Zaher Zak Kassas

Differential ranging measurements from ground based receivers to low Earth orbit (LEO) satellites with erroneous ephemerides (e.g., non-cooperative satellites) are studied and a method to compensate for differential ranging measurement errors is developed. A single-difference framework is proposed in which a base receiver with a known position communicates pseudorange measurements from overhead LEO space vehicles (SVs) with erroneous ephemerides to a rover receiver, with an unknown position. It is shown that the ephemeris error impact on the single difference measurement can be characterized in terms of one sufficient parameter: the ephemeris error magnitude, which can be estimated using differential measurements via a batch weighted nonlinear least-squares (B-WNLS) estimator. The estimated parameter is employed in a proposed differential measurement correction algorithm to accurately localize the rover receiver. The consistency of an extended Kalman filter (EKF) for receiver positioning that fuses differential pseudorange measurements is evaluated, showing that single-difference range-type measurements in the presence of ephemeris errors yield suboptimal estimator performance and large estimation bias. However, employing the proposed ephemeris error correction scheme is able to mitigate the effect of the ephemeris errors on the differential measurements. Next, the influence of the baseline orientation and distance on the differential range error is examined, showing that the ephemeris error magnitude and the baseline distance do not affect the differential residual along specific baseline orientations, which can be characterized by the angle formed between the line-of-sight vectors at both receivers. Finally, experimental results are presented where differential carrier phase measurements from 10 Starlink, 4 OneWeb, and 2 Orbcomm LEO SVs are used to localize a stationary rover receiver via a B-WNLS. Using Monte Carlo analysis with an average 3-D initial position error of 126.84 km, utilizing erroneous LEO SV ephemerides from two-line element (TLE) files, propagated with SGP4, resulted in a 3-D positioning error of 2,752 m. In contrast, using differential carrier phase measurements from a base with a known position, 6.92 km away from the rover, resulted in a 3-D positioning error of 31.3 m. However, utilizing the proposed correction method reduced the error to 5.3 m.

This letter presents the first stationary user equipment (UE)-based positioning framework that blindly estimates both always-on and on-demand 5G downlink signals with multiple 5G gNBs, transmitting on the same channel. The framework opportunistically exploits the full bandwidth of downlink 5G signals. In the acquisition stage, the maximum likelihood function of the beamformed signal is computed to differentiate the gNBs in both carrier frequency offset and angular domains, followed by blind beacon estimation of each gNB. Carrier-aided code delay tracking loops are developed to track the carrier phase and code delay to extract navigation observables. The Cram´ er–Rao lower bounds (CRLBs) for carrier frequency offset, azimuth, and elevation angles are derived. Experimental results are presented demonstrating that the estimated beacon exhibits a narrower autocorrelation function compared to that of always-on signals, due to the exploitation of on-demand signals, leading to higher time resolution estimation. Monte Carlo (MC)–based positioning results for a stationary UE using pseudorange and azimuth angle measurements from two co-channel 5G gNBs are presented. With initial positions randomly located within a 99% confidence circle of 2.1 km radius, the mean final position estimate across MC realizations was within 8.6 m of the true UE position.

A framework that could detect the presence of repetitive features in unknown signals is developed and experimentally demonstrated with non-terrestrial (NTN) sources, namely GPS and low Earth orbit (LEO) satellites. In modern communication systems, the existence of repetitive feature (i.e., the beacon) in the transmitted signals is inherited either implicitly; due to the transmitter’s source and channel coding, modulation, and multiplexing schemes; or explicitly, by broadcasting repetitive sequences for synchronization purposes. Upon detecting an unknown source, this framework, termed cognitive beacon detection and estimation, is capable of estimating the beacon, regardless of the adopted modulation scheme by the source. First, a model that is adequate to describe received signals from highly dynamic satellite channels is presented. The model parametrizes signals received from multiple unknown sources in terms of their time-varying carrier power, delay, Doppler, and user data. Second, a sequential beacon detection and estimation approach is developed, which is agnostic to the modulation scheme employed by the transmitter. The proposed cognitive framework allows for opportunistic exploitation of salient information embedded in the estimated beacon, such as beam, sector, and transmitter identification sequences. Third, the proposed framework is shown to converge almost surely to the correct beacon one at a time, until all sources are detected. Fourth, experimental results are presented demonstrating the efficacy of the developed cognitive framework in blindly detecting and estimating beacons of NTN sources, namely GPS and 5 LEO constellations: NOAA, Orbcomm, Iridium, Starlink, and OneWeb. These sources transmit in a diverse swath of modulation schemes: AM/FM, M-PSK, SC-FDMA, and OFDM. Finally, experimental results are presented demonstrating the applicability of the developed framework in navigating a ground vehicle with multi-constellation LEO satellite signals. The pseudorange rate measurements produced by the framework to 2 Orbcomm, 1 Iridium, 4 Starlink, and 1 OneWeb were fused with altimeter measurements via an extended Kalman filter to estimate the vehicle’s nearly 1 km trajectory, achieving a three-dimensional position root mean squared error of 4.15 m.

Four frameworks for LEO PNT (low Earth orbit positioning, navigation, and timing) with pseudorange or Doppler measurements from non-cooperative satellites with poorly known ephemerides are developed. The first utilizes publicly available ephemerides information from two-line element (TLE) files, propagated in an open-loop fashion via the simplified general perturbations 4 (SGP4) model. The second utilizes the simultaneous tracking and navigation (STAN) framework, in which the LEO space vehicles' (SVs') position and velocity are simultaneously estimated with the rover's states along with the clock error difference between the rover and LEO SVs. The third is a differential framework, which utilizes measurements made by a base station with a known position. Here, the rover estimates its states along with its clock error difference with that of the base, while the LEO SVs' states are obtained from SGP4. The fourth is differential STAN (DSTAN)– a hybrid of the second and third frameworks. Simulation results are presented comparing frameworks' performance. An aerial vehicle; equipped with a tactical-grade inertial measurement unit (IMU), an altimeter, and global navigation satellite system (GNSS) and LEO receivers; navigates for 28 km, the last 23 km of which are without GNSS signals. During GNSS unavailability, the vehicle aids its IMU with pseudorange or Doppler measurements from five LEO constellations: Starlink, OneWeb, Iridium NEXT, Orbcomm, and Globalstar. The efficacy of the frameworks are compared with various combinations of LEO constellations, revealing that (i) using more SVs with SGP4 exacerbates the PNT errors; (ii) submeter-level accuracy is achievable with DSTAN with pseudorange measurements; (iii) meter-level accuracy is achievable with pseudorange or Doppler measurements with STAN; and (iv) while differential SGP4 is effective in significantly reducing the effect of ephemerides error on PNT, with a relatively low number of SVs, it ceases to be effective with a large number of SVs. Two sets of experimental results are presented of a ground vehicle navigating with LEO Doppler measurements via the four frameworks. The vehicle was equipped with an industrial-grade IMU, an altimeter, and GNSS and LEO receivers. In the first experiment, the vehicle navigated for 540 m, the last 492 m of which without GNSS, while receiving signals from 2 Starlink, 1 OneWeb, 1 Iridium NEXT, and 2 Orbcomm LEO SVs, achieving a 3-D position root-mean squared error (RMSE) of 41.3, 10.7, 7.1, and 6.8 m. In the second, the vehicle navigated for 486 m, the last 376 m of which without GNSS, while receiving signals from 2 Starlink, 1 Iridium NEXT, and 1 Orbcomm LEO SVs, achieving a 3-D position RMSE of 54.4, 21.6, 11.7, and 10.6 m.

This paper presents a navigation framework, complemented with real-world experiments, for exploiting uncooperative low Earth orbit (LEO) satellites. To deal with the unknown nature of the satellite's signals, a receiver capable of acquiring and tracking the satellite's Doppler frequency is developed. A sequential matched subspace detector is derived to estimate the number of active LEO satellites. A generalized likelihood ratio (GLR)-based algorithm is developed to estimate the Doppler frequency of LEO satellites with and without integer constraint modulation. A Kalman filter-based tracking loop is designed to track the Doppler. To deal with the poorly known satellites' ephemerides, a differential Doppler LEO-aided inertial measurement unit (IMU) framework is developed, comprising a stationary base with a known position and a mobile rover. Experimental results are presented demonstrating the proposed framework, where the base and the rover acquired and tracked 5 LEO satellites (1 OneWeb, 1 Starlink, 1 Iridium, and 2 Orbcomm). The rover (ground vehicle) was equipped with an altimeter, an industrial-grade IMU, a global navigation satellite systems (GNSS) receiver, and the proposed LEO receiver. The vehicle traversed a trajectory of 540 m in 60 seconds. GNSS signals were available for the first 20 seconds but were fictitiously cut off for the last 40 seconds, during which the vehicle traveled 492 m. The differential LEO-aided IMU navigation system yielded a threedimensional (3-D) position root mean squared error (RMSE) of 7.6 m, compared to 87.7 m with the GNSS-aided IMU

The ephemeris and timing errors of low Earth orbit (LEO) satellites are modeled, leading to an approach to disambiguate these errors from pseudorange-type measurements. First, a model is derived describing the ephemeris error's impact on ranging measurements from LEO space vehicles (SVs) with imprecise ephemerides. A simulation study is presented comparing the impact of ephemeris error on ranging error for 5 LEO constellations (Statlink, OneWeb, Orbcomm, Iridium, and Globalstar) and 5 medium Earth orbit (MEO) constellations (GPS, GLONASS, Galileo, BeiDou-3, and O3B). Second, it is shown that for a particular SV position, the ephemeris error has no effect on range measurements. Next, the ephemeris and timing errors are parametrized by the three-dimensional (3-D) ephemeris error magnitude and its direction angle from the in-track axis. This parametrization is exploited in a proposed algorithm to disambiguate the ephemeris and timing error from the LEO SVs' pseudorange measurements at a reference receiver. The two parameters can be communicated to any unknown receiver listening to the same LEO SVs to correct for ephemerides ranging error, leading to improved positioning, navigation, and timing (PNT) precision. Monte Carlo simulation results are presented demonstrating the efficacy of the proposed algorithm. The simulations considered a reference receiver tracking via pseudorange measurements 22 Starlink and 4 OneWeb LEO SVs with poorly known ephemerides (obtained from two-line element (TLE) files, propagated with SGP4). The proposed algorithm reduced the 3-D position error of all SVs from a few kilometers to less than 120 m. The parameters were communicated to an unknown receiver to correct the LEO ephemerides, after which the receiver estimated its position by fusing its LEO pseudoranges via an extended Kalman filter (EKF), resulting in a horizontal position error of 0.91 m, as compared to 213 m utilizing TLE+SGP4 ephemerides. Two sets of experimental results are presented where the ephemeris correction method was applied to carrier phase measurements: (i) ephemeris parameters were estimated at a reference receiver from 3 Starlink and 7 OneWeb LEO SVs, and used to localize the same receiver, achieving a horizontal final position error of 0.85 m, compared to 7 km utilizing TLE+SGP4 ephemerides; and (ii) the two parameters of 7 Starlink SVs were estimated and communicated from St. Louis, Missouri, to an unknown receiver in Columbus, Ohio, over a baseline distance of 635 km, achieving a horizontal final position error of 8.78 m, compared to 2.41 km utilizing TLE+SGP4 ephemerides.

The modeling and compensation of timing and spatial ephemeris errors of low Earth orbit (LEO) satellites is considered. First, models are derived capturing the effect of temporal and spatial errors of publicly available uncertain LEO ephemerides on pseudorange, carrier phase, and Doppler measurements. Next, a scheme is developed to enable rapid compensation of timing and spatial ephemeris errors. The scheme utilizes a stationary receiver with a known position, extracting opportunistically pseudorange, carrier phase, or Doppler measurements from LEO downlink signals. An unscented Kalman filter-based LEO tracking framework is developed, which employs the derived spatial and temporal error models. A simulation study is presented to evaluate the developed scheme with multiconstellation LEO satellites: Starlink, OneWeb, Orbcomm, and Iridium NEXT. It is demonstrated that the proposed scheme reduces the satellite's initial position error from several kilometers to hundreds of meters. It is also demonstrated that the proposed scheme is more robust to initial satellite position error than direct LEO satellite tracking. Monte Carlo experimental results are presented to demonstrate the efficacy of the error compensation scheme to localize a stationary receiver with 1) carrier phase; and 2) Doppler measurements from three Starlink and two OneWeb noncooperative LEO satellites. Starting with an initial 3-D error of 11 316 m, it is shown that utilizing SGP4-propagated LEO ephemerides results in an error of 1) 1186 m; and 2) 1109 m, respectively; while the proposed refined ephemerides results in an error of 1) 3.18 m; and 2) 7.91 m, respectively.