(Georgia Institute of Technology, 2020-03)
Jun, William W.; Cheung, Kar-Ming; Milton, Julia; Lightsey, E. Glenn; Lee, Charles
With 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.