Extended Kalman filter-based angle-of-arrival estimation for optical inter-satellite tracking

Abstract

Accurate angle-of-arrival (AOA) estimation is essential for acquisition and tracking in free-space optical (FSO) inter-satellite links operating in low Earth orbit (LEO), where rapid relative motion, sensor noise, and nonlinear spherical geometry complicate real-time beam pointing. This paper presents a causal Extended Kalman Filter (EKF) framework for recursive AOA tracking using normalized sensor responses from a spherical photodetector (PD) array distributed via a Fibonacci lattice. The EKF estimates azimuth and elevation directly as the system state and supports nonlinear measurement relationships by linearizing the angle-to-intensity mapping with a Jacobian evaluated at each time step. Simulation over a nominal 1 kHz sample sequence for 100 seconds (100,000 samples) under zero-mean Gaussian angular perturbations with a standard deviation of 0.1° demonstrates sub-degree mean tracking error using a 64-sensor array: 0.025115° azimuth and 0.025052° elevation. A reduced-sensor case (40 sensors) produced mean absolute errors (MAE) of 0.024258° in azimuth and 0.024192° in elevation, demonstrating comparable tracking performance under reduced sensing density for the tested trajectory. Results show stable estimation and effective noise suppression, supporting EKF-based nonlinear estimation as a viable path toward onboard, real-time optical beam tracking.