23-EFT.WP.Metrology.PathCorrection v1.0 | Chapter 15 — Use Cases and Reference Implementations

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Chapter 15 — Use Cases and Reference Implementations

One-Sentence Goal
Provide three representative end-to-end, executable paths—from modeling → correction → publication—for (1) GNSS-style free space, (2) White Rabbit / fiber round trip, and (3) metro-area NLOS microwave links, including aligned P/S/M/I/C items and example manifest.path fragments.

I. Scope and Objects

1. Covers three canonical paths:
   • GNSS-style free-space path (ground station ↔ satellite).
   • White Rabbit / fiber links (round-trip symmetry with micro-asymmetry correction).
   • Metro-area NLOS microwave links (multipath suppression and arrival-time harmonization).
2. Outputs (per use case): T_parts, T_corr, u/U, contracts.*, tags, and excerpts of manifest.path.*.
3. Common constraints: dual-form evaluation in parallel; explicit RefCond; check_dim passes; cross-volume citations use the fixed style.

II. Terms and Variables

1. Common: gamma(ell), L_gamma, n_eff(f,x), c_ref, T_arr, delta_form, tol_Tarr, RefCond, u(x), U = k * u_c.
2. Case-specific:
   • GNSS: elev, mapping(elev), TEC, clk_tx/rx (clock-bias fields persisted only; computation per TimeBase/Sync).
   • WR/Fiber: RTT, T_fixed (sum of device fixed delays), Δasym (TX/RX and wavelength asymmetry), n_g(f,T).
   • NLOS Microwave: h(t), T_mpath, specular_k, RAKE/SAGE tags and suppression thresholds.

III. Axioms P815-*

• P815-1 (End-to-End Coherent Convention) — All three use cases decompose with T_arr = T_geom + T_med + T_inst + T_proc and run dual forms in parallel (Chs. 2 & 10).
• P815-2 (Traceable Reference Conditions) — RefCond must include data sources and versions for temperature/pressure/humidity or TEC/cable thermal spectra, as applicable.
• P815-3 (Uncertainty Publication) — Publish U only when delta_form ≤ tol_Tarr and u_num is accounted for (Ch. 13).
• P815-4 (Bounded Fallback) — On missing data, apply the fallback matrix (Ch. 14) and inflate U and guardbands.
• P815-5 (Unit Checks) — Every quantity entering equations declares unit/dim and passes check_dim.

IV. Minimal Equations S815-*

• S815-1 (Generic Dual-Form Arrival Time)
  T_arr = ( 1 / c_ref ) * ( ∫_{gamma} n_eff d ell ) + T_inst + T_proc
  T_arr = ( ∫_{gamma} ( n_eff / c_ref ) d ell ) + T_inst + T_proc
  delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |.
• S815-2 (GNSS-Style Free-Space Components)
  T_med = T_tropo + T_iono, with T_tropo = T_hydro + T_wet;
  T_iono ∝ TEC / f^2 (Ch. 6), elevation mapping M(elev) applied to ground-zenith delays.
• S815-3 (WR/Fiber One-Way Solution)
  T_one = 0.5 * ( RTT - T_fixed ) + Δasym + T_env,
  where T_env = ( 1 / c_ref ) * ( ∫ n_g(f,T) d ell ) - T_ref (relative to reference conditions, Ch. 8).
• S815-4 (NLOS Multipath Suppression)
  With LOS term p0 and specular cluster {p_k}: observed h(t) = ∑ a_k δ( t - τ_k ) + n(t);
  estimate T_mpath = f( {τ_k, a_k}, policy ) and form the suppressed arrival time T_arr' = T_arr - T_mpath (Ch. 7).
• S815-5 (Uncertainty Combination)
  All three use u_c^2 = J V_x J^T + u_num^2 or MC quantiles (Ch. 13), with U = k * u_c.

V. Metrological Workflow M80-15 (Common Frame for All Three)

• Ready — Assemble the execution graph G = (V,E) and policies; bind data sources and RefCond.
• Modeling — By case, choose model_troposphere / model_ionosphere / model_fiber / estimate_multipath, etc.
• Dual-Form Integration — integrate_path(n_eff, gamma, c_ref) → { T_form1, T_form2, delta_form }.
• Composition — compose_path_correction(parts) aggregates T_geom / T_med / T_inst / T_proc.
• Uncertainty — propagate_gum / propagate_mc to obtain U and guardband.
• Checks — assert_path_contracts(ds, rules) applies C80-*; on failure, fallback or recompute.
• Persist & Publish — emit_path_manifest(results, policy) writes manifest.path and manifest.path.rt; push to dashboards.

VI. Contracts and Assertions (C80-15xx)

• C80-1501 GNSS: age(TEC) ≤ Δt_TEC, age(met) ≤ Δt_met, declared version of M(elev); delta_form ≤ tol_Tarr.
• C80-1502 WR/Fiber: |Δasym| ≤ asym_max; u(T_one) includes u(RTT), u(T_fixed), u(Δasym), u_env; loopback-calibration version is traceable.
• C80-1503 NLOS: specular_k ≤ K_max; residual_p95 ≤ thr_res; suppression policies and thresholds are persisted.
• C80-1504 Common: check_dim(T_arr) = "[T]"; U/g consistent with risk parameters; contracts.pass = true before publication.

VII. Implementation Bindings I80-15*

• I80-151 run_case_gnss(obs, met, TEC, geom, policy) -> { T_parts, T_corr, u, manifest }
  Internals: model_troposphere, model_ionosphere, solve_ray (optional), integrate_path, compose_path_correction, propagate_*, assert_path_contracts, emit_path_manifest.
• I80-152 run_case_wr(fiber, rtt, fixed, temp_profile, cable_spec, policy) -> { T_one, T_parts, u, manifest }
  Internals: model_fiber, calibrate_loopback, regress_inst, integrate_path (optional validation), propagate_*.
• I80-153 run_case_nlos(obs, geom, dem, policy) -> { T_mpath, T_corr, tags, u, manifest }
  Internals: estimate_multipath(method∈{RAKE,specular-fit,SAGE}), solve_ray (optional NLOS refraction), integrate_path, compose_path_correction, propagate_*.
• Invariants: non_decreasing(ell); delta_form ≤ tol_Tarr; RefCond and method persisted; idempotent per trace_id.

VIII. Cross-References
Geometry & coordinates (Ch. 3); medium-field construction (Chs. 4–6, 8); ray tracing (Ch. 9); dual forms & integration (Ch. 10); environmental fusion (Ch. 11); instrument chain (Ch. 12); uncertainty & runtime dashboards (Chs. 13–14); time base/sync: EFT.WP.Metrology.TimeBase v1.0, …Sync v1.0.

IX. Quality & Risk Control (Suggested Use-Case SLOs)

• GNSS: p95(|map_residual|) ≤ 1.5 ns, p99(delta_form) ≤ tol_Tarr, age(TEC) ≤ 30 min.
• WR/Fiber: p95(|T_one_error|) ≤ 0.3 ns, tau_ripple_p2p ≤ 0.1 ns, online thermal coefficient |k_T| controlled.
• NLOS: p95(|T_mpath|) ≤ 3 ns (post-suppression residual), specular_k ≤ 3, alarm.mpath triggers fallback.
• Fallback strategy: on source outage or contract failures, revert to model / climatology / reference and inflate U & guardbands per Ch. 13.

Summary
Three runnable reference links reuse the P/S/M/I/C system and produce a unified manifest.path. Once closed-loop with the models and contracts in Chs. 2–14, this volume serves directly as an engineering blueprint.

Use Case A: GNSS-Style Free-Space Path Correction (Guided Example)
I. Inputs: obs = { elev, f, r_tx, r_rx, ts }, met = { T, P, RH }, TEC grid / ray mapping, RefCond, policy.
II. Core Steps

• T_tropo = model_troposphere(met, elev, f, model);
• T_iono = model_ionosphere(TEC, f, mapping);
• T_med = T_tropo + T_iono;
• T_geom (geometric / relativistic minor terms as needed);
• Dual-form integration and delta_form gating (optional solve_ray for refraction).
  III. Publication Fragment (manifest.path example)

{

"TraceID": "gnss-2025-09-02T10:00:00Z-001",

"gamma.hash": "...e3b9",

"RefCond": { "met.ver": "gpt3w-2025.08", "tec.ver": "igsg-2025.09", "ts": "2025-09-02T10:00:00Z" },

"T_parts": { "T_geom": 0.000067321, "T_tropo": 0.000007842, "T_iono": 0.000001235, "T_inst": 0.000000300 },

"T_form": { "form1": 0.000076698, "form2": 0.000076699, "delta_form": 1.2e-12, "tol_Tarr": 5e-12 },

"u": { "u_c": 8.5e-10, "U": 1.7e-9, "nu_eff": 56, "method": "MC", "u_num": { "u_q": 2.0e-12, "u_form": 7.0e-13 } },

"contracts": { "freshness": true, "form_ok": true, "units_ok": true },

"tags": ["gnss", "free-space", "mapping=VMF3"]

}

【Dashboard hooks: delta_form_p99, age(TEC), U, map_residual time-series】

Use Case B: White Rabbit / Fiber Round-Trip Symmetry Correction (Guided Example)
I. Inputs: RTT, T_fixed, temp_profile(x,t), cable_spec, Δasym (SFP/wavelength asymmetry estimate), RefCond.
II. Core Steps

• Device loopback/interconnection yields T_fixed and partial T_inst (Ch. 12).
• Thermal field drives model_fiber(temp, f, cable_spec) → T_env.
• One-way delay T_one = 0.5*(RTT - T_fixed) + Δasym + T_env.
• Run validation integration on the fiber segment and record delta_form.
  III. Publication Fragment (manifest.path example)

{

"TraceID": "wr-2025-09-02T10:05:00Z-042",

"RefCond": { "T0": 293.15, "cable_spec": "G652D", "ver": "lab-1.4" },

"fiber": { "L_gamma": 10_000, "n_g_model": "Sellmeier+thermo", "temp_profile.hash": "...a71" },

"T_parts": { "T_one": 0.000050312, "T_env": 1.8e-10, "Delta_asym": -2.5e-10, "T_inst": 3.2e-10 },

"T_form": { "form1": 0.0000503123, "form2": 0.0000503122, "delta_form": 1.1e-13, "tol_Tarr": 1e-12 },

"u": { "u_c": 2.2e-10, "U": 4.4e-10, "method": "GUM", "u_num": { "u_q": 3e-13, "u_form": 6e-14 } },

"contracts": { "loopback_traceable": true, "asym_bound_ok": true, "form_ok": true },

"tags": ["white-rabbit", "fiber", "symmetry-correction"]

}

【Dashboard hooks: RTT, T_one, temp_coeff_drift, tau_ripple】

Use Case C: Metro NLOS Microwave — Multipath Suppression & Arrival-Time Harmonization (Guided Example)
I. Inputs: obs(t) (impulse response / correlation), geom (sites & obstructions), dem, f, policy (suppression thresholds / max clusters).
II. Core Steps

• estimate_multipath(obs, geom, method="specular-fit") -> { τ_k, a_k }.
• Compute T_mpath and suppress: T_arr' = T_arr - T_mpath.
• If needed, solve_ray for non-uniform atmospheric refraction paths.
• Online dual-form monitoring; residuals feed the map_residual metric.
  III. Publication Fragment (manifest.path example)

{

"TraceID": "nlos-2025-09-02T10:12:30Z-207",

"geom": { "los": false, "specular_k": 2, "dem.hash": "...19f" },

"T_parts": { "T_geom": 0.000003941, "T_med": 0.000000992, "T_mpath": -2.8e-09, "T_inst": 6.0e-10 },

"T_form": { "form1": 0.0000049322, "form2": 0.0000049322, "delta_form": 3.0e-12, "tol_Tarr": 1e-11 },

"u": { "u_c": 1.9e-09, "U": 3.8e-09, "method": "MC", "q": [-2.0e-09, 4.1e-09] },

"contracts": { "specular_k<=3": true, "residual_p95_ok": true, "form_ok": true },

"tags": ["microwave", "NLOS", "multipath-suppression", "SAGE"]

}

【Dashboard hooks: specular_k, residual_p95, delta_form, SLI_latency】

P/S/M/I Cross-Walk & Checklist (Excerpt)

• P815-* ↔ unified use-case conventions & bounded fallback.
• S815-* ↔ use-case equations (GNSS / WR / NLOS specifics).
• M80-15 ↔ shared workflow for all three.
• I80-151/152/153 ↔ single-entry runners per use case.
• C80-1501/1502/1503/1504 ↔ use-case-level contracts.
• Runtime fields and dual-form assertions are reused from Chs. 10, 13, 14—no reimplementation.

Final Summary
The three use cases traverse the volume’s methodology—from geometry/medium/instrument modeling to dual-form integration, MC/GUM uncertainty, and runtime dashboards—supporting deployable, auditable results.
Minimal merged view:
manifest.path = { TraceID, gamma.hash, RefCond, T_parts, T_form:{ form1, form2, delta_form, tol_Tarr }, u:{ u_c, U, nu_eff, method, u_num|q }, contracts.*, tags, signature }.
Readers can directly connect real data sources via I80-151/152/153 to reproduce dashboards and compliance outcomes.