Unified Orbit-Attitude Estimation and Sensor Tasking Framework for Autonomous Cislunar Space Domain Awareness Using Multiplicative Unscented Kalman Filter

This paper presents a unified framework for autonomous cislunar space domain awareness that optimizes sensor architecture and tasking strategies using the Tree of Parzen Estimators and mutual information, respectively, while employing a multiplicative unscented Kalman filter to manage the complex non-linear dynamics of orbit-attitude state estimation.

The Gist

Imagine the space between the Earth and the Moon as a busy, expanding highway system. In the past, this "cislunar" highway was mostly empty, but with the Artemis program and commercial companies planning to build lunar bases, it's about to get incredibly crowded.

The problem? We don't have a good traffic control system for this new highway yet. Unlike the space near Earth, where satellites follow predictable, circular paths, the space between Earth and the Moon is chaotic. The gravity of both planets pulls on objects in complex, twisting ways, making it hard to predict where things are or how they are spinning.

This paper proposes a smart, automated system to act as the "traffic cop" for this new lunar highway. It solves two main problems: Where should we put our cameras? and What should those cameras look at, and when?

Here is the breakdown of their solution, using some everyday analogies:

1. The Challenge: The "Twisty" Highway

Imagine driving a car on a road that constantly shifts and bends due to invisible forces. If you try to guess where another car is based on a simple map, you'll be wrong.

• The Reality: In cislunar space, objects don't just orbit in circles; they dance in complex loops influenced by Earth and Moon gravity.
• The Visibility Issue: It's also hard to see anything. The Sun might be blinding you, the Moon might block your view, or the object might be too far away to see clearly. Plus, we don't know how shiny or dark the objects are, which affects how bright they appear.

2. Task 1: Designing the Camera Network (The "Where")

Before we can track anything, we need to decide where to place our "security cameras" (sensors).

• The Old Way: You could just throw cameras at random spots and hope for the best. This is like trying to find a lost key in a dark room by waving a flashlight randomly.
• The New Way (The Paper's Solution): The authors used a super-smart algorithm (called a "Tree of Parzen Estimators") to find the perfect spots.
  • The Analogy: Imagine you are trying to watch a flock of birds in a park. You don't just stand in one spot. You figure out the best 10 spots on a hill where, if you place a camera at each, you can see the most birds for the longest time, without the trees blocking your view.
  • The Result: They found that placing cameras on specific, stable "loops" (orbits) around the Earth-Moon system works best. They also figured out that you don't need thousands of cameras; a carefully chosen group of about 20 to 40 is enough to cover the area efficiently.

3. Task 2: The Smart Camera Manager (The "What" and "When")

Once the cameras are in place, they can't look at everything at once. They have to decide what to focus on.

• The Problem: If you have 20 cameras and 100 spaceships to track, you can't look at all of them every second. If you switch targets too slowly, you might lose track of a fast-moving ship. If you switch too often, you waste energy.
• The Solution: The system uses a "Mutual Information" strategy.
  • The Analogy: Think of a security guard with a walkie-talkie. Instead of staring at one door for an hour, the guard constantly calculates: "If I look at Door A for the next 5 minutes, how much more do I learn about the thief's location compared to looking at Door B?"
  • The system picks the target that gives the most new information at that exact moment. It's like a game of "Where's Waldo," but the computer is constantly asking, "Which part of the picture should I zoom in on right now to find Waldo fastest?"

4. The "Brain" of the System: The Kalman Filter

Even with the best cameras and the smartest manager, the data will be noisy. The system needs a way to guess the true position and spin of a spaceship even when the view is blurry.

• The Tool: They used a Multiplicative Unscented Kalman Filter.
• The Analogy: Imagine you are trying to guess the path of a ball thrown in a strong, gusty wind. You can't see the ball perfectly.
  • The "Kalman Filter" is like a super-smart coach. It takes your blurry guess, combines it with the physics of how the ball should move, and corrects your guess every time you get a new glimpse of the ball.
  • The Twist: This specific filter is great at tracking two things at once: where the ball is (orbit) and how it's spinning (attitude).

5. What They Discovered

The authors ran thousands of computer simulations to test their system. Here is what they found:

• Position is Easy, Spin is Hard: The system is excellent at tracking where a spaceship is. However, tracking how it is spinning is much harder.
• The "Crowded Room" Effect: If you have 20 cameras and 20 spaceships, the system works perfectly. But if you have 20 cameras and 100 spaceships, the system starts to get confused about the spinning of the ships, even though it still knows where they are.
• Timing Matters: If the cameras switch targets too slowly (e.g., every 4 hours), the system loses track of the spinning motion. If they switch faster (every 30 minutes), the tracking stays accurate.

The Big Picture

This paper provides a blueprint for building an autonomous "traffic control" system for the Moon. It tells us:

1. Don't waste money: You don't need a massive fleet of sensors; a small, smartly placed group is enough.
2. Be smart about focus: Don't stare at everything; focus on what gives you the most new information.
3. Watch your timing: You need to update your "gaze" frequently, especially if you are tracking many objects at once, or you will lose track of how they are spinning.

In short, they've built the software and strategy to keep the future "lunar highway" safe, ensuring that as we travel to the Moon, we know exactly where everything is and how it's moving.

Technical Summary

1. Problem Statement

The paper addresses the critical need for Cislunar Space Domain Awareness (SDA) as human and commercial activity in the Earth-Moon system increases. Unlike Near-Earth Orbit (NEO), the cislunar environment presents unique challenges:

• Dynamics: Strongly non-linear, non-Keplerian dynamics (governed by the Circular Restricted Three-Body Problem, CR3BP) complicate uncertainty propagation and state estimation.
• Observation Constraints: Long observation ranges lead to poor signal-to-noise ratios, restrictive viewing geometries, and frequent occultations (Sun, Earth, Moon exclusion zones).
• Resource Limitations: There is a lack of established heuristics for placing sensors and a need to optimize limited sensing assets across a vast volume.
• Estimation Complexity: Simultaneously estimating both orbital (translational) and attitude (rotational) states is difficult, particularly for passive optical sensors where attitude observability is often weak.

The authors propose a unified framework to solve two coupled problems:

1. Task 1: Optimizing the observer architecture (selecting orbits and the number of sensors) to maximize coverage and stability.
2. Task 2: Developing an integrated sensor tasking and state estimation strategy to track multiple targets and estimate their full state (position, velocity, attitude, angular velocity) efficiently.

2. Methodology

A. Dynamical and Sensing Models

• Dynamics: The Earth-Moon system is modeled using the CR3BP in a rotating frame. Both observer and target trajectories are propagated using these equations.
• Sensing: The study focuses on passive electro-optical sensing from space-based platforms.
  • Brightness Modeling: Uses the Cook-Torrance Bidirectional Reflectance Distribution Function (BRDF) for high-fidelity simulation (microfacet model, specular/diffuse reflection). For optimization speed, an analytical Lambertian sphere model is used.
  • Measurements: Sensors provide Right Ascension (RA), Declination (DEC), and apparent magnitude (brightness).
• State Estimation: An Error-State Multiplicative Unscented Kalman Filter (UKF) is employed.
  • State Vector: Includes translational position/velocity (CR3BP frame) and attitude/angular velocity.
  • Attitude Representation: Global attitude is a unit quaternion; local attitude errors are parameterized using Generalized Rodrigues Parameters (GRPs) to avoid singularities and maintain a minimal 3-parameter representation.

B. Task 1: Observer Architecture Optimization

• Objective: Select 10 distinct periodic orbits from a library of 302 candidates (derived from 13 CR3BP families like Halo, Lyapunov, Butterfly, Dragonfly) and assign an integer number of satellites (1–10) to each.
• Target Set: Static targets are generated based on Jacobi constants of past/future missions, clustered via k-means into three density scenarios: Sparse (100), Moderate (2,000), and Dense (10,000).
• Cost Function ($J$): A novel composite cost function minimizes the product of six terms:
  1. Satellite Count: Penalizes excessive hardware.
  2. Orbital Stability: Penalizes unstable orbits (based on monodromy matrix eigenvalues).
  3. Cumulative Observability: Total number of observable targets over 30 days.
  4. Target Re-observability: Frequency of observation per target (log-scaled).
  5. Proximity: Penalizes orbits far from Earth/Moon.
  6. Feasibility: Ensures orbit uniqueness.
• Algorithm: Solved using Bayesian Optimization via the Tree-structured Parzen Estimator (TPE) algorithm (via the Hyperopt package), which outperforms random search in high-dimensional, discontinuous design spaces.

C. Task 2: Integrated Sensor Tasking and Estimation

• Tasking Strategy: A greedy, single-step optimization maximizes Mutual Information between the prior and posterior covariance of the targets.
  • Assumption: Targets are independent (block-diagonal joint covariance).
  • Constraint: One-to-one sensor-target assignment.
• Temporal Cadence:
  • Tasking Update: Coarse interval (e.g., 30 mins to 4 hours).
  • State Estimation: Fine interval (30 seconds) using UKF updates between tasking steps.
• Implementation: Tasking uses the analytical brightness model for speed; the UKF update uses the high-fidelity Cook-Torrance model for accuracy.

3. Key Contributions

1. Unified Framework: First work to jointly optimize cislunar observer architecture and perform integrated orbit-attitude tasking/estimation in a non-Keplerian environment.
2. Novel Cost Function: Introduces a multi-objective cost function balancing hardware cost, orbital stability, coverage, and proximity, solved via TPE.
3. Attitude-Oriented Estimation: Demonstrates the application of an Error-State Multiplicative UKF with GRPs for simultaneous orbit and attitude estimation in cislunar space.
4. Scalability Analysis: Provides a systematic analysis of how estimation performance scales with Target-to-Observer ratios and Tasking Intervals.

4. Key Results

Architecture Optimization (Task 1)

• Performance: The TPE-based optimizer consistently found architectures with lower cost values and fewer sensors compared to Random Search baselines.
  • Example (Sparse Scenario): TPE used 20 satellites vs. 51 for Random Search, achieving a better cost function value.
• Orbit Selection: The optimal architectures heavily favored L2 Halo (North/South) and L3 Halo orbits, which provide diverse viewing geometries and stability.
• Scalability: As target density increased (100 $\to$ 10,000), the optimal number of observers increased (20 $\to$ 43), but the TPE algorithm efficiently managed the combinatorial complexity.

Sensor Tasking & Estimation (Task 2)

• Translational vs. Rotational Sensitivity:
  • Translational States: Remained satisfactorily estimated across a wide range of target-to-observer ratios and tasking intervals.
  • Rotational (Attitude) States: Highly sensitive to resource constraints.
• Impact of Target Density: As the number of targets exceeded the number of observers, attitude estimation performance degraded significantly, leading to divergence in rotational states for high target counts.
• Impact of Tasking Interval:
  • Increasing the tasking interval (e.g., from 30 mins to 4 hours) caused only modest degradation in translational accuracy.
  • However, attitude estimation suffered significantly, with increased uncertainty and frequent divergence, especially at high target-to-observer ratios.
• Observability Limit: The study highlights that passive optical measurements provide strong constraints on position (via line-of-sight angles) but weak constraints on attitude, particularly when tasking updates are infrequent.

5. Significance and Conclusion

This paper provides a critical roadmap for autonomous cislunar SDA. It demonstrates that while translational state estimation is robust even with sparse sensor networks and infrequent updates, attitude estimation is the limiting factor for system performance.

• Operational Insight: To maintain accurate attitude knowledge, sensor tasking must be frequent, and the ratio of observers to targets must be carefully managed.
• Future Directions: The authors suggest that future frameworks must explicitly prioritize attitude observability in the tasking cost function (currently based on orbital covariance) and consider heterogeneous sensor fusion to overcome the limitations of passive optical sensing in the cislunar regime.

The work establishes a foundational methodology for designing scalable, cost-effective, and high-performance space domain awareness systems for the upcoming era of lunar exploration.