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Lightsey,
E. Glenn
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ItemAutonomous Navigation for Crewed Lunar Missions with DBAN(Georgia Institute of Technology, 2020-03) Jun, William W. ; Cheung, Kar-Ming ; Milton, Julia ; Lightsey, E. Glenn ; Lee, CharlesWith the recent push for a crewed Lunar mission to descend, land, and ascend from the Moon, there is a need for real-time position, velocity, and orientation knowledge of a Lunar spacecraft. Proposed approaches to achieve this include the use of weak-signals received from GPS and Deep Space Network (DSN)-aided measurements, but these all require significant hardware development and active tracking from multiple ground stations. Additionally, these solutions may be unavailable during close approach and landing. This paper extends the previously published relative Doppler-based positioning scheme (Law of Cosines – LOC) and an absolute Doppler-based scheme (Conic Doppler Localization – CDL) with the aid of range measurements and an inertial measurement unit (IMU) to create the Doppler Based Autonomous Navigation (DBAN) architecture. DBAN allows for real-time, autonomous positioning with as few as one Lunar orbiter and a reference station on the surface of the Moon. The LOC scheme is a relative navigation architecture that converts Doppler measurements into Doppler-based range measurements with the aid of a reference station and at least one satellite. In addition, the CDL scheme is an absolute navigation architecture that converts Doppler measurements into conic sections for angle-based positioning. These schemes allow for localization with solely Doppler measurements that can be made using existing hardware, with significant performance improvements when including range measurements. However, the existing drawback with these schemes is that they require a static user; they can be biased through the Doppler shift produced by a dynamic user. However, with the aid of range measurements, an IMU, and a non-linear Kalman filter, DBAN can correct these biases and provide continuous Doppler-based navigation. In this analysis, the Lunar Gateway and the Lunar Relay Satellite (LRS) were used with a pre-existing reference station located on the south pole of the Moon to localize a user during orbit, descent, and landing. A surface constraint assumption was optionally implemented using the knowledge of the altitude of the user as a constraint. Satellite ephemeris, velocity, and external and internal measurement errors were modeled as Gaussian variables and embedded in Monte Carlo simulations to increase fidelity. An Extended Kalman Filter (EKF) was used to ensure quick convergence without effects from linearization during intervals of high user dynamics. Ultimately, the DBAN architecture may provide real-time positioning, velocity, and orientation knowledge with a minimal navigation infrastructure that relaxes hardware requirements and utilizes as few as one orbiter.
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ItemLocalizing in Urban Canyons using Joint Doppler and Ranging and the Law of Cosines Method(Georgia Institute of Technology, 2019-09) Jun, William W. ; Cheung, Kar-Ming ; Lightsey, E. Glenn ; Lee, CharlesThe performance of Global Navigation Satellite System (GNSS) based navigation can be limited in urban canyons and other regions with narrow satellite visibility. These regions may only allow for less than the minimum of four satellites to be visible, leading to a decay of positional knowledge. A scheme with Joint Doppler and Ranging (JDR) and relative positioning, known as the Law of Cosines (LOC) method, is introduced in this paper that utilizes Doppler and pseudorange measurements from a minimum of two GNSS satellites to obtain a position fix. The user’s GNSS receiver was assumed to output both corrected pseudorange and Doppler shift measurements for each tracked satellite. The velocity vector of each satellite was calculated using broadcast satellite ephemerides. Additionally, the location of the reference station was known and Doppler measurements from the GNSS receiver at the reference station were transmitted to the user. Ephemerides from eight GNSS satellites were simulated with the user and reference station approximately 12 km apart in San Francisco. Gaussian error sources were modelled and randomized in Monte Carlo simulations, adding error to the receiver’s known satellite ephemeris, satellite velocity, Doppler, and pseudorange measurements. Each unique pair of 2 satellites was employed for the positioning of the user using the LOC method for over 10,000 Monte Carlo simulations. With reasonable assumptions on measurement error, the average 2D topocentric Root-Mean-Square-Error (RMSE) performance of all pairs of satellites was 23 meters, reducing to 10 meters by removing specific pairs with poor geometry. However, with a new technique called Terrain Assisted – JDR (TA-JDR), which uses accurate topographic information of the user’s region as a faux pseudorange measurement, the average RSME of the satellite pairs was reduced to approximately 7 meters. The use of the JDR-LOC scheme and its variants may not only be useful in urban canyons, but also in other GPS-denied unfriendly environments. Ultimately, the JDR-LOC scheme was capable of achieving navigational solutions with an RMSE as low as 7 meters for users with limited GNSS satellite visibility, with only the use of a GNSS receiver and a reference station.
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ItemSingle-Satellite Doppler Localization with Law of Cosines (LOC)(Georgia Institute of Technology, 2019-03) Cheung, Kar-Ming ; Jun, William W. ; Lee, Charles ; Lightsey, E. GlennModern day localization requires multiple satellites in orbits, and relies on ranging capability which may not be available in most proximity flight radios that are used to explore other planetary bodies such as Mars or Moon. The key results of this paper are: 1. A novel relative positioning scheme that uses Doppler measurements and the principle of the Law of Cosines (LOC) to localize a user with as few as one orbiter. 2. The concept of “pseudo-pseudorange” that embeds the satellite’s velocity vector error into the pseudorange expressions of the user and the reference station, thereby allowing the LOC scheme to cancel out or to greatly attenuate the velocity error in the localization calculations. In this analysis, the Lunar Relay Satellite (LRS) was used as the orbiter, with the reference station and the user located near the Lunar South Pole. Multiple Doppler measurements by the stationary user and the reference station at different time points from one satellite can be made over the satellite’s pass, with the measurements in each time point processed and denoted as from a separate, faux satellite. The use of the surface constraint assumption was implemented with this scheme; using the knowledge of the altitude of the user as a constraint. Satellite’s ephemeris and velocity, and user’s and reference station’s Doppler measurement errors were modeled as Gaussian variables, and embedded in Monte Carlo simulations of the scheme to investigate its sensitivity with respective to different kinds of errors. With only two Doppler measurements, LOC exhibited root mean square (RMS) 3D positional errors of about 22 meters in Monte Carlo simulations. With an optimal measurement window size and a larger number of measurements, the RMS error improved to under 10 meters. The algorithm was also found to be fairly resilient to satellite velocity error due to the error mitigating effects in the LOC processing of the pseudo-pseudorange data type. A sensitivity analysis was performed to understand the effects of errors in the surface constraint, showing that overall position error increased linearly with surface constraint error. An analysis was also performed to reveal the relationship between the distance between the user and the reference station; a distance of up to 100 km only lead to an increase of 10 meters in RMS 3D position error. Ultimately, the LOC scheme provides localization with a minimal navigation infrastructure that relaxes hardware requirements and uses a small number of navigation nodes (as small as one).
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ItemAccuracy/Computation Performance of a New Trilateration Scheme for GPS-Style Localization(Georgia Institute of Technology, 2018-03) Cheung, Kar-Ming ; Lightsey, E. Glenn ; Lee, Charles H.We recently introduced a new geometric trilateration (GT) method for GPS-style positioning. Preliminary single-point analysis using simplistic error assumptions indicates that the new scheme delivers almost indistinguishable localization accuracy as the traditional Newton-Raphson (NR) approach. Also, the same computation procedure can be used to perform high-accuracy relative positioning between a reference vehicle and an arbitrary number of target vehicles. This scheme has the potential to enable a) new mission concepts in collaborative science, b) in-situ navigation services for human Mars missions, and c) lower cost and faster acquisition of GPS signals for consumer-grade GPS products. The new GT scheme differs from the NR scheme in the following ways: 1. The new scheme is derived from Pythagoras Theorem, whereas the NR method is based on the principle of linear regression. 2. The NR method uses the absolute locations (xi, yi, zi)’s of the GPS satellites as input to each step of the localization computation. The GT method uses the Directional Cosines Ui’s from Earth’s center to the GPS satellite Si. 3. Both the NR method and the GT method iterate to converge to a localized solution. In each iteration step, multiple matrix operations are performed. The NR method constructs a different matrix in each iterative step, thus requires performing a new set of matrix operations in each step. The GT scheme uses the same matrix in each iteration, thus requiring computing the matrix operations only once for all subsequent iterations. In this paper, we perform an in-depth comparison between the GT scheme and the NR method in terms of a) GPS localization accuracy in the GPS operation environment, b) its sensitivity with respect to systematic errors and random errors, and c) computation load required to converge to a localization solution.