L1 ⚛ L1-466 ⊙ Testnet

GNSS Positioning and Navigation

Geodesy · Satellite positioning

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⬇ L1-466.md

# ⚛ L1 Principle — GNSS Positioning and Navigation **ID:** `L1-466` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geodesy — *Satellite positioning* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D position velocity > **📡 Carrier:** RF · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555298 --- ## 🧠 1. Introduction **GNSS Positioning and Navigation** is a **linear inverse problem** whose unknown lives in **3D position velocity** space, within the **Satellite positioning** sub-domain of **Geodesy**. Measurements consist of RF coil signals (typical of MRI) via a **pseudorange doppler measurement** sensing mechanism. The forward operator applies, in order: Pi · geometry operator; S · kalman · navigation operator; O · least squares · weighted operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D_position_velocity 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 ~= 10); ionospheric_model_error_m 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** → Pi · geometry → O · least squares · weighted → **y** (detector). ``` y = `O.least_squares.weighted` `Pi.geometry` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `Pi.geometry` | Pi · geometry operator | | `O.least_squares.weighted` | O · least squares · weighted operator | **🛰 Estimator components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `S.kalman.navigation` | S · kalman · navigation operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geodesy | | Sub domain | Satellite positioning | | Carrier | RF | | Problem class | linear_inverse | | Solution space | 3D_position_velocity | | Noise model | gaussian | | Integration axis | temporal_navigation | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered 3D_position_velocity 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 ~= 10); ionospheric_model_error_m dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | position_RMSE_m | | Secondary | PDOP | ## 📏 5. Operating Range (Ω) **Center problem class:** `linear_inverse` · **Forward operator:** `pseudorange_doppler_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | N sat | — | 8 | | Ionospheric tecu | — | 5 | | Multipath sigma m | m | 0.5 | | Elevation cutoff deg | deg | 15 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N sat | — | 4 – 30 | | Ionospheric tecu | — | 0.5 – 50 | | Multipath sigma m | m | 0.1 – 5.0 | | Elevation cutoff deg | deg | 5 – 30 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.5 position_RMSE_m | Metric | Range | |---|---| | Position rmse m | 0.01 – 10.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **position_RMSE_m**, with κ = `100` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x0a9120762927c26e70273d9422745920b65641572cdabb858e1e6c38fb79dce6` - **Chain tx hash:** `0xa3fb986ef0e11cc0baca6524e8d2d21e9d13700aed0b33f989e747e94b1db584` - **Chain block:** `41555298` --- ## File Mapping This bundle consists of: `L1-466.md`, `L1-466.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-466.md` | Source of truth — edit this | Human or LLM | | `L1-466.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 `L1-466`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-466.md).
Regenerate L1-466.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-466-001 GNSS Positioning and Navigation — Nominal + Mismatch Specs

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📋 JSON metadata

{
  "artifact_id": "L1-466",
  "chain_block": 41555298,
  "chain_hash": "0x0a9120762927c26e70273d9422745920b65641572cdabb858e1e6c38fb79dce6",
  "chain_tx_hash": "0xa3fb986ef0e11cc0baca6524e8d2d21e9d13700aed0b33f989e747e94b1db584",
  "domain": "Geodesy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 100,
    "metric": "position_RMSE_m",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "position_RMSE_m",
    "regime": "Existence of the recovered 3D_position_velocity 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 ~= 10); ionospheric_model_error_m dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "PDOP"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "RF",
    "difficulty_delta": 3,
    "domain": "Geodesy",
    "integration_axis": "temporal_navigation",
    "noise_model": "gaussian",
    "primitives": [
      "Pi.geometry",
      "S.kalman.navigation",
      "O.least_squares.weighted"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "pseudorange_doppler_measurement",
    "solution_space": "3D_position_velocity",
    "sub_domain": "Satellite positioning",
    "title": "GNSS Positioning and Navigation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "pseudorange_doppler_measurement"
    ],
    "allowed_omega_dimensions": [
      "N_sat",
      "elevation_cutoff_deg",
      "ionospheric_TECU",
      "multipath_sigma_m"
    ],
    "allowed_problem_classes": [
      "linear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.5 position_RMSE_m",
      "forward_operator": "pseudorange_doppler_measurement",
      "input_format": "measurement_only",
      "omega": {
        "N_sat": 8,
        "elevation_cutoff_deg": 15.0,
        "ionospheric_TECU": 5.0,
        "multipath_sigma_m": 0.5
      },
      "problem_class": "linear_inverse"
    },
    "epsilon_bounds": {
      "position_RMSE_m": [
        0.01,
        10.0
      ]
    },
    "omega_bounds": {
      "N_sat": [
        4,
        30
      ],
      "elevation_cutoff_deg": [
        5,
        30
      ],
      "ionospheric_TECU": [
        0.5,
        50
      ],
      "multipath_sigma_m": [
        0.1,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Satellite positioning",
  "title": "GNSS Positioning and Navigation"
}

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