L1 ⚛ L1-428 ⊙ Testnet

Extended Kalman Filter (EKF)

Control Theory · Nonlinear estimation

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⬇ principle.md ⬇ principle.json

Fork L1-428

⬇ L1-428.md ⬇ L1-428.json

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You are helping me submit a MODIFICATION of L1-428 (Extended Kalman Filter (EKF)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-428.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-428.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = `O.innov.consistency_check` `D.time.explicit` `S.ekf.jacobian_linearization` x + n,    n ~ 𝒩(0, σ²)

world state x (nonlinear state estimate)

→

S · ekf · jacobian linearization `S.ekf.jacobian_linearization`

→

D · time · explicit `D.time.explicit`

→

O · innov · consistency check `O.innov.consistency_check`

→

observation y (N/A detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-428.md

# ⚛ L1 Principle — Extended Kalman Filter (EKF) **ID:** `L1-428` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Control Theory — *Nonlinear estimation* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** nonlinear state estimate > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555240 --- ## 🧠 1. Introduction **Extended Kalman Filter (EKF)** is a **nonlinear inverse problem** whose unknown lives in **nonlinear state estimate** space, within the **Nonlinear estimation** sub-domain of **Control Theory**. Measurements consist of N/A via a **linearized nonlinear estimation** sensing mechanism. The forward operator applies, in order: S · ekf · jacobian linearization operator; D · time · explicit operator; O · innov · consistency check operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered nonlinear_state_estimate 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 ~= 100); strong_nonlinearity 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 · ekf · jacobian linearization → D · time · explicit → O · innov · consistency check → **y** (detector). ``` y = `O.innov.consistency_check` `D.time.explicit` `S.ekf.jacobian_linearization` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.ekf.jacobian_linearization` | S · ekf · jacobian linearization operator | | `D.time.explicit` | D · time · explicit operator | | `O.innov.consistency_check` | O · innov · consistency check operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Control Theory | | Sub domain | Nonlinear estimation | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | nonlinear_state_estimate | | Noise model | gaussian | | Integration axis | discrete_time | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered nonlinear_state_estimate 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 ~= 100); strong_nonlinearity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | RMSE_state_estimation | | Secondary | filter_consistency_NEES | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `linearized_nonlinear_estimation` **Center point:** | Parameter | Unit | Value | |---|---|---| | N steps | — | 200 | | Q r ratio | — | 1 | | N state dim | — | 6 | | Nonlinearity degree | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N steps | — | 20 – 5000 | | Q r ratio | — | 0.01 – 100 | | N state dim | — | 2 – 20 | | Nonlinearity degree | — | 0.1 – 3.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.08 RMSE_state_estimation | Metric | Range | |---|---| | Rmse state estimation | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **RMSE_state_estimation**, with κ = `2000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc51b690c1f98e27dfc3162de4531fb67d8322b788a352e92951a47d10a1b8c75` - **Chain tx hash:** `0xb17130492a353b9b7fcd21bedeaee0aea2e1ee1db791159919a62f10fbb64d8b` - **Chain block:** `41555240` --- ## File Mapping This bundle consists of: `L1-428.md`, `L1-428.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-428.md` | Source of truth — edit this | Human or LLM | | `L1-428.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 `L1-428`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-428-001 Extended Kalman Filter (EKF) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "artifact_id": "L1-428",
  "chain_block": 41555240,
  "chain_hash": "0xc51b690c1f98e27dfc3162de4531fb67d8322b788a352e92951a47d10a1b8c75",
  "chain_tx_hash": "0xb17130492a353b9b7fcd21bedeaee0aea2e1ee1db791159919a62f10fbb64d8b",
  "domain": "Control Theory",
  "hardness_fn": {
    "delta": 3,
    "kappa": 2000,
    "metric": "RMSE_state_estimation",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "RMSE_state_estimation",
    "regime": "Existence of the recovered nonlinear_state_estimate 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 ~= 100); strong_nonlinearity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "filter_consistency_NEES"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Control Theory",
    "integration_axis": "discrete_time",
    "noise_model": "gaussian",
    "primitives": [
      "S.ekf.jacobian_linearization",
      "D.time.explicit",
      "O.innov.consistency_check"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "linearized_nonlinear_estimation",
    "solution_space": "nonlinear_state_estimate",
    "sub_domain": "Nonlinear estimation",
    "title": "Extended Kalman Filter (EKF)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "linearized_nonlinear_estimation"
    ],
    "allowed_omega_dimensions": [
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      "nonlinearity_degree",
      "Q_R_ratio",
      "N_steps"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.08 RMSE_state_estimation",
      "forward_operator": "linearized_nonlinear_estimation",
      "input_format": "measurement_only",
      "omega": {
        "N_steps": 200,
        "Q_R_ratio": 1.0,
        "n_state_dim": 6,
        "nonlinearity_degree": 0.5
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "RMSE_state_estimation": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "N_steps": [
        20,
        5000
      ],
      "Q_R_ratio": [
        0.01,
        100
      ],
      "n_state_dim": [
        2,
        20
      ],
      "nonlinearity_degree": [
        0.1,
        3.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Nonlinear estimation",
  "title": "Extended Kalman Filter (EKF)"
}

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