Mark Moretto, North Carolina State University; Katherine Melbourne, University of Colorado Boulder; Marcus Holzinger, University of Colorado Boulder
Keywords: Event camera, non-resolved object characterization, SSA, vibrations, rotational state
Abstract:
Space situational awareness (SSA) requires the correlation of measurements to specific objects – debris or spacecraft. The rotational state and vibrational modes of these objects can help resolve ambiguities in this association process and provide additional information about the properties and operational state of the object. Event, also known as neuromorphic, cameras have shown promise in rapidly quantifying the rotation and vibration of spacecraft from ground-based observations [1, 2].
Event cameras are collections of circuits that are sensitive to changes in flux and that operate independently [3]. The circuits report “events” when the voltage changes by plus or minus a tunable percentage threshold, generating positive or negative events, respectively. Events are reported with microsecond precision. Benson & Holzinger [1,2] derived equations for the mean voltage under certain periodic signals, as well as providing proof-of-concept analysis of observations of the ISS [1] and Ajisai [1,2]. The goal of this work is to quantify the sensitivity to and recoverability of periodic signals from event camera data to inform the design and tuning of these devices, as well as to demonstrate these results on empirical data.
This work will present analytical advances in the event camera’s sensitivity to frequency content and on the recovery of frequency content from event data. First, an analytical formulation of the event rate computed from the mean voltage and it’s time derivative derived by Benson & Holzinger [1,2] will be described. Next, the voltage normalized by its value at the initial epoch, a proxy for the voltage in the circuit computed from event data, will be introduced. The frequency content of the analytical event rate, the proxy voltage, the mean voltage, and idealized events, will be compared for known inputs. The separability of multiple frequencies using different analysis techniques will be explored.
The event camera circuit will be analyzed using controls techniques. Bode plots are used to quantify the sensitivity of the circuit to specific frequencies and the phase of the output. Analytical bounds on the frequency sensitivity are found from a transfer function approximation of the event camera circuits. These analytical results will inform the tuning of event cameras to target specific frequency content. Furthermore, these analytical results will inform the minimum magnitude of periodic signals that can be recovered from event data.
Finally, these results will be verified using empirical observations of satellites, stars, and other periodic signals in-lab. The recovery of known signals will demonstrate the validity of this methodology. The repeatability of observations of objects without known characteristics and the consistency of those results with analytical models will provide confidence that these techniques can be used operationally. Results will be compared with truth data when available.
There are four contributions of this work. The first contribution is the use of analytical event rates to approximate discrete event data and the use of a proxy voltage for frequency analysis. The second contribution is a comparison of frequency analysis techniques. The third contribution is the treatment of the event camera circuit as a classical controls problem to derive analytical insights into the observability of frequency content. Finally, the fourth contribution is the demonstration of these results using empirical data of known and unknown signals.
[1] Benson, C.J. and Holzinger, M.J., 2022. Simulation and Analysis of Event Camera Data for Non-Resolved Objects. Advanced Maui Optical and Space Surveillance Technologies Conference 2022
[2] Benson, C.J. and Holzinger, M.J., 2023. Simulation and Analysis of Event Camera Data for Non-Resolved Objects. The Journal of the Astronautical Sciences, 71(3), pp. 1-25.
[3] Lichtsteiner, P., Posch, C., and Delbruck, T., 2008. A 128×128 120 db 15 microsecond latency asynchronous temporal contrast vision sensor. IEEE J. Solid State Circ., 43(2), pp. 566–576.
Date of Conference: September 17-20, 2024
Track: SDA Systems & Instrumentation