APOGEE: Orbital Intelligence for a Crowded Sky

1The orbital-safety problem

Orbit is a shared, finite resource filling faster than it can be managed. Tens of thousands of tracked objects, and far more too small to track, cross paths at kilometres per second, and a single collision can render a band of orbit hazardous for decades.

The problem has three distinct computational faces. First, knowing where everything is: objects are seen only in brief, noisy passes from radar and optical sensors, and their positions must be inferred and propagated forward against imperfectly-known forces. Second, knowing what will come close: screening every object against every other is a combinatorial screening problem, and turning a close approach into a defensible probability of collision requires propagating uncertainty, not just nominal positions. Third, acting in time: an avoidance maneuver must be minimal and coordinated across a constellation, and when a spacecraft is out of ground contact it must decide for itself.

These are different problems, statistical estimation, combinatorial optimization, and real-time control, and APOGEE pairs each with the appropriate method rather than forcing one tool across all three.

2System overview

APOGEE runs a loop from sensor to spacecraft and back: observations become a catalog, the catalog is screened for risk, risk becomes maneuvers, and what the spacecraft does refines the catalog. Part of the loop runs on the ground; part runs onboard.

2.1Ground plane and flight plane

APOGEE separates a ground plane (the full catalog, screening, and optimization) from a flight plane (the onboard subset: health monitoring, fault response, and pre-authorized autonomy). The flight plane degrades gracefully: if the ground link or a quantum backend is unavailable, the spacecraft keeps monitoring and can execute the last approved safe action. Nothing on the safety-critical path depends on a quantum backend being reachable.

3Track — orbit determination

Track turns sparse, noisy observations into a precise, uncertainty-aware estimate of every object's orbit, and propagates it forward against the forces that perturb it.

3.1Observation and estimation

Each sensor pass yields a measurement z (range, angles, range-rate) related to the object's state x (position and velocity) through a nonlinear observation model with noise:

A recursive Bayesian estimator fuses each new pass with the propagated prior, updating both the state estimate and its covariance:

The covariance P is a first-class output, not an afterthought. It is what makes conjunction assessment (§4) a probability rather than a guess.

3.2Propagation

Between observations the state is propagated under the real force environment, two-body gravity plus the perturbations that dominate in each regime:

and the covariance is propagated with the state-transition matrix Φ, so predicted uncertainty grows honestly with time:

Drag depends on poorly-known atmospheric density and object attributes, so Track estimates ballistic coefficients online and is the largest error source in low orbit, a fact §10 does not hide.

3.3Sensor tasking

Sensors are scarce and the sky is large. Track decides which object to observe next to reduce catalog uncertainty the most, an active-learning loop that prioritizes objects whose covariance is growing toward a conjunction, so observation effort follows risk.

4Predict — conjunction assessment

Predict screens the full catalog for close approaches and converts each into a defensible probability of collision, days before the moment of closest approach.

4.1All-versus-all screening

Comparing every object against every other is quadratic, hundreds of billions of pairs per screening cycle. APOGEE reduces it with coarse geometric pre-filters (apogee/perigee overlap, orbit-plane geometry) that discard the vast majority of pairs cheaply, leaving a small set of true candidates for precise analysis.

4.2Probability of collision

The nominal miss distance is not the risk; the risk is the miss distance relative to the combined position uncertainty. Projecting both objects' covariances into the encounter (B-)plane and combining them gives a 2D distribution C; the probability of collision integrates it over the combined hard-body radius R_HB:

This is why Track's covariance matters: a small miss with a large, well-characterized uncertainty can be lower risk than a larger miss with a tight covariance. Where the linear-encounter assumptions break down (slow, long encounters), APOGEE falls back to Monte-Carlo integration of the propagated states.

4.3Lead time and triage

Screening runs continuously, so a conjunction is flagged days ahead and its P_c tracked as new observations tighten the covariance. Events are triaged by P_c and consequence, so operators act on a short, ranked list rather than a flood of low-risk close approaches.

5Optimize — maneuvers and coverage

Optimize plans the smallest maneuver that makes an object safe, and coordinates maneuvers and phasing across a whole constellation, exactly the combinatorial structure where quantum and hybrid solvers earn their place.

5.1Fuel-optimal avoidance

An avoidance maneuver is an optimization: minimize the propellant cost (the velocity change Δv) subject to driving collision probability below an operator threshold and respecting mission, pointing, and timing constraints:

For a single object this is small; across a constellation, where one satellite's burn changes coverage that others must restore, the coupled assignment and scheduling problem grows combinatorial.

5.2Quantum formulation

The assignment and scheduling decisions, which satellite maneuvers, into which slot, in what order, are encoded as binary variables in a QUBO, with constraints as quadratic penalties:

and solved with QAOA, a depth-p circuit alternating a cost and a mixing unitary whose angles a classical optimizer tunes:

A classical relaxation warm-starts the solve, and the CVaR of the measured energy distribution is minimized to concentrate on the best samples. Continuous burn magnitudes and timing are then refined by a classical trajectory optimizer.

5.3Coverage and contacts

Beyond avoidance, the same machinery optimizes constellation phasing for coverage and schedules ground-station contacts, allocating scarce passes across the fleet, as coupled combinatorial problems.

6Autonomy — onboard intelligence

A spacecraft is in ground contact for only minutes per orbit. For the rest, APOGEE runs onboard: it watches telemetry, diagnoses faults, and takes safe, bounded action in real time.

6.1Learned health envelopes

Fixed red-line limits miss the subtle, correlated drifts that precede a failure. Onboard models learn each subsystem's normal operating envelope and score live telemetry against it, flagging a deviation as an anomaly when it departs the learned distribution, earlier and with fewer false alarms than static thresholds.

6.2Fault detection, isolation, and recovery

A flagged anomaly enters an FDIR loop: the fault is detected, isolated to a subsystem, and met with a recovery action drawn from a pre-authorized, operator-approved playbook, without waiting for the next ground pass. When confidence is high and the action is within limits, APOGEE acts; otherwise it safes the vehicle and reports.

6.3Bounded autonomy

Autonomy is deliberately bounded. Every autonomous action is constrained to an operator-defined envelope, is reversible or safe by construction, and is logged for review on the next contact. The engine is designed to never take an irreversible action it is not explicitly authorized for.

7Hybrid orchestration

The "quantum only where it pays" principle is enforced in code by a router that chooses, per job, between classical and quantum solvers and between ground and onboard execution, always guaranteeing a usable result in time.

7.1The router

Every job carries a class, a size, and a deadline. Real-time safety and estimation are always classical and, where needed, onboard. Maneuver and scheduling jobs are sized: small ones go to a classical solver; large ones to the quantum/hybrid solver when a backend and time budget allow; and when a deadline looms, the router returns the best classical result. The router is free to choose classical, and for single-object avoidance it usually does.

Optimize / safety router (simplified)def route(job):
    if job.kind in ("orbit_det", "fdir", "conjunction"):
        return Classical(job.kind)          # never on the QPU path
    if job.kind == "constellation":
        n = job.sats * job.slots
        if n <= CLASSICAL_LIMIT:
            return Classical(solver="milp")
        if backend.available() and job.deadline > QPU_MIN:
            return Hybrid(qaoa_depth=6, warm_start=True)
        return Classical(solver="milp_heuristic")  # graceful fallback

7.2Backends and mitigation

One circuit interface runs across simulators and gate-model QPUs, so operators are not locked to a vendor and benefit as hardware improves. On real hardware APOGEE applies readout-error calibration and zero-noise extrapolation, and records which backend and mitigations produced each plan in the audit trail.

8Deployment and integration

APOGEE deploys where operations already run, behind the operator's security perimeter, speaking standard space-data protocols, with the option to fly a thin autonomy layer onboard.

8.1Topology

The ground plane runs on-premises or in an air-gapped enclave; ephemerides and telemetry never leave the operator's boundary. Only abstracted optimization instances (a cost matrix, a constraint set) are brokered to a quantum backend over an encrypted channel, never raw catalog or mission data.

8.2Digital-twin validation

Before any recommendation drives an operational decision, APOGEE runs against a high-fidelity simulation of the catalog and the vehicle, replaying historical conjunctions and stress scenarios. New models are shadow-deployed, advising without acting, until they earn operational trust; onboard autonomy is proven on a hardware-in-the-loop twin first.

8.3Security and audit

Access is role-based; every catalog update, conjunction message, maneuver plan, and autonomous action, with the compute path that produced it, is written to an append-only audit log. The system is auditable end to end, as operators and regulators require.

9Validation and benchmarks

We benchmark against strong operational baselines, standard conjunction pipelines and classical flight-dynamics planners, and report where quantum does not yet win.

9.1Methodology

• Orbit determination is scored by position error against precision ephemerides and by covariance realism (are the error bars honest?).
• Conjunction assessment is scored against reference P_c tools and, where available, known events.
• Optimization is measured by Δv and objective value at a fixed wall-clock budget, and by feasibility against all constraints.

The verdict column is the point: learning and pre-filtering carry tracking and screening; quantum optimization earns its place as constellation coordination grows, and on small avoidance problems APOGEE routes to the classical solver.

10Limitations and current maturity

This section is deliberately blunt. Spaceflight is unforgiving and conservative for good reason; credibility with operators depends on candor.

• NISQ reality. Quantum hardware is noisy and limited in scale. APOGEE's quantum advantage on constellation optimization is demonstrated in simulation and on small instances; classical solvers carry production planning today, and the router falls back automatically.
• Data drives everything. Track is only as good as the sensor data feeding it. Sparse coverage, especially over some regions and for small objects, bounds catalog accuracy no algorithm can recover.
• Drag is hard. Atmospheric density is variable and imperfectly modelled, so low-orbit predictions carry irreducible along-track uncertainty; this is why Pc, not nominal miss, drives decisions.
• Autonomy is bounded on purpose. Onboard autonomy is intentionally narrow and reversible; APOGEE is not an autonomous mission planner and does not seek open-ended control of a vehicle.
• Simulated figures. Every number here is illustrative of the target. Production performance depends on sensors, orbit regime, and backend, and is established per deployment against the operator's own data.

11Responsible use and safety

Space situational awareness is dual-use. APOGEE is operated for spaceflight safety and traffic coordination under partner and, where applicable, government agreements, with export-control (ITAR/EAR) awareness built into deployment. The system is oriented toward collision avoidance and sustainability of the orbital environment; onboard autonomy is bounded, reversible, and auditable by design. Partner ephemerides and mission data remain the partner's property and stay within their enclave; models are not shared across partners. Full provenance is retained so every catalog value, conjunction message, and action can be traced.

12Roadmap

—References and further reading

1. Vallado, D. Fundamentals of Astrodynamics and Applications. 4th ed., Microcosm Press, 2013.
2. Montenbruck & Gill. Satellite Orbits: Models, Methods and Applications. Springer, 2000.
3. Foster & Estes. A parametric analysis of orbital debris collision probability. NASA JSC-25898, 1992.
4. Alfano, S. Review of conjunction probability methods for short-term encounters. AAS 07-148, 2007.
5. Klinkrad, H. Space Debris: Models and Risk Analysis. Springer, 2006.
6. Kessler & Cour-Palais. Collision frequency of artificial satellites: the creation of a debris belt. J. Geophys. Res. 83 (1978).
7. Farhi, Goldstone, Gutmann. A Quantum Approximate Optimization Algorithm. arXiv:1411.4028.
8. Barkoutsos et al. Improving Variational Quantum Optimization using CVaR. Quantum 4, 256 (2020).
9. CCSDS. Conjunction Data Message, Recommended Standard 508.0-B-1.
10. Kalman, R. E. A New Approach to Linear Filtering and Prediction Problems. J. Basic Eng. 82 (1960).

This brief describes a system and design intent. All performance figures are illustrative and simulated for demonstration; production characteristics are established per deployment and validated on the operator's own data. © Ace Hacker Research & Development Lab.