EBS-EKF: Accurate and High Frequency Event-based Star Tracking

TL;DR

This work tackles the challenge of high-frequency, accurate star tracking with event-based sensors by developing EBS-EKF, which couples a physics-informed centroiding model that accounts for low-light circuit dynamics with an asynchronous EKF on the rotation-velocity state. The key innovations are an intensity-dependent event likelihood model and a 3D attitude EKF that estimates both orientation and angular velocity at up to $1 kHz$, validated on real night-sky data with ground-truth APS references. The authors provide a ground-truth night-sky dataset and open-source code, demonstrating up to an order of magnitude accuracy improvement over prior EBS methods and superior motion tolerance compared to APS trackers. This approach enables robust, high-rate attitude updates for star tracking applications in space navigation and related fields, especially where power and latency constraints are critical.

Abstract

Event-based sensors (EBS) are a promising new technology for star tracking due to their low latency and power efficiency, but prior work has thus far been evaluated exclusively in simulation with simplified signal models. We propose a novel algorithm for event-based star tracking, grounded in an analysis of the EBS circuit and an extended Kalman filter (EKF). We quantitatively evaluate our method using real night sky data, comparing its results with those from a space-ready active-pixel sensor (APS) star tracker. We demonstrate that our method is an order-of-magnitude more accurate than existing methods due to improved signal modeling and state estimation, while providing more frequent updates and greater motion tolerance than conventional APS trackers. We provide all code and the first dataset of events synchronized with APS solutions.

Figures (36)

• Figure 1: We present EBS-EKF, an event-based star tracking algorithm that combines a novel centroiding technique with an extended Kalman filter and is validated using the first ground-truthed dataset of event streams from real stars. (a) Our centroiding technique accounts for event camera behavior in low light, enabling more accurate tracking. (b) We develop a data collection setup of a EVK4-HD event camera that is rigidly mounted and synchronized with a space-ready APS star tracker. The insets show APS (top) and event camera (bottom) pixels for 8 Cygni, a subgiant star in the constellation Cygnus. (c) We demonstrate that our attitude estimates (red) are more accurate than existing methods (purple) Ng2022, and that we can operate above the 3 deg/sec cutoff of the APS star tracker, highlighting the utility of our method for high-frequency star tracking.
• Figure 2: Measurement model for event-based star tracking. (a) depicts the coordinate systems used; (b) depicts an example operation of an EBS pixel as a star's projection passes over it.
• Figure 3: In low-light conditions, a star's brightness introduces a variable delay between the observed peak of positive events and its true locations. (a) depicts the numerical solution of event likelihood $E_{\text{LL}}(t)$ in Eq \ref{['eq:methods:diffeq']} compared to star intensity $I(t)$ for a single pixel. Bright stars produce a distribution of positive and negative events that follows the derivative of the intensity. Dim stars, however, yield a distribution of positive events that peaks nearer to the peak intensity, and the negative events fall to the tail of the distribution. (b) compares the theoretical spatial positive event likelihood distribution (calculated by solving Eq \ref{['eq:methods:complete_spatial_likelihood']}) to those measured in our night sky dataset. (c) depicts the offset $z(m_s)$ between the centroid of the positive events and the star's true centroid as a function of the star's brightness (i.e. relative magnitude $m_s$). The offsets are normalized to have a minimum offset of 0.
• Figure 4: Testing the centroiding accuracy of Eqs \ref{['eq:methods:complete_spatial_likelihood']} and \ref{['eq:methods:gauss_approx_likelihood']} via an LCD monitor. (a) depicts the hardware setup. (b) depicts the centroiding experiment on the high-update rate monitor, where the star is moving at 35 pixels per second and has a 2.5 pixel standard deviation to emulate stars in our night sky dataset. (c) depicts the centroiding accuracies of our methods (blue and orange curve) compared to those of previous works. The black dotted line depicts zero centroiding error. Details about the synchronization and other aspects are included in supplementary.
• Figure 5: Our night sky data collection system with key components labeled. The sync pulse generator ensures that we can temporally correlate the Rocket Lab APS measurements with the EVK4-HD event camera measurements. The Pan and Tilt Motors are used to sweep both star trackers across the sky based on pre-defined motion patterns.