GNSS-based relative navigation for LEO nanosatellite laser communications

Abstract

The Size, Weight, and Power (SWaP) efficiency of laser communications make it a good fit for development in concert with rising interest in small satellite mission concepts. The CubeSat Laser Infrared CrossinK (CLICK) mission has the objective of demonstrating the first Low-Earth orbit (LEO) nanosatellite crosslink. The need for precise and accurate pointing with laser instruments motivates a formalized, systematic approach to fulfilling this need called Pointing, Acquisition, and Tracking (PAT). The focus of this work is the initial Global Navigation Satellite System (GNSS) based relative navigation pointing process for LEO crosslinks and downlinks. In Chapter 2, the baseline CLICK pointing budgets are given for crosslink and downlink relative navigation based body pointing. For crosslink, the 9 9 th percentile angular relative navigation errors are 1367 [mu]rad & 76.58 [mu]rad for the minimum 25 km range and maximum 580 km range cases, respectively.

The corresponding 99.7% pointing losses are -0.278 dB & -0.182 dB, with margins of 1.222 dB & 1.318 dB relative to the -1.5 dB requirement. For downlink, the 9 9 th percentile angular relative navigation error is 17.29 [mu]rad, with a corresponding 99.7% pointing loss of -0.189 dB and margin of 1.311 dB. The crosslink and downlink access durations are also determined by simulation. In Chapter 3, using Cowell's method with only an appropriate central body gravity model, model-induced propagation error is maintained to less than 50 m for intervals up to 90 minutes and less than 25 m for intervals up to 30 minutes. This corresponds to crosslink 9 9 th percentile angular errors of less than 600 [mu]rad at 25 km and less then 40 [mu]rad at 580 km. Earth-Centered-Inertial (ECI) to Earth-Centered-Earth-Fixed (ECEF) transformations are discussed for ground station position prediction, and even with the simplest transformation formulation, position error remained less than 16 m.

Model-induced error for all downlink cases had a 9 9 th percentile error of less than 32 [mu]rad. The relative navigation error for crosslinks is analyzed for the baseline CLICK configuration of directly propagating GPS fixes. For crosslinks across all configurations, the 9 9 th percentile angular errors are less than ~2000 [mu]rad at 25 km and less then ~200 [mu]rad at 580 km, corresponding to 99.7% pointing losses less than -1.235 dB at 25 km and -0.427 dB at 580 km and corresponding margins greater than 0.265 dB and 1.073 dB, respectively. For downlinks, the 9 9 th percentile error across all cases is less than ~45 [mu]rad, which corresponds to 99.7% pointing losses of less than -0.434 dB with margins greater than 1.066 dB across all cases, including simplified Earth rotation models. In Chapter 4, Kalman filtering algorithms are explored to improve GNSS-based orbit determination for relative navigation in LEO.

Three different formulations of the Extended Kalman Filter (EKF) correction and prediction subroutines are explored in depth: 1) the Conventional EKF (CEKF); 2) the Joseph Sequential EKF (JSEKF); 3) the UD Sequential EKF (UDSEKF). Implementation and time complexity differences are discussed for Runge-Kutta methods used to solve state prediction problem and for matrix exponential methods used to approximate continuous-time covariance prediction. The EKF for orbit determination using GNSS measurements is formulated using the ECI position and velocity, a central body gravity model, and nondimensionalization. The CEKF, JSEKF, and UDSEKF filter formulations are evaluated on three metrics: efficiency as per analytical time complexity results, consistency, and orbit determination accuracy. The overall ranking is 1) UDSEKF, 2) CEKF, 3) JSEKF.

With the addition of Kalman filtering, across all crosslink configurations, the 9 9 th percentile angular errors are less than -1000 [mu]rad at 25 km and less then ~100 [mu]rad at 580 km, and the 99.7% pointing losses are less than -0.623 dB at 25 km and -0.421 dB at 580 km with corresponding margins greater than 0.877 dB and 1.079 dB, respectively. This corresponds to improvements of at least 50% for the angular error across all cases. For the CLICK hardware configuration, filtering has a significantly greater effect on pointing loss at shorter ranges. Applying filtering for downlinks yields an improvement in the overall 9 9 th percentile error across all cases by at least 22.2% to less than ~35 [mu]rad. As anticipated from previous analysis, filtering has a negligible impact on pointing loss for downlink due to the dominance of mechanical and spacecraft errors in the CLICK downlink pointing budget. Filtering had the greatest impact for short range crosslinks.

Nevertheless, for future missions with more stringent requirements, narrower beams, improved mechanical errors, and/or significantly worse GPS measurement errors, filtering may also have significant benefit for long range crosslinks and for downlinks.