# ⚛  L1 Principle — Spacecraft Attitude Determination

**ID:** `L1-454` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Robotics — *Spacecraft dynamics*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** quaternion attitude
> **📡 Carrier:** N/A · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555278

---

## 🧠 1. Introduction

**Spacecraft Attitude Determination** is a **parameter-estimation problem** whose unknown lives in **quaternion attitude** space, within the **Spacecraft dynamics** sub-domain of **Robotics**.

Measurements consist of N/A via a **star tracker magnetometer attitude** sensing mechanism.

The forward operator applies, in order: S · quest · quaternion estimator operator; time evolution of the state; O · ekf · attitude ekf operator.

Observations are corrupted by additive Gaussian noise. Existence of the recovered quaternion_attitude is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); gyro_bias_estimation_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → S · quest · quaternion estimator → Time derivative → O · ekf · attitude ekf → **y** (detector).

```
y = `O.ekf.attitude_ekf` ∂_t `S.quest.quaternion_estimator` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.quest.quaternion_estimator` | S · quest · quaternion estimator operator |
| `D.time` | Time evolution of the state |
| `O.ekf.attitude_ekf` | O · ekf · attitude ekf operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Robotics |
| Sub domain | Spacecraft dynamics |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | quaternion_attitude |
| Noise model | gaussian |
| Integration axis | time |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered quaternion_attitude is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); gyro_bias_estimation_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | attitude_error_arcsec |
| Secondary | gyro_bias_estimation_error_deg_hr |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `star_tracker_magnetometer_attitude`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Update rate hz | Hz | 10 |
| N stars tracked | — | 10 |
| Gyro noise deg hr | — | 0.01 |
| Star tracker noise arcsec | — | 2 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Update rate hz | Hz | 0.1 – 100 |
| N stars tracked | — | 3 – 50 |
| Gyro noise deg hr | — | 0.001 – 1.0 |
| Star tracker noise arcsec | — | 0.5 – 30.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.0 attitude_error_arcsec

| Metric | Range |
|---|---|
| Attitude error arcsec | 0.1 – 60.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **attitude_error_arcsec**, with κ = `500` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xfd81afc26fbdf7c38a0f782e8ea081d453eb660d3302cd94e780cbc8cba7bdfb`
- **Chain tx hash:** `0xcb45855bac3df78f636be77bbe6b5acb248689909dc32403b8f2683e2b78b281`
- **Chain block:** `41555278`

---

## File Mapping

This bundle consists of: `L1-454.md`, `L1-454.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-454.md` | Source of truth — edit this | Human or LLM |
| `L1-454.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-454`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._