Figure 1: Diagram of cis-lunar space, which includes the real GPS sidelobe data collected on an HEO space vehicle. (All figures provided by the authors)

As part of NASA’s increased interest in returning to the moon, the ability to acquire accurate, onboard navigation solutions will be indispensable for autonomous operations in cis-lunar space (see Figure 1). Artemis I recently made its weeks-long journey to the Moon, and spacecraft carrying components of the Lunar Gateway and Human Landing System are planned to follow suit. During launch and within the GNSS space service volume, space vehicles can depend on the robust navigation signals transmitted by GNSS constellations (GPS, GLONASS, BeiDou, and Galileo). However, beyond this region, NASA’s Deep Space Network (DSN) serves as the system to track and guide lunar spacecraft through the dark regions of cis-lunar space. Increasingly, development of a lunar navigation satellite system (LNSS) that relies on a low size, weight and power (SWaP) “smallSat” constellation is being discussed for various possible orbits such as low lunar orbit (LLO), near rectilinear halo orbit (NRHO) and elliptical frozen orbit (ELFO).

Figure 2: DPE 3D (left) and 2D (right) spatial correlogram shown on a 3D north-east grid.

We have implemented direct positioning estimation (or collective detection) techniques to make the most of the limited and weak GPS signals (see Figure 2) that have been employed in other GNSS-degraded environments such as urban canyons. The algorithm used in conventional GNSS positioning employs a two-step method. In the first step, the receiver acquires signals to get a coarse estimate of the received signal’s phase offset. In the second step, the receiver tracks the signals using a delay lock loop coupled with a phase or frequency lock loop. The second step enables the receiver to get fine measurements, ultimately used to obtain a navigation solution. In the scenario addressed in our work, where a vehicle is navigating beyond the GPS satellite constellation, the signals are weak and sparse, and a conventional GPS receiver may not be able to acquire or maintain a lock on a satellite’s sidelobe signals to form a position solution. For a well-parameterized region of interest (that is, having a priori knowledge of the vehicle orbital state through dynamic filtering), and if the user’s clock error is known within a microsecond, a direct positioning estimator (DPE) can be used to improve acquisition sensitivity and obtain better position solutions. DPE works by incorporating code/carrier tracking loops and navigation solutions into a single step. It uses a priori information about the GPS satellites, user location, and clocks to directly estimate a position solution from the received signal. The delay-Doppler correlograms are first computed individually for the satellites and are then mapped onto a grid of possible candidate locations to produce a multi-dimensional spatial correlogram. By combining all signals using a cost function to determine the spatial location with the most correlation between satellites, the user position can be determined. As mentioned, signals received beyond the constellation will be sparse and weak, which makes DPE a desirable positioning method.

BACKGROUND

The proposed techniques draw from several studies exploring the use of weak signals and provide a groundwork for developing robust direct positioning methods for navigating beyond the constellation. NASA has supported and conducted several of the studies in developing further research into the use of signals in this space.

A study done by Kar-Ming Cheung and his colleagues at the Jet Propulsion Laboratory propagates the orbits of satellites in GPS, Galileo, and GLONASS constellations, and simulates the “weak GPS” real-time positioning and timing performances at lunar distance. The authors simulated an NRHO lunar vehicle based on the assumption that the lunar vehicle is in view of a GNSS satellite as long as it falls within the 40-degree beamwidth of the satellite’s antenna. The authors also simulate the 3D positioning performance as a function of the satellites’ ephemeris and pseudorange errors. Preliminary results showed that the lunar vehicle can see five to 13 satellites and achieve a 3D positioning error (one-sigma) of 200 to 300 meters based on reasonable ephemeris and pseudorange error assumptions. The authors also considered using relative positioning to mitigate the GNSS satellites’ ephemeris biases. Our work differs from this study in several key ways, including using real data collected beyond the GNSS constellations and investigating the method of direct positioning estimation for sparse signals.

Luke Winternitz and colleagues at the Goddard Space Flight Center described and predicted the performance of a conceptual autonomous GPS-based navigation system for NASA’s planned Lunar Gateway. The system was based on the flight-proven Magnetospheric Multiscale (MMS) GPS navigation system augmented with an Earth-pointed high-gain antenna, and optionally, an atomic clock. The authors used high-fidelity simulations calibrated against MMS flight data, making use of GPS transmitter patterns from the GPS Antenna Characterization Experiment project to predict the system’s performance in the Gateway NRHO. The results indicated that GPS can provide an autonomous, real-time navigation capability with comparable, or superior, performance to a ground-based DSN approach using eight hours of tracking data per day.

In direct positioning or collective detection research, Penina Axelrad and her colleagues at the University of Colorado at Boulder and the Charles Stark Draper Laboratory explored the use of GPS for autonomous orbit determination in geostationary orbit (GEO). They developed a novel approach for directly detecting and estimating the position of a GEO satellite using a very short duration GPS observation period that had been presented and demonstrated using a hardware simulator, radio-frequency sampling receiver, and MATLAB processing.

Ultimately, these studies and more have directed our research in exploring novel methods for navigating beyond the constellation space.

DATA COLLECTION

The data we used was collected as part of the U.S. Air Force Academy-sponsored Falcon Gold experiment and the data was also post-processed by analysts from the Aerospace Corporation. A few of the key notions behind the design of the experiment was to place an emphasis on off-the-shelf hardware components. The antenna used on board the spacecraft was a 2-inch patch antenna and the power source was a group of 30 NiMH batteries. To save power, the spacecraft collected 40-millisecond snapshots of data and only took data every five minutes. The GPS L1 frequency was down-converted to a 308.88 kHz intermediate frequency and was sampled at a low rate of 2 MHz (below the Nyquist rate) and the samples were only 1- bit wide. Again, the processing was designed to minimize power requirements.

METHODS AND SIMULATIONS

To test our techniques, we used real data collected from the Falcon Gold experiment on a launch vehicle upper stage (we’ll call it the Falcon Gold satellite) which collected data above the constellation on a HEO orbit. The data collected was sparse, and the signals were weak. However, the correlation process has shown that the collected data contained satellite pseudorandom noise codes (PRNs). Through preliminary investigation, we find that the acquired Doppler frequency offset matches the predicted orbit of the satellite when propagated forward from an initial state. The predicted orbit of the satellite was derived from the orbital parameters estimated using a batch least-squares fit of range-rate measurements using Aerospace Corporation’s TRACE orbit-determination software. The propagation method uses a Dormand-Prince eighth-order integration method with a 70-degree, first-order spherical harmonic gravity model and accounting for the gravitation of the Moon and Sun. The specifics of this investigation are detailed below.

Figure 3: GPS constellation “birdcage” (grey tracks), with regions of visibility near the GPS antenna boresight in blue and green for the given line-of-sight from the Falcon Gold satellite along its orbit (orange).

The positions of the GPS satellites are calculated using broadcast messages (combined into so-called BRDC files) and International GNSS Service (IGS) precise orbit data products (SP3 files). GPS satellites broadcast signals containing their orbit details and timing information with respect to an atomic clock. Legacy GPS signals broadcast messages contain 15 ephemeris parameters, with new parameters provided every two hours. The IGS supports a global network of more than 500 ground stations, whose data is used to precisely determine the orbit (position and velocity in an Earth-based coordinate system) and clock corrections for each GNSS satellite. These satellite positions, along with the one calculated for the Falcon Gold satellite, allowed for the simulation of visibility conditions. In other words, by determining points along the Falcon Gold satellite trajectory, we determine whether the vehicle will be within the 50° beamwidth of a GPS satellite that is not blocked by Earth.

Figure 3 shows a plot rendering of the visibility conditions of the Falcon Gold satellite at a location along its orbit to the GPS satellite tracks. Figure 4 depicts three of the 12 segments where signals were detected and compares the predicted visibility to the satellites that were actually detected. A GPS satellite is predicted to be visible to the Falcon Gold satellite if the direct line-of-sight (DLOS) is not occluded by Earth and if the DLOS is within 25° of the GPS antenna boresight (see Figure 5).

Figure 4: Predicted visibility of direct line-of-sight to each GPS satellite where a blue line indicates the PRN is predicted to be visible but undetected. A green line is predicted to be visible and was detected, and a red line indicates that the satellite is predicted to not be visible, but was still detected.

Figure 5: Depiction of the regions of a GPS orbit where the Falcon Gold satellite could potentially detect GPS signals based on visibility.

As a preliminary step to evaluate the Falcon Gold data, we analyzed the Doppler shifts that were detected at 12 locations along the Falcon Gold trajectory above the constellation. By comparing the Doppler frequency shifts detected to the ones predicted by calculating the rate of change of the range between the GPS satellites and modeled Falcon Gold satellite, we calculated the range rate root-mean-square error (RMSE). Through this analysis, we were able to verify the locations on the predicted trajectory that closely matched the detected Doppler shifts.

These results are used to direct our investigations to regions of the dataset to parameterize our orbit track in a way to effectively search our delay and Doppler correlograms to populate our spatial correlograms within the DPE. Figure 6 shows the time history of the difference of predicted range rates on the trajectory and the detected range rates on the trajectory. That is, a constant detected range rate value is subtracted from a changing range rate for the duration of the trajectory and not just at the location on the trajectory at the detect time (dashed vertical line). From this we can see that the TRACE method gives range rates near the detected ranges at the approximate detection time for the 12 different segments.

Figure 6: Plots depicting the 12 segments of detection and the corresponding time history of differences of range-rate values for each GPS PRN detected. The time history is of the range-rate difference between the predicted range rate from the TRACE-estimated trajectory and the constant detected range rate at the detection time (vertical line).

Excluding Segment 12, which was below the MEO constellation altitude, Segment 6 has more detected range rates than that of the other segments. On closer inspection of this segment, and using IGS precise orbit data products, it appears that the minimum RMSE of the range rates from the detected PRNs is off from the reported detection time by several seconds (see Figure 7). Investigating regions along the Falcon Gold TRACE-estimated trajectory and assuming a mismatch in time tagging results in a location (in Earth-centered Earth-fixed coordinates) with a lower RMSE for the predicted range rates compared to detected range rates.

Figure 7: Range-rate difference between the predicted range rate from the TRACE-estimated trajectory and the constant detected range rate at the detection time (left). A portion of the trajectory around Segment 6 with the TRACE-estimated location at the time of detection (red) and the location with the minimum RMSE of range rate (black).

To determine the search space for the DPE, we first determine the location along the original TRACE-estimated trajectory with the minimum RMSE of range rates for each segment. Then we propagate the state (position and velocity) at the minimum location to the Segment 6 time stamp. If the time segment has more than three observed range rates (Segment 6 and Segment 12), we perform a least squares velocity estimate using the range-rate measurements, using the locations along the trajectory and selecting the location with the smallest RMSE. Then, for Segment 12, the position and velocity obtained from least squares is propagated backwards in time to the Segment 6 timestamp. All of these points along the trajectory as well as the original point from the TRACE estimated trajectory are used in a way similar to the method of using a sigma point filter. Specifically, the mean and covariance of the position and velocity values are used to sample a Gaussian distribution. This distribution will serve as the first iteration of the candidate locations for DPE. There were a total of three iteration steps and at each iteration the range of clock bias values over which to search was refined from a spacing of 1,000 meters, 100 meters, and 10 meters. Also on the third iteration, the sampled Gaussian distribution was resampled with 1,000 times the covariance matrix values in the directions perpendicular to the direction to Earth. This was done to gain better insight into the GPS satellites that were contributing to the DPE solution.

RESULTS

Figure 8 shows the correlation peaks for each of the signals reported to be detected using a 15-millisecond non-coherent integration time within the DPE acquisition. Satellite PRNs 4, 16 and 19 are clearly detected. Satellite PRN 29 is less obviously detected, but the maximum correlation value is associated with the reported detected frequency. However, this is the peak detected frequency only if the Doppler search band is narrowly selected around the reported detected frequency. Similarly, while the peak code delay shows a clear acquisition peak for PRNs 4, 16 and 19, for PRN 29 the peak value for code delay is more ambiguous with many peaks of similar magnitude of correlation power. Figure 8 depicts the regions around the max peak correlation chip delay.

Figure 8: Acquisition peak in frequency (left) and time (right) for PRN 4, 16, 19 and 29. The correlograms are centered on the frequency predicted from the range rate calculated along the trajectory.

For the first iteration of DPE, the peak coordinated acquisition values for PRN 16 and PRN 4 are chosen for the solution space. From the corresponding spatial correlogram, the chosen candidate solution is roughly 44 kilometers away from the original position estimated using TRACE.
For the second iteration of DPE, the clock bias is refined to search over a 100-meter spacing. The peak values for PRN 16 and PRN 19 are chosen for the solution space and the chosen candidate solution is roughly 38 kilometers away from the original position estimated using TRACE.
For the final iteration, Figures 9 and 10 depict the solutions with the 10-meter clock bias spacing and the approach of spreading the search space over the dimension perpendicular to the direction of Earth. Again, this was done to illustrate how the peak correlations appear to be drawing close to a single intersection location. However, the results fall short of the type of results shown in the spatial correlogram previously depicted in Figure 2 when many satellite signals were detected.

Figure 9: Acquisition peaks plotted in the time domain with the candidate location chosen at the location of the vertical black line for the detected PRNs for the third iteration of the DPE method.

Figure 10: Spatial correlogram with the candidate location chosen at the location of the black circle for the detected PRNs for the third iteration of DPE method. The original TRACE-estimated position is indicated by a red circle. The two positions are approximately 28 kilometers apart.

A similar iterative method was followed using not just the four detected PRNs, but any satellite that was predicted to be visible with the relaxed criteria allowing for visibility based on receiving signals from the first and second sidelobes of the antenna. This is predicted using a larger 40° away from the GPS antenna boresight criterion. The final spatial correlogram (Figure 11) shows similar results to the intersections shown in Figure 10. However, there is potentially another PRN shown with a peak contribution near the original intersection point. These results are somewhat inconclusive and will need to be investigated further.

Figure 11: Spatial correlogram with the candidate location chosen at the location of the black circle for the detected PRNs for the third iteration of DPE method using additional satellites. The original TRACE-estimated position is indicated by a red circle. The two positions are approximately 24 kilometers apart.

CONCLUSIONS AND FUTURE WORK

Our research investigated the DPE approach of positioning beyond the GNSS constellations using real data. We will further investigate ways to parameterize our estimated orbit for use within a DPE algorithm in conjunction with other orbit determination techniques (such as filtering) as our results were promising but inconclusive. Some additional methods that may aid in this research include investigating the use of precise SP3 orbit files over the navigation message currently used (BRDC) within our DPE approach. Also, some additional work will need to be completed in determining the possibility of time tagging issues that could result in discrepancies and formulating additional methods related to visibility prediction that could aid in partitioning the search space. Additionally, we plan to investigate other segments where few signals were detected, but where more satellites are predicted to be visible (a better test of DPE). Finally, using full 40-millisecond data segments rather than the 15 milliseconds used to date may provide the additional signal strength needed to give more conclusive results.

ACKNOWLEDGMENTS

This article is based on the paper “Direct Positioning Estimation Beyond the Constellation Using Falcon Gold Data Collected on Highly Elliptical Orbit” presented at ION ITM 2023, the 2023 International Technical Meeting of the Institute of Navigation, Long Beach, California, January 23–26, 2023.

KIRSTEN STRANDJORD is an assistant professor in the Aerospace Engineering Department at the University of Minnesota. She received her Ph.D. in aerospace engineering sciences from the University of Colorado Boulder.

FAITH CORNISH is a graduate student in the Aerospace Engineering Department at the University of Minnesota.

<p>The post Far Out: Positioning above the GPS constellation first appeared on GPS World.</p>

The Moonlight initiative will provide sustainable lunar data-relay services for communication and navigation around the Moon. (ESA Moonlight Study conceptual drawing.) (Image: SSTL/Airbus/ESA)

GNSS researchers presented hundreds of papers at the 2022 Institute of Navigation (ION) GNSS+ conference, which took place Sept. 19–23 in Denver, Colorado, and virtually. The following five papers focused on lunar and space applications. The papers are available now.

MTO Navigation Using Lunar Signals

The moon transfer orbit (MTO) is becoming increasingly important as several national space agencies are planning moon exploration soon, with projects such as NASA’s Artemis. In previous research, the GPS navigation accuracy on the MTO reached 200 m at the moon altitude by using GPS signals emitted from the far side of Earth. As accuracy on a low-Earth orbit (LEO) using GPS is a few meters, 200 m accuracy is not accurate enough to support lunar exploration. The deterioration of accuracy is due to the poor geometry of the GPS satellites that became visible from the MTO.

The authors want to achieve an accuracy of less than 100 m in MTO by using other navigation sources, including the lunar navigation satellite system (LNSS) to be deployed in the moon’s orbit. The LNSS signals will come from the far side of the moon, similar to the signals of GPS satellites coming from the opposite side of Earth. Its satellites will be pointed towards the moon to provide positioning, navigation and timing services on the moon surface, especially at the lunar South Pole region

The researchers have been conducting the simulation evaluation for the MTO navigation accuracy using signals coming from the moon and assume that these signals will be emitted from beacons on the moon surface or the LNSS.

Murata, Masaya; Kogure, Satoshi; “Moon Transfer Orbit Navigation Using Signals Coming from the Moon.”

Designing the Smallsat-Based LNCSS

There is growing interest in the use of a smallsat platform for the future lunar navigation and communication satellite system (LNCSS); however, many design considerations are not finalized for the smallsat-based LNCSS, such as choice of the satellite clock, satellite orbital parameters and the constellation size.
Using the Systems Tool Kit simulation software, the authors examined various LNCSS constellation case studies based in elliptical lunar frozen orbit and with a low-grade chip-scale atomic clock.

They evaluated case studies of navigation design considerations including position and timing accuracy, lunar user equivalent ranging error, and dilution of precision. As for case studies of communications design considerations, the authors examined daily data volume, availability and data rate. Finally, they examined smallsat factors including the cost, size, weight and power of the satellite payload.

The paper includes trade-off analysis in satisfying the preliminary design criteria outlined by international space agencies and commercial space companies.

Bhamidipati, Sriramya; Mina, Tara; Sanchez, Alana; Gao, Grace; “A Lunar Navigation and Communication Satellite System with Earth-GPS Time Transfer: Design and Performance Considerations.”

Developing an SDR for Space

A geostationary satellite (GEO) equipped with the satellite-based augmentation system (SBAS) function has a transmitter for GNSS correction signals at the L1 and L5 bands. This transmitter could interfere with the GNSS space service volume (SSV) receiver in the same satellite, so L1 and L5 signals cannot be used for the GEO SBAS satellite. However, the use of GPS L2C signals can be an alternative.

The authors of this paper present the development of a GPS L2C signal generator for the SSV in GEO simulation. They present the simulation process for GEO satellites and the structure of the GPS L2C signal generator.

In this study, a verification through the receiver test with a GNSS software-defined receiver is included to show the possibility of the designed signal simulator. The validation is performed by analyzing the programmable system device, the results of the acquisition, code/carrier tracking, and the C/N0 estimation.

Lee, Hak-beom; Choi, ByeongHyun; Song, Young-Jin; Won, Jong-Hoon; Kwon, Ki-Ho; “Development of GPS L2C Signal Generator for SSV in Geostationary Orbit Simulation.”

Differential Positioning on the Moon

This paper introduces a new concept of delivering the pseudorange correction calculated at a reference station on the lunar surface, as a part of the lunar navigation satellite system (LNSS) navigation message. The concept enables LNSS users to apply differential positioning using pseudorange correction without adding new hardware to their receivers.

The authors propose the differential positioning technique to reduce the signal-in-space range error of LNSS satellites and the coordinate transformation errors from Earth-centered fixed frame to lunar reference frame — the dominant errors in satellite positioning by LNSS.

The proposed reference station is equipped with instruments to externally estimate its own position relative to the lunar reference frame. The user on the lunar surface would then perform differential positioning using the station coordinate and pseudorange correction obtained at the reference station.
In this study, the simulation results using eight elliptical lunar frozen orbit satellites show that the real-mean-squared values for both horizontal and vertical positioning errors with differential correction are reduced to 1/10 of those without differential correction, even at 10 degrees latitude from the reference station at the lunar South Pole.

Akiyama, Kyohei; Murata, Masaya; Kogure, Satoshi; “Differential Positioning Performance on Lunar South Pole Region Using Lunar Navigation Satellite System.”

GEO Precise Orbit Determination

Using GPS in satellites in geostationary (GEO) orbits provides advantages by improving position, velocity and timing data, reducing operating costs and providing autonomous orbit control for station keeping. This paper presents the result of the onboard data evaluation and precise orbit determination of an optical data-relay satellite (ODRS) using GPS L1 C/A code and carrier-phase observations for 74 days.

As a result of precise orbit determination, the authors found that both code- and carrier-phase observations are affected by the ionospheric delay when signals pass through the plasmasphere located above the ionosphere.

Several methods were implemented during this research to reduce the effect of the plasmasphere, including setting a higher cut-off altitude, applying correction sequences generated from orbit determination residuals, and applying a new observation noise model depending on the GPS off-nadir angle. Results show that the correction sequences and the new noise model improve the internal orbit consistency. The authors also found that the orbit bias in radial direction due to negatively biased carrier-phase observations is mitigated from –51 cm to –17 cm by setting a higher cut-off altitude and applying correction sequences.

Matsumoto, Takehiro; Sakamoto, Takushi; Yoshikawa, Kazuhiro; Kasho, Sachiyo; Nakajima, Ayano; Nakamura, Shinichi; “GEO Precise Orbit Determination Using Onboard GPS Carrier Phase Observations of Optical Data Relay Satellite.”

<p>The post Research roundup: Space and lunar applications first appeared on GPS World.</p>

Artist’s impression of the Lunar Pathfinder satellite built by Surrey Satellite Technology Ltd. (SSTL) that will provide communications and navigation services for the Moon.

NASA and its international partners are planning a return to our natural satellite. The following three papers — presented at the Institute of Navigation (ION) GNSS+ conference Sept. 20–24, 2021 — discuss the role of GNSS in lunar exploration. The full papers are available at www.ion.org/publications/browse.cfm.

Using GPS for Time Transfer

NASA and the European Space Agency have conceptualized the initial framework for a GPS-like constellation for the Moon, which will ensure uninterrupted navigation and communication services for future lunar missions. The authors designed a smallsat-based Lunar Navigation Satellite System (LNSS) with time-transfer from Earth-GPS to alleviate the size, weight and power (SWaP) and timing stability requirements of the onboard clocks. A timing filter corrects the lower grade clock when Earth-GPS signals are available and propagates these clock estimates forward in time when no Earth-GPS signals are available. The authors analyzed their proposed time-transfer technique using high-fidelity simulations of an LNSS satellite with an onboard chip-scale atomic clock for three cases of elliptical lunar frozen orbits.

Bhamidipati, Sriramya, Mina, Tara, Gao, Grace, “Design Considerations of a Lunar Navigation Satellite System with Time-Transfer from Earth-GPS,” https://doi.org/10.33012/2021.18021

GNSS Nav for Moon Missions

The authors show the potential of autonomous GNSS signal-based navigation for a set of Moon scenarios. This technology could be a game changer for the future of lunar exploration, representing an extremely low cost and effective alternative for Moon navigation. Results show that not only autonomous GNSS navigation for lunar orbiters is possible, but it also delivers good navigation performance. In fact, navigation with root-mean-square (RMS) errors on the order of 50–100 meters were obtained for scenarios of high interest, such as for the planned Lunar Pathfinder and near-rectilinear halo orbit of the Lunar Gateway space station around the Moon.

Mangialardo, Marco, Jurado, María Manzano, Hagan, David, Giordano, Pietro, Ventura-Traveset, Javier, “The full Potential of an Autonomous GNSS Signalbased Navigation System for Moon Missions,” https://doi.org/10.33012/2021.18040

Finding the best lunar orbit

A continuous and reliable lunar positioning and timing system, such as a GNSS-like constellation, is considered essential infrastructure for lunar exploration. The authors focus on halo orbits with the aim of defining an optimal halo constellation for supporting and delivering a navigation service on the Moon. This paper shows the performance of a GNSS-like constellation deployed in Halo orbits around Earth-Moon L1 and L2 collinear libration points. Different phases have been considered, from a minimum number of satellites able to provide a local PNT service on the South Pole (Initial Operational Capability), to a final, extended constellation able to cover the whole lunar surface (Final Operational Capability).

Musacchio, Daniele, Iess, Luciano, Carosi, Mattia, Capolicchio, Jacopo, Eleuteri, Massimo, Stallo, Cosimo, Di Lauro, Carmine, “Design of Earth Moon Halo Orbits for a Global Lunar PNT Service,” https://doi.org/10.33012/2021.18020

<p>The post Research Roundup: Lunar GNSS applications first appeared on GPS World.</p>