L1 ⚛ L1-454 ⊙ Testnet

Spacecraft Attitude Determination

Robotics · Spacecraft dynamics

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⬇ L1-454.md

# ⚛ 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._

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Read the attached Markdown (L1-454.md).
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L2-454-001 Spacecraft Attitude Determination — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555278,
  "chain_hash": "0xfd81afc26fbdf7c38a0f782e8ea081d453eb660d3302cd94e780cbc8cba7bdfb",
  "chain_tx_hash": "0xcb45855bac3df78f636be77bbe6b5acb248689909dc32403b8f2683e2b78b281",
  "domain": "Robotics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "attitude_error_arcsec",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "attitude_error_arcsec",
    "regime": "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.",
    "secondary": "gyro_bias_estimation_error_deg_hr"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Robotics",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "S.quest.quaternion_estimator",
      "D.time",
      "O.ekf.attitude_ekf"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "star_tracker_magnetometer_attitude",
    "solution_space": "quaternion_attitude",
    "sub_domain": "Spacecraft dynamics",
    "title": "Spacecraft Attitude Determination"
  },
  "size_tiers": {
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      "star_tracker_magnetometer_attitude"
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    "allowed_omega_dimensions": [
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      "gyro_noise_deg_hr",
      "star_tracker_noise_arcsec",
      "update_rate_Hz"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0 attitude_error_arcsec",
      "forward_operator": "star_tracker_magnetometer_attitude",
      "input_format": "measurement_only",
      "omega": {
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        "gyro_noise_deg_hr": 0.01,
        "star_tracker_noise_arcsec": 2.0,
        "update_rate_Hz": 10
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "attitude_error_arcsec": [
        0.1,
        60.0
      ]
    },
    "omega_bounds": {
      "N_stars_tracked": [
        3,
        50
      ],
      "gyro_noise_deg_hr": [
        0.001,
        1.0
      ],
      "star_tracker_noise_arcsec": [
        0.5,
        30.0
      ],
      "update_rate_Hz": [
        0.1,
        100
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Spacecraft dynamics",
  "title": "Spacecraft Attitude Determination"
}

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