal locked loop (RSLL), and iteratively tracking phases and delays of the received signals with respective phase lock loops and delay lock loops.

[0142] In another embodiment, the receiver includes a carrier phase discriminator 470 hardware assembly receiving a sample of the received signal for carrier phase determination.

[0143] In another embodiment, the receiver includes a code phase discriminator 465 hardware assembly utilizing the delay lock loop to track a rate of change of delay during a time length of coherent accumulation of the sequential reference signal sample data.

[0144] FIG. 4C illustrates a flow chart of one embodiment of this disclosure. A computer implemented method of navigating user equipment according to received signals proximate the user equipment includes using a receiver connected to the user equipment to process the received signals with a computer having a processor and computer memory storing software implementing computer software steps. The receiver acquires (405) respective received signals having reference signals and synchronization signals within the received signals. The method includes autocorrelating (410) the synchronization signals to form a train of periodic impulse waveforms corresponding to an autocorrelation function of the received signals; estimating a frame length (415) of the received signals as a distance between two of the periodic impulse waveforms; using sequential matched subspace detection to identify a number of sources (420) of the received signals and estimating corresponding reference signals (425) in each received signal, wherein the subspace to be calculated is defined as a set of chirp parameters corresponding to each source; utilizing a general linear detector method to sequentially test the received signals at the user equipment and using a likelihood function with the general linear detector to rank the received signals according to a presence of a corresponding signal source and a respective power level of the corresponding signal source; evaluating a maximum of the likelihood function to determine, for each received signal, an estimated coherent processing interval (CPI) and estimated chirp parameters including initial Doppler frequency (fo) and Doppler rate (P); providing estimated corresponding reference signals, estimated chirp parameters, the likelihood function and the estimated coherent processing interval for each received signal to a reference signal locked loop (440); iteratively tracking the corresponding reference signals for each source with the reference signal locked loop (RSLL), iteratively tracking phases and delays of the received signals with respective phase lock loops and delay lock loops (44) ; and calculating (450), for each received signal, carrier phase, code phase, and Doppler frequency as navigation data (460)for the user equipment.

[0145] V. EXPERIMENTAL RESULTS

[0146] The performance of the proposed receiver is assessed in three different scenarios: (i) to navigate a UAV with terrestrial 5GNR signals, (ii) to localize an unknown 5G gNB in the environment from measurements made by a mobile ground vehicle, and (iii) to localize a stationary receiver with Starlink LEO SV downlink signals. The objectives of the experiments are to: (i) demonstrate the performance of the acquisition of unknown signals in the almost static and intensive Doppler rate scenarios, (ii) assess the effect of CPI estimation on thenavigation performance, (iii) examine the effect of the proposed RSLL tracking loop on the quality of RS estimation, and (iv) analyze the transmission of Starlink unknown signals to detect the always-on and on-demand modes of Starlink LEO SVs. In the following experiments, (20) is used to calculate the threshold qi for a probability of false alarm of 10-4 for all the stages.

[0147] A. Experiment 1 : UAV Navigation With 5G NR Signals

[0148] An Autel Robotics X-Star Premium UAV equipped with a single-channel Ettus 312 universal software radio peripheral (USRP) connected to a consumer-grade 800 / 1900 MHz cellular antenna. The cellular receivers were tuned to the cellular carrier frequency 632.55 MHz, which is a 5G NR frequency allocated to the U.S. cellular provider T-Mobile. Samples of the received signals were stored for off-line post-processing.

[0149] The experimental layout is presented in Fig. 5. During the course of the experiment, the receiver was listening to two gNBs referred to as gNBl and gNB2 in FIG. 5. The ground-truth reference trajectory was taken from the on-board Ettus 312 USRP GPS solution. The main limitations of the algorithm are: (i) the proposed receiver, requires periodic RSs in the downlink signal, and (ii) in the signal model, a single tap channel which corresponds to the LOS path with arbitrary channel gain a is considered. More precisely, the channel impulse response is modeled as h[n] = a5[n-nd], where a is the complex channel gain between the transmitter and the receiver, and nd is the code-delay corresponding to the transmitter and the receiver.

[0150] This channel model considers a flat fading scenario, where the effect of multiple “close” paths is considered in a single path gain a. Based on the underlying distribution of a, the considered h[n] can model a Rayleigh or Rician flat fading channel. Recall from (16) and (17) that when the apparent Doppler frequencies of the unknown sources are close to each other, the effective SNR, i.e., pi defined in (18), will have a small value which in turn results in a poor detection / acqui sition performance. Therefore, in order for the unknown sources to have enough separation in the Doppler subspace, it is practically preferred to perform the acquisition stage then the UAV is moving. However, to challenge the proposed receiver, the acquisition is performed in the starting phase of the flight when the UAV is almost stationary. The Doppler frequency depends on the LOS velocity between the UAV and the gNBs. When the UAV is almost stationary, the Doppler subspaces of the two gNBs will overlap which results in a small pi. It will be seen that in the starting phase of the flight, there is only going tobe a very slight separation in the Doppler subspace (on the order of 1 Hz) which is due to very small movements of the UAV.

[0151] 1) Detection and Tracking: The ML estimate of the CPI was obtained to be 100 for both gNBs. The likelihoods in the two different stages of the acquisition are plotted in Fig. 6(a). The blue curve demonstrates the likelihood in the first stage. It can be seen that the only one peak at -1 Hz is observed in the blue curve which corresponds to the first detected gNB. Due to the mentioned Doppler subspace overlap, the two sources are masking each other in the Doppler subspace. In the second stage the first gNB is nulled (red curve in 6(a)). After nulling the first gNB, a second peak appears in the likelihood function which is located at 0 Hz and corresponds to the second gNB. Fig. 6(b) demonstrates the carrier-phase errors corresponding to the two gNBs, showing that the two gNBs are being tracked.

[0152] 2) Post- Acquisition and Post-Tracking Reconstructed

[0153] Frame: After the detection of each gNB, (21) is used to estimate the corresponding RS. In this subsection, the reconstructed RS frame structure is presented for the postacquisition stage where the estimate of the RS is given in (21), and after the estimated RS is refined in the tracking loops using (22). Fig. 7 demonstrates the frame structure of the estimated RS for gNBl. Fig. 7(a) shows the resulting RS frame structure after acquisition, and Fig. 7(b) shows the refined estimated RS after tracking. Comparing the reconstructed frame in 7 with Fig. 2 shows that other than the broad cast signals (SS / PBCH blcok), several on- demand active subcarriers are also detected. As discussed in Section III, the subcarriers indicated with dark blue color code in the OFDM frame are the subcarrier that do not correspond to the RSs. Ideally, in the estimated RS, the energy of these subcarriers should be zero (darker blue). However, due to the effect of noise, these subcarriers may not appear in dark blue color. It can also be observed that the post-tracking estimated RS is less noisy (darker) than the RS obtained by (21) in the acquisition.

[0154] 3) Navigation Framework: Next, the pseudorange observables from the two gNBs will be used to estimate the 2D position of the UAV-mounted receiver, denoted by rr. The code-phase in (23) can be used to readily deduce the pseudorange observables. The pseudorange, expressed in meters, from the n-th gNB can be modeled as Formula 24 of FIG. 19A, where rsn is the 2D position of the n-th gNB, c is the speed of light, Str and Stsn are the receivers and n-th gNB’s clock biases, respectively, and vn is the measurement noise, which is modeled as a zero-mean white Gaussian sequence with variance c2n. The location of the gNBs were mapped prior to the experiment, therefore, rsn is known. The terms c • [5tr(k) -5tsn(k)] are combined into one term as they do not need to be estimated separately, yielding Formula 25 of FIG. 19B.

[0155] Cellular gNBs possess tighter carrier frequency synchronization than time (codephase) synchronization - the code-phase synchronization requirement as per the cellular protocol is typically within 1.1 ps

[0043] , It is assumed that the resulting clock biases in the TOA estimates will be very similar, up to an initial bias. Consequently, one may leverage this relative frequency stability to eliminate parameters that need to be estimated. The reparametrization is proposed as Formula 26 of FIG. 19A, where c5t is a time-varying common bias term independent of the nth gNB, and m is the deviation of c 5tn from this common bias and is treated as measurement noise. Using Formula 26, the TOA measurement of Formula 24 can be re-parameterized as Formula 27 of FIG. 19C, where cStOn = c6tn(0) and qn(k) = en(k) + vn(k) is the overall measurement noise. Note that cStOn can be obtained by knowing the initial receiver’s position and from the initial measurement zn(0), according to cStOn ~ zn(0) - ||rr(0) - rsnll . The TOA measurements were fed to an extended Kalman filter (EKF) to estimate the state vector x =[ rTr , r Tr , c5t, c'5t]T, where rr is the UAV’s 2-D velocity vector and '51 is the clock drift. A white noise acceleration model was used for the UAV’s dynamics, and a standard double integrator driven by process noise was used to model the clock bias and drift dynamics

[0044] , As such, the discrete-time dynamics model of x is given by Formula 28 and Formula 29 of FIG. 19C and T is the time interval between two measurements; and w(k) is the process noise, which is modeled as a zero-mean white random sequence with covariance matrix Q = diag [Qpv,Qclk] where Formula 30 and Formula 31 of FIG. 19C proceed.

[0156] ~Q xy = diag [~qx, ~qy], and the x, y acceleration process noise spectra of the white noise acceleration model were set to ~qx = ~qy = 5 m2 / s3, the time interval between two measurements was T = 0.0267 s, and the receiver’s clock process noise spectra were chosen to be S ~ w5t = 1.3 x 1022and S ~ w'5t = 7.9 x 1025which are that of a typical temperature- compensated crystal oscillator (TCXO)

[0045] , Note that rr is expressed in an east-north-up (ENU) frame centered at the UAV’s true initial position. The EKF state estimate was initialized at x(0) = 06x 1 with an initial covariance of P(0) = diag[3 • 12x2, 12x2, 10-2,I O4]. The measurement noise covariance was set to R = 12x2. Effect of RSLL loop gain on the navigation results: Next, the effect of the RSLL loop gain on the navigation results is assessed. The RSLL loop gain is set to be Gi = ILK x 1 / L*I = 0.002, and G2 = 1 / K2 x 1 / L2 =0.005, To assess the effect of the loop gain on the navigation RMSE, the loop gain for the second RS is set to 0.002, and the loop gain for the first RS is swept between different orders of magnitude as 5 * [10-6, 10-5, . . . , 10-1] (blue curve). Similarly, the loop gain for the first RS is set to be 0.005, and sweeping the loop gain for the second RS different orders of magnitude as 2 * [10-6, 10-5, . . . , 10-1], It can be seen that the least navigation RMSE is obtained by selecting G1 = I A< • 1 / L*1 , and G2 = 1 / K2 • 1 / L*2 as the loop gains corresponding to the first and the second sources, respectively. Effect of CPI on the navigation solution: Next, the effect of CPI selection on the navigation results is assessed.

[0157] Fig. 9(a) compares the RMSE for different values of CPI. It can be seen that if one selects a CPI which is less than a particular value, the navigation solution does not converge. It can also be observed that for a range of CPIs the error would be bounded between 4.2 to 5.8 m in the 416 m of flight trajectory. Fig. 9(b) shows the estimated trajectories via the proposed receiver and the receiver in

[0046] which only uses the SS / PBCH block, and the ground truth trajectory. Fig. 8 demonstrates the position RMSE in terms of the RSLL loop gain.

[0158] B. Experiment 2: Cognitive Sensing a 5GNR gNB on a Ground Vehicle A ground vehicle was equipped with a quad-channel National Instrument (NI) USRP-2955 and two consumer grade 800 / 1900 MHz cellular antennas to sample 5G signals near Ohio Stadium in Columbus, Ohio, USA. One channel from the USRP was tuned to a 632.55 MHz carrier frequency, which is a 5G NR frequency allocated to the U.S. cellular provider T-Mobile. The sampling rate was set to 20 mega-samples per second (MSps) and the sampled 5G signals were stored on a laptop for post-processing.

[0159] In order to obtain the vehicle’s trajectory, the vehicle was equipped with a Septentrio AsteRx SBi3 Pro+ with a dual antenna multi -frequency GNSS receiver with realtime kinematic (RTK) and an industrial-grade inertial measurement unit (IMU). The vehicle’s traversed a trajectory of 1.79 km. Fig. 10 shows the environment layout, the vehicle trajectory, and the experiment setup.

[0160] The location of the gNB and the transmitted RS from the gNB were unknown to the receiver. The goal of this experiment was to cognitively sense the location of the gNB via the proposed receiver. Only the carrier frequency of the transmitted signal was known to the receiver. Fig. 11 demonstrates the acquisition results. It can be seen that five sources were detected by the receiver. The detected sources could correspond to either gNBs or false alarm due to multipath. The first detected source in Stage 1 of the acquisition algorithm has the largest likelihood, therefore, it corresponds to the strongest path.

[0161] The transmitter and receiver clock terms, i.e., 5tr(k) and 5tsn(k) in Formula 24, are both unknown to the receiver. Assuming a first-order clock model for both the gNB and the receiver, the combined clock term in Formula 24 can be written as c5tn(k) = c • [5tr(k) -5tsn(k)] = + q / k where S, is the clock bias and y is the clock drift

[0047] , Note that rr(k) is known and the receiver uses pseudorange observables to estimate the gNB’s position rs. Next, define the parameter vector x = [rTs ,y]T. Let z denote the vector of all the pseudorange observables stacked together. Then, one can write the measurement equation given by z = g(x)+vz, where g(x) is a vector-valued function that maps the parameter vector x to the pseudorange observables according to (24), and vz denotes the vector of all measurement noises stacked together. Next, a nonlinear least-squares (NLS) estimator was used to estimate x denoted by x. The estimated position was validated by onsite verification. The 2D position error of the estimated gNB found to be 5.83 m. The true location of the gNB and the estimated location of the gNB are shown in Fig. 13.

[0162] Fig. 12 demonstrates the delay tracking results for each source versus the true delay which was obtained according to the true location of the gNB and the ground truth trajectory of the receiver. In this paper, cognitive sensing of the gNB is considered. The cognitive sensing of multipath and other interfering components can be considered in future work. Fig. 14(a) demonstrates the autocorrelation of the estimated RS in comparison with the autocorrelation of the always-on signals (PSS, SSS, and PBCH block). It can be seen that the autocorrelation function of the estimated RS is sharper in comparison with the autocorrelation of the always-on signals which results in a better TOA tracking performance. In order to demonstrate the effect of better autocorrelation properties the estimated RS in comparison with the always-on components, the estimated Doppler is plotted in Fig. 14(b). It can be seen that the tracked Doppler using the method in

[0046] which only relies on always-on signals has a larger estimation variance compared to the proposed method.

[0163] C. Experiment 3: Stationary Positioning With Starlink LEO SV Signals

[0164] A stationary National Instrument (NI) universal software radio peripheral (USRP) 2945R was equipped with a consumer grade Ku antenna and low-noise block (LNB) downconverter to receive Starlink signals in the Ku-band. The sampling rate was set to 2.5 MHz and the carrier frequency was set to 11.325 GHz to record Ku signals over a period of 800 s. Six SVs were detected this period. To avoid redundancy, the acquisition and tracking results of one of the Starlink SVs are presented next.

[0165] 1) Acquisition: The acquisition stages in the proposed receiver is shown in Fig. 15.As it can be seen in this figure, in the first stage of the acquisition, one source is detected at the normalized Doppler frequency of 199 Hz. Finally, in the second stage, the Doppler subspace of the first source is nulled and the resulting likelihood is less than the threshold or equivalently N = 1.

[0166] 2) The Effect of CPI on Tracking Performance: Fig. 16 demonstrates the carrierphase error for the different values of KI = 40 and the KI = 300 which was the ML estimate of the CPI obtained by maximizing (15) over different values of CPI. As it can be seen in Fig. 16, the standard deviation of the carrier-phase error for KI = 300 is smaller than that of the case where CPI is arbitrary selected to be KI = 40.

[0167] 3) Navigation Results: The navigation results can be seen in Fig. 17. The experimental setup and the navigation framework is similar to the setup in

[0037] , Six starlink satellite was tracked using the proposed receiver. The receiver position was initialized as the centroid of all SV positions, projected onto the surface of the earth, yielding an initial position error of 179 km. The final two dimensional error was 6.5 m using the six Starlink LEO SVs. Table I compares the 2D positioning results for different values of CPI. It can be seen that if one select CPI = 30, the 2D navigation solution does not converge. The skyplot of the satellites and the navigation results are shown in Fig. 17.

[0168] An adaptive cognitive receiver architecture was proposed to extract navigation observables from Starlink LEO SV and 5GNR signals, without requiring knowledge of the RSs. The cognitive nature of the proposed receiver enables estimating both always-on and on- demand RSs which are not necessarily always-on. The parameters of the proposed receiver is designed to enable deciphering RSs in both intensive and non-intensive Doppler scenarios. It was shown that the estimated RSs contain both always-on and on-demand component of the transmitted signals. The proposed cognitive structure was modified based on an iterative algorithm for the ML CPI estimator. Tracking loops were also designed in order to refine and maintain the estimates of the RS provided by the acquisition stage and follow the delay and Doppler of the received signals. Experimental results were presented showing the performance of the proposed receiver by: (i) enabling an unmanned aerial vehicle (UAV) to detect and exploit terrestrial 5G NR cellular signals for navigation purposes showing a root-mean-square error (RMSE) which is bounded between 4.2m and 5.8 m in a total trajectory of 416 m, (ii) enabling a ground vehicle to cognitively sense (detect blindly, exploit all the information, and track) an unknown gNB in a traversed trajectory of 1.79 km, and estimating the position of thegNB with a two-dimensional error of 5.83 m in a blind fashion, and (iii) exploiting Starlink OFDM signals for positioning a stationary receiver showing a two-dimensional error of 6.5 m when the initial estimate is 179 km away from the true position of the receiver.

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[0218] It is important to note that the construction and arrangement of the sensing system for described herein as shown in the various exemplary embodiments is illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting or layering arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter described herein. For example, elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes and omissions may also be made in the design, operating conditions and arrangement of the various exemplary embodiments without departing from the scope of the present embodiments.

[0219] Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.

[0220] The embodiments of the method, system and computer program product described herein are further set forth in the claims below.

Claims

CLAIMS1. A computer implemented method of navigating user equipment according to received signals proximate the user equipment, the method comprising: using a receiver connected to the user equipment to process the received signals with a computer having a processor and computer memory storing software implementing the following steps: acquiring, at the user equipment, respective received signals having reference signals and synchronization signals within the received signals; autocorrelating the synchronization signals to form a train of periodic impulse waveforms corresponding to an autocorrelation function of the received signals; estimating baseband data for the received signals, wherein the baseband data comprises a frame length of the received signals as a distance between two of the periodic impulse waveforms; using sequential matched subspace detection to identify a number of sources of the received signals, wherein the subspace domain is defined as a set of chirp parameters corresponding to each source; utilizing a general linear detector method to sequentially test the received signals at the user equipment and using a likelihood function with the general linear detector to rank a corresponding signal source according to a respective power level of the corresponding signal source; iteratively evaluating the received signals with the computer and calculating a maximum of the likelihood function to estimate, for each received signal, an estimated coherent processing interval (CPI), estimated chirp parameters including initial Doppler frequency (fo) and Doppler rate (P), and estimated sample data for a corresponding reference signal; providing initial estimated sample data of the corresponding reference signal, estimated chirp parameters, the likelihood function and the estimated coherent processing interval for each received signal to a reference signal locked loop;iteratively tracking the corresponding reference signals for each source with the reference signal locked loop (RSLL), iteratively tracking phases and delays of the received signals with respective phase lock loops and delay lock loops; and calculating, for each received signal, a carrier phase, a code phase, and a Doppler frequency as navigation data for the user equipment.

2. The computer implemented method of Claim 1, wherein the Doppler frequency is equal to a sum of an initial Doppler frequency and a Doppler rate of change.

3. The computer implemented method of Claim 1, further comprising using the frame length to determine a sampling period of at least one reference signal.

4. The computer implemented method of Claim 1, further comprising iteratively evaluating the received signals with the computer in an order of the rank of the corresponding signal source.

5. The computer implemented method of Claim 1, wherein estimating the baseband data further comprises sampling the received signals at a time instant and for the received signals, using the computer to perform steps of : estimating a code delay at the time instant; estimating a carrier phase at the time instant; and estimating a code phase at the time instant.

6. The computer implemented method of Claim 5, further comprising estimating a complex channel gain between the user equipment and a corresponding signal source at the time instant.

7. The computer implemented method of Claim 1, further comprising, utilizing the likelihood function as an indicator of performance of signal acquisition; and adjusting a gain of the reference signal locked loop according to the performance.

8. The computer implemented method of Claim 7, further comprising maximizing a contribution of a particular received signal in the calculating of the carrier phase, code phase,and Doppler inputs when the likelihood function is above a threshold for the particular received signal and minimizing contributions from other received signals.

9. The computer implemented method of Claim 1, wherein the received signal is modeled by the computer as an equivalent summation of the reference signals totaling a baseband signal with a complex channel gain alpha (a) between a satellite source of the received signal and the user equipment.

10. The computer implemented method of Claim 1, comprising estimating a Doppler rate of respective received signals as the Doppler rate that results in the autocorrelation function exhibiting signal pulses of constant amplitude.

11. The computer implemented method of Claim 1, further comprising comparing the likelihood function to a threshold to determine the corresponding source and the power level.

12. The computer implemented method of Claim 1, further comprising: calculating a matrix of samples of periodic reference signals within the received signals; calculating a scalar value, lambda (X), as a function of Doppler frequency differences between respective corresponding sources; and modeling the likelihood function as a function of lambda (X).

13. The computer implemented method of Claim 1, further comprising loop filters connected to the delay locked loop and the phase locked loop to minimize variability of respective loop outputs.

14. The computer implemented method of Claim 1, wherein estimating corresponding reference signals comprises estimating at least one of demodulation reference signals, phase tracking reference signals, sounding reference signals, or channel state information reference signals.

15. The computer implemented method of Claim 1, wherein identifying a number of sources of the received signals comprises evaluating the received signals when the estimated Doppler rate is wiped off of the received signal.

16. The computer implemented method of Claim 1, wherein autocorrelating the synchronization signals comprises acquiring the received signals for a time period that is longer than an estimated period of the received signals.

17. The computer implemented method of Claim 1, further comprising iteratively updating the initial estimated sample data of the corresponding reference signal by: attenuating a code delay and the Doppler frequency of the estimated sample data of the reference signal; and accumulating measurements of a next sample.

18. The computer implemented method of Claim 17, further comprising setting a loop gain of the reference signal locked loop (RSLL) according to the likelihood function value and applying the loop gain to the next sample before accumulating the estimated sample data.

19. The computer implemented method of Claim 1, further comprising iteratively updating the Doppler frequency of the reference signals by dividing a rate of change of carrier phase error in radians per second by 2K.

20. The computer implemented method of Claim 1, further comprising iteratively updating a carrier phase of the reference signals by adding a product of a rate of change of carrier phase error and a time length of coherent accumulation.

21. The computer implemented method of Claim 20, further comprising: tracking a delay of each time length of coherent accumulation; and calculating a change of the code phase of the received signal.

22. A receiver for navigating user equipment according to received signals proximate the user equipment, the receiver comprising: at least one data connection to a computer having a processor and computer memory in data communication with the receiver; a correlator hardware assembly configured to receive inputs from the computer wherein the inputs comprise, for a respectively received signal, initial estimated sample data of at least one corresponding reference signal, an estimated initial Doppler frequency for therespectively received signal, and broadband data comprising at least an estimated frame length of the respectively received signal; and a reference signal locked loop assembly iteratively updating the initial estimated sample data of the at least one corresponding reference signal with a coherent accumulation of sequential reference signal sample data; a phase locked loop assembly tracking updated phases of the received signals; and a delay locked loop assembly tracking delays over a time length of the coherent accumulation, wherein the computer is configured to calculate, for each received signal, a carrier phase, a code phase, and a Doppler frequency as navigation data for the user equipment.

23. The receiver of Claim 22, further comprising: software stored in the memory performing a computer implemented method comprising steps of: acquiring, at the user equipment, respective received signals having reference signals and synchronization signals within the received signals; autocorrelating the synchronization signals to form a train of periodic impulse waveforms corresponding to an autocorrelation function of the received signals; estimating baseband data for the received signals, wherein the baseband data comprises a frame length of the received signals as a distance between two of the periodic impulse waveforms; using sequential matched subspace detection to identify a number of sources of the received signals, wherein the subspace domain is defined as a set of chirp parameters corresponding to each source; utilizing a general linear detector method to sequentially test the received signals at the user equipment and using a likelihood function with the general linear detector to rank a corresponding signal source according to a respective power level of the corresponding signal source;iteratively evaluating the received signals with the computer and calculating a maximum of the likelihood function to estimate, for each received signal, an estimated coherent processing interval (CPI), estimated chirp parameters including initial Doppler frequency (fo) and Doppler rate (P), and estimated sample data for a corresponding reference signal; providing initial estimated sample data of the corresponding reference signal, estimated chirp parameters, the likelihood function and the estimated coherent processing interval for each received signal to a reference signal locked loop; iteratively tracking the corresponding reference signals for each source with the reference signal locked loop (RSLL), iteratively tracking phases and delays of the received signals with respective phase lock loops and delay lock loops.

24. The receiver of Claim 22, further comprising a carrier phase discriminator hardware assembly receiving a sample of the received signal for carrier phase determination.

25. The receiver of Claim 24, further comprising a code phase discriminator hardware assembly utilizing the delay lock loop to track a rate of change of delay during a time length of coherent accumulation of the sequential reference signal sample data.

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