L1 ⚛ L1-427 ⊙ Testnet

Kalman Filter State Estimation

Control Theory · Optimal estimation

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⬇ L1-427.md

# ⚛ L1 Principle — Kalman Filter State Estimation **ID:** `L1-427` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Control Theory — *Optimal estimation* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** state estimate covariance > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555240 --- ## 🧠 1. Introduction **Kalman Filter State Estimation** is a **parameter-estimation problem** whose unknown lives in **state estimate covariance** space, within the **Optimal estimation** sub-domain of **Control Theory**. Measurements consist of N/A via a **linear optimal state estimation** sensing mechanism. The forward operator applies, in order: S · kalman · predict update operator; computes eigen-pairs of a linear operator; O · innov · sequence whiteness operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered state_estimate_covariance 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); Q_R_mismatch 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** → O · innov · sequence whiteness → **y** (detector). ``` y = `O.innov.sequence_whiteness` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `O.innov.sequence_whiteness` | O · innov · sequence whiteness operator | **🛰 Estimator components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `S.kalman.predict_update` | S · kalman · predict update operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `E.eigensolve` | Computes eigen-pairs of a linear operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Control Theory | | Sub domain | Optimal estimation | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | state_estimate_covariance | | Noise model | gaussian | | Integration axis | discrete_time | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered state_estimate_covariance 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); Q_R_mismatch dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | NEES_normalized_estimation_error_squared | | Secondary | NIS_normalized_innovation_squared | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `linear_optimal_state_estimation` **Center point:** | Parameter | Unit | Value | |---|---|---| | Q r ratio | — | 1 | | P obs dim | — | 2 | | N state dim | — | 4 | | N time steps | — | 100 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Q r ratio | — | 0.01 – 100 | | P obs dim | — | 1 – 10 | | N state dim | — | 1 – 20 | | N time steps | — | 10 – 10000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.05 NEES_normalized_estimation_error_squared | Metric | Range | |---|---| | Nees normalized estimation error squared | 0.5 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **NEES_normalized_estimation_error_squared**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf5cd46a31ed61e959fa019a451146c1450dd7a58403e6fee6bd587f387f79ab5` - **Chain tx hash:** `0x11d69e8fba7258e0d52bb6102493e3eedc3ff24fac63196e993c1f646f3780a4` - **Chain block:** `41555240` --- ## File Mapping This bundle consists of: `L1-427.md`, `L1-427.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-427.md` | Source of truth — edit this | Human or LLM | | `L1-427.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 `L1-427`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-427-001 Kalman Filter State Estimation — Nominal + Mismatch Specs

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📋 JSON metadata

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  "domain": "Control Theory",
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    "L_DAG": 2.8,
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    "integration_axis": "discrete_time",
    "noise_model": "gaussian",
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      "E.eigensolve",
      "O.innov.sequence_whiteness"
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    "sensing_mechanism": "linear_optimal_state_estimation",
    "solution_space": "state_estimate_covariance",
    "sub_domain": "Optimal estimation",
    "title": "Kalman Filter State Estimation"
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      "input_format": "measurement_only",
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        3.0
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      "n_state_dim": [
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        20
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      "p_obs_dim": [
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        10
      ]
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Optimal estimation",
  "title": "Kalman Filter State Estimation"
}

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