Incorporation of GNSS Multipath to Improve Autonomous Rendezvous, Docking and Proximity Operations in Space

Accurately model the raw GNSS signal received during rendezvous and close proximity operations around large space structures and use this information to improve relative navigation accuracy and integrity. An outline of material developed under this grant is shown below in Figure 1. The project components are color-coded as follows: green and blue indicate actual and simulated data respectively, both used as software inputs; salmon indicates original software; yellow indicates software outputs. Hubble Servicing Mission 4 (HSM4) was used as a case study for this research because of unique, sampled intermediate frequency Global Positioning System (GPS) data obtained from the mission. During HSM4, the Relative Navigation Sensor (RNS) experiment collected several hours of imagery and other data for estimating the space telescope’s relative position and attitude from the shuttle cargo bay. Two GPS antennas were included as part of this experiment, one right-hand circularly polarized (RCP), intended for receiving direct signals, the other left-hand circularly polarized (LCP), intended for receiving reflected signals. The two resulting data sets cover several hours of rendezvous, docking and deploy of the Hubble Space Telescope (HST) and are represented in Figure 1 by the “HSM4 Data” block. In order to estimate receiver environment features from multipath, such as the distance of a reflecting “target” spacecraft from a receiver, it is necessary to characterize the relationship between the environment features of interest and the observable multipath signal properties. First the “truth” geometry of HSM4 was constructed. Absolute position and attitude of the shuttle was taken from the United Space Alliance’s Post-flight Attitude and Trajectory History (PATH) data product, a standard product for shuttle missions. The position of HST relative to the shuttle was computed from a composite of the United Space Alliance product Relative Best Estimate Trajectory (RELBET) and vision processing estimates from the RNS experiment. The truth geometry was used to construct a simulation in Simulation Tool Kit (STK) in order to visualize the mission and compute geometric features such as GPS satellite visibility. Using the truth geometry and a model of HST, a simulation was constructed in electromagnetic (EM) ray trace software, WinProp. In collaboration with Professor Penina Axelrad and Jeanette Veldman at the University of Colorado Boulder, a ray trace simulation was run to find all ray paths of GPS signals reflected off HST and their properties (PRN source, azimuth, elevation, relative delay, relative E field strength, type of interaction, time of arrival). These reflected signal properties relative to the line of sight (LOS) signals were combined with scenario geometry in a MATLAB GPS signal simulator to simulate HSM4 data, shown in Figure 1 as “Simulated Raw Measurements.” The signal simulator, GSFC Siggen, was developed in collaboration with fellowship mentor Dr. Luke Winternitz. A custom MATLAB software receiver was constructed, the Relative Navigation Sensor Software Defined Radio (RNS SDR), and used to produce code pseudorange measurements from both the simulated and experimental data. A model was derived for the effect of reflected signals, or “multipath,” on the code correlations at the output of the Delay Lock Loop (DLL), where M is the number of multipath rays, τe the delay estimate error, τd the early-late correlator spacing of the DLL (in chips), αi the ratio of the i-th multipath ray amplitude to the LOS ray amplitude, and δi and ψi the code delay and carrier phase of the i-th multipath signal relative to the LOS signal respectively. The error due to multipath in the propagation delay measurement (i.e., pseudorange) can be calculated by finding the null of Equation 1. In the simulation case, the scenario geometry can be used to calculate a true pseudorange. The differences between the measured and true pseudoranges were shown to agree with Equation 1 for the true multipath parameters from ray tracing supplied to the signal simulator. An example with a single reflected ray is shown in Figure 2 for PRN 9 starting at 16:23:45 UTC during docking. In the top plot the excess pseudorange measured from tracking simulated data is plotted with that calculated using Equation 1 from the reflected signal’s relative code and carrier phases (middle plot) and amplitude (bottom plot). Excess pseudorange measurements have not yet been made from the HSM4 data; the narrow front-end bandwidth used in collecting the data (2 MHz) had a smoothing effect on the code correlations so other techniques for extracting multipath observables are being pursued. In the meantime, a navigation algorithm was developed using an Extended Kalman Filter (EKF) to estimate receiver and target spacecraft states. In a rendezvous and docking scenario, the target spacecraft is the non-cooperative space vehicle that the controlled spacecraft, or “chaser,” is docking with. Using original code, as well as programs from Goddard’s Orbit Determination Toolbox (ODTBX), a simulation of HSM4 was constructed. As an initial step, direct and reflected pseudoranges are used as measurements and modeled using the Bistatic Radar Equation and a perfectly conducting sphere for HST’s radar cross section. Position errors are shown in Figure 3 for the receiver and target for fifty different runs demonstrating successful estimation of both spacecraft to meter-level accuracy under these simplified conditions.