Angles-Only Navigation System for Nanosatellites

The goal of this work is to develop an angles-only navigation system compatible with the on-board resource constraints of nanosatellites or CubeSats. This system uses measurements from a monocular camera to perform autonomous far- to mid-range relative navigation with a non-cooperative target, serving the needs of future on-orbit servicing and debris removal missions. Furthermore, the small mass and power budgets of the resulting system are expected to reduce the cost of future formation-flying missions. The proposed work aims at the development of a complete navigation system, including new overall concept, algorithms, software, customized commercial-off-the-shelf hardware, interfaces, integration, and a rigorous validation using a high-fidelity optical stimulator testbed at Stanford University. The end goal of this project is a flight demonstration in the Starling Formation-flying Optical eXperiment (StarFOX), which is part of the Starling1 mission in development at NASA Ames Research Center. Multiple flight demonstrations of angles-only navigation have performed during the ARGON and AVANTI experiments. However, these experiments relied on a common recipe that includes accurate a-priori information (e.g. NORAD two-line elements) and use of translational maneuvers to resolve the weakly observable range. This work aims to overcome the limitations of the state-of-the-art to enable angles-only navigation without translational maneuvers and without a-priori relative state information. These developments would enable use of angles-only navigation in a broader range of space missions. To meet these objectives, this research has provided several contributions to the state-of-the-art in closed-form astrodynamics models, angles-only navigation algorithms, and sensor-in-the-loop verification and validation for vision-based navigation systems. Previous angles-only navigation demonstrations relied on translational maneuvers because the bearing angle trajectories to nearby resident space objects exhibit little sensitivity to the separation. To resolve the separation without performing translational maneuvers, it is necessary to use an accurate, nonlinear model of spacecraft relative motion in perturbed orbits. A closed-form model is ideal to minimize computation cost. To meet this need, a new methodology was developed for derivation of state transition matrices for spacecraft relative motion for states based on relative orbital elements. Unlike prior approaches, this method can incorporate conservative and non-conservative perturbations in orbits of arbitrary eccentricity. This method was used to produce for the first time in literature STMs that include the secular and long-period effects of both earth oblateness and differential drag on orbits of arbitrary eccentricity. In addition to their use in angles-only navigation, these models can be leveraged to inform the design of a wide range of future spacecraft formation-flying and swarming missions. These dynamics models are leveraged to develop a new initial relative orbit determination algorithm that does not require any a-priori information. The relative orbit is computed in three steps. First, a coarse estimate of the range is computed from the secular drift of the elevation angle. Second, an estimate of the unit vector aligned with the relative state is computed using a linearized measurement model. Finally, the initial estimate is refined using iterative regularized batch least squares. Monte Carlo simulations have demonstrated that this approach provides an initial relative orbit estimate with a range error of 25% or less in a wide range of scenarios. Next, a new sequential filter architecture was developed to enable angles-only navigation without requiring translational maneuvers. To enable robust convergence in the presence of realistic measurement errors and operational limitations, it is necessary to ensure that the propagation of the state estimate and covariance is as accurate as possible. An unscented Kalman filter was selected for this purpose because the unscented transform captures nonlinearities in the propagated probability density function. This filter architecture has exhibited reliable maneuver-free convergence to steady state range estimation errors of 2% or less. To ensure that the navigation algorithms behave as intended in flight, it is necessary to test them in a representative environment. The Space Rendezvous Laboratory has developed a high-fidelity optical stimulator testbed to facilitate testing of this filter and other vision-based navigation systems. The testbed includes a small 1.2-megapixel OLED display, two collimating optics, and a sensor. The testbed is calibrated to render point sources such as stars with accuracy on the order of tens of arsceconds after calibration. This testbed was used to test the combined image processing, initial relative orbit estimation, and sequential filtering algorithms. Sensor-in-the-loop tests have demonstrated that the developed angles-only navigation algorithms function as intended in a high-fidelity replication of the space environment.