Position and Time Determination without Prior State Knowledge via Onboard Optical Observations of Delta Scuti Variable Stars

TL;DR

The paper tackles autonomous recovery from lost in space and time by leveraging onboard optical observations of δ Scuti variable stars to extract time-of-arrival information. It develops a TOA-based navigation framework consisting of TOA estimation, a closed-form 4D (space and time) linear solution, and an ambiguity-resolution search using wavefront intersections, validated via simulations with OSIRIS-APEX. Key contributions include explicit light-curve modeling for δ Scuti stars, a weighted least-squares observer-state estimator, and an XNAV-inspired ambiguity-resolution approach, demonstrating feasibility within about $0.03$ au and $3$ s (3σ) using only existing optical sensors. The work suggests a practical, autonomous capability to re-establish state after clock or navigation failures, potentially complementing higher-accuracy methods and enabling resilient deep-space operations.

Abstract

We present a navigation concept for solving the lost in space and time problem using optical observations of $δ$ Scuti variable stars. Only a small number of techniques exist that allow a spacecraft to recover from being lost in both space and time, which can be caused by a failure of the onboard clock and navigation systems. Optical observations of $δ$ Scuti stars, which can be collected onboard from star trackers or navigation cameras, may enable autonomous position and time determination without requiring additional equipment or external communication. Our results indicate that less than one day of observation by the OSIRIS-APEX PolyCam may enable position and time determination accuracy within 0.03 au (3$σ$) and 3 seconds (3$σ$).

Figures (12)

• Figure 1: Normalized light curve of X Caeli.
• Figure 2: Pulsation spectra of X Caeli. The dominant frequencies --- 7.392, 6.046, and 13.980 cycles per day --- are in close agreement with results from Ref. mantegazza1999simultaneous.
• Figure 3: Diagram of measurement time transfer between a spacecraft and the reference observatory. Parallax and relativistic perturbations are neglected. A signal traveling along $-\hat{\mathbf{u}}$ can be measured at time $t$ at the spacecraft, and at time $T$ at the reference observatory.
• Figure 4: Illustration of a three-dimensional light cone originating from a $\delta$ Scuti star, representing the set of possible spacecraft coordinates given a signal measurement known to pass through the SSB at time $T$.
• Figure 5: Two-dimensional example of wavefront intersection. The $\delta$ Scuti star lines of sight are indicated by $\hat{\mathbf{u}}$. The observer's true spacetime coordinate is in green. The observer's spacetime coordinate can be on an infinite number of wavefronts --- shown in red --- when only observing the light curve of one $\delta$ Scuti star (a). Adding wavefronts from observations of other $\delta$ Scuti stars reduces set of feasible spacetime coordinates to intersections of wavefronts as shown in (b)-(c) lohan2021methodology.