System and method for multi-constellation blind beacon estimation, doppler tracking, and positioning

Abstract

An exemplary system and method that provide blind beacon estimation and Doppler tracking that is agnostic to the modulation and multiple access scheme adopted by LEO satellites. The exemplary system and method can generate navigation observables from broadband LEO satellites without the need to know the signal specifications using repetitive sequence observed from the high dynamics between the LEO satellite and a terrestrial receiver to induce a prominent feature in the received spectrum. The exemplary system and method can lock on the satellite's feature in the frequency domain and uses the cross-correlation method to track the Doppler shift.

Description

Attorney Docket No. 103361-500WO1 T2023-353 SYSTEM AND METHOD FOR MULTI-CONSTELLATION BLIND BEACON ESTIMATION, DOPPLER TRACKING, AND POSITIONING Statement Regarding Federally Sponsored Research or Development

[0001] This invention was made with government support under Contract No. DOT 69A3552047138 and Contract No. FA9550-22-1-0476, awarded by the Air Force Office of Scientific Research, and Contract No. N00014-22-1-2242 and Contract No. N00014-19-1-2511, awarded by the Office of Naval Research. The government has certain rights in the invention. Related Application

[0002] This PCT application claims priority to, and the benefit of, U.S. Provisional Patent Application No. 63 / 498,189, filed April 25, 2023, entitled, “First Multi-Constellation Blind Beacon Estimation Doppler Tracking, and Opportunistic Positioning with OneWeb, Starlink, Iridium Next, and Orbcomm LEO satellites,” which is incorporated by reference herein in its entirety. Background

[0003] There are benefits for positioning, navigation, and timing (PNT) using low Earth orbit (LEO) satellites as the satellites would send a plethora of signals, diverse in frequency and direction, to the Earth. Such satellites are currently owned by private operators that typically do not disclose crucial information about the satellite’s ephemerides, clock synchronization and stability, and signal specifications.

[0004] Recent approaches allowed for the exploitation of unknown Starlink LEO satellites, from which navigation observables were produced via a carrier phase tracking approach and a generalized likelihood ratio (GLR) Doppler detection. The former was reported to localize a receiver to within a two-dimensional (2D) error of 25.9 meters, while the latter achieved a 2D error of 10 meters.

[0005] There is a need and benefit to improve navigation and Doppler estimation measures from low Earth orbit satellites. Summary

[0006] An exemplary system and method are disclosed that provide blind beacon estimation and Doppler tracking that is agnostic to the modulation and multiple access scheme adopted by LEO satellites. The exemplary system and method can generate navigation observables fromAttorney Docket No. 103361-500WO1 T2023-353 broadband LEO satellites without the need to know the signal specifications using a repetitive sequence (also known as a beacon) observed from the high dynamics between the LEO satellite and a terrestrial receiver to induce a prominent feature in the received spectrum. The exemplary system and method can lock on the satellite’s feature in the frequency domain and uses the cross- correlation method to track the Doppler shift.

[0007] The exemplary system and method employs an analytical approximation of the received signal frequency spectrum under a high dynamics channel to provide a blind Doppler estimator using spectral cross-correlation and a Kalman filter (KF)-based tracking loop. A study was conducted that demonstrated the successful acquisition, tracking, and positioning of multi- constellation LEO satellites, including, but not limited to, Orbcomm, Iridium NEXT, Starlink, and OneWeb, using the exemplary system and method.

[0008] The blind navigation beacon estimator can estimate the time-domain waveform of the repetitive sequence present in the LEO signals even when the signal structure employed by the satellite changes. While decoding the repetitive sequence using its modulation scheme can be subsequently performed, the refined time-domain waveform alone is sufficient to be used to generate navigation observables from LEO satellites.

[0009] It is expected that broadband LEO satellite constellations will move to adopt the 5G new radio (NR) (and generally, the third-generation partnership project (3GPP)) standards for cellular communications. Simulation results presented herein show successful beacon estimation and Doppler tracking of Starlink LEO satellites transmitting 5GNR OFDM signals.

[0010] Experimental results also demonstrated the efficacy of the exemplary blind receiver system and method on multi-constellation LEO satellites, including OneWeb, Starlink, Orbcomm, and Iridium NEXT. The exemplary blind receiver system and method was capable of successfully estimating the beacon and tracking the Doppler, in a blind fashion, of eight LEO satellites (two OneWeb, four Starlink, an Iridium NEXT, and an Orbcomm) over a period of about 560 seconds with Hz-level accuracy, each having different modulation and multiple access transmission schemes. The produced Doppler measurements were fused through a nonlinear least-squares estimator to localize a stationary receiver to an unprecedented level of accuracy. With an initial estimate of about 3,600 km away, experimental results show a final three-dimensional (3D) position error of 5.8 m, and a 2D position error of 5.1 m was achieved. Aside from achieving thisAttorney Docket No. 103361-500WO1 T2023-353 unprecedented accuracy, the results represent the first successful opportunistic tracking of unknown OneWeb LEO signals and their exploitation for positioning.

[0011] The exemplary system and method may be used for the commercialization of vehicular navigation (manned or unmanned), including aerial, ground, and maritime. It can also be commercialized for consumer devices (iPhones, tablets).

[0012] In an aspect, a method is disclosed of estimating a beacon in a blind fashion, the method comprising receiving an RF signal (e.g., Ku-band) (e.g., 5G NR OFDM signals); identifying existence of one or more repetitive sequences in the received RF signal, one of the repetitive sequences being associated with a satellite in low Earth Orbit (LEO) having an unknown modulation or access scheme; performing blind beacon estimation and Doppler tracking agnostic to the modulation and the access scheme of the LEO satellite to generate an estimation of the beacon and a tracked Doppler by: locking, via a spectral cross-correlation and a Kalman filter (KF)-based tracking loop, on a satellite feature in the received RF signal in the frequency domain; iteratively evaluating a carrier phase (!") based on the locked satellite feature; and generating navigation observables from the LEO satellite based on the carrier phase.

[0013] In some embodiments, the navigation observables include a measure of Doppler of the LEO satellite, the measure of Doppler being employed for positioning, navigation, and timing (PNT) application of a receiver (e.g., LEO-based global positioning application or navigation based application based on the LEO-based global positioning).

[0014] In some embodiments, the navigation observables include a measure of Doppler, the measure of Doppler being employed in the correction or adjustment of decoding of digital communication channel.

[0015] In some embodiments, the RF signal at the receiver is modeled as having a shifted and dilated version of the frequency spectrum of the repetitive sequence, alongside some noise, wherein the shift in the received spectrum is estimated, for a moving time window, as a residual Doppler parameter (!$#") in the spectral cross-correlation and a Kalman filter (KF)-based tracking loop, and wherein the dilation is estimated, for the same moving time window, as a residual Doppler rate parameter (!$%") in the spectral cross-correlation and a Kalman filter (KF)-based tracking loop.

[0016] In some embodiments, the spectral cross-correlation and a Kalman filter (KF)-based tracking loop includes a nonlinear least-squares (NLS) estimator and a Kalman-based filter,Attorney Docket No. 103361-500WO1 T2023-353 wherein the residual Doppler parameter is determined by the nonlinear least-squares (NLS) estimator of the received signal’s sequence after a carrier wipe-off in the frequency domain, the NLS estimator iteratively evaluating a Doppler ambiguity parameter (!$#&) corresponding to a true carrier phase (!"), based on an energy evaluation.

[0017] In some embodiments, the energy evaluation comprises the NLS estimator iteratively evaluating an energy parameter of an estimated sequence for an estimated beacon corresponding to an LEO satellite until a steady-state value equal to the energy of the true beacon (i.e., carrier phase) is reached.

[0018] In some embodiments, the Kalman-based filter is configured to track one or more carrier phase states ('") comprising at least one of a true carrier phase (!"), true ambiguity-free Doppler shift (!#"), and Doppler rate (!%"), the Kalman-based filter being configured to update, for each time window, the tracked carrier phase state with a state transition matrix and a zero-mean white random sequence.

[0019] In some embodiments, outputs of the Kalman-filter comprising tracked Doppler are employed by the NLS estimator in a carrier wipe-off adjustment to generate an estimated signal sequence.

[0020] In some embodiments, outputs of the spectral cross-correlation and a Kalman filter (KF)-based tracking loop (e.g., tracked Doppler (!(#")) are employed in a Doppler ambiguity resolution operation.

[0021] In some embodiments, the method includes performing code phase tracking of the blind beacon estimation and Doppler tracking.

[0022] In some embodiments, the code phase tracking comprises determining, via a carrier phase change parameter, whether the NLS estimator of the Doppler tracking loop is locked to adjust the carrier phase estimation, wherein the carrier phase change parameter is used to adjust weights or usage of the residual carrier phase sequence generated by the Doppler tracking loop.

[0023] In some embodiments, the steps of claim 1 are performed for a second LEO satellite.

[0024] In some embodiments, the steps of claim 1 are performed for multiple LEO satellites in a batch operation.

[0025] In some embodiments, the RF signal comprises Ku-band frequencies.

[0026] In some embodiments, the RF signal comprises 5G NR OFDM signals.Attorney Docket No. 103361-500WO1 T2023-353

[0027] In another aspect, a system is disclosed comprising: a processor; and a memory having instructions stored thereon, wherein the instructions, when executed by the processor, cause the processor to perform steps for any one of the above-discussed methods.

[0028] In some embodiments, the system is a transceiver chip for a global positioning transceiver.

[0029] In some embodiments, the system further includes a network transceiver, the network transceiver being configured to receive the measure of Doppler to use in a compensation parameter in the network transceiver. In some embodiments, the system is a navigation software.

[0030] In another aspect, a global positioning transceiver (e.g., a universal GNSS RF receiver) is disclosed comprising: a processor (digital signal processor, ASIC, or combination thereof); a memory having instructions stored thereon, wherein the instructions, when executed by the processor, cause the processor to perform steps for any one of the above-discussed methods.

[0031] Other systems, methods, features, and / or advantages will be or may become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and / or advantages be included within this description and be protected by the accompanying claims. BRIEF DESCRIPTION OF DRAWINGS

[0032] The components in the drawings are not necessarily to scale relative to each other. Like reference, numerals designate corresponding parts throughout the several views.

[0033] Fig. 1 shows a system comprising a blind beacon estimation and Doppler tracking module that is configured to generate navigation observables from broadband LEO satellites using repetitive sequences (also known as a beacon) observed from the high dynamics between the LEO satellite and a terrestrial receiver in accordance with an illustrative embodiment.

[0034] Figs. 2A and 2B show an example blind beacon estimation and Doppler tracking module comprising a blinder Doppler tracker, a code phase tracker, and a Doppler Ambiguity Resolver, and their associated operation, in accordance with an illustrative embodiment.

[0035] Fig. 3A shows an example multi-constellation positioning receiver configured to execute the blind Doppler tracker of Fig. 2A in accordance with an illustrative embodiment.Attorney Docket No. 103361-500WO1 T2023-353

[0036] Figs. 3B and 3C show examples of opportunistic differential frameworks employing the carrier phase observable generated by the blind Doppler tracker of Fig. 2 in accordance with an illustrative embodiment.

[0037] Fig. 4 shows the simulation results of the exemplary blind receiver system and method and demonstrates its ability to successfully estimate the 5G frame transmitted by a Starlink LEO satellite.

[0038] Fig. 5 shows hardware components employed in a study to evaluate the exemplary blind receiver system and method.

[0039] Figs. 6A – 6G show experimental results of Blind beacon estimation of four LEO satellite signals in accordance with an illustrative embodiment.

[0040] Figs. 7A – 7C show experimental results for multi-constellation satellite positioning measurement in accordance with an illustrative embodiment.

[0041] Figs.8A and 8B each shows parameters of various LEO satellite constellation networks that were employed in the study, and that can be used in the exemplary system and method described herein. DETAILED DESCRIPTION

[0042] To facilitate an understanding of the principles and features of various embodiments of the present invention, they are explained hereinafter with reference to their implementation in illustrative embodiments.

[0043] Some references, which may include various patents, patent applications, and publications, are cited in a reference list and discussed in the disclosure provided herein. The citation and / or discussion of such references is provided merely to clarify the description of the present disclosure and is not an admission that any such reference is “prior art” to any aspects of the present disclosure described herein. In terms of notation, “[n]” corresponds to the n-th reference in the list. All references cited and discussed in this specification are incorporated herein by reference in their entirety and to the same extent as if each reference was individually incorporated by reference.

[0044] Example System

[0045] Fig. 1 shows a system 100 comprising a blind beacon estimation and Doppler tracking module 102 that is configured to generate navigation observables from broadband LEO satellitesAttorney Docket No. 103361-500WO1 T2023-353 using repetitive sequences (also known as a beacon) observed from the high dynamics between the LEO satellite and a terrestrial receiver agnostic to the modulation and multiple access operation of the LEO satellite. The exemplary system and method can generate navigation observables from broadband LEO satellites without the need to know the signal specifications using such repetitive sequences.

[0046] In the example shown in Fig. 1, the blind beacon estimation and Doppler tracking module 102 are operatively coupled to a receiver 104 that is configured to observe and receive RF transmission having frequencies and bands allocated to LEO satellites. Plot 106 shows a time- frequency plot of an example RF signal observed in the frequency and bands associated with LEO satellites. The module 102 includes a blinder Doppler tracker 108 comprising a spectral cross- correlation and Kalman filter (KF)-based tracker 110 (shown as a “KF-based tracker” 110), a code phase tracker 112, and a Doppler Ambiguity Resolver 114.

[0047] The spectral cross-correlation and Kalman filter (KF)-based tracker 110 is configured to lock on a candidate feature in the received RF signal in the frequency domain having high dynamics as a potential satellite feature. After the blind Doppler tracking loop 110 achieves lock, the code phase tracker 112 starts to correct the carrier phase changes and track the code phase of the repetitive sequence. The Doppler Ambiguity Resolver 114 operates with the spectral cross- correlation and Kalman filter (KF)-based tracker 110 and the code phase tracker 112 to blindly estimate the deterministic repetitive sequence present and resolve for the Doppler ambiguity associated with the estimated repetitive sequence.

[0048] In Fig. 1, the receiver 102 is shown to receive signals 116 from (i) Satellite #1 (118) (shown as time t 118a, and time t+1118b) and (ii) Satellite #2 (120) to track repetitive sequence (122) s[n].

[0049] Example Blind Beacon Estimation and Doppler Tracking

[0050] Fig. 2A shows an example blind beacon estimation and Doppler tracking module 102 (also referred to as a blind receiver 200) comprising the blinder Doppler tracker 108 (shown as 202), the code phase tracker 112 (shown as 204), and a Doppler Ambiguity Resolver 114 (shown as 206).

[0051] Blind Doppler Tracking. The blind Doppler tracking operation 202 employs a frequency-domain-based Doppler discriminator and Kalman-filter-based Doppler tracking loop. The loop includes a frequency-domain-based Doppler discriminator 208 and a Kalman-filterAttorney Docket No. 103361-500WO1 T2023-353 Doppler tracker 210 configured in loop 212 that removes carrier wipe-off from the received signal. The blind Doppler tracking operation relies on the existence of a repetitive sequence in the signal transmitted by the LEO satellite.

[0052] The first step in the process of blindly estimating the beacon is to perform a Doppler wipe-off. After a successful Doppler wipe-off, the receiver begins the estimation and refinement of the repetitive sequence.

[0053] Repetitive sequence. The existence of repetitive sequences in a communication system can inherently exist in the source and channel encoding, modulation, and multiplexing schemes or abundantly transmitted by the communication source for synchronization purposes at the UE. For example, code division multiple access (CDMA), e.g., in cellular 3G

[0045] , GPS

[0046] , and Globalstar LEO

[0047] , can employ repetitive sequences in the form of pseudorandom noise (PRN) codes to spread the data before transmission. In OFDM used in 4G long-term evolution (LTE)

[0048] and 5G

[0049] , the primary synchronization sequence (PSS) and secondary synchronization sequence (SSS) define repetitive sequences in the signal transmitted by cellular towers.

[0054] Moreover, repetitive sequences can be defined as permanently or temporarily repeated patterns in the transmitted user data. As an example, Orbcomm LEO satellites transmit their ephemeris packets every 4 seconds

[0050] . The ephemeris packet contains the current date and time, which is temporarily repetitive (the same), along with the symbols corresponding to the day, month, and year.

[0055] Baseband Received Signal Model. The blind Doppler tracking operation can operate based on a signal model in which x(t) is an unknown signal transmitted by a LEO satellite before carrier modulation. The blind Doppler tracking operation does not assume knowledge of any particular modulation or multiplexing scheme. The signal model is written as x(t) = s(t)+nd(t), where s(t) is a deterministic repetitive signal, and nd(t) is a random signal driven by the user data. The blind Doppler tracking operation can operate if s(t): (i) is periodic with period T0, (ii) is uncorrelated with the user data nd(t), and (iii) is zero-mean and has a stationary power spectral density (PSD) *+{,-.) / 01-.)}*2= 34-5), where / 01-.) is a windowing function that is unity within

[0056] The unknown signal x(t) is transmitted at a carrier frequency fc. The apparent delay τd(t) between a transmitted signal denoted as xc(t) 6 x(t) exp(j2πfct) and a received signal 78-.)9at the receiver’s antenna can be the composition of multiple effects: (i) the time-of-flight along theAttorney Docket No. 103361-500WO1 T2023-353 line-of-sight (LOS) between the transmitter and receiver (e.g., dLOS(t) / c, where dLOS(t) is the LOS distance between the LEO satellite’s transmitter and the receiver and c is the speed of light); (ii) combined effect of the transmitter’s and receiver’s clock biases, denoted asionospheric and tropospheric delays δtiono(t) and δttropo(t), respectively; and (iv) other unmodeled errors. After propagating in an additive white Gaussian channel, the resulting received signal 78-.)9beforebaseband mixing can be expressed as Equation 1A.78-.) = :8--. ; <>-.)).) ? @8-.).)(Eq. 1A)

[0057] In Equation 1A, @8-.) is complex, zero-mean, white Gaussian noise with two-sided PSD N0 / 2. The received signal r−(t) after baseband mixing and filtering can be expressed asEquation 1B.7F-.) 6 78-.) exp-;CDE58.)=:-. ; <>-.)) exp[C!-.)] ? @F-.)(Eq. 1B)

[0058] In Equation 1B, @F-.)is a lowpass-filtered version of @8-.), and !-.)is the carrierphase of the received signal expressed as Equation 1C.!-.) 6 ;DG58<>(t)(Eq. 1C)

[0059] Using a Taylor series expansion (TSE), at time instant ."= .&? HI&, where k is thesub-accumulation index, and .&9is some initial time; the carrier phase of the received signal!"-.) 6 !-. ? .")J01-.)9for t Î [0, T0) can be approximated per Equation 2.!"L-K !-? !#-." . ? .2(Eq. 2)

[0060] The apparent Doppler shift 5M-.)9can be expressed as 5M- 6N# -O), and the apparent Doppler rate 5#-.)9 express#--O)M ed as 5M9. The channel satellite and theopportunistic receiver is highly dynamic; thus, high Doppler shift and rate would be observed by the receiver.Attorney Docket No. 103361-500WO1 T2023-353

[0061] At a given k-th sub-accumulation, the apparent delay <>(t) can be approximated by its zero-order TSE term Q"K <>-.") and the higher-order terms can be dropped to simplify the following signal analysis. The higher-order terms in the code phase can account for compression and dilation of the code in the time-domain and can be ignored for the analysis per experimental results described later herein, which observed such effect to be negligible for the Orbcomm,Iridium NEXT, Starlink, and OneWeb LEO constellations. The expression of the received signal7F" -.) before carrier wipe-off at the k-th sub-accumulation can be expressed per Equation 3.7F" -.) 6 7F-. ? .") / 01-.).)^ (Eq. 3)

[0062] In Equation 3, ,"-.) 6 ,-. ; Q")9 / 01-.) is the lumped user data, and @F"-.) 6[@F-. ; Q") ? @>-. ; Q")] / 01-channel noise. The blind Doppler trackingoperation can determine !("-.) as the received signal 7"-.) after the carrier wipe-off using the carrier phase estimate in a tracking loop per Equation 4A, where^the residual carrier phase !$"canbe defined as !$" = !"-.) ; !(".7"-.) = 7F" -.) expR;C!("-.)S^.)^(Eq. 4A) >^^^^@ Frequency Spectrum of the Received Signal. The received signal’s frequency spectrum at the k-th sub-accumulation 3TU-5)can be determined as 3TU-5)=|+{7"-.)}|2. Using the third property of ,-.), a Wigner distribution function (WDF) of ,"-.) for t V [0, T0) can be written per Equation 4B.^ _ <<=I&(Eq. 4B)Attorney Docket No. 103361-500WO1 T2023-353

[0064] In Equation 4B, s^denotes the complex conjugate of s. It can be shown that the WDF of the residual carrier phase at the k-th sub-accumulation `"-.) = exp9-C!$"-.)), for t Î [0, T0), can be expressed as Equation 4C. $Wa9 # $%U-.X 5) = 9b c5 ;!";99!".d9(Eq. 4C)

[0065] In Equation 4C, the second property of 3-.), the WDF of 7"-.)^in Equation 4A, for t V [0, T0), becomes Equation 4D. WTU-5) =34-5)g b c5 ;9!$#";99!$%".d ? Wh -.X 5)(Eq. 4D)In Equation 4D, 5 g i Q. = _

[0066] - ) jF_ 5-<)i-. ; <)Q< 9is the convolution of 5 and i, andW -.X 5) is the WDF of the noise andat the k-th sub-accumulation. Using theof WDF, the frequency spectrum 3TU-5) =j01& WTU-.X 5) 9can be further expressed per Equation 5. 0134-5) 9!$#" 99!$%5) )(Eq. 5)

[0067] Equation 5 implies that the received signal’s frequency spectrum can include a shifted and dilated version of the repetitive sequence’s frequency spectrum alongside noise. The shift inAttorney Docket No. 103361-500WO1 T2023-353 the received spectrum is due to the residual Doppler !$#", while the dilation is due to the residualDoppler rate !$%".

[0068] Frequency Domain-Based Doppler Discriminator. The nonlinear least-squares (NLS) estimator (208) of the residual Doppler !$#"(214) at the k-th sub-accumulation can be derivedfrom Equations 6 and 7 to provide Equation 8.!$# = q^^^^r ^3 -5) ; # %2" TU 34-5) g l-^m ! X !)^N#6)7)

[0069] In Equation 8, -5 ^ i)-<)= j_F_5^-.)i-. ? <)Q. is the cross-correlation of 5 and i. The first two terms in theEquation 7 are a constant function of the optimization parameter !#, therefore, they can be ignored. Since the blind receiver (200) does not have prior knowledge of 34(f), it can start with an initial estimate 3^4-5) ^ 3T^-5) and refines the repetitive sequence’s spectrum with every sub-accumulation. This initialization approach introduces a Doppler ambiguity !$#&invoked by taking 3T^-5) as initial spectral reference for Doppler tracking. The Doppler ambiguity can then be resolved. The assumption !$%"K ^ (i.e., regime of small residual Doppler rate values) invoked in Equation 8 is a reasonable assumption since the Doppler rate between two consecutive sub-accumulations can be considered to be nearly constant for LEO satellite channels.

[0070] KF-Based Tracking Loop. The continuous-time signal in Equation 4A can be sampled at a constant sampling interval I4= L^^4. The discrete-time received signal before carrier wipe- off at the k-th sub-accumulation 7"F[@] (216) can be written per Equation 9.Attorney Docket No. 103361-500WO1 T2023-353 7"F[@] = ,[@ ; Q"] exp-C^"[@]) ? @"F[@] (Eq. 9)

[0071] In Equation 9, n Î [0, L − 1]; s[n] is the discrete-time equivalent of s(t) with period L = T0 / Ts; ^k[n] and dkare the discrete-time carrier phase and code phase, respectively, of the received signal at the k-th sub-accumulation; and @"F[@]is the discrete-time equivalent of @"F-.).

[0072] The continuous-time carrier phase state vector may be defined as !-.) 6R!-.)X !#-.)X !%-.)S0^^ with dynamics modeled as Equation 10.!#-.) = ^!-.) ? 9^ / -.),^^ ^^^ ^ L(Eq. 10)

[0073] In Equation 10, / -.) is a zero-mean white noise process with PSD ^^. The continuous- time model in Equation 10 can be discretized at a constant sampling time T0= LTs, leading toEquation 11.'"^^ = ^'" ?9 / "(Eq. 11)

[0074] In Equation 11, '"6 R!"X !#"X !%"S (218) is the carrier phase state at the k-th sub- accumulation, ^ 6 o^01is thematrix, and / "is a discrete-time process noise inwhich a zero-mean white random sequence with covariance ^ can be defined as ^ =^ 01^ j& o^^^-o^^^)^Q.. The reconstructed sequence of the carrier phase '^"[r] that is used toperform carrier wipe-off can be written as a second-order piecewise polynomial given by '^"[r] =!("F^ ? !(#"@I4 ? ^2 !(%"-@I4)2, n ę [0, L-1]. In Fig. 2A, a numerically controlled oscillator (221) isto a tracked residual carrier phase !("[r] of the KF 224.carrier wipe-off, the received signal’s sequence 7"[@] (220) can be expressed per Equation 12.7"[@] = 7F" [@]exp9[;C'^"[@]]= ,[@ ; Q"]o:  ¡;C'^"[@]¢ ? @"[@](Eq. 12)Attorney Docket No. 103361-500WO1 T2023-353

[0075] Equation 12 can be used to determine the residual Doppler !$#"(214) at the k-th sub- accumulation, which is fed to the KF loop 212 that uses the observation model, e.g., described perEquation 13.£" = ¤'" ? ¥"X ¤ 6 [^ L ^](Eq. 13A)

[0076] In Equation 13A, vk is a discrete-time zero-mean white noise sequence with variance¦2N#. The KF innovation vk (shown “Kalman Filter” 224) is the fast Fourier transform (FFT)-baseddiscrete version of Equation 8 per Equation 13B.¥-H) = !$# = DG q | |2 ^ 2§¨ " ^^^qx 9 ©"[5] ^ 9 *3"[5]* 9^(Eq. 13B)

[0077] In Equation 13B, ©"[5] (shown as ©"[ / ] (226)) and 3^"[5] (shown as 3^"[ / ] (228)) are the FFT of 7"[@] (220) and ,[n], respectively. The blind Doppler tracking loop (212) can be considered to be in the locked regime whenever the innovation sequence vk(e.g., in 224) becomes nearly white and its variance stabilizes. In this regime, '^"Ĭ [0, 0, 0]Tand 7"[@] Ĭ s [n − dk]+nk[n].

[0078] The KF (224) can be initialized with '^&^ ¡!(&X !(#&X !(%&¢ that gives rise to an initial ^ carrier phase state error 'ª&^ ¡!$&X !$#&X !$%&¢ . For theC defined in Equation 13A, the initial carrier phaseunobservable, which can induce a shift in the phase of the estimated repetitive sequence, causing the initial Doppler error !$#&to persist as an ambiguity in a tracked Doppler !(#"9(222) since it is embedded into the first received sub-accumulation, which is taken as a reference for tracking. But to the linearity and time-invariance of Equations 11 and 13A, the residual carrier phase state vector '^"could converge to zero.

[0079] Code Phase Tracking. After the blind Doppler tracking loop (212) achieves lock, the code phase tracking portion (204) of the blind receiver (200) can start to correct the carrier phase changes and track the code phase of the repetitive sequence. Given Equation 12, the NLS estimate (from estimator 208) of the tracked code phase Q^"(228) at the k-th sub-accumulation can beexpressed per Equation 14.Q^" = «7"[@] ; ,[@ ; Q]«2Attorney Docket No. 103361-500WO1 T2023-353 =q^^>^^r {«7"[@]]«2 ? «,[@ ; Q]«2 ; D-7" ^ ,)[Q]}(Eq. 14)

[0080] The NLS code phase estimator (208) given by Equation 14 is only valid while the Doppler tracking loop 212 is locked and the carrier phase changes (e.g., !") are tracked and wiped-off at every sub-accumulation. Without the lock condition, the residual carrier phase sequence'^"[n] (e.g., maintained in KF 224) present in Equation 12 could deteriorate the NLS estimator(208) performance (Fig. 2B).

[0081] Furthermore, as the blind receiver (200) does not have prior knowledge of deterministicrepetitive beacon sequence s[n], it starts with an initial estimate of the beacon sequence ,¬[@] ^7&[@] and uses it as a reference to track the code phase Q^". The initialization introduces a codephase ambiguity d0. After tracking the code phase Q^"(228), the receiver (200) can correct for thecode phase shift 7"[@] (230) per Equation 15.7"[@] 6 7"[@]9®9Q^"= ,R@ ; Q^"So:  ¡;C'^"[@]¢ ? @"[@](Eq. 15)

[0082] In Equation 15, -:[@]®Q)denotes the circular shift operation (232) that shifts the sequence x[n] by d samples, and the code phase error Q¯"(234) at the k-th sub-accumulation can be determined as Q¯"= Q"; Q^".

[0083] Blind Navigation Beacon Estimation. In module 206, given Equation 9, the time- varying parameters modulating the deterministic repetitive beacon sequence s[n] may be determined as: (i) the carrier phase state vector '"(218) and (ii) the code phase Q"(228). Based on the blind Doppler tracking (202) and the code phase tracking (204) to track and wipe-off theeffect of the time-varying parameters in the regime of successful Doppler and code phase tracking,°'ª"[@] K ^X Q¯" K ^±, Equation 15 can be simplified to 7"[@] K ,[@] ? @"[@]. At this stage, the(200) is ready to (i) blindly estimate the deterministic repetitive sequence present in Equation 15 and (ii) resolve the Doppler ambiguity associated with the estimated repetitive sequence.Attorney Docket No. 103361-500WO1 T2023-353

[0084] Beacon Estimator Formulation. Let 7", @", ,, ², H, and / denote the equivalentcomplex vector form of the terms in Equation 15 such that³" 6 [7 ^"[^] ´ X 7"[µ ; L]] ,¶" 6 [@·"[^] ´ X @·"[µ ; L]]^,¸ 6 [,[^] ´ X ,[µ ; L]]^,¹ 6 [³^^ X ´ X ³^º ]^,´ ^ ^,

[0085] where ½¾denotes the L; ³"9and ¶"9denotes the vectors ofobserved and noise samples at the k-th sub-accumulation, respectively; ¹ and » denote the vectors of concatenated observations and noise of M sub-accumulations, respectively; s denotes the vector of the deterministic repetitive sequence present in the received signal that is sought to be estimated; and ¼^denotes the observation matrix of the M^sub-accumulations in the regime of Doppler andcode phase tracking lock. The vector ¹ of observed samples can be expressed per Equation 16.¹= ¼¸ ? »

[0086] In Equation 16, »^is as zero-as¿ = ¦2h½¾×º. Given the observation model in Equation 16, the least-squares estimate of therepetitive sequence s may be expressed as Equation 17. º L(Eq. 17)

[0087] In Equation 17, -f)Ádenotes the Hermitian transpose operator.

[0088] Convergence Property. The convergence property for the beacon estimator given in Equation 17 can be employed as the stopping criterion. The energy in the estimated sequence À¸ºafter M sub-accumulations can be expressed as Equation 18A. º ºAttorney Docket No. 103361-500WO1 T2023-353 º º º = «,«2?DÄÆ{¸Á}L Áà ¶"? Ã2ÄÄÆ°¶È¶"± (Eq. 18A)

[0089] The fact that = ^ follows from the second and third properties of s(t), whileÆ°¶ Á 2È ¶"± = µ¦hbÊÈ, where bÊÈ is the Kronecker delta function, follows from the assumedwhiteness of the noise. According to Equation 18,2 2h Ë^Ì^_Æ{«,¬º]« }=«,«9. Therefore, the energy in the estimated beacon decreases with every additional observeduntil reaching a steady-state value equal to the energy of the true beacon «,«2. The stopping criterion for thebeacon estimator may then be given per Equation 18B.«,¬º«2Í ÎOÏX^(Eq. 18B)

[0090] In Equation 18B, ÎOÏ^is a predetermined constant, e.g., chosen to be 0.9. Other constant values may be used. >^^^^@ Doppler Ambiguity Resolution. To resolve the Doppler ambiguity !$#&present in the estimated repetitive sequence, the receiver relies on the relationship between the carrier and code phase tracking loops (212, 236), respectively. ^

[0092] Let !#"= !(#"; !$#&? ¥N# X"99denotes the true ambiguity-free Doppler shift, where ¥N# X"is a discrete-time frequency noise. Therefore, the true carrier phase !"can be expressed as Equation 19. º º(Eq. 19)

[0093] In Equation 19, !&is the initial carrier phase ambiguity. Let the true code phase Q"be defined as Q"= Q^"+ Q&+ ¥>X", where ¥>X"is the discrete-time code phase noise. The discretization of Equation 1C relating to the code and carrier phase yields Equation 20.Attorney Docket No. 103361-500WO1 T2023-353 !"= ;DG58Q"= ;D9G58-Q^"? Q&?9¥>X")) (Eq. 20)

[0094] Equating (19)²" = !$#&-HI&) ? Ð& ? ¥"(Eq. 21)

[0095] In Equation 21, the is a function of the ambiguous Doppler term !$#&, can be determined as ²"= !("? DG58Q^". The lumped ambiguity term Ð&can be determined as Ð&=9;-!&? DG58Q&). The lumped code and carrier phase noise ¥"can be determined as ¥"= -¥NX"; DG58¥>X"). With sufficient sub-accumulations M, the initial Doppler error Doppler ambiguity !$#&can be estimated from Equation 21 by fitting a linear regression model with ²"as the target variable and HI&as the regressor.

[0096] Multi-Constellation Satellite Positioning Measurement

[0097] Fig. 3A shows an example multi-constellation positioning receiver configured to execute the blind Doppler tracker of Fig. 2A in accordance with an illustrative embodiment. The carrier phase navigation observables produced by the exemplary blind beacon estimation and Doppler tracker, are implemented and shown for each individual constellation, as well as a fusion from all four constellations, to localize a stationary receiver.

[0098] Carrier Phase Measurement Model. Let i Î [1, L] denote the satellite’s index, where L is the total number of satellites. The carrier phase observable ÑÊ-H) can be determined as ÑÊ-H) 6 ÒÈÅ&^ÓN^"F #ÔI&for each satellite via a model per Equation 22 by integrating the Dopplerk, which represents the discrete-time instant tk= t0+kT0 for an initial time t0, e.g., expressed in meters.ÑÊ-H) = ^³T ; ³ÖØÙ-HÚ)^2 ? Ó f Rb.T-H) ; b.ÖØÙ-HÚ)S ? Ó f Rb.OTÛÜÙ-H) ? b.ÊÛhÛÙ-H)S ? ÝÊÞÊ(Eq. 22)

[0099] In Equation 22, ³T6 [:TX ²TX £T]^is the stationary receiver’s position vector in the East- North-Up (ENU) frame; ³ÖØÙ6 [:ÖØÙX ²ÖØÙX £ÖØÙ]^is the i-th satellite’s position vector in the ENUframe; bOT and bÖØÙ are the receiver’s and i-th satellite’s clock biases, respectively; b.OTÛÜÙ andb.ÊÛhÛÙ are the ionospheric and tropospheric delays between the receiver and i-th satellite,Attorney Docket No. 103361-500WO1 T2023-353 respectively; c is the speed-of-light; ÝÊis the wavelength of the i-th satellite’s signal; ÞÊis the carrier phase ambiguity between the receiver and i-th satellite; and ¥Êis the measurement noise, which is modeled as a discrete-time mean white sequence with variance ¦ß2XÊ.

[0100] In Equation 22, the time index HÚrepresents discrete step ."= .&? HI&? b.0àáÙ, where b.0àáÙis the time-of-flight of the signal from the i-th satellite to the receiver. The operation can assume HÚK H for the formulation of the NLS positioning framework. The approximation introduces an error in the LEO satellite position and clock bias. The error introduced by the approximation in the LEO satellite position is negligible compared to the position error in TLE files, which can be as high as a few kilometers. The error introduced by this approximation in the LEO satellite clock can be lumped into a combined term and estimated as described next.

[0101] The receiver and LEO satellite clock error states (bias and drift) may be modeledaccording to the standard double integrator model [3]. The terms b.T-H), b.ÖØÙ-H), b.ÊÛhÛÙ-H),b.OTÛÜÙ-H) may be lumped together and approximated as a first-order TSE, to approximateEquation 22, per Equation 23.ÑÊ-H) K ^³T ; ³ÖØÙ-H)^2 ? âÊ ? ÐÊHI& ? ¥Ê-H)(Eq. 23)

[0102] In Equation 23, âÊ 6 Ó ã -b.T ; b.ÖØÙ ? b.ÊÛhÛÙ ? b.OTÛÜÙ) and ÐÊ 6 Ó ã -b#.T ; b#.ÖØÙ ?b#.ÊÛhÛÙ ? b#.OTÛÜÙ) are the zero- and first-order TSE terms, respectively, of the lumped clock errorsanddelays.

[0103] Batch NLS Estimator. Next, the state vector x can be defined as : 6[³ ^T X â^X Ð^X ´ X â¾ X о]^. Let z(k) denote the vector of carrier phase observables from all LEOsatellites, available at time-step k, stacked together, i.e., £-H) 6 [Ñ ^^-H)X´ XѾ-H)] . The vector£ of all available observables is defined as £ 6 [£-^)X ´ X £-Ã)]^, where M is the total number ofobservations during the satellite’s pass. Let vzof all measurement noises stacked together. Then, the measurement equation can be expressed z = g(x)+9 ¥ä, where g(x) is the nonlinear mapping from the state space x^to the measurement space z. The positioning solutionmay be achieved by iterating over the NLS update equation per Equation 24.åæç = A¼^¼ BF^¼^Ü Ü Ü Ü A£ ; è-:ÀÜ)BAttorney Docket No. 103361-500WO1 T2023-353 (Eq. 24)

[0104] In Equation 24, p Î {1, 2, . . . , p^} denotes the recursion index; p^ is the index when^æç 2 − éê-ë)Ü^ reaches a predetermined stopping criterion (e.g., chosen to be 10 6); ¼Ü 6 éë |æÅæçì is themeasurement Jacobian matrix.

[0105] Global Positioning Transceiver

[0106] Fig.3A shows an example multi-constellation positioning receiver 300. In the example shown in Fig. 3A, the carrier phase observable ÑÊ-H)is determined for one or more LEO constellation satellites via a set of transceiver 302 as 302a, 302b, 302c). The output carrierphase observable can then be fused, via a controller 304, to output localization data (e.g., 2D or 3D global positioning coordinates) for the receiver.

[0107] The Starlink transceiver 302a includes a low-noise receiver 306 that operates with a base receiver 307 that couples to a Ku-band antenna 305. In the example shown in Fig. 3A, the low-noise receiver 306 includes a bandpass filter 308, a low noise amplifier 310, a demodulator 312, a second bandpass filter 314, and a second low-noise amplifier 316. The low-noise receiver 306 is coupled to a baseband receiver 307 comprising a demodulator 320 and an analog-to-digital converter 322. The sampling bandwidth Fs may be set to 500 MHz, the carrier frequency fc set to 11.325 GHz, to correspond to the center of one of Starlink’s downlink channels in the Ku-band.

[0108] The Orbcomm transceiver 302b includes a receiver comprising a demodulator 320 (shown as 320’) and an analog-to-digital converter 322 (shown as 322’). The sampling bandwidth Fs may be set to 2.4 MHz and the carrier frequency fc set to 137 MHz.

[0109] The Iridium NEXT transceiver 302c includes a receiver comprising a demodulator 320 (shown as 320”) and an analog-to-digital converter 322 (shown as 322”). The sampling bandwidth Fs may be set to 2.4 MHz, the carrier frequency fc set to 1626.2708 MHz in the L̢band.

[0110] In some embodiments, a global positioning transceiver (e.g., a universal GNSS RF receiver) may be implemented using an architecture shown in Fig. 3A. The global positioning transceiver may be employed as a processor (e.g., digital signal processor, ASIC, or combination thereof) having memory with instructions stored thereon to execute the operation described in relation to Fig. 2. In some embodiments, the global positioning transceiver is implemented as a single chip integrated circuit (IC).Attorney Docket No. 103361-500WO1 T2023-353

[0111] The processor may represent a single processing device or multiple processing devices. Similarly, memory may represent a single memory device or multiple memory devices. Processor can be a microcontroller, microprocessor, an ASIC, one or more FPGAs, a group of processing components, or other suitable electronic processing structures. In some embodiments, the processor is configured to execute program code stored in memory to cause the controller to perform one or more operations, as described below in greater detail. It will be appreciated that, in embodiments where the controller is part of another computing device, the components of a controller may be shared with, or the same as, the host device.

[0112] Memory can include one or more devices (e.g., memory units, memory devices, storage devices, etc.) for storing data and / or computer code for completing and / or facilitating the various processes described in the present disclosure. In some embodiments, the memory includes tangible (e.g., non-transitory), computer-readable media that store code or instructions executable by the processor. Tangible, computer-readable media refers to any physical media that is capable of providing data that causes the controller to operate in a particular fashion. Examples of tangible, computer-readable media may include, but are 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. Accordingly, memory can include RAM, ROM, hard drive storage, temporary storage, non- volatile memory, flash memory, optical memory, or any other suitable memory for storing software objects and / or computer instructions. Memory can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present disclosure. Memory can be communicably connected to a processor, such as via a processing circuit, and can include computer code for executing one or more processes described herein.

[0113] Opportunistic Differential Framework

[0114] Figs.3B and 3C show example of opportunistic differential frameworks employing the carrier phase observable ÑÊ-H)í In Fig. 3B, the blind navigation beacon estimator is shown used for real-timeof communication protocol and opportunistic navigation. The navigating receiver may be employed, e.g., in a GNSS-challenged environment. The system includes vehicles such as land-based vehicles, water-based vehicles, or aerial vehicles. In some embodiments, the system includes unmanned aerial vehicles (UAV). The various vehicles canAttorney Docket No. 103361-500WO1 T2023-353 employ the LEO satellite blind Doppler receiver (e.g., 300), executing the blind beacon estimation for navigation or location.

[0115] Fig. 3C shows an example differential simultaneous tracking and navigation using the exemplary blind beacon estimation in combination with GNSS. In the example shown in Fig.3C, the system 330 includes a GNSS receiver 332 coupled to a GNSS antenna 334 that communicate with base stations 336 (shown as “Base 1” (336a), …, “Base N” (336b)).

[0116] The system 330 includes a LEO satellite receiver 338 (e.g., 300) having one or more receiver modules for at least one LEO satellite constellation network. The receiver 338 is coupled to a LEO satellite antenna 340 that communicates with the LEO satellite constellation network 342 (shown as “LEO SV 1” (340a), …, “LEO SV L” (340b)).

[0117] The receiver 338 provides the discrete-time received signal before carrier wipe-off at the k-th sub-accumulation 7"F[@] (e.g., 216), as described in relation to Fig.2, to the blind Doppler tracker 202 (shown as “Leo Propagation” 342). The Kalman filter 344 (shown as “EKF Prediction”) includes the blind Doppler tracker 342, Inertial Navigation System (INS) states 346, and clock models 348. In this example, the INS states 346 are updated from inertia measurement unit (IMU) 350. The EKF updates module 352 then fuse the Doppler measurements from module 342, the GNSS receiver 332, and the INS state 346.

[0118] The differential simultaneous tracking and navigation can be employed for differential pseudo-ranging measurement per equation model 354 or for differential Doppler measurement per equation model 356. The Doppler or localization from the LEO satellites and GNSS networks can be stacked together to provide zl.

[0119] Experimental Results and Additional Examples

[0120] A study was conducted to develop and evaluate a framework for blind beacon estimation and Doppler tracking of LEO satellites. The study developed a derivation of an analytical expression for the received signal frequency spectrum. The study also developed a frequency-based Doppler discriminator. The study also developed a KF-based Doppler tracking algorithm. The study developed a blind beacon estimation framework and demonstrated the operation on four LEO constellation networks, including Orbcomm, Iridium NEXT, Starlink, and OneWeb. The study also showed the first result of stationary receiver localization with multi- constellation LEO satellites, including OneWeb, achieving a 2–D position error of 5.1 m.Attorney Docket No. 103361-500WO1 T2023-353

[0121] Numerical Simulation. The study demonstrated, via numerical simulations, the ability of the exemplary system and method to blindly estimate the beacon transmitted by an LEOsatellite. Following the notation described in Equation 9 (reproduced).7F" [@] = ,[@ ; Q"] exp-C^"[@]) ? @F"[@](Eq. 9)

[0122] In this example, the deterministic repetitive sequence s[n] is chosen to be the Synchronization Sequence Block (SSB) of the 5G-NR frame structure with period T0, bandwidth B, and energy ||s||2, e.g., as described by the 3GPP. The phase ^k[n] can be assumed to follow the Doppler a Starlink LEO satellite, and the noise component of the signal @"F[@] is modeled as a white random process with PSD µ¦h2. Table I summarizes the simulation parameters. Table 1 Parameter Value Unit 2

[0123] The first step in the process of blindly estimating the beacon is to perform a Doppler wipe-off, e.g., as described in relation to Fig.2. The exemplary blind receiver system and method (e.g., 200) only relies on the assumption that the PSD of the deterministic repetitive sequence in a received signal is stationary. Therefore, the exemplary blind receiver system and method is capable of tracking and wiping off the Doppler with no a priori knowledge of the temporal or spectral signal structure. After the successful Doppler wipe-off, the receiver begins the estimation and refinement of the repetitive sequence.Attorney Docket No. 103361-500WO1 T2023-353

[0124] Fig. 4 shows the simulation results of the exemplary blind receiver system and method and demonstrates its ability to successfully estimate the 5G frame transmitted by a Starlink LEO satellite. Specifically, Fig.4 shows simulation results showing successful blind beacon estimation and Doppler tracking of emulated 5G-NR signals transmitted by Starlink LEO satellites: (a) Left: frame of an observed sample sub-accumulation on the left, Middle: refined repetitive sequence after M sub-accumulations, Right: ground truth repetitive sequence’s frame. (b) In-phase and quadrature (IQ) components of the estimated sequence and the true sequence. (c) Black: true repetitive sequence’s energy. Blue: the energy of the realization shown in (a) and (b). Orange: the expected energy (cf. Equation 18A) of the estimated sequence «,¬º«2versus the number of observed sub-accumulations M, respectively. (d) The correlation functionbetween the estimated and true repetitive sequence. (e) The error between the true Doppler shift and the one estimated using the proposed blind Doppler tracker.

[0125] In particular, Fig. 4, subpanel A shows the frame of (i) an observed sample sub- accumulation rk (402) that includes the repetitive sequence alongside data and channel noise, (ii) the refined repetitive sequence À¸ºafter M sub-accumulations (404), and (iii) the ground truth repetitive sequence (406).

[0126] Fig.4, subpanel B, compares the IQ components of the estimated sequence (408) versus the true sequence (410). The 5G-NR SSB, which was taken as the repetitive sequence for the simulation, included 4 OFDM symbols, including (i) PSS at symbol 1, (ii) SSS at symbol 3, and (iii) a physical broadcast channel (PBCH) at symbols 2 to 4. Moreover, Fig. 4, subpanel B shows the unobservable constant phase shift !$&, which is embedded into the estimated sequence relative to the true sequence’s constellation.

[0127] Fig.4, subpanel C, shows a plot in line 412 the energy of the estimated sequence«,¬º]«versus the number of observed sub-accumulations M (y-axis). The curve followed the shape of the theoretical curve Æ{«,¬º]«2}9(Equation 18A) shown in line 414. The line 416 represents the true repetitive sequence’s energy, «,«2, which lower-bounds the energy of the estimated sequence.

[0128] Fig. 4, subpanel D,normalized cross-correlation function (418) between the estimated and true repetitive sequence. The prominent cross-correlation peak (420) is an indicator of successful beacon estimation.

[0129] Fig. 4, subpanel E shows the error (422) between the true Doppler shift and the one estimated using the exemplary blind Doppler tracker during a satellite pass, indicating theAttorney Docket No. 103361-500WO1 T2023-353 exemplary blind receiver system and method is capable of tracking the Doppler with Hz-level accuracy. Experimental results are later shown for four LEO constellations: Orbcomm, Iridium NEXT, Starlink, and OneWeb.

[0130] Beacon Estimation and Blind Doppler Tracking of Orbcomm, Iridium NEXT, Starlink, and OneWeb. Experimental results demonstrating successful beacon estimation and blind Doppler tracking are shown for four LEO constellations, namely Orbcomm, Iridium NEXT, Starlink, and OneWeb, which transmit their downlink signals according to different modulation schemes. The receiver initialized with and tracked the signal’s stationary PSD to generate Doppler observables. Finally, a positioning solution was generated using the estimated observables. Fig. 5 shows an overview of the hardware components used to receive downlink signals from the four LEO constellations. The captured samples were stored and then processed via a software-defined radio implementation (SDR) of the exemplary blind receiver system and method.

[0131] Specifically, Fig. 5 shows a block diagram of signal capture setup for Orbcomm satellites (502), Iridium NEXT satellites (504), Starlink satellites (506), and OneWeb satellites (508).

[0132] Orbcomm LEO Constellation. The exemplary blind receiver system and method was applied to downlink Orbcomm LEO satellite signals. A stationary National Instrument (NI) universal software radio peripheral (USRP) E312 was equipped with a commercial Orbcomm antenna to receive signals in the VHF-band. The sampling bandwidth Fs was set to 2.4 MHz, and the carrier frequency fcwas set to 137 MHz. The duration of the recorded data was 900 seconds. Orbcomm satellites transmit at a predefined set of frequency pairs in the user downlink spectrum with an effective channel bandwidth B = 4.8 kHz. Fig.8A shows parameters 802 of the Orbcomm LEO constellation satellites.

[0133] After collection, the Orbcomm signal was fed to the exemplary blind receiver system and method, as described in relation to Fig. 2A (e.g., 200). For comparative purposes, the true transmitted data of the Orbcomm satellites was decoded using the scheme described in

[0051] .

[0134] After decoding, the signal auto-correlation showed repetitive behavior every T0intervals equating to 1 second. The decoded data was averaged in a T0-window over a sufficient number of sub-accumulations to increase the effective energy of the repetitive sequence. The blindly estimated beacon was compared against the true sequence obtained by the averaging process.Attorney Docket No. 103361-500WO1 T2023-353

[0135] Fig. 6A shows the experimental results of Blind beacon estimation of Orbcomm LEO satellite signals. Specifically, Fig. 6A, subpanel A shows the true versus estimated sequences in- phase time-domain waveform. Fig. 6A, subpanel B shows the IQ plot of the estimated repetitive sequence. The plot reveals that the modulation scheme of the repetitive sequence for Orbcomm is 4-PSK. Fig. 6A, subpanel C shows the cross-correlation function between the true and estimated sequence. The prominent peak indicates successful estimation of the repetitive sequence. The bottom figure is a zoomed version of the peak in the top figure, which confirms successful beacon estimation. Fig. 6B shows the result of correlating the estimated repetitive sequence with the collected Orbcomm data. The correlation peaks confirm the correct estimation of the repetitive sequence.

[0136] Iridium NEXT LEO Constellation. The NI-USRP E312 was also used to capture raw signal measurements received by a commercial Iridium NEXT antenna. The sampling bandwidth Fs was set to 2.4 MHz, the carrier frequency fc was set to 1626.2708 MHz in the L̢band, which coincides with the ring alert (RA) channel of Iridium satellites, and the total capture duration was 600 seconds. Iridium NEXT satellites employ both time division multiple access (TDMA) and frequency division multiple access (FDMA). The Iridium spectrum includes multiple channels, including the RA channel, paging channel, voice channel, and duplex user channels. The RA channel bandwidth is B = 41.667 kHz, and the repetitive sequence period is T0 = 90 ms. Fig. 8A shows the parameters 804 of the Iridium NEXT LEO constellation satellites.

[0137] Executing the exemplary blind receiver system and method on the collected signal resulted in the repetitive sequence estimate shown in Fig. 6C, subpanel A. Specifically, Fig. 6C, subpanel A shows the In-phase waveform (601) of the estimated Iridium NEXT’s repetitive sequence.

[0138] Taking a closer look at the estimated sequence reveals a pure tone sequence (602) followed by an alternating Binary Phase Shift Keying (BPSK) sequence (604). The specific estimated repetitive sequence is well-known in the communication literature: it is the typical TDMA synchronization preamble employed in TDMA-based satellite systems

[0052] .

[0139] Fig. 6C, subpanel B shows the IQ plot of the estimated repetitive sequence, which indeed matches the figure in

[0052] .

[0140] Fig. 6C, subpanel C shows the auto-correlation profile of the estimated preamble sequence, which confirms successful sequence estimation. Furthermore, Fig. 6D shows the resultAttorney Docket No. 103361-500WO1 T2023-353 of an auto-correlation function of the estimated repetitive sequence with the collected Iridium NEXT data. The correlation peak (606) confirms the correct estimation of the repetitive sequence.

[0141] Starlink LEO Constellation. The signal capture setup for Starlink utilized the NI-USRP x410 to collect raw IQ measurements. The sampling bandwidth Fswas set to 500 MHz, and the carrier frequency fc was set to 11.325 GHz, which is roughly at the center of one of Starlink’s downlink channels in the Ku-band. According to the Federal Communications Commission (FCC), the Starlink user downlink signal spectrum spans the 10.7 - 12.7 GHz frequency band. The spectrum is dissected into 8 equidistant channels, each with bandwidth B = 240 MHz. Fig. 8A shows the parameters 806 of the Starlink LEO constellation satellites.

[0142] The period of the repetitive sequence was determined by inspecting the auto-correlation function of a data snapshot that entails many frames. The repetitive sequence present in the frames of the data snapshot induces an impulse train in the auto-correlation function with spacing equal to T0, which was recorded to be equal to 4 / 3 ms for Starlink downlink signals. A low-noise block (LNB) downconverter was coupled with a 30 dBi conversion gain Ku-band parabolic dish in order to improve the received SNR. The dish was continuously pointed towards the Starlink satellite throughout its passing - propagating the satellite’s trajectory from the publicly available TLE files governs the direction in which the dish should be pointed. The NI-USRP x410 was set to record for a duration of 900 seconds.

[0143] Next, the exemplary blind receiver system and method were used to acquire and track the signals present in the collected data. Taking a closer look at the estimated Starlink repetitive sequence reveals the signal structure.

[0144] Fig.6E, subpanel A, shows the auto-correlation profile (608) of the estimated sequence. The different peaks in the figure reveal unique values in Starlink’s OFDM frame structure, such as the symbol duration, cyclic prefix duration (which is defined as the number of samples taken from the end of a symbol and repeated at its beginning), and the frame duration.

[0145] Fig.6E, subpanel B, shows that the estimated sequence has repetitive components (610) in symbols [1, 2, 3, 5, 7]. The parameter estimates from Fig. Fig. 6E, subpanel A are sufficient to allow for the removal of the cyclic prefix from each symbol, which is then followed by applying a short-term Fourier transform (STFT) to the sequence estimate, e.g., as described in relation to Fig. 2A. This allows for spectral analysis of the repetitive sequence, which, as shown in Fig. 6E,Attorney Docket No. 103361-500WO1 T2023-353 subpanel C, shows 4 silent subcarriers in the middle of the signal bandwidth. In fact, this is the bandwidth location where some tones can be observed sometimes.

[0146] Fig. 6E, subpanel D, shows the IQ plot of the first three symbols within the synchronization sequence-bearing symbols. In observing the constellations, it can be observed that the synchronization symbols use a 4-quadrature amplitude modulation (QAM) scheme. The first plot (612) is derived from the time domain representation of the symbol, whereas the other two symbols (614, 616) are derived from the frequency domain representation of the symbols. The estimated repetitive sequences are comparable to the synchronization sequences employed in a 5G-NR (PSS, SSS, and PBCH) frame according to the 3GPP standard.

[0147] OneWeb LEO Constellation. The signal capture setup for OneWeb downlink signals was the same as that of Starlink, with the sampling frequency Fsset to 50 MHz and the carrier frequency fc set to 11.075 GHz. According to the FCC, OneWeb’s user downlink signal spectrum spans the 10.7-12.7 GHz frequency band. The spectrum is dissected into 8 equidistant channels, each with bandwidth B = 250 MHz. The repetitive sequence period was estimated to be T0= 10 ms from the data snapshot autocorrelation function. Fig. 8B shows the parameters 808 of the OneWeb LEO constellation satellites.

[0148] The exemplary blind receiver system and method was capable of estimating a repetitive sequence, which can be used to generate Doppler and code phase observables.

[0149] To the authors’ knowledge, the achieved acquisition and tracking of OneWeb signals is unprecedented in the literature. Fig. 6G shows the result of correlating the estimated repetitive sequence with the collected OneWeb data. The clean correlation peaks separated by T0seconds confirm the correct estimation of the repetitive sequence. Furthermore, Fig.6F shows the result of correlating the estimated repetitive sequence with the collected Starlink data. The clean correlation peaks separated by T0seconds confirm the correct estimation of the repetitive sequence.

[0150] Multi-Constellation Satellite Positioning Measurement Results. Multi- constellation positioning results, e.g., of the operation described in relation to Fig. 3, are experimentally shown to exploit signals from Orbcomm, Iridium NEXT, Starlink, and OneWeb LEO constellations. The carrier phase navigation observables produced by the proposed blind beacon estimation and Doppler tracking framework for each individual constellation, as well as fused from all four constellations, are used to localize a stationary receiver.Attorney Docket No. 103361-500WO1 T2023-353

[0151] Experimental Results. Signals from 1 Orbcomm, 1 Iridium NEXT, 4 Starlink, and 2 OneWeb LEO satellites were collected via the setup described in Fig. 3.

[0152] Fig. 7A, subpanel A shows the skyplot of the LEO satellites, while Fig. 7A, subpanel B shows the hardware used for data collection. The hardware included: (i) an LNB with a conversion gain of 50 dB and noise figure of 2.5 dB connected to a Ku-band 60 cm parabolic offset dish with a gain of 30 dBi to receive Starlink and OneWeb satellite signals, (ii) a commercial Orbcomm antenna, and (iii) a commercial Iridium NEXT antenna. The satellite positions,°7 îÖØÙ±ÊÅ^ , were obtained from TLE files and an SGP4 orbit determination software. The TLE epochadjusted for each satellite to account for ephemeris errors. This was achieved byminimizing the carrier phase residuals for each satellite

[0027] . The blind Doppler tracking operation, as described in relation to Fig. 2A, was used to acquire and track satellite signals with qw = (0.1)2rad2 / s6and ¦N#=ïð rad / s. Fig. 7A shows the results of 8 different satellites.

[0153] Specifically, Fig. 7A shows the Doppler shift profiles (701) for two OneWeb, four Starlink, an Iridium NEXT, and an Orbcomm LEO satellite. The solid curves (704) denote the estimated Doppler from the exemplary blind receiver system and method, while dotted curves (702) denote the predicted Doppler from TLE+SGP4.

[0154] It is likely that the cut-offs in Doppler tracking for OneWeb and Starlink are caused by the inability to continuously point the highly directional dish manually toward the satellite position. The bottom graphs (706) show the KF innovation νKF(k) (e.g., in KF 224) during the tracking period. Even though the studied LEO constellations had high Doppler (up to f250 kHz), the exemplary blind receiver system and method were able to track the Doppler with an error of less than 10 Hz.

[0155] Next, the batch NLS estimator described in Equation 24 was employed using measurements from all LEO satellites to obtain the final estimate æçÜ^. The receiver’s initial position estimate, ³ÀTX&was set on the roof of a building at the University of California, Irvine, USA, approximately 3,600 km away from the true position, which was on the roof of a building at the Ohio State University, Columbus, Ohio, USA.

[0156] Fig. 7C summarizes the positioning results. Specifically, Fig. 7C, subpanel A shows the trajectories of the 8 satellites from the 4 LEO constellations, and Fig. 7C, subpanel B shows the initial and final position estimates. Fig.7C, subpanel C shows the true and estimated receiver’sAttorney Docket No. 103361-500WO1 T2023-353 position. The final 3D position error was found to be 5.8 m, while the 2D position error was 5.1 m (i.e., upon considering only the east and north coordinates in the ENU frame). For comparative purposes, the batch NLS estimator was employed with the individual LEO constellations. Table 2 shows a summary of the results. Table 2 Constellation Visibility [seconds] 2D Error [meters] OneWeb 132 3068

[0157] Discussion

[0158] Navigation from low Earth orbit (LEO) will usher in a new era for positioning, navigation, and timing (PNT). Mega-constellations of LEO satellites are being born (e.g., Starlink, OneWeb, and Kuiper), joining existing LEO constellations (e.g., Orbcomm, Globalstar, Iridium NEXT, among others) [1]. These satellites will shower the Earth with a plethora of signals, diverse in frequency and direction, which could be utilized for PNT in a dedicated fashion [2] or opportunistically [3].

[0159] To compensate for the limitations of global navigation satellite systems (GNSS) [4], [5], researchers over the past decade studied the exploitation of terrestrial signals of opportunity (SOPs) for PNT. SOPs include: (i) AM / FM radio [6]; (ii) digital television [7]; (iii) WiFi [8]; and (iv) cellular 3G [9],

[0010] , 4G

[0011] ,

[0012] , and 5G

[0013] ,

[0014] ; with cellular SOPs showing the most promise, as they achieved lane-level positioning on ground vehicles

[0015] ,

[0016] , meter-level positioning on high-altitude aircraft

[0017] , and submeter-level positioning on low-altitude unmanned aerial vehicles

[0018] ,

[0019] , and are usable in environments under intentional GPS jamming

[0020] . Exploiting SOPs did not stay earthly, as LEO satellites have received considerable attention recently as potential SOPs

[0021] . Many theoretical and experimental studies have been conducted on LEO-based PNT

[0022] –

[0027] .

[0160] LEO satellites possess desirable attributes for PNT [2], [3]: (i) they are around twenty times closer to the Earth compared to GNSS satellites, which reside in medium Earth orbit (MEO),Attorney Docket No. 103361-500WO1 T2023-353 which could yield significantly higher carrier-to-noise ratio; (ii) they are becoming abundant as tens thousands of broadband Internet satellites are expected to be deployed into LEO; and (iii) they transmit in different frequency bands and are placed in varying orbits, making LEO satellite signals diverse in frequency and direction. However, exploiting broadband LEO satellite signals for PNT purposes comes with challenges

[0028] , as they are owned by private operators that typically do not disclose crucial information about the satellites’, including (i) ephemerides, (ii) clock synchronization and stability, and (iii) signal specifications.

[0161] To address the first challenge, several approaches have been recently proposed, including differential navigation utilizing a known base receiver

[0029] ,

[0030] , simultaneous tracking and navigation (STAN)

[0031] , and analytical / machine-learning satellite orbit tracking

[0032] ,

[0033] . Approaches to address the second challenge have been offered in

[0024] ,

[0034] . To address the third challenge, the paradigm of cognitive opportunistic navigation, which estimates the minimally known LEO satellite signals in a blind fashion, has been showing tremendous promise

[0035] . Most recently, this paradigm allowed for the exploitation of unknown Starlink LEO satellites, from which navigation observables were produced via (i) a carrier phase tracking approach

[0027] and (ii) a generalized likelihood ratio (GLR) Doppler detection approach

[0036] , with the former localizing a receiver to within a two-dimensional (2D) error of 25.9 m, while the latter achieving a 2D error of 10 m.

[0162] The instant study addressed the third challenge by developing a blind beacon estimation and Doppler tracking framework that is agnostic to the modulation and multiple access scheme adopted by LEO satellites. The exemplary blind receiver system and method generates navigation observables from broadband LEO satellites without the need to know their signal specifications.

[0163] Previous researchers have proposed frameworks for blind estimation of spreading sequences in direct sequence spread spectrum in communication systems

[0037] and for GPS signals under non-cooperative conditions

[0038] . However, these approaches cannot be applied to LEO because they do not account for the high dynamics channel between the LEO satellite and a terrestrial receiver. Previous literature has proposed methods for Doppler tracking with M-ary phase shift keying (MPSK) and orthogonal frequency division multiplexing (OFDM) signals

[0039] –

[0041] . The aforementioned approaches aim to generate a peak in the frequency-domain by either relying on nonlinear operations (for M-PSK signals) or increasing the coherent processing interval (CPI) (for OFDM signals). After generating the peak, the methods track it using a peak trackingAttorney Docket No. 103361-500WO1 T2023-353 algorithm to estimate the Doppler shift. However, using nonlinear operations could degrade the signal-to-noise ratio (SNR), while increasing the CPI is not straightforward with the highly dynamic channels encountered with LEO satellites. Also, peak tracking is prone to generate invalid observables and even divergence whenever the spectrum is contaminated by noisy DC peaks.

[0164] The instant study developed a spectral-based framework to mitigate the above challenges. The exemplary blind receiver system and method rely on the presence of a repetitive sequence (also referred to as a beacon) in the signal transmitted by the LEO satellite that will induce a prominent feature in the received spectrum. The exemplary blind Doppler tracker (e.g., 202) locks on the satellite’s feature in the frequency domain and uses the cross-correlation method to track the Doppler shift. Spectral cross-correlation has been studied in the literature

[0042] and used for noise reduction in speech

[0043] and detection of stars and planets

[0044] .

[0165] The instant study (i) developed an analytical approximation of the received signal frequency spectrum under a high dynamics channel, (ii) developed a blind Doppler estimator using spectral cross-correlation and a Kalman filter (KF)-based tracking loop, (iii) demonstrated successful acquisition, tracking, and positioning with multi-constellation LEO satellite, namely Orbcomm, Iridium NEXT, Starlink, and OneWeb. The instant study was, to the inventor’s knowledge, the first to additionally show tracking and navigation solution results with the OneWeb LEO constellation.

[0166] The exemplary blind navigation beacon estimation framework can estimate the time- domain waveform of the repetitive sequence present in the LEO signals. In addition, decoding the repetitive sequence using its modulation scheme can be additionally or optionally performed. That is, the refined time-domain waveform alone is sufficient to be used to generate navigation observables from LEO satellites. The exemplary blind receiver system and method can notably estimate the transmitted beacon on-the-fly even if the signal structure employed at the satellite’s end changes.

[0167] Conclusion

[0168] Throughout the description and claims of this specification, the word “comprise” and other forms of the word, such as “comprising” and “comprises,” means including but not limited to, and are not intended to exclude, for example, other additives, segments, integers, or steps. Furthermore, it is to be understood that the terms comprise, comprising, and comprises as theyAttorney Docket No. 103361-500WO1 T2023-353 relate to various aspects, elements, and features of the disclosed invention also include the more limited aspects of “consisting essentially of” and “consisting of.”

[0169] As used herein, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to a “polymer” includes aspects having two or more such polymers unless the context clearly indicates otherwise.

[0170] Ranges can be expressed herein as from “about” one particular value and / or to “about” another particular value. When such a range is expressed, another aspect includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another aspect. It should be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0171] As used herein, the terms “optional” or “optionally” mean that the subsequently described event or circumstance may or may not occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0172] For the terms "for example" and "such as," and grammatical equivalences thereof, the phrase "and without limitation" is understood to follow unless explicitly stated otherwise.

[0173] The following patents, applications and publications as listed below and throughout this document are hereby incorporated by reference in their entirety herein. Reference list [1] G. Curzi, D. Modenini, and P. Tortora, “Large constellations of small satellites: A survey of near future challenges and missions,” Aerospace, vol. 7, no. 9, pp. 1–18, September 2020. [2] T. Reid, T. Walter, P. Enge, D. Lawrence, H. Cobb, G. Gutt, M. O’Conner, and D. Whelan, “Position, navigation, and timing technologies in the 21st century,” J. Morton, F. van Diggelen, J. Spilker, Jr., and B. Parkinson, Eds. Wiley-IEEE, 2021, vol. 2, ch. 43: Navigation from low Earth orbit – Part 1: concept, current capability, and future promise, pp. 1359–1379. [3] Z. Kassas, “Position, navigation, and timing technologies in the 21stcentury,” J. Morton, F. van Diggelen, J. Spilker, Jr., and B. Parkinson, Eds. Wiley-IEEE, 2021, vol. 2, ch. 43: Navigation from low Earth orbit– Part 2: models, implementation, and performance, pp. 1381–1412.Attorney Docket No. 103361-500WO1 T2023-353 [4] R. Faragher, “Effects of multipath interference on radio positioning systems,” Ph.D. dissertation, University of Cambridge, England, 2007. [5] R. Ioannides, T. Pany, and G. Gibbons, “Known vulnerabilities of global navigation satellite systems, status, and potential mitigation techniques,” Proceedings of the IEEE, vol. 104, no. 6, pp. 1174–1194, February 2016. [6] X. Chen, Q. Wei, F. Wang, Z. Jun, S. Wu, and A. Men, “Super-resolution time of arrival estimation for a symbiotic FM radio data system,” IEEE Transactions on Broadcasting, vol. 66, no. 4, pp. 847–856, December 2020. [7] L. Chen, P. Thevenon, G. Seco-Granados, O. Julien, and H. Kuusniemi, “Analysis on the TOA tracking with DVB-T signals for positioning,” IEEE Transactions on Broadcasting, vol. 62, no. 4, pp. 957–961, December 2016. [8] R. Faragher and R. Harle, “Towards an efficient, intelligent, opportunistic smartphone indoor positioning system,” NAVIGATION, Journal of the Institute of Navigation, vol. 62, no. 1, pp. 55–72, 2015. [9] J. Khalife, K. Shamaei, and Z. Kassas, “A software-defined receiver architecture for cellular CDMA-based navigation,” in Proceedings of IEEE / ION Position, Location, and Navigation Symposium, April 2016, pp. 816–826.

[0010] C. Yang, T. Nguyen, and E. Blasch, “Mobile positioning via fusion of mixed signals of opportunity,” IEEE Aerospace and Electronic Systems Magazine, vol. 29, no. 4, pp. 34–46, April 2014.

[0011] J. del Peral-Rosado, J. L´opez-Salcedo, F. Zanier, and G. Seco-Granados, “Position accuracy of joint time-delay and channel estimators in LTE networks,” IEEE Access, vol. 6, pp.25185–25199, 2018.

[0012] K. Shamaei and Z. Kassas, “A joint TOA and DOA acquisition and tracking approach for positioning with LTE signals,” IEEE Transactions on Signal Processing, pp. 2689–2705, 2021.

[0013] A. Xhafa, J. del Peral-Rosado, J. L´opez-Salcedo, and G. Seco-Granados, “Evaluation of 5G positioning performance based on UTDoA, AoA and base-station selective exclusion,” Sensors, vol. 22, no.1, pp. 101–118, 2021.

[0014] A. Abdallah, J. Khalife, and Z. Kassas, “Exploiting on-demand 5G downlink signals for opportunistic navigation,” IEEE Signal Processing Letters, 2023, accepted.Attorney Docket No. 103361-500WO1 T2023-353

[0015] J. Peral-Rosado, J. Lopez-Salcedo, S. Kim, and G. Seco-Granados, “Feasibility study of 5G-based localization for assisted driving,” in Proceedings of International Conference on Localization and GNSS, June 2016, pp. 1–6.

[0016] M. Maaref, J. Khalife, and Z. Kassas, “Lane-level localization and mapping in GNSS- challenged environments by fusing lidar data and cellular pseudo-ranges,” IEEE Transactions on Intelligent Vehicles, vol. 4, no. 1, pp. 73–89, March 2019.

[0017] Z. Kassas, A. Abdallah, C. Lee, J. Jurado, J. Duede, Z. Hoeffner, T. Hulsey, R. Quirarte, S. Wachtel, and R. Tay, “Protecting the skies: GNSS-less aircraft navigation with terrestrial cellular signals of opportunity,” in Proceedings of ION GNSS Conference, September 2022, pp. 1014–1025.

[0018] J. Del Peral-Rosado, P. Nolle, S. Razavi, G. Lindmark, D. Shrestha, F. Gunnarsson, F. Kaltenberger, N. Sirola, O. S¨arkk¨a, J. Rostr¨om, K. Vaarala, P. Miettinen, G. Pojani, L. Canzian, H. Babaroglu, E. Rastorgueva-Foi, J. Talvitie, and D. Flachs, “Design considerations of dedicated and aerial 5G networks for enhanced positioning services,” in Proceedings of Workshop on Satellite Navigation Technology, April 2022, pp. 1–12.

[0019] J. Khalife and Z. Kassas, “On the achievability of submeter-accurate UAV navigation with cellular signals exploiting loose network synchronization,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 5, pp. 4261–4278, October 2022.

[0020] Z. Kassas, J. Khalife, A. Abdallah, and C. Lee, “I am not afraid of the GPS jammer: resilient navigation via signals of opportunity in GPS-denied environments,” IEEE Aerospace and Electronic Systems Magazine, vol. 37, no. 7, pp. 4–19, July 2022.

[0021] N. Jardak and Q. Jault, “The potential of LEO satellite-based opportunistic navigation for high dynamic applications,” Sensors, vol. 22, no. 7, pp. 2541–2565, 2022.

[0022] F. Farhangian, H. Benzerrouk, and R. Landry, “Opportunistic in-flight INS alignment using LEO satellites and a rotatory IMU platform,” Aerospace, vol. 8, no. 10, pp. 280–281, 2021.

[0023] M. Psiaki, “Navigation using carrier Doppler shift from a LEO constellation: TRANSIT on steroids,” NAVIGATION, Journal of the Institute of Navigation, vol. 68, no. 3, pp. 621–641, September 2021.Attorney Docket No. 103361-500WO1 T2023-353

[0024] K. Wang and A. El-Mowafy, “LEO satellite clock analysis and prediction for positioning applications,” Geo-spatial Information Science, vol. 25, no. 1, pp. 14–33, 2022.

[0025] M. Hartnett, “Performance assessment of navigation using carrier Doppler measurements from multiple LEO constellations,” Master’s thesis, Air Force Institute of Technology, Ohio, USA, 2022.

[0026] P. Iannucci and T. Humphreys, “Fused low-Earth-orbit GNSS,” IEEE Transactions on Aerospace and Electronics Systems, 2022, accepted.

[0027] J. Khalife, M. Neinavaie, and Z. Kassas, “The first carrier phase tracking and positioning results with Starlink LEO satellite signals,” IEEE Transactions on Aerospace and Electronic Systems, vol. 56, no. 2, pp. 1487–1491, April 2022.

[0028] Z. Kassas, M. Neinavaie, J. Khalife, N. Khairallah, J. Haidar-Ahmad, S. Kozhaya, and Z. Shadram, “Enter LEO on the GNSS stage: Navigation with Starlink satellites,” Inside GNSS Magazine, vol. 16, no. 6, pp. 42–51, 2021.

[0029] J. Khalife and Z. Kassas, “Performance-driven design of carrier phase differential navigation frameworks with megaconstellation LEO satellites,” IEEE Transactions on Aerospace and Electronic Systems, pp. 1–20, 2023, accepted.

[0030] C. Zhao, H. Qin, N. Wu, and D. Wang, “Analysis of baseline impact on differential doppler positioning and performance improvement method for LEO opportunistic navigation,” IEEE Transactions on Instrumentation and Measurement, pp. 1–10, 2023.

[0031] Z. Kassas, J. Morales, and J. Khalife, “New-age satellite-based navigation – STAN: simultaneous tracking and navigation with LEO satellite signals,” Inside GNSS Magazine, vol. 14, no. 4, pp. 56–65, 2019.

[0032] D. Shen, J. Lu, G. Chen, E. Blasch, C. Sheaff, M. Pugh, and K. Pham, “Methods of machine learning for space object pattern classification,” in Proceedings of IEEE National Aerospace and Electronics Conference, 2019, pp. 565–572.

[0033] J. Haidar-Ahmad, N. Khairallah, and Z. Kassas, “A hybrid analytical-machine learning approach for LEO satellite orbit prediction,” in Proceedings of International Conference on Information Fusion, 2022, pp. 1–7.Attorney Docket No. 103361-500WO1 T2023-353

[0034] N. Khairallah and Z. Kassas, “An interacting multiple model estimator of LEO satellite clocks for improved positioning,” in Proceedings of IEEE Vehicular Technology Conference, 2022, pp. 1–5.

[0035] S. Kozhaya and Z. Kassas, “Blind receiver for LEO beacon estimation with application to UAV carrier phase differential navigation,” in Proceedings of ION GNSS Conference, 2022, pp. 2385–2397.

[0036] M. Neinavaie, J. Khalife, and Z. Kassas, “Acquisition, Doppler tracking, and positioning with Starlink LEO satellites: First results,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 3, pp. 2606–2610, June 2022.

[0037] H. Choi and H. Moon, “Blind estimation of spreading sequence and data bits in direct- sequence spread spectrum communication systems,” IEEE Access, vol. 8, pp. 148 066–148074, 2020.

[0038] Z. Rui, X. Ouyang, F. Zeng, and X. Xu, “Blind estimation of GPS M-Code signals under non-cooperative conditions,” Wireless Communications and Mobile Computing, vol. 2022, 2022.

[0039] J. Khalife, M. Neinavaie, and Z. Kassas, “Blind Doppler tracking from OFDM signals transmitted by broadband LEO satellites,” in Proceedings of IEEE Vehicular Technology Conference, April 2021, pp. 1–5.

[0040] C. Zhao, H. Qin, and Z. Li, “Doppler measurements from multi-constellations in opportunistic navigation,” IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1–9, 2022.

[0041] C. Huang, H. Qin, C. Zhao, and H. Liang, “Phase - time method: Accurate Doppler measurement for Iridium NEXT signals,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 6, pp. 5954–5962, 2022.

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[0043] S. Vaseghi, Advanced digital signal processing and noise reduction. John Wiley & Sons, 2008.

[0044] S. Zucker, “Cross-correlation and maximum-likelihood analysis: a new approach to combining cross-correlation functions,” Monthly Notices of the Royal Astronomical Society, vol. 342, no. 4, pp. 1291–1298, 2003.Attorney Docket No. 103361-500WO1 T2023-353

[0045] 3GPP2, “Physical layer standard for cdma2000 spread spectrum systems (C.S0002-E),” 3rd Generation Partnership Project 2 (3GPP2), TSC.S0002-E, June 2011.

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Claims

Attorney Docket No. 103361-500WO1 T2023-353 What is claimed is:

1. A method of estimating a blind beacon, the method comprising: receiving an RF signal; identifying existence of one or more repetitive sequences in the received RF signal, one of the repetitive sequences being associated with a satellite in low Earth Orbit (LEO) having an unknown modulation or access scheme; performing blind beacon estimation and Doppler tracking agnostic to the modulation and the access scheme of the LEO satellite to generate an estimation of the beacon and a tracked Doppler by: locking, via a spectral cross-correlation and a Kalman filter (KF)-based tracking loop, on a satellite feature in the received RF signal in the frequency domain; iteratively evaluating a carrier phase (!") based on the locked satellite feature; generating navigation observables from the LEO satellite based on the carrier phase.

2. The method of claim 1, wherein the navigation observables include a measure of Doppler of the LEO satellite, the measure of Doppler being employed for position, navigation, and timing (PNT) application of a receiver.

3. The method of claim 1, wherein the navigation observables include a measure of Doppler, the measure of Doppler being employed in the correction or adjustment of decoding of a digital communication channel.

4. The method of claim 1, wherein the RF signal is modeled as having a shifted and dilated version, alongside noise, of a repetitive sequence frequency spectrum of the repetitive sequence in the received RF signal, and wherein the shift in the received spectrum is estimated, for a moving time window, as a residual Doppler parameter (!$#")in the spectral cross-correlation and a Kalman filter-based tracking loop, and wherein the dilation is estimated, for the same moving time window, as a residual Doppler rate parameter (!$%") in the spectral cross-correlation and a Kalman filter-based tracking loop.Attorney Docket No. 103361-500WO1 T2023-353 5. The method of claim 4, wherein the spectral cross-correlation and a Kalman filter (KF)- based tracking loop includes a nonlinear least-squares (NLS) estimator and a Kalman-based filter, wherein the residual Doppler parameter is determined by the nonlinear least-squares estimator of the received signal’s sequence after a carrier wipe-off in the frequency domain, the NLS estimator iteratively evaluating a Doppler ambiguity parameter (!$#&) corresponding to a true carrier phase (!"), based on an energy evaluation.

6. The method of claim 5, wherein the energy evaluation comprises the NLS estimator iteratively evaluating an energy parameter of an estimated sequence for an estimated beacon corresponding to an LEO satellite until a steady-state value equal to the energy of the true beacon (i.e., carrier phase) is reached.

7. The method of claim 5, wherein the Kalman-based filter is configured to track one or more carrier phase states ('") comprising at least one of a true carrier phase (!"), true ambiguity- free Doppler shift (!#"), and Doppler rate (!%"), the Kalman-based filter being configured to update, for each time window, the track carrier phase state with a state transition matrix and a zero-mean white random sequence.

8. The method of claim 5, wherein outputs of the Kalman filter comprising tracked Doppler are employed by the NLS estimator in a carrier wipe-off adjustment to generate an estimated signal sequence.

9. The method of claim 1, wherein outputs of the spectral cross-correlation and a Kalman filter-based tracking loop are employed in a Doppler ambiguity resolution operation.

10. The method of claim 1, comprises: performing code phase tracking of the blind beacon estimation and Doppler tracking.

11. The method of claim 1, wherein the code phase tracking comprises: determining, via a carrier phase change parameter, whether the NLS estimator of the Doppler tracking loop is locked to adjust the carrier phase estimation, wherein the carrierAttorney Docket No. 103361-500WO1 T2023-353 phase change parameter is used to adjust weights or usage of the residual carrier phase sequence generated by the Doppler tracking loop.

12. The method of any one of claims 1-11, wherein the steps of claim 1 are performed for a second LEO satellite.

13. The method of any one of claims 1-11, wherein the steps of claim 1 are performed for multiple LEO satellites in a batch operation.

14. The method of any one of claims 1-13, wherein the RF signal comprises Ku-band frequencies.

15. The method of any one of claims 1-14, wherein the RF signal comprises 5G NR OFDM signals.

16. A system comprising: a processor; a memory having instructions stored thereon, wherein the instructions, when executed by the processor, cause the processor to perform steps for any one of the methods for claims 1-13.

17. The system of claim 16, wherein the system is a transceiver chip for a global positioning transceiver.

18. The system of claim 16 further comprising: a network transceiver, the network transceiver being configured to receive the measure of Doppler to use in a compensation parameter in the network transceiver.

19. The system of claim 16, wherein the system is a navigation software.

20. A global positioning transceiver comprising: a processor;Attorney Docket No. 103361-500WO1 T2023-353 a memory having instructions stored thereon, wherein the instructions, when executed by the processor, cause the processor to perform steps for any one of the methods for claims 1-13.

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