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Optimal Search for Finding Satellites Post-Launch

Carlo Schreiber, Duncan Eddy, Mahdi Al-Husseini, Derek Woods, Araz Feyzi, Mykel J. Kochenderfer

arXiv:2610.07300v1eess.SYcs.SY

TL;DR

After launch, operators must search for spacecraft whose actual positions may differ from uncertain orbit estimates, while misses inform the search and antenna motion limits future reachability. The paper introduces BC-MPC, which replans antenna pointings after misses while retaining a feasible sweep continuation. Across 96 simulated deployments, it improves acquisition probability and reduces restricted mean acquisition time relative to ATUS.

  • Problem

    Launch and deployment errors can leave spacecraft far enough from predicted positions that operators must search during ground contacts to establish communications.

    Source: §1 · p. 1

  • Method

    BC-MPC updates a particle-based orbital belief after misses and replans near-term antenna pointings while retaining a feasible baseline sweep continuation.

    Source: §1 · p. 1

  • Results

    83.3% to 90.2% acquisition probability and 89.8 s to 78.3 s RMST with BC-MPC relative to ATUS across 96 simulated deployments.

    Source: §5 · p. 7

  • Takeaways & Limitations

    The retained, motion-feasible continuation lets BC-MPC evaluate replanned pointings together with the remaining sweep over the full contact window.

    Source: Operational search strategies · p. 4

    The evaluated initial beliefs use equally weighted particles with independent Gaussian perturbations around the nominal orbit and specified standard deviations.

    Source: §4 · p. 4

Abstract

from arXiv · show

This paper introduces Bayesian Continuation Model Predictive Control (BC-MPC), an adaptive method that replans near-term antenna pointings while continuing a feasible baseline sweep, for finding and establishing contact with spacecraft immediately after launch when their true positions are most uncertain. After separation, launch and deployment errors can leave the spacecraft sufficiently far from its predicted position that operators must actively search for it during ground contacts to establish communications. Each missed detection provides information about which orbital hypotheses remain plausible, but searching one part of the uncertainty region can consume the time needed to reach another. BC-MPC updates a particle-based orbital belief after missed detections and replans antenna pointing guidance while retaining feasibility. Its continuation helps preserve future search coverage that greedy and short-horizon methods can sacrifice for immediate acquisition gains. We compare BC-MPC against the operationally prevalent along-track sweep and additional search algorithms under common search-time budgets, initial uncertainty, and antenna constraints. Across 96 simulated deployments with matched uncertainty, BC-MPC improves acquisition probability over the along-track sweep and reduces restricted mean acquisition time. We additionally evaluate the method using pre-launch, post-launch, and initial acquisition ephemerides for 83 spacecraft from the Transporter-16 rideshare launch. Using either pre-deployment or post-deployment two-line element sets (TLEs) for planning, BC-MPC improves modeled acquisition probability over the along-track sweep by approximately 12 percentage points under the commonly assumed uncertainty model.

1. INTRODUCTION

After launch, operators must find spacecraft whose actual positions may differ substantially from their orbit estimates, while working within limited contact windows and antenna-motion constraints. The paper introduces BC-MPC to adapt search pointings after misses while preserving a feasible continuation of the sweep.

Motivation

  • Launch and deployment errors can make a spacecraft’s position uncertain enough that operators must search around an estimated orbit to establish contact and assess spacecraft health.Pre-launch orbit parameter messages provide an expected deployment state, but not the exact post-launch position.Source: §1 · p. 1, Figure 1 · p. 2

Existing procedures

  • Traditional predetermined scans along or around the predicted trajectory are simple and predictable, but generally do not use missed detections to adapt the next search location.The paper situates this problem within Bayesian search and related methods while focusing on antenna-motion constraints and finite contact duration.Source: §1 · p. 1

Search challenge

  • Search decisions must use limited ground-contact time efficiently because antenna motion can make later locations unreachable after searching elsewhere.Misses provide information about plausible trajectories, but moving toward one part of the uncertainty region can consume time needed to reach another.Source: §1 · p. 1

Contributions

  • BC-MPC updates a particle-based trajectory belief after misses and replans near-term antenna pointings while retaining a feasible baseline sweep as continuation.The paper formulates acquisition as a sequential decision problem and evaluates the method in simulations, sensitivity studies, fleet experiments, and Transporter-16 replay.Source: §1 · pp. 1–2

2. PROBLEM FORMULATION

The formulation selects antenna search actions to maximize acquisition probability during contact, given an uncertain spacecraft state and antenna-motion constraints. It represents uncertainty with orbit hypotheses, updates their weights after misses, and accounts for reachable pointings and contact timing.

2. PROBLEM FORMULATION

  • The decision problem selects an antenna-action sequence that maximizes the probability of acquiring a spacecraft within a contact window, given a belief about its state.Actions consist of pointing, settling, and listening, subject to antenna motion constraints.Source: §2 · p. 2

Contact windows

  • A predicted contact window is planned from the nominal state, but actual visibility can differ; failed searches resume at the next available contact with an updated belief.The window spans the interval when the spacecraft is above the station’s elevation mask.Source: Contact windows · p. 2

Orbital uncertainty

  • Orbital uncertainty is represented by weighted particles, each describing a possible trajectory propagated through the contact window with SGP4.The nominal orbit comes from pre-deployment or post-deployment OPMs, while the true state remains uncertain because of launch and deployment errors, limited tracking, and prediction error.Source: Orbital uncertainty · p. 2
  • Each orbit hypothesis maps to an antenna pointing direction by propagating its state, transforming its position to Earth-fixed coordinates, and expressing the line of sight in the station’s local frame.The resulting pointing direction can be represented by azimuth and elevation.Source: Orbital uncertainty · p. 2

Search actions and observations

  • A search action commands a pointing, allows the antenna to settle, and listens; its detection probability depends on pointing error, range, elevation, and listening duration.The model uses a Gaussian angular profile with a 2° full width at half maximum, and an on-axis probability that decreases with range and decreasing elevation.Source: Search actions and observations · p. 3
  • After a miss, particle weights are updated using Bayes’ rule, shifting belief away from trajectories for which the executed pointing likely would have produced acquisition.The model treats successive attempts as independent for each trajectory, ignoring persistent propagation losses or beacon outages.Source: Search actions and observations · p. 3
  • The sequence objective accounts for the probability of acquisition across the planned search actions.It evaluates acquisition within the contact window rather than treating each action in isolation.Source: §2 · p. 2, Search actions and observations · p. 3

Antenna motion feasibility

  • A pointing is reachable only when the slew, settling, and listening time fit the decision interval, so each choice can restrict later feasible actions.Slews are modeled as great-circle transfers subject to maximum slew rate and angular acceleration.Source: Antenna motion feasibility · p. 3

3. BAYESIAN CONTINUATION MPC

The section contrasts operational search policies with Bayesian greedy search and MPC, then introduces BC-MPC, which replans near-term antenna pointings while retaining a feasible ATUS continuation. After a missed detection, it updates the orbital belief and repeats the optimization.

Operational search strategies

  • Operational alternatives include nominal tracking from the predicted state and a uniform grid sweep over a fixed region that does not exploit orbital-uncertainty structure.The grid may spend time on locations where the spacecraft is unlikely to be.Source: Operational search strategies · p. 3
  • ATUS sweeps evenly spaced candidates along predicted along-track uncertainty in a fixed repeating order, selecting reachable pointings or partially slewing toward the preferred one.Missed detections do not change the sweep order.Source: Operational search strategies · p. 3
  • Bayesian greedy search updates its belief after a miss and selects the feasible pointing with the highest immediate acquisition probability, without accounting for later opportunities.Source: Operational search strategies · pp. 3–4
  • MPC optimizes a sequence of H upcoming pointings but executes only the first; a short horizon can leave later contact opportunities outside the optimization.BC-MPC retains the ATUS continuation to evaluate beyond that horizon.Source: Operational search strategies · p. 4
  • BC-MPC reoptimizes the next H pointings from an ATUS schedule, evaluates them with the retained continuation across all remaining stages, and preserves antenna-motion feasibility.Only the first optimized pointing is executed.Source: Operational search strategies · p. 4
  • After a miss, BC-MPC updates particle weights, shifts the optimized schedule into the next continuation, and replans using the updated belief.Source: Operational search strategies · p. 4

4. EVALUATION

The evaluation tests single-contact search, repeated-contact and fleet acquisition, and an operational replay under shared search assumptions. BC-MPC outperforms ATUS in the reported full-window, fleet, and Transporter-16 comparisons.

4. EVALUATION

  • The primary evaluation used 2,773 attempts across 96 deployments and compared BC-MPC with a uniform grid sweep, ATUS, Bayesian greedy, and MPC without continuation.The shared configuration used six illustrative ground stations and equally weighted particles initialized by Gaussian perturbations around the nominal orbit; acquisition probability and RMST were the evaluation metrics.Source: Single-spacecraft search · p. 4, §4 · p. 4

Single-spacecraft search

  • Over 192 s, BC-MPC achieved acquisition probability 0.902 versus 0.833 for ATUS, a 6.9-percentage-point improvement, and reduced RMST from 89.8 s to 78.3 s, a reduction of 11.5 s.The confidence intervals were 6.7–7.0 percentage points for the acquisition improvement and 11.4–11.7 s for the RMST reduction.Source: Table 2 · p. 4, Single-spacecraft search · pp. 4–5
  • By 60 s, Bayesian greedy and MPC without continuation had higher cumulative acquisition than BC-MPC, but BC-MPC led by the end of the 192 s contact window.The comparison illustrates the value of retaining effective search opportunities for later in the contact when early pointings do not detect the spacecraft.Source: Single-spacecraft search · p. 5, Figure 4 · p. 5
  • Across repeated contacts in 16 spacecraft scenarios, BC-MPC acquired more spacecraft during the earliest opportunities, while the difference narrowed as more opportunities became available.Missed detections over a contact window inform the belief used to guide subsequent contacts.Source: Single-spacecraft search · p. 5, Figure 5 · p. 5
  • BC-MPC maintained lower RMST than ATUS across tested confirmation-time multipliers and retained an average 5.1 s RMST saving with a 100 s mean signal-availability delay.As mean signal-availability delay increased, RMST rose for both controllers and BC-MPC’s advantage gradually narrowed.Source: Single-spacecraft search · p. 6, Figure 6 · p. 6, Figure 7 · p. 6

Fleet acquisition after launch

  • With six ground-station sites, BC-MPC increased the expected fraction of spacecraft acquired within 24 hours from 89.5% with ATUS to 94.2%.The advantage was largest with limited ground-station opportunities and narrowed as the network expanded, with both controllers approaching 99% acquisition for the largest tested networks.Source: Figure 9 · p. 7, Fleet acquisition after launch · p. 7

Kayhan Space LEOP replay

  • Across pre- and post-deployment planning cases using operational orbit products, BC-MPC improved modeled acquisition over ATUS by approximately 12 percentage points in both cases while also reducing RMST.Source: Kayhan Space LEOP replay · p. 7

5. CONCLUSION

BC-MPC adapts antenna pointings using Bayesian belief updates while retaining an operational sweep’s structure. Simulated deployments and a Transporter-16 replay show improved acquisition over ATUS, with the advantage narrowing as more ground-station opportunities become available.

5. CONCLUSION

  • Acquisition probability rose from 83.3% to 90.2% and RMST fell from 89.8 s to 78.3 s versus ATUS across 96 simulated deployments.The paper also reports improved modeled acquisition over ATUS by 12.0 and 12.4 percentage points for pre- and post-deployment ephemerides, respectively.Source: §5 · p. 7
  • Transporter-16 replay data for 83 spacecraft showed modeled acquisition gains over ATUS of 12.0 and 12.4 percentage points using pre- and post-deployment ephemerides.The gains used the commonly assumed uncertainty model and were accompanied by reduced RMST.Source: §5 · p. 7
  • Repeated-contact and fleet experiments found that contact-level improvements translated into earlier fleet acquisition, while the advantage narrowed as additional ground-station opportunities became available.Source: §5 · p. 7
  • BC-MPC updates a particle-based belief after missed detections and replans antenna pointings while accounting for future antenna reachability and retaining an operational sweep’s structure.Future work could validate with vehicle GNSS measurements and extend the controller to variable listening times, partial signal-strength feedback, and reservation reassignment after early acquisition.Source: §5 · p. 7

BIOGRAPHY[

The biographies describe the authors’ academic roles, research interests, and professional experience.

BIOGRAPHY[

  • Carlo Schreiber is an electrical-engineering M.S. student and graduate researcher at Stanford, focusing on decision-making under uncertainty, planning, and control.Source: BIOGRAPHY[ · p. 8
  • Duncan Eddy is a Stanford research fellow and Center for AI Safety executive director whose research focuses on decision-making in safety-critical, climate, and space systems.Source: BIOGRAPHY[ · p. 8
  • Mahdi Al-Husseini is a Stanford Ph.D. candidate developing models and algorithms for semidecentralized multi-agent systems under communication constraints.Source: BIOGRAPHY[ · p. 8
  • Derek Woods manages Kayhan Space customer success for spaceflight safety integrations, with prior astrodynamics engineering experience focused on high-accuracy force modeling and code reliability.Source: BIOGRAPHY[ · p. 8
  • Araz Feyzi is Kayhan Space’s co-founder and CTO, with more than 10 years of technology and analytics experience.Source: BIOGRAPHY[ · p. 9
  • Mykel J. Kochenderfer is a Stanford professor and director of the Stanford Intelligent Systems Laboratory, researching robust decision-making systems.Source: BIOGRAPHY[ · p. 9
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